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GRADE 9 TERM 4 MATHEMATICS

Grade 9Term 4MathematicsTeaching Plan

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Mathematics Teaching Plan: Term 4 Grade 9 (ATP)

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LESSON 1: 1

Practice Exams in Number systems, financial contexts, including ratio and rate, integers, exponents 1 0.5LESSON 2: 1 Practice Exams in Number systems, financial contexts, including ratio and rate, integers, exponents 1 1.0 LESSON 3: 1 Practice Exams in Number systems, financial contexts, including ratio and rate, integers, exponents 1 1.6LESSON 4: 1 Practice Exams in Geometry of Straight lines, 2D Shapes, Pythagoras and Constructions 1 2.1LESSON 5: 1 Practice Exams in Geometry of Straight lines, 2D Shapes, Pythagoras and Constructions 1 2.6LESSON 6: 1 Practice Exams in Geometry of Straight lines, 2D Shapes, Pythagoras and Constructions 1 3.1LESSON 7: 1 Practice Exams in Expressions, Equations, Functions and Graphs 1 3.6LESSON 8 : 1 Practice Exams in Expressions, Equations, Functions and Graphs 1 4.2LESSON 9 Weekly Assessment

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LESSON 1: 1

Practice Exams in Expressions, Equations, Functions and Graphs 1 4.7LESSON 2: 1 Practice Exams in Expressions, Equations, Functions and Graphs 1 5.2 LESSON 3: 1 Practice Exams in Number systems, Integers, Common Fractions, Decimal Fractions, Financial Contexts, including ratio and rate, 1 5.7LESSON 4: 1 Practice Exams in Number systems, Integers, Common Fractions, Decimal Fractions, Financial Contexts, including ratio and rate, 1 6.3LESSON 5: 1 Practice Exams in Number systems, Integers, Common Fractions, Decimal Fractions, Financial Contexts, including ratio and rate, 1 6.8LESSON 6: 1 Practice Exams in Geometric Patterns, Numeric Patterns and Functions 1 7.3LESSON 7: 1 Practice Exams in Geometric Patterns, Numeric Patterns and Functions 1 7.8LESSON 8 : 1 Practice Exams in Geometric Patterns, Numeric Patterns and Functions 1 8.3LESSON 9 SBA Assessment

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LESSON 1: 1

Practice Exams in Data Handling and Probability 1 8.9LESSON 2: 1 Practice Exams in Data Handling and Probability 1 9.4LESSON 3: 1 Practice Exams in Data Handling and Probability 1 9.9LESSON 4: 1 Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 10.4LESSON 5: 1

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Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 10.9LESSON 6: 1 Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 11.5 LESSON 7: 1 Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 12.0LESSON 8 : 1 Practice exams in Expressions and Equations 1 12.5LESSON 9 SBA Assessment - Project

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LESSON 1: 1

Practice exams in Expressions and Equations 1 13.0LESSON 2: 1 Practice exams in Expressions and Equations 1 13.5 LESSON 3: 1 Practice Exams in Expressions, Equations, Functions and Straight line Graphs 1 14.1LESSON 4: 1 Practice Exams in Expressions, Equations, Functions and Straight line Graphs 1 14.6LESSON 5: 1 Practice Exams in Expressions, Equations, Functions and Straight line 1 15.1LESSON 6: 1 Practice Exams in Data Handling and Probability 1 15.6 LESSON 7: 1 Practice Exams in Expressions, Equations, Functions and Straight line 1 16.1LESSON 8: 1 Practice Exams in Expressions, Equations, Functions and Straight line 1 16.7LESSON 9 Weekly Assessment

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Week 5 (05 Nov-09 Nov)

Lesson 1&2 : 1

Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 17.2Lesson 3&4 : 1 Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 17.7Lesson 5&6 : 1 Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 18.2Lesson 7&8 : 1 Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 18.8LESSON 9 Weekly Assessment

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Lesson 1&2: 1

Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and graphs 1 19.3Lesson 3&4: 1 : Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and straight line graphs 1 19.8Lesson 5&6: 1 Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and straight line graphs 1 20.3Lesson 7&8: 1 Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and straight line graphs 1 20.8LESSON 9 Weekly Assessment

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Lesson 1&2: 1

Practice exams on Constructions, Straight line Geometry and 2D shapes. 1 21.4Lesson 3&4: 1 Practice exams on Constructions, Straight line Geometry and 2D shapes. 1 21.9Lesson 5&6: 1 Practice exams on Area and Perimeter, 3-D objects, Surface Area and volume and Data handling including probability 1 22.4Lesson 7&8: 1 Practice exams on Area and perimeter, 3-D objects, Surface Area and volume and Data handling including probability 1 22.9LESSON 9 Weekly Assessment

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Lesson 1&2: 1

Practice exams on Transformations and Straight line Graphs 1 23.4Lesson 3&4: 1 Practice exams on Transformations, Straight line Graphs exponents and Probability 1 24.0Lesson 5&6: 1 Practice exams on Expressions and Equations 1 24.5Lesson 7&8: 1 Practice exams on Expressions and Equations 1 25.0LESSON 9 Weekly Assessment

TOTAL OF SUB-TOPICS 48 Type of Assessment

Concepts & Skills Assessed Date to be completed

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FORMAL ASSESSMENT: TEST (END OF THE TERM)Important considerations: • Include Multiple Choice Questions.• Ensure coverage of Cognitive levels as prescribed in CAPS p157.• Ensure that the questions are grade-appropriate.• The test and the memo should be moderated.

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Grade 9Term 4MathematicsLesson Plans

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SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 1

TOPIC: Number systems, financial contexts, including ratio and rate, integers.

CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:

Define and apply rules for number systems

RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1

WHAT YOU SHOULD KNOW (Knowledge)

Describe the real number system by recognising, defining and distinguishing properties of: natural numbers whole numbers integers rational numbers irrational numbers

WHAT YOU SHOULD BE ABLE TO DO (skills)

Use the definitions in the real number system to identify the different types of numbers by using their properties

COMPONENTS TIME TASKS/ACTIVITIES CAPS

REVIEW AND CORRECTION OF HOMEWORK

This is the first lesson of the term thus there will be no homework

LESSON PRESENTATION/ DEVELOPMENT

20minThe following tables should be revised with the learners. They could present it to each other with some concepts blocked and fill in the blanks.

Natural Numbers(N ): The most basic type of number.

N = { 1; 2; 3; 4; 5; …}

CAPSTerm: 1Page reference:119

9


Even Numbers are a subset of Natural numbers or the numbers that are divisible by 2 or multiples of 2.

{2; 4; 6; 8; …}

Odd numbers are a subset of Natural numbers or any integer that cannot be divided exactly by 2.

{1; 3; 5; 7; 9; …}

Prime numbers are numbers greater than 1 which can only be divided by itself and 1, without a remainder. They have two factors, the number itself and 1

{ 2; 3; 5; 7; 11; …)

Composite numbers can be divided by 1, itself and at least one other number without a remainder. They have more than two factors.

{4; 6; 8; 9; 10; …}

1 is neither a prime number nor a composite numbers, but is a factor of every natural number

1 = 1 × 1; 2 = 1 × 2; 3 = 1 ×3; 201

=20

1 is the identity element of multiplication and division.15=1 ;√1=1 ; 3√1=1; ;etc .

Whole numbers (N 0): The set of natural numbers together with 0.Whole numbers also consist of odd, even and prime numbers, and 1 and 0

{0; 1; 2; 3; 4; 5; 6; …}

0 is neither a prime number nor composite. 4 + 0 = 4; 5 – 0 = 5; 0 is the identity element for multiplication 03=0 ;0×5=0 , but 4

0isundefined

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Integers (Z):The set of integers consists of the positive whole numbers, zero and the negative numbers

{…; -3; -2; -1; 0; 1; 2; 3; …}

Rational numbers (Q): Any number that can be

written in the form ab , where a and b are

integers but b≠0.Recurring decimal : a decimal fraction in which a figure or group of figures is repeated indefinitely, as in 0.666

Integernon−zeronumber ,

Finite decimals: 75100

=34=75 % ;

−1,5=−1510

=−32

;

Recurring decimals:

0 , 3=13;−0 , 8=−8

9;

Irrational numbers (Q'): They are numbers with infinite non-terminating decimals, whose numbers goes on forever.

In practice we use rounded off values: √2≈1,414 , which is a rational approximation of the real value of √2.

Pi (π ¿ , 227

=3,141592…

Real numbers (R): Consist of all the numbers that we use and include all the numbers

Real number system:

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NON-REAL NUMBERS: These numbers are generally powered roots of negative numbers.

Examples or non-real numbers are:√−3√−4 ; 10√−100 ; √−2 ; 4√−20 ;

UNDEFINED NUMBERS: Division by zero is undefined.

50 ;

00 ;

CLASSWORK 10 min Give the learners the following exercise to complete in class:Complete the following table of numbers:

Number N N0 Z Q Q' Non-Real Undefined15 Yes Yes Yes Yes No No No√3

0,14287

√ 14

−√1443√−1√−1

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CONSOLIDATION/CONCLUSION AND OR HOMEWORK

Homework will follow in the next lesson

REFLECTION

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Answers: Term 4 Grade 9 Week 1 Lesson 1

Class work

Number N N0 Z Q Q' Non-Real Undefined15 Yes Yes Yes Yes No No No√3 No No No No Yes No No

0,14287 No No No Yes No No No

√ 14

No No No Yes No No No

−√144 No No Yes Yes No No No3√−1 No No Yes Yes No No No

√−1 No No No No No Yes No

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solve problems in contexts involving: Ratio and rate Direct and indirect proportion

by recognising and using calculation techniques.

FINANCIAL MATHS profit, loss, discount and VAT budgets accounts and loans rentals exchange rates and commission

by using the appropriate formulae



How to solve problems in contexts involving: Ratio and rate Direct and indirect proportion by recognising and using calculation techniques. FINANCIAL MATHS

profit, loss, discount and VAT budgets accounts and loans rentals exchange rates and commission by using the appropriate formulae

WHAT YOU SHOULD BE Use the appropriate formulae and conversion techniques to solve problems in contexts involving:

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ABLE TO DO (skills) Ratio and rate Direct and indirect proportion FINANCIAL MATHS

profit, loss, discount and VAT budgets accounts and loans rentals exchange rates and commission exchange rates and commission



20 min RateThe comparison of two amounts with different units. Notice that any rate uses the word per to indicate that it compares one quantity to one unit of another quantityWe use ratios to calculate rate.e.g: There are 96 boys and 120 girls in Grade 9. Write down, in the simplest form, the ratio of the number of boys to the number of girls in the grade.

Solution:96:120 = 8:10 = 4:5

Financial MathsKnow the following formulae:A=P(1+¿), where = final amount; = Initial amount, =interest rate and = number of periods.

Use this only for simple interest

CAPSTerm: 1Page reference:121

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, where = final amount; = Initial amount, =interest rate and = number of periods.Use this only for compound interest

Exchange rates:Write the knowns under each other and solve for the unknown by cross multiplying. E.g. :

Make use of the exchange rate table below to calculate each of the given transactions

(a) Mr. D from Germany bought rands with 4500 euros from Mary.(b) Mr. H from South Africa bought Pula with R1 000 from Mary.(c) Mary sells R 4 000 worth of dollars to Ms. B

Solutions:a) If Mr. D bought rands with 4500 euros, it means that Mary bought 4500 euros. 4500 × 11,2780 = R50751,00 b) If Mr. H bought Pula with R1000, it means that Mary sold Pula. 1000 ÷ 0,8080 = 1237,62 P c) 4000 ÷ 8,4586 = $ 472,89

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CLASSWORK 9 min 1. Divide R5 600 in the ratio 3: 4: 2.

2. A car travels a distance of 440 km at an average speed of 80 km/h. How long does it take the car to travel this distance? Round off your answer to the nearest hour.

3. Calculate the amount that will be in the bank after 5 years if R3500 was invested at 9% p.a. simple interest.

4. Calculate the interest if R10 000 is invested at 10 % per annum compound interest for

3 years.


1min 1. Simplify the ratio R250:R150:R1002. Divide 240g in the ratio 5 : 3 : 43. Calculate the interest if R6500 is invested for 3 years at 7,7% per annum compound

interest.4. Calculate the amount that will be in the bank after 5 years if R9500 was invested at

8% p.a. simple interest. 5. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange

rates are shown on the electronic notice board below.

CurrencyBuy (R) Sell (R)

US Dollar $ 1 8,1090 8,4586

British Pound ￡ 1

12,7850 13,4767

Euro 1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080

Mary buys $500 from a customer: How much did she pay in rand?

REFLECTION

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Answers: Term 4 Grade 9 Week 1 Lesson 2Class work

1. Divide R5 600 in the ratio 3: 4: 2.39×R5600=R1866,67

49×R5600=R2488,89

29×R5600=R1244,44


time=distancespeed

= 440 km80km /h

∴time=6hours


A=P(1+¿) and i= 9100

=0,09

∴ A=3500 (1+5×0,09 )=R5 075

4. Calculate the interest if R10 000 is invested at 10 % per annum compound interest for 3 years.

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TOPIC: Number systems, financial contexts, including ratio and rate, integers, exponents


Use laws and rules to do calculations involving integers and exponents



INTEGERS Commutative property

This law applies to addition and multiplication of numbers; it tells us that even if we change the order of the numbers we still get the same answer.

Associative propertyThis rule also applies to addition and multiplication; it allows us to group numbers when adding or multiplying and still get the same answer.

Distributive propertyWhen multiplying across addition or subtraction this property allows us to redistribute the numbers and still get the same answer.

Additive inverse: Is the number that is added to another to get 0 Examples: (1) 6 and -6, 6 + (-6) = 0 (2) –a and a, a + (-a) = 0 (3) 4b and -4b, 4b + (-4b) = 0

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Order of operation (BODMAS):B – BracketsO – of/ other(exponents and surds)D – Division,M – multiplicationA – additionS – Subtraction

EXPONENTSProduct of powers: am×an=am+n , a > 0

Quotient of powers: am÷an=am−n , if m>n

Exponent zero a0=1 am÷am=am−m=a0 ,a>0

am

am=1


Apply all the rules and laws above in order to do calculations



8min 1. Simplify the ratio R250:R150:R100

= 5:3:2

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2. Divide 240g in the ratio 5 : 3 : 45 : 3 : 4

First mass :

Second mass :

Third mass : 3. Calculate the interest if R6500 is invested for 3 years at 7,7% per annum compound interest.

A=P¿A=6500 ¿A=R8120.08


A=P(1+¿) and i=8

100=0,08

∴ A=9500 (1+5×0,08 )=R13 3005. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange rates are

shown on the electronic notice board below.


US Dollar $ 1 8,1090 8,4586

British Pound ￡ 1

12,7850 13,4767

Euro €1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080


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500 × 8,1090 = R4 054,50 Mary sells ￡400 to a customer. How much did she receive in rand? 400 × 13,4767= R5390,68

LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK

15 min Place learners in groups and allow for the following exercises to be completed.Stop learners at intervals of 5 min and answer questions with them.

EXERCISE:1. The weather forecast for the world on TV shows the following temperatures:

Minimum MaximumJohannesburg -4 0C 15 0CBloemfontein -10 0C -1 0CLondon -3 0C 14 0C

(a) What is the difference between the minimum temperatures in Johannesburg and the minimum in Bloemfontein?

(b) What is the rise in temperature from minimum to maximum in Johannesburg?(c) What is the rise in temperature from minimum to maximum in Bloemfontein?

2. Simplify the following:a) 4m5×3m7×−2m3

b) a7×a6

a8×a3

c) ¿

d) (−2 x2)¿

e) 2n8n+2

43n2−2n

CAPSTerm: 1Page reference: 119- 122

CONSOLIDATION/CONCLUSION

2min 1. Calculate:a)– 3(-11 + 5)

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AND OR HOMEWORK2. The minimum and maximum temperatures in Sutherland , Western Cape are shown in the table:

TEMPERATURES FOR SUTHERLAND:

January August October

Min 0C 120 -160 50

Max 0C 290 00 220

(a) What was the coldest temperature in Sutherland?

(b) What was the warmest temperature in Sutherland?

(c) What is the difference between the two temperatures?

3.a)

4 x2 y3

2x y5

b)

2 p8q4

8 p3qr÷ 16 p4

4 r

c)2x+1

3.2x−1

REFLECTION

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Answers: Term 4 Grade 9 Week 1 Lesson 3Class work Homework

1.a) - 40C – (- 100C) = 6 0Cb) 150C – (-40C) = 19 0Cc) -10C – ( -100C) = 9 0C

2.a) 4m5×3m7×−2m3

b) a7×a6

a8×a3

c) ¿

d) (−2 x2 )¿

=−2x2

4 x2

¿ −24

=−12

1. Simplify the ratio R250:R150:R100

= 5:3:2 2. Divide 240g in the ratio 5 : 3 : 4

5 : 3 : 4

First mass :

Second mass :

Third mass : 3. Calculate the interest if R6500 is invested for 3 years at 7,7% per annum compound interest.

A=P¿A=6500 ¿A=R8120.08


A=P(1+¿) and i=8

100=0,08

∴ A=9500 (1+5×0,08 )=R13 300

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e) 2n8n+2

43n2−2n

¿2n (23 )n+2

(22 )3n2−2n= 2n23n+6

26n2−2n

¿ 2n+3n+6

26n−2n =24 n+6

24n

¿24n+6−4n=26=64

5. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange rates are shown on the electronic notice board below.


US Dollar $ 1 8,1090 8,4586

British Pound ￡ 1

12,7850 13,4767

Euro €1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080


500 × 8,1090 = R4 054,50 Mary sells ￡400 to a customer. How much did she receive in rand? 400 × 13,4767= R5390,68

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TOPIC: Geometry of Straight Lines, 2D shapes, Pythagoras and Constructions


Apply themselves using the theory of : Geometry of Straight Lines

RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 2 Disc 1 ; Grade 9 Term 2 Disc 2


Vertically opposite angles; Corresponding angles; alternate angles; co-interior angles


Identify and apply the properties of: Vertically opposite angles are equal Corresponding angles are equal Alternate angles are equal Co-interior angles are supplementary



10 min 1. Calculate:a) – 3(-11 + 5) = - 3 × - 11 + - 3 × 5 = 33 +(-15) = 18

2. The minimum and maximum temperatures in Sutherland , Western Cape are shown in the table:

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January August October

Min 0C 120 -160 50

Max 0C 290 00 220

(a) What was the coldest temperature in Sutherland? -16 0C in August

(b) What was the warmest temperature in Sutherland? 29 0C in January

(c) What is the difference between the two temperatures? 29 – (-16) = 45 0C

3.

a) 4 x2 y3

2x y5

¿2 x2−1 y3−5

¿ 2 xy2

b) 2 p8q4

8 p3qr÷ 16 p4

4 r

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c) 2x+1

3.2x−1

LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK

20 min Get learners into groups and ask them to do the following problems and have group leaders present to the class, while educator guides them. The educator should ensure that the notation for geometry is maintained at all times.Stop learners at 10 minute intervals to give feedback.

1.

CAPSTerm: 2Page reference:134-138

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In the figure, AB//ED, Determine the size of and

2.

Calculate the values of and if

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.



REFLECTION Answers: Term 4 Grade 9 Week 1 Lesson 1

Class work

1.

In the figure, AB//ED, Determine the size of and

32


2.

Calculate the values of and if B2=x , D2= y , D1=44 ° ,C1=75 °∧AD‖BC

33


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Apply themselves using the theory of : 2D shapes



Properties of and conditions for: Triangles Quadrilaterals Congruency and Similarity


Identify and apply the properties of: Triangles Quadrilaterals Congruency and Similarity

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10 Min Revise the conditions for congruency and similarity.Emphasise the notation for this section while doing the examples one at a time in class. Allow learners to write answers before assiting with corrections.

1. Determine whether the following are congruent, similar or neithera)

b)

CAPSTerm: 2Page reference: 134-138

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c)

d)

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1. Consider the triangles below. Prove Δ ABD≡ ΔCDB

2. Prove that


Homework follows in the next lesson

REFLECTION

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1.

a)

b) .c) Not congruent

d)2.

In

(common)

(given) (given)

( ;H; S)

3.

In

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Apply themselves using the theory of : Pythagoras Constructions



How to use a protractor and compass to construct angles and shapes Use the Theorem of Pythagoras to solve right angles triangles


Use a protractor and compass to construct angles and shapes Apply the Theorem of Pythagoras to solve right angles triangles



10 minEnsure that learners know the following steps for constructions:

Bisecting a line segment with a ruler and a compass.

Step 1: Place the compass on one end point of the line segment (Point A).Draw an arc above and below the line. Step 2: Without changing the compass width place the compass on point


40


B. Draw an arc below and above the line so that the arcs cross the first two.

Step 3: Use a ruler to join the points where the arcs intersect. This line segment known as BD is the bisector of AB.

*the perpendicular is a line that meets another line at 90˚.

Theorem of Pythagoras:In any right angled triangle:

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Place learners in groups to complete the classwork.

CLASSWORK 10 min 1. Use a pair of compass and a ruler to make accurate constructions of the following:

2.

42


Calculate the value of the unknown side.


2 min 1. Use a pair of compass and a ruler to make accurate constructions of the following:

a) angle

2. Calculate the value of the unknown side.a)

b)

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REFLECTION

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1. Use a pair of compass and a ruler to make accurate constructions of the following:

2.

45



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TOPIC: Expressions, Equations, Functions and graphs

CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs

RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2

47



Rules for integers Factorisation ( all methods)


Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations.



5min 1.Use a pair of compass and a ruler to make accurate constructions of the following:A angle

3. Calculate the value of the unknown side.c)

d)

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25min Educator should give learners this activity to do in pairs:1. Simplify:

a) 2a2(a−2)+2a(a2−3a )

2. If x=5 and y=−4 , find the value of

4 x2+3 y2

3. Calculate the value of :; if

4. If and ,calculate the value of

5. If , calculate the value of

6. Solve for x:a) 4 x−1=−9

b)


49


c)

d)

e)

f)



REFLECTION

50


Answers: Term 4 Grade 9 Week 1 Lesson 7Homework

1. 2a2 (a−2)+2a(a2−3a )


3. ; if ¿−2¿¿−16−12−18+2¿−44

4. If and ,find the value of

51



6. If and y = -3 ,calculate the value of


52


b)

c)

d)

e)

53


f)

54


55











25 min Do the following examples with the learners, they should answer individually, one at a time, then the educator provides answers

1. Give the equation of the following:

CAPSTerm: 1,3Page reference: 130-131


56



1. Give the equations of the following:

y=x

2. Sketch the graph of y=−2

57

x

y

y

x


3. On the grid, draw the graphs defined by and . Label each graph and clearly mark the points where each graph cuts the axis and the axis.

58


4. Study the straight line graphs below and answer the questions that follow

Complete:a) The equation of line CD is b) The equation of line AB is … c) The length of CE = …

a)

b) c) CE = 6 units

59


Homework

1.Use a pair of compass and a ruler to make accurate constructions of the following:A angle


60


b)

61



TOPIC: WEEKLY ASSESSMENT AND REMEDIAL TEACHING

Grade 9

WEEKLY ASSESSMENT

QUESTION 1

In each of the questions below choose the correct answer.1.1 2a2 (a−2)+2a(a2−3a ) (2)

ABCD1.2 If x=5 and y=−4 , find the value of

4 x2+3 y2

(2)

A -148B 140C 148D -140

62


1.3 Solve for x: 3 x−1=−9

(2)

A.

B.

C.

D.

1.4 (2)

A.B.C.D.

63


1.5 Sketch the graph of (2)A.

B.

C.

64

y

y

y

x

x

x


D.

1.6

Calculate the value of .

(2)

ABCD

65

x

y


1.7

Choose a correct statement to describe the relationship between the above two triangles.

(2)

A

B

C They are not congruent

D They are neither congruent nor similar

1.8 Simplify : √ x8 + √ x16

A.B.C.D.

(2)

[16]

66


QUESTION 2

2.1 Complete the following statements:

2.1.1 ABC is an acute angled triangle because_______________ (1)

2.1.2 DEF is a _____angled triangle because it has a 90° angle. (1)

2.1.3 GHI is an obtuse angled triangle because ______________ (1)

QUESTION 3

3.1 Calculate the interest if R1250 is invested for 3 years at 9% per annum compound interest. (4)

3.2 Calculate the amount that will be in the bank after 4 years if R6500 was invested at 5% p.a. simple interest.

(4)

[8]TOTAL 25

67


Grade 9WEEKLY ASSESSMENTMEMORANDUM

QUESTION 11.1 B (2)1.2 C (2)1.3 A (2)1.4 D (2)1.5 A (2)1.6 C (2)1.7 D (2)1.8 A (2)

[14]QUESTION 2

2.1 Complete the following statements:2.1.1 ABC is an acute angled triangle because all interior angles are smaller than 90° (1)2.1.2 DEF is a right angled triangle because it has a 90° angle. (1)2.1.3 GHI is an obtuse angled triangle because one of the interior angles is larger than 90° (1)

QUESTION 33.1 A=P¿

A=R1250 ¿A=R1618.79

(4)

3.2 A=P(1+¿) and i=

5100

=0,05

∴ A=6500 (1+4×0,05 )¿R7800

(4)

[8]TOTAL 25

68




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: manipulate expressions, solve equations.

RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1







5min Revise the memo for the previous weeks test – only do the questions that were poorly answered or learners found difficult.


20min The following must be done as individual examples, give learners 30 to 60 seconds to answer each question and then provide the answer, with explanation.

1. Factorise the following expressions:a) 2 x2−8 xb) mx−my+5x−5 yc) 3m−3d−4de+4med) tv−uv−tw+uw

2. Solve for

CAPSTerm: 1 and 3Page reference:130-131 and 141-145

69


a)

b)



REFLECTION

70


Answers: Term 4 Grade 9 Week 2 Lesson 11. Factorise the following expressions:

a)

b) mx−my+5x−5 y

c) 3m−3d−4de+4me

d) tv−uv−tw+uw

2. Solve for a)

71


b)

72







Types of Graphs Scale factor Identify dependent and independent variables


Recognise and interpret graphs Draw conclusions from graphs regarding the dependent and independent variables



25min Use the following graph on the chalkboard. Ask learners for the dependant and independent variables and then ask learners the questions to interpret the graphs.

1. The graph below represents the charge per day from two car rental companies. Company A charges an initial fee of R120 and then charges R25 per day. Company B charges no initial fee, but charges R75 a day. According to the graph...

CAPSTerm: 1 and 3Page reference:130-131 and 141 - 145

73


A.Company A is cheaperB. Company B is cheaper C. Company B is cheaper if you hire the car for two days.D.Company A is cheaper if you hire the car for more than two days

Solution: D.

2. A Businessman earns a basic salary of R1 000 plus R500 commission for every item he sells.

2.1 Write a function for calculating the salesman’s salary (y) if he sells x items.

74


2.2 Complete the table of values using your function from Question 1.

2.3

Draw a grid using a scale of 0 to 10 on the x-axis and 0 to 5 000 (with intervals of 500) on the y-axis, and plot a graph based on your table.

2.4 Use the graph to find out how much the salesman would be paid if he sold 7 items


5min 1. Draw the graph of 2. Find the equation of the graph passing through (2;3) and (-4;2)

REFLECTION

75

X1 2 3 4 5

Y



1. D- Company A is cheaper if you hire the car for more than two days 2.

2.12.2

2.3

2.4

76

x1 2 3 4 5

y 1500 2000 2500 3000 3500




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: calculate using number systems, integers, common fractions, decimal fractions.



The rules for the real number system Integers


Apply the rules and simplify / solve using *integers*the real number system



5min 1.

77


2.

78



25min The following must be done by individual learners, one at a time, provide answers with explanations after each is completed. Revise defination of rational numbers as well.

1. Calculate, without the use of a calculator:

a)

b)c)

d)2. Write down any 5 rational numbers that will fit between the following integers:

a) -1 ; -2b) 2,3 ; 2,4




REFLECTION

79



1.

a)

b)

c)

80


d)

2.

a)

b)

81




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: calculate using number systems, integers, common fractions, decimal fractions, financial context, including ratio and rate



Square roots , cube roots Decimal fractions Common fractions


Apply the rules and simplify / solve using *integers*the real number system*common and decimal fractions*squares, cubes, square roots and cube roots



25min 1.a)

b)

c)


82


d)

2.Study the following table:A B C0,825 4,2367 3,452.1 Round off 0,825 to the nearest :

a) unit b) tenth c) hundredth

2.2 What is the place value of 2 in 0,825? 2.3 What is the number value of 2 in 0,825?2.4 What is the number value of 6 in 4,2367?


1. Calculate the following, without the use of a calculator:a)

b)

c)

d)

83


2. Calculate the following: (Round your answers off to 2 decimal places)a)

b)

c)

REFLECTION

84



1.a)

b)

c)

1. a.

b.

c.

85


d)

2.a) 1,0b) 0,8c) hundredths (h)

d)

e)6

1000(6 thousandths)

d.

or

2. a.

b.

c.

86




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: calculate using number systems, integers, common fractions, decimal fractions, financial context, including ratio and rate



Square roots , cube roots Decimal fractions Common fractions


Apply the rules and simplify / solve using *integers*the real number system*common and decimal fractions*squares, cubes, square roots and cube roots



5min 3. Calculate the following, without the use of a calculator:

a)

87


b)

c)

d)

88



b)

c)


25min 1. If 1 of petrol weighs 0,6798 . What will of petrol weigh? (round off your answer to 3 decimal places.

2. Mashudu bought a cooldrink for R7,50 ; a chocolate for R5,75 and a packet of chips for R6,00. He paid with a R50,00 note.

a) How much did he spend?b) How much change did he get?

3. The reading on a water meter at the beginning of the month was 322,573 .


89


At the end of the month the reading is 332,523 . The municipality charges R1,25 per 200

a) How much water was used during this month?b) How much will be paid for this month’s water .

4. Water drips from a tap at a rate of 15 of water per minute. How many litres of water drips from the tap in a day?


Homework will follow in the next lesson.

REFLECTION

90



1. 1 l=0 ,679 kg30 ,52l=xx=0 ,6798×30,52¿20 ,747 kg

2.a)

b)

3.a)

b)

1. Calculate the following, without the use of a calculator:a)

b)

c)

d)

91


4. 60 min in 1hr x 24 hrs = 1 440 minutes in a day

Water wasted in a day


b)

c)

92



TOPIC: Geometric patterns; Numeric patterns and Functions

CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to identify and use geometric patterns; numeric patterns and functions in calculations

RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1 ; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2


Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values


Apply the rules and simplify/ solve using Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values



25min Give learners time to discuss answers with a partner then give them opportunities to present their answers on the board, while guiding them.

1. a) Complete the table below described by the function , show only 2 calculations.

Input Value

-3 -2 -1 0 1 2


93


Output Value

b) draw a flow diagram to show the 2 calculations.

2. Find the output values in a flow diagram below for the rule

3. Use and to determine the corresponding output values ( values). Represent the input and output values in :a) A flow diagram


5min 1. Study the following diagram:

a) Draw the 4th diagramb) Complete the table:

Position 1st 2nd 3rd 4thValue 1

REFLECTION

94



1.Input Value

-3 -2 -1 0 1 2

Output Value

5 10 15 20 25 30

2

95


3.


96








Apply the rules and simplify / solve using Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values

97




5min 1.a)

b)Position 1st 2nd 3rd 4thValue 1 4 9 16


25min Allow learners to complete individually and give different learners opportunity to present to class.

1. Copy and complete the table:Input Value

1 2 3 4 5 6

Output Value

4 7 10 19

2. Determine the rule for the relationship between the inputs and output values of the table

3. Find the values of and respectively-2 -1 0 1 12-7 -5 -3 -1 27



Homework to follow in the next lesson

REFLECTION

98



1.Input Value

1 2 3 4 5 6

Output Value

4 7 10 13 16 19

2. 3.

99









Apply the rules and simplify / solve using Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values



25min 1. Determine the rule to describe the relationship between the input and

output values of the table below.

-2 -1 0 1 2-3 -1 1 3 5

2.


100


In each of the following trms you can determine the next term by applying a rule to the previous term. Describe the rule in words in each case:

a)

b)

c)

d)3. Calculate the output values:

0 1 2 3 4-8


5min Prepare for the weekly assessment on*expressions; equations; functions and graphs*number systems; integers; common fractions; decimal fractions; financial contexts including ratio and rate* geometric patterns; Numeric patterns

REFLECTION

101



1.2.

a) Add three to the previous termb) Multiply the previous term by 2c) Subtract 4 from the previous term

d) Multiply the previous term by 3.

0 1 2 3 4-8 -12 -16 -20 -24

102



TOPIC: WEEKLY ASSESSMENT AND REMEDIAL TEACHING

Grade 9

WEEKLY ASSESSMENT

QUESTION 11.1 Which of the following equations is equivalent to the equation (2)

ABCD1.2 Look at the first two patterns, how many sticks will Pattern 3 have? (2)

A 6B 9C 2D 151.3 Choose the function that represents the following graph: (2)

103


A.B.C.D.

[6]QUESTION 2Write down the next two terms of the following patterns:

2.12.2 (1)2.3 (2)2.4 (2)

[7]QUESTION 3

3.1 Complete the following pattern by drawing the next three terms: (3)

104


3.2 Complete the table :

x -2 -1 0 1 2 4 n

y 15 12 -9 -24

(8)

[11]

TOTAL 25

105


Grade 9

WEEKLY ASSESSMENT

MEMORANDUMQUESTION 1

1.1 B (2)1.2 B (2)1.3 C (2)


2.1 (2)2.2 (2)2.3 (2)2.4 (2)

[8]QUESTION 3

3.1 (3)

3.2 x -2 -1 0 1 2 4 7 12 n

y 18 15 12 9 6 0 -9 -24 -3x +12

(8)

[11]TOTAL 25

106



TOPIC: Data handling and Probability

CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should know and be able to organise data using a stem and leaf, calculate measures of central tendency and determine the probability of an event)



Mean; mode; range Stem and leaf diagram Different graphs to represent data Probability definition and equation


Use the definitions and formula as well as knowledge on graphs to work out problems related to data handling and probability



10min Review the previous weekly assessment. Do the examples that learners found difficult and/or the ones they struggled in after marking.


20min Using their previous knowledge and notes ask learners to answer the following questions individually and provide answers in between.

1. The given data set represents the weight to the nearest kg of a group of learners.82 73 6542 55 6265 58 6851 65 72


107


63 48 65a) Draw a stem and leaf diagram for the datab) Determine the range of the datac) Determine the moded) Determine the meane) Determine the median

2. An 8-sided die has the numbers 1 to 8 on its faces. When thrown, it has as equal chance of landing on any one of its facesa) How many possible outcomes are there?b) What is the probablility that it will land on a prime number?c) What is the probablility that it will land on a prime number?

1.a)

Stem Leaf8 27 2 36 2 3 5 5 5 5 85 1 5 84 2 8

b) Range ¿82−42=40

c) Mode ¿65

d) Mean

¿

e) Arrange data : 42 48 51 55 58 62 63 65 65 65 65 68 72 73 82

Media ¿ 65

2.

108


a) 8 possible outcomes

b) P(prime number) = c) P(number less than 0)= 0



REFLECTION

109



Classwork

1.a)

Stem Leaf8 27 2 36 2 3 5 5 5 5 85 1 5 84 2 8

b) Range ¿82−42=40

c) Mode ¿65

d) Mean ¿

e) Arrange data : 42 48 51 55 58 62 63 65 65 65 65 68 72 73 82 Media ¿65

2.a) 8 possible outcomesb) P(prime number) ¿c) P(number less than 0¿=0



110


CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should know and be able to represent data using a scatterplot, analyse data, calculate measures of central tendency and determine the probability of an event)








25min 1. A group of 14 learners measure their height and foot sizes and tabulate their results.Height 174 158 163 175 140 126 153 160 160Foot 27 24 24 26 23 23 22 25 24

Height 131 156 165 158 120Foot 20 23 25 24 20a) Draw a scatterplot for the data collected.b) According to the graph, do taller people have longer feet lengths and why?

2. There are eight balls in a basket. 2 are green, 3 are blue and the rest are white.a) Calculate how many white balls there are.b) What is the probability of picking a blue ball?c) What is the probability of picking a green ball?


CONSOLIDATION/CONCLUSION AND OR

5 min 1. A survey was conducted to test the relationship between the hand and shoe size. The table below shows 10 measurements of different hand lengths and shoe sizes.

Hand 5 7 2 9 6 7 4 9 8 5

111


HOMEWORK lengthShoe size 12 13 10 15 12 15 11 16 15 11

a) Draw a scatter plot using the information in the table.b) Draw a line of best fit.c) What conclusion can you draw about the relationship between a hand length and a shoe size?d) Find the mode for the shoe size.e) Calculate the mean for the shoe size.f) Determine the range for the hand size.

2. There are 25 learners in a class. If a learner is chosen at random, what is the probability that a girl is chosen if there are 11 boys?

REFLECTION

112



Classwork Homework1. a)

a) A positive correlation. Taller people do have longer feet length.

2.a) 8−(2+3)=3b) P(B)=¿c) P(G)=¿

1. a) and b)

1 2 3 4 5 6 7 8 9 10024681012141618

Relationship between hand and shoe size

Hand Length

Shoe

Size

c) The length of the hand is in direct proportion with the shoe size d) Mode ¿15

e) Mean ¿ 12+13+10+15+12+15+11+16+15+11

10=13

f) Range ¿9 –2=7

2. Girls: 25−11=14 P(G) ¿

113




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to read the bar graph and scatterplot and answer related questions and be able to use a tree diagram to find possible outcomes of an event)






114




10min a) and b)

1 2 3 4 5 6 7 8 9 10024681012141618

Relationship between hand and shoe size

Hand Length

Shoe

Size

c) The length of the hand is in direct proportion with the shoe size d) Mode ¿15

e) Mean ¿ 12+13+10+15+12+15+11+16+15+11

10=13

f) Range ¿9 –2=7

2. Girls: 25−11=14 P(G) ¿


20min 1. Study the bar graph below taken from the 2009 South African Census@School results. It shows the modes of transport to school from home of the learners who participated in the Census@School.

a) What is the graph about?b) What information is shown on the axes?

CAPSTerm: 4Page reference:

115


c) Is the scale clear and easy to read?d) What conclusions can the graph help you make?

Stem Leaf1 1 2 5 7 2 0 1 3 4 83 2 9

149-153

116


4 3 3 5 6 85 0 1 6

a) What is the range for the stem and leaf plot? b) What is the median value for the stem and leaf plot? c) What is the mode for the stem and leaf plot below? d) What is the mean value?

3. Represent the following 2-way table on a tree diagram:

T-shirt JeansBlack Blue Red

Green Black/green Blue/green Red/greenWhite Black/white Blue/white Red/white

1.a) In order to find out what the graph is about, we look at the title. The title tells us that the

graph shows how learners get to school each day.b) The axes are clearly labelled. The horizontal axis shows the different forms of transport:

walk, car, train, bus, bicycle, scooter, taxi and other. The vertical axis shows percentage.c) The scale is clear and easy to read. You cannot read exact percentages for the number of

learners walking to school, but it is easy to estimate that nearly 80% (or over 70%) walk to school.

d) You can immediately see that most of the learners in the census walk to school from home. The other learners mostly use car, bus or taxis to get to school

2. a) 56 – 11 = 45

117


b)

39−322 = 3,5

c) 43 d) 624 ÷ 19 = 32,8

.



REFLECTION

118



Class work

1.a) In order to find out what the graph is about, we look at the title.

The title tells us that the graph shows how learners get to school each day.

b) The axes are clearly labelled. The horizontal axis shows the different forms of transport: walk, car, train, bus, bicycle, scooter, taxi and other. The vertical axis shows percentage.

c) The scale is clear and easy to read. You cannot read exact percentages for the number of learners walking to school, but it is easy to estimate that nearly 80% (or over 70%) walk to school.

d) You can immediately see that most of the learners in the census walk to school from home. The other learners mostly use car, bus or taxis to get to school

2. a) 56 – 11 = 45

b)

39−322 = 3,5

c) 43 d) 624 ÷ 19 = 32,8

3.

119



TOPIC: Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations

CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to identify properties of solids, calculate the area, reflect and translate geometric figures, determine coordinates of images of transformation, compare and identify solids from their properties)



Formulae for: Area and Perimeter Surface Area Volume

3-D objects Conversions Transformations e.g. reflection and rotation


Use formulae and conversions to solve problems involving : Area and Perimeter Surface Area Volume

3-D objects Do any transformation of points and shapes and write down coordinates

120




25min First tell the learners what the topics for the lesson is then hand out the classwork and allow them to complete, question at a time. Give answers after each question revising some theory as you go along.

1. Complete the following table:

Platonic Solid Name of solid Number of edges

Number of vertices

Number of faces

a) b) c) d)

2. In the figure below, AP= 5m; AS = SB = 2m; PT = 12m and PS ⊥ AB

Calculate the area of the figure correct to 2 decimal places.

CAPSTerm: 3 & 4Page reference:146-148

121


3. Reflect ∆≝¿ in the x-axis; y−¿axis and in the line y=x .


5min 1.a) Draw line segment PQ with P (2;3) and Q(5;5) on a Cartesian planeb) Translate line PQ 2 units to the right and 2 units upwards and label the image P 'Q'c) Write down the coordinates of P'∧Q '

2. Which of the following polyhedral are prisms

122

A B C D E F


REFLECTION

123



Class work

1.

Platonic Solid Name of solid Number of edges Number of vertices Number of facesa)Dodecahedron

b) 30 c) 20 d) 12

2. Area of kite

124


3.

125


Homework

1.

a) and b)

c ¿P ' (4 ;5) and Q '(7;7)

2. A, B, C are Prisms

D, E , F are pyramids

126

x

y




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to reflect geometric figures, determine coordinates of images of transformation, identify prisms and calculate volume)



Formulae for: Area and Perimeter Surface Area Volume 3-D objects conversions Transformations e.g. reflection and rotation


Use formulae and conversions to solve problems involving : Area and Perimeter Surface Area Volume 3-D objects Do any transformation of points and shapes and write down coordinates

127




10min 1. a) and b)

c) P '(4 ;5) and Q '(7 ;7)

2. A, B, C are Prisms D, E , F are pyramids


20min 1.a) Draw the Cartesian planeb) Draw rectangle JKLM with the following coordinates:

J (−5 ; 4) ,K (−3 ;4) , L(−3 ;1)∧M (−5;1)


128

y

x


c) Shade half of the rectangled) Reflect the rectangle along the y-axis and label the image J ' ,K ' , L' , M ' and write down the

coordinates of each vertexe) Reflect the rectangle J ' ,K ' , L' , M ' along the x-axis and label the image J K L M and write

down the coordinates of each vertex.

2. What is a prism? 3. Calculate the volume of the following:



REFLECTION


Classwork

129


1.

2. A prism is a polyhedral with two identical and parallel faces called bases.

3.



130


CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to reflect geometric figures, determine coordinates of images of transformation, express the transformation algebraically, identify properties of solids and calculate volume)




3-D objects conversions Transformations e.g. reflection and rotation




131




20min 1.a) Draw a Cartesian plane on the grid provided and label the axesb) Draw the figure SAMP with vertices S(1 ;−2) , A (2 ;−1) and

M (3 ;−2) and P(2 ;−5)c) Reflect the figure along the y-axis and label it S' A 'M ' P 'd) Write down the coordinates of S' A 'M 'P’ e) Compare the coordinates of SAMP and S' A 'M ' P 'f) What is the relationship between the coordinates of the object and the coordinates of the

image? g) Complete: (x ; y)→¿

2. Complete the table:


132


3. Calculate the volume of the following object:


1. Calculate the volume of the following, use π=3,14

133


2. Describe the transformation if the coordinates of the original point and its image are:

a)

b)

c)

3.

a) Name the shapeb) What is the shape of its faces?c) How many faces does the shape have?d) How many edges does the shape have?e) How many vertices does the shape have?f) Draw the net of the shape.

REFLECTION

134



Class work Homework

1. a) , b) and c)

d) S' (−1;−2 ) , A ' (−2 ;−1 ) , M ' (−3 ;−2 ) ,P '(−2;−5)

e) x−¿coorinates change a sign and y−¿coordiantes remain the same.

f) (x ; y) →(−x ; y)2.

1. V=π r2×h ¿3,14× ¿ ¿339,12 cm3

2. a) Translation 2 units downwardsb) Translation 10 units to the left and 7 units upwardsc) Translation 13 units to the right and 9 units upwards.

3. a) Dodecahedronb) Pentagonsc) 12 Facesd) 30 Edgese) 20 Vertices

f)

135

y

x


3.

136




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to enlarge geometric figures, determine scale factors of transformations, express, identify properties of solids and calculate area and volume)




3-D objects Conversions Transformations e.g. reflection and rotation




137




10min 1. V=π r2×h ¿3,14× ¿ ¿339,12 cm3

2. a) Translation of 2 units downwardsb) Translation of 10 units to the left and 7 units upwardsc) Translation of 13 units to the right and 9 units upwards.

3.a) Dodecahedronb) pentagonc) 12d) 30e) 20f)


20min 1. Study the diagram below: CAPSTerm: 3Page reference:146-148

138


Complete the following:a) AB= 3cm A ' B' = 6cm therefore A ' B' = ------× ABb) BC= 2cm B' C ' = 4cm therefore B' C ' = ------× BCc) CD= 3cm C ' D ' = 6cm therefore C ' D ' = ------× CDd) AD= 2cm A ' B' = 4cm therefore A ' B' = ------× AD

2. Refer to question 1.a) Calculate the ratio of the area of Figure B to the area of Figure A.b) Simplify the ratio in question 2.a) above.


139


Name Shape of faces

No of faces (F)

No of vertices (V)

No of edges (E)

F+V-E

4. The area of the base of a rectangular prism is 32mm2 and its height is 12mm. What is its volume?5. The volume of a cube is 216m3. What is the length of one of its edges?



REFLECTION


140


Classwork Homework

1.a) AB= 3cm A ' B' = 6cm therefore A ' B' = --2----× ABb) BC= 2cm B' C ' = 4cm therefore B' C ' = --2----× BCc) CD= 3cm C ' D ' = 6cm therefore C ' D ' = --2----× CDd) AD= 2cm A ' B' = 4cm therefore A ' B' = --2----× AD

2.a) b)

Area of ABCD = 6cm2

Area of A ' B' C ' D'=24 cm2

Ratio of the area of figure B to the area of figure A = 24 cm2 : 6 cm2

The ratio in simplest form is:

4 : 1

22 : 1

Emphasise to learners that the area of the image = 4 times the area of an objectThis means that area of the image = 22× area of the objectIn general, if a shape enlarges by a factor of k, then the area of the image = k2 × area of the object



141


4. V=32mm2×12mm=384mm3

5. Length of edge = 3√216m3=6m

142



TOPIC: Expressions, Equations

CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to find products of algebraic expressions, factorise, simply algebraic expressions and solve algebraic equations)

RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 4 Disc 1 GDE 16-01-2014 2014







20min Place the learners in groups with the classwork and allow them to do the exercises. Walk around and facilitate where necessary.

1. Expand and simplify:a) 2 (x2+4 x+8 )b) (x+2)( x+5)

2. Factorise:

CAPSTerm: Page reference:

143


a) 25a2−9b) 1−16 x2

c) 2 x2−2d) ( x+ y )2−b2

e) 4 x6−19

f) −(x+ y )2+1g) x2+5 x+6h) x2−5 x+6i) 2 x2+10 x+12j) −2b2+6b−4

3. Simplify:

a) x2−9x2+x−6

÷ x2−3 xx+1

b)2

x2+4 x−12

−1x−2

4. Solve the following equations:

a) 4(2m – 5) = 5 – 2(m + 1) b) 3(x – 1) – 4x = 5 – 2(x+ 1)c) 2(x – 3) = x- 3(x+ 2)


Learners must bring all materials for the SBA task – Project in the next lesson.e.g: cardboard; scissors; glue etc…

144


REFLECTION


Class work

1. Expand:a)

2 (x2+4 x+8 )

b)(x+2)( x+5)

2. Factorise:a)

25a2−9

b)1−16 x2

c)2 x2−2

d)

145


( x+ y )2−b2

e) 4 x6−19

f) −(x+ y )2+1

g) x2+5x+6

h) x2−5 x+6(x−3)(x−2)

i) 2 x2+10 x+12

j) −2b2+6b−4¿−2 (b2−3b+2 )¿−2 (b−1 ) (b−2 )

146


3. Simplify:

a) x2−9

x2+x−6 ÷ x

2−3 xx+1

b) 2

x2+4 x−12

−1x−2

147


4. Solve the following equations:a) 4(2m – 5) = 5 – 2(m + 1)

8m−20=5−2m−28m+2m=5+20−210m=23

m=2310

¿2 310

b) 3(x – 1) – 4x = 5 – 2(x+ 1)3 x−3−4 x=5−2 x−2

3 x−4 x+2 x=5+3−2 x=6

c) 2(x – 3) = x- 3(x+ 2)

148


149


Grade 9 Project Geometry of 3D Objects Marks: 48

1. Use the following nets to build 1.1 A rectangular prism1.2 A triangular prism1.3 A cylinder

2. Change all the dimensions by multiplying by 2 and build another rectangular prism in each – build again.3. Work out the surface area and volume of both sets of prisms and compare them.

a)

150


b)

c)

151


Use the following rubric to allocate marks for learners’ objects:

1.1 A rectangular prism. Criteria

Neatness (3)

Accuracy (4) (original + enlarged)

Materials used (2)

Due date (2)

Answers (5)

Total [16]

1.2 A triangular prismCriteria

Neatness (3)


Materials used (2)

Due date (2)

Answers (5)

Total [16]

152


1.1.1.1.2.1.3. A cylinder

Criteria

Neatness (3)

Accuracy (4)(original + enlarged)

Materials used(2)

Due date ( 2 )

Answers (5 )

Total [16 ]

153



TOPIC: Expressions, Equations


manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs





Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations.



5min Give learners their SBA project marks and correct answers


25min Give the exercise and allow learners to explain to each other how to do them, also revise the examples given in term 4; week 3 lesson 8.1. Simplify:

a)b)c) ( 4a2+2b ) ( 4a−2ab+9c )

CAPSTerm: 1 and 3Page :130-131141 -145

154


d) 9 x2( 13x+2x3)−4 x( 1

2x4−3 x2)

2. Solve the following equations:1. 4 ( x+2 )−3=2 (3−x )

2.



REFLECTION

155



Classwork

1.a)

b)

c)( 4a2+2b ) ( 4a−2ab+9c )

¿16a3−8a3b+36a2c+8ab−4ab2+18bc

d)9 x2( 1

3x+2x3)−4 x(1

2x4−3 x2)

¿3 x3+18 x5−2 x5+12x3

¿16 x5+15x3

156


2.a) 4 ( x+2 )−3=2 (3−x )

4 x+8−3=6−2x4 x+2 x=6−8+3.6 x=1

x=16

b)

157



TOPIC: Expressions, Equations, Functions and Straight Lines





Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines


Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines


LESSON PRESENTATION/ DEVELOPMENT/CLASSSWORK

25min 1. Simplify:

a)

2. Solve for :

a)b)

CAPSCAPSTerm: 1 and 3Page :130-131141 -145

158


a) Use the graph to calculate the gradient of the straight line.b) Determine the equation of the straight line.c) Write down the gradient of any other straight line which can be drawn parallel to the given

line

159



5min 1. Solve for :

a) 2.

a) Write down the defining equation of each of the following straight line graphs.

b) What can you deduce about the lines AD and BC. Give a reason for your answer.

REFLECTION

160



Classwork Homework

1.a)

OR x2−4 x+4−4¿ x2−4 x¿ x (x−4)

2.a)

b)

3.

1.a)

2.

a) mBC=−4−00−(−2 )

=−2

∴ y BC=−2 x−4

mAD=4−00−2

=−2

∴ y AD=−2 x+4

b) AD‖BC because the gradients are equal to each other

161


a)

b) c)

162











163




5min 1.a)

2. a) mBC=−4−00−(−2 )

=−2

∴ y BC=−2 x−4

mAD=4−00−2

=−2

∴ y AD=−2 x+4

b) AD//BC because the gradients are equal to each other


25min Allow learners to engage with each other in groups on methods of solving the exercise:1.Simplify the following expressions

a)b)

CAPSTerm: 1 and 3Page reference:130-131

141 -145

164


2. Solve the following equations:a) b)

3. Determine the gradient of the following straight line:

, as well as the intercept and the intercept



REFLECTION

165



Classwork Homework

1.a)

b)

2.a)


166


b)

3.

intercept: Let :

intercept:

intercept: Let :

intercept:

167











168




25min Do each example on the board after giving learners 30-60seconds to solve. Explain how the problems were solved using previous rules learnt.

1. Factorise the following expressions fully, using any suitable method:a) 3 x2 y−9x y2+12x3 y3

b)

2. Simplify the expression below:

a)

3. Draw the graph of

CAPSCAPSTerm: 1 and 3Page :130-131141 -145


1. Factorise the following expressions fully, using any suitable method:

a)b)


a)3. Find the equation of the graph

REFLECTION

169

x

y



Classwork Homework

1.a)

b)

2. a)

1. a) (2 x− y )(2x+ y )

b) (x−2)(x−9)

2. 9 y2

7

3. y=−x+3

170


3

171













5min 1.a) 4 x2− y2

(2 x− y )(2x+ y )

b)

2.

172


a)

3. m=0−33−0

=−1

∴ y=−x+3


25min Do each example on the board after giving learners 30-60seconds to solve. Explain how the problems were solved using previous rules learnt.

1. Simplify:

a)

b)

c)

2. Factorise

a)

b)

3. Solve for :

a)

CAPSCAPSTerm: 1 and 3Page reference:130-131141-145

173


4. Study the graph below:

a) What type of graph is this?b) Is it an increasing or decreasing function?c) Approximately what ℉ is freezing point?


Homework follows in the next lesson.

REFLECTION

174

x

y


175



1.a)

b)

c)

2. a)

b)

1.a) 4 x2− y2=(2x− y )(2 x+ y )

b)

2.a)

3. m=0−33−0

=−1

∴ y=−x+3

176


3.a)

4. a) Linearb) Increasingc) 30℉

177











178




25min Allow learners to work in pairs to complete the exercise. Stop learners after 5 minutes and answer questions, allow for further questions from the learners as well.

1. Simplify:

a)

b)

2. Solve for

a) x2 = 25

3 What is the equation of the graph drawn below?

CAPSTerm: 1 and 3Page reference:130-131141-145

179


4.

a) At how many minutes do both companies charge the same rate?b) When is company T’s rates lower than that of Company S?


1. Simplify:

2. , calculate , when .

3. Complete the table below and draw the graph.-3 -2 -1 0 1 2 3

REFLECTION

180



Classwork

1.a)

b)

2.a)

3.

4.a) At 20 minutesb) From 0 and 20 minutes

181










Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight linesInterpret straight lines



5min 1. Simplify

2.

3.

182


-3 -2 -1 0 1 2 3-2 -1 0 1 2 3 4


25min Give learners exercise to complete individually for 15 min then answer with explanations.

1. Simplify:

a)

b)

c)

CAPSCAPSTerm: 1 and 3Page reference:130-131141-145

183


2. Solve for if :

3. , calculate , when

4. Use the given coordinates to find the equation of the straight line graphs passing through them.

a) (16; 5) and (7; 2)

b) (−12;8) and (-6; -3)


Homework follows in the next lesson.

REFLECTION

184



Class work

1.a)

b)

c)

2.a)

1.

a)

2.

3.

-3 -2 -1 0 1 2 3-2 -1 0 1 2 3 4

185


b)

3.a)

m=y2− y1

x2−x1

m= 5−216−7

m=13

∴ y=13x+c

∴5=13

(16 )+c

∴ c=−13

b)

m=y2− y1

x2−x1

m=8−(−3)−12

− (−6 )

∴m=2∴ y=2x+c

186


∴−3=2 (−6 )+c∴ c=9∴ y=2x+9










187




25min Learners should work at the exercise in pairs and assist each other with methodology. The educator should walk around the class to ensure that all the work is completed and understood.

1. Simplify

a)

b) 9 x2( 13x+2x3)−4 x( 1

2x4−3 x2)

c)12abc ( 14a2b

c+ 8ac3

b−22c3b3

a )2. Given that a=−1 ;b=7∧c=0 find the value for each of the following expressions:

a) 17abcb) 3a+2b−7 c

3. Solve for :

a) 4 ( x+2 )−3=2 (3−x )

b) 4 ( x−7 )+6 (2−3x )=5 (x−6 )

4. a) On the same Cartesian plane draw the graphs y = 4 and x = 4.

b) What is the gradient for each graph?

c) What do you notice about these two graphs?

CAPSCAPSTerm: 1 and 3Page :130-131141-145


Learners must prepare for weekly test on expressions, equations, functions and straight line graphs

188


REFLECTION


Classwork

1.a)

b)

9 x2( 13x+2x3)−4 x( 1

2x4−3 x2)

¿3 x3+18 x5−2 x5+12x3

¿16 x5+15x3

c)

12abc ( 14a2b

c+ 8ac3

b−22c3b3

a ) ¿7a3b2+4a2 c4−11b4 c4

2.a)

17abc ¿17 (−1 ) (7 ) (0 ) = 0

b)

189


3a+2b−7 c

¿3 (−1 )+2 (7 )−7 (0 )¿−3+14

3.a) 4 ( x+2 )−3=2 (3−x )

4 x+8−3=6−2x4 x+2 x=6−8+36 x=1

x=16

b) 4 ( x−7 )+6 (2−3x )=5 (x−6 )4 x−28+12−18 x=5 x−304 x−18 x−5x=−30+28−12

−19 x=−14

x=1419

4.

For y = 4, the gradient is 0

For x = 4, the gradient is undefined

They are perpendicular to each other

190



Grade 9Weekly AssessmentTerm 4 - Week 4 15min

QUESTION 11.1 Calculate the intercept of the line (3)

[3]QUESTION 2

2.1 Simplify2.1.1 (2)

2.1.2 (2)2.1.3 (3)

2.2 Factorise:2.2.1

Solve for x :(2)

2.2.2 (3)[12]

TOTAL : 15

191


Grade 9Weekly AssessmentMEMORANDUMTerm 4 15min

QUESTION 11.1 intercept: Let :

intercept:

(3)

[4]QUESTION 2

2.12.1.1 (2)

2.1.2 (2)

2.1.3 (3)

2.22.2.1 (2)

2.2.2 (3)

[12]TOTAL : 16

192


SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 5 LESSONS 1 & 2

TOPIC: Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions





Rules for integers Conversion between decimal and common fractions Financial maths formulae Percentage, ratio and rate Highest Common Factor and Lowest Common Multiple


Apply all the knowledge when doing calculations Recall and apply formulae, where necessary.



10 min Revise the weekly assessment from the previous week


20min Give learners the exercise to do in groups to revise the topics for this week, then allow them to present to the class.1. Which of the following numbers belong to each group below?

−2 13

9π √20 1,23 .. . −3 √16


193


a) Integersb) Rational numbersc) Irrational numbers

2. List the following:a) The factors of 15b) The first four multiples of 6c) Find two rational numbers between -1,36 and -1,35

3. Calculate:

a) 1 12−1

6+5

3

b) 3 56−3 1

3

c) -9 – (21 – 4)d) 3 + 3 - (-7) – 8e) (450-349) x 2 + (-101)

4.US Dollar $8,4916 R11,78British Pound £13,7697 R7,26Euro €8,9 R11,24Jamie is travelling to Europe. She has R2 000 for spending.

a) How much will Jamie get in Euros?b) Will it be cheaper for her to go to London and use the British pound? Explain fully



REFLECTION

194


195


Answers: Term 4 Grade 9 Week 5 Lessons 1 & 2Classwork

1.

a) −3 ; √16

b) −2 1

3−3 √16

c) 9 π √20 1 ,23. . .

2.

a) 1 ; 3 ; 5 ; 15b) 6 ; 12; 18 ; 24c) −1 ,359 ; −1 ,358; −1 ,357 ; −1,356 ; −1 ,355 ; −1 ,354 ; −1,353 ; −1 ,352 ; −1 ,351

3.

a) 1 12−1

6+5

3

¿32– 1

6+ 5

3

¿ 9−1+106

¿ 186

¿3

b)3 56−3 1

3

¿ 236

−103

196


¿ 236

−10×23×2

¿ 236

−206

¿ 36=1

2a) -9 – (21 – 4)

= - 26

b) 3 + 3 - (-7) - 8=5

c) (450-349) x 2 + (-101)=101

4.a)

8,9=11 ,24x=200011 ,24 x=2000×8,9

x=2000×8,911 ,24

x=1583 ,63

b)

197


13 ,7697=7 ,26x=20007 ,26 x=2000×13 ,7697

x=2000×13 ,76977 ,26

x=3793 ,31She will get £3793,31Thus it will be cheaper.

198








Rules for integers Conversion between decimal and common fractions Financial maths formulae Percentage, ratio and rate Highest common factor and lowest common multiples





5 min Revise the weekly assessment from the previous week


20minGive the exercise to learners in their groups to come up with solutions; assign group leaders to present to the class:

1. Simplify:

a) (3 12+3 1

2 )÷1 34


199


b) 3 56−2 1

3

c) (-3)3

2. Calculate:a) 3 – (-9)b) -1 + 2 – 3 x 4c) 3 x 3 + 1 x 11 – 6d) √90−9

3. Don bought a music set for R199 and sold it to Tumi for R250. Thando bought a TV for R800 and sold it for R850.a) Calculate the profit that each one made.b) Calculate the percentage profit that each person made. (correct to one decimal place)c) Who made the larger profit?d) Who made the larger percentage profit?


REFLECTION

200


Answers: Term 4 Grade 9 Week 5 Lesson 3 and 4

Class work

1. Simplify:

a) (3 12+3 1

2 )÷1 34

¿( 72+ 7

2 )÷ 74

¿ 142× 4

7¿4

b) 3 56−2 1

3

¿ 236

−73

¿ 236

−7×23×2

¿ 236

−146

¿ 96=3

2=1 1

2

c) (-3)3

= -27

201


2. Calculate:a) 3 – (-9) =12

b) -1 + 2 – 3 x 4 =-11

c) 3 x 3 + 1 x 11 – 6 = 14

d) √90−9 = 93.a) Don: R250 –R199 = R51Thando R850-R800 =R50

b)Don:

51199

×100

=25 ,6 %

Thando:

50800

×100

=13 ,3 %

c) Dond) Thando

202











203




5 min Do homework – previous lesson


20min Learners work in pairs and educator assists with solutions individually, clarifying misconceptions when checking how learners are working out solutions

1. Simplify:

a) 3 37×(4 2

3−11

5 )b)

45+1 7

10c) -(3)2

d) 1,5 : 3

2. Calculate:a) 80 – 0

b)c) 11 + 12 + 13 + 14 + 115

3. Jabu deposits R2 000 into a savings account where the interest is 15% p.a. compounded annually.a) How much interest did he receive?

4. You receive R500 for your birthday. You decide to invest it for 15% p.a. for 3 years.a) Calculate the interest after 3 years.b) The final amount he will receive after 3 years.


CONSOLIDATION/CONCLUSION AND OR


204


HOMEWORK

REFLECTION Answers: Term 4 Grade 9 Week 5 Lesson 5 and 6

Class work Homework

1.

a) 3 37×(4 2

3−11

5 )

b)45+1 7

10

205


c) -(3)2

d) 1,5 : 3=1 : 2

2.a) 80 – 0 = 80

b)

c) 11 + 12 + 13 + 14 + 115=165

206


3.a)

A=P(1+ i)n

=2000 (1+15100

)12

=10700 ,50

b) Interest = R10 700 ,50 – 2 000 = R8 700,504.

a)

SI=Pr t100

=500×15×3100

=225

b) Interest : Initial amount + interest = R500 + R225 = R725

207













5 min


20minGive learners the exercise to work with in pairs, then provide answers, with explanations at intervals.



208


2.Si

mplify:

a)23× 9

10

b)24+ 4

4

3. Calculate:

a) 4 × - 5 = - 20 b) (-135) +145c) 20 – (8)(0) ÷ 2(-10)(-1)

4. Johnny borrows R800 from his brother to buy a new i-pod. The agreement is that he will pay the money back together with 12% p.a. simple interest after two years. How much will he have to pay back?

5. A car costs R90 000. Calculate the value of the car after 10 years if the rate of depreciation is 12% p.a. on a reducing balance.

6. Your dad bought a laptop for R11000. It depreciates in value on a simple interest basis. Calculate

209

Number N N0 Z Q Q' Non-Real Undefined

0

√0,9

10

−3111


the value of the new computer after 3 years.


Learners must prepare for the weekly assessment on : Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions

REFLECTION

210



Class work Homework


2. Simplify:

a)23× 9

10

23× 9

10=18

30

211

Number N N 0 Z Q Q' Non-Real

Undefined

0 No Yes Yes Yes No No No

√0,9 No No No No Yes No No

10

No No No No No No Yes

−311

No No No Yes No No No

1 Yes Yes Yes Yes No No No


b)24+ 4

4

¿ 2+44

3. Calculate:a) 4 × - 5 = - 20 b) (-135) +145 =10c) 20 – (8)(0) ÷ 2(-10)(-1)

4.

SI=Pr t100

=800×12×2100

=192

Total= R800 +R192 = R992

212


5.

A=P(1−i)n

=90000(1−12100

)10

=25065 ,096.

Dep=P×r×t100

=11000×24×3100

=7920New value = R 11 000 – R7 920 =R3 080

213


GRADE 9 WEEKLY ASSESSMENTMAX: 25TIME: 30min

QUESTION 1Which of the following numbers belong to each group below?

−2 13

9π √20 1,23 .. . −3 √16

1.1.1 Integers (1)1.1.2 Rational numbers (2)1.1.3 Irrational numbers (2)

1.2 List the following:1.2.1 The factors of 15 (3)1.2.2 The first four multiples of 6 (2)1.2.3 The prime factors of 36 (1)1.2.4 Find two rational numbers between -1,36 and -1,35 (2)

[13]QUESTION 2Find the selling price if 2.1 cost price is R720 with a profit of 40% (2)2.2 Price marked at R85 with VAT included. (2)2.3 Jamie buys 10 pens and sells them for R5 each. If the 10 pens cost him R52

calculate his profit or loss per pen.(2)

[6]QUESTION 3

3.1 A flight from Durban to Cape Town takes 1 hour if an aeroplane flies at 800km/h. At what speed will it fly if the same flight takes 2 hours?

(2)

3.2 John and Jane are two brands of shoes. John sells for R7,20 for 8 pairs while Jane sells for R7,76 for 9 pairs. Which brand is the cheapest?

(4)

[6]TOTAL: 25

214


GRADE 9 WEEKLY ASSESSMENT - MemorandumMAX: 25

QUESTION 11.1.1 −3 ; √16 (1)

1.1.2−2 1

3−3 √16 (1)

1.1.3 9 π √20 1 ,23. . . (1)

1.21.2.1 1 ; 3 ; 5 ; 15 (2)1.2.2 6 ; 12; 18 ; 24 (2)1.2.3 2×2×3×3 (2)1.2.4 −1 ,359 ; −1 ,358; −1 ,357 ; −1,356 ; −1 ,355 ; −1 ,354 ; −1,353 ; −1 ,352 ; −1 ,351

[13]QUESTION 22.1 40

100×720

1=R288Selling Pr ice =R720+R288=R 1066

(2)

2.2 14100

×851

=R11 ,90Selling Pr ice =R85+R11 ,90=R 96 ,90

(2)

2.3 Cost Pr ice : R52÷10=R5 ,20R5−R5 ,20=−R 0 ,20He makes a loss of 20c .

(2)

[6]QUESTION 33.1

Speed=8002

km/h

=400km/h

(2)

3.2John=R7 ,20

8=90 c

Jane=R7 ,769

=86 cJane is the cheapest

(4)

[6]TOTAL: 25

215


216


SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 6 LESSON 1 & 2

TOPIC: GEOMETRIC AND NUMERIC PATTERNS, FUNCTIONS, EXPRESSIONS AND GRAPHS


Define and apply rules for number systems Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs


PRIOR KNOWLEDGE Concepts and skills relating to Numeric and Geometric patterns, Input and Output values, Functions and graphs.



10 min Revise the weekly assessment form the previous week Page 126-129 &141-145


20min Give the learners the exercise to do in pairs and exchange answers. Provide answers with explanations every few minutes.

1. Consider the following pattern:1; 4; 9; 16; ….a) Find the next 3 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.

217


2. 7; 11; 15; 19; …a) Find the next 3 terms of the pattern

3.

a) Draw the next three patterns for the above.b) Describe in words the pattern.

3. If y=12 x−10 and x=−3 , x=−1 , x=0 , x=2 , x=4 , x=12. draw a graph to represent the above information. HINT: Draw a table of values first.



REFLECTION

Answers: Term 4 Grade 9 Week 6 Lesson 1& 2

Class work

1.a) 25; 36; 49b) The position of the term squaredc) 100

d)

218


2.a) 23; 27; 31

3.

a) b) Add one more circle than was added to the previous row, to the new row.

4.a)

x -3 -1 0 2 4 12

y 46 -22 -10 14 38 134

219


220

y




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: Define and apply rules for number systems Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs





20min Give the learners the exercises to do in groups and then present to each other.Walk around the class, providing guidance where necessary.

1. Study the pattern below:

a) Draw the next three patterns for the above.b) Write down in words what the pattern is.

Page 126-129 &141-145

221


2. Complete the following tables by filling in the missing input and output values and the formula for the pattern.a)

x-2 -1 0 1 2 7 n

y -7 -4 -1 26 44

b) Give the formula that defines the above table.c) Draw the graph of y=−3x+8.

3.Find the value of b 2 -6 3 b 4 ×(−3) -12 5 a

222



1. Find the next two terms of the pattern: 1; 2 ; 4; 8;….2. Find the equations of the following graphs:

a)

b)

REFLECTION

223


Answers: Term 4 Grade 9 Week 6 Lesson 3 & 4

Class work

1. a)

c) Add another E to the previous E’s.

2.a)

x -2 -1 0 1 2 7 10 16 n

y -10 -7-

4-1 2 17 26 44 3n – 4

b)T n=3n−4

224


3.b = 9

225

y

x




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: Define and apply rules for number system Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs





10 min 1. 16; 322.

3.

Page 126-129 &141-145


20min Allow learners to work in pairs and then provode answers after they have completed each example.

1. Consider the values in the following table. The rule for finding y is: divide x by −2 and subtract 4.

2 0 2 5-1 -3 -4 48

a) Use the rule to determine the missing values in the table, and write them in.

2. Sketch the graph of y=−x

226


3. Consider the following pattern: 7; 11; 15; 19; …a) Find the next 4 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.



REFLECTION

227


Answers: Term 4 Grade 9 Week 6 Lesson 5 & 6Class work

1.

-6 2 0 2 5 -104-1 -3 -4 -5 -6,5 48

2.

3.a) 23; 27; 31 ; 23b) Add 4 to the previous termc) 4(10) + 3 = 43

228

x

y




CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: Define and apply rules for number systems Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs





20min 1. Consider the following pattern: 8; 15; 22; 29; …a) Find the next 4 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.

2. Complete the following table of values

3. If y=−2x+7 and

x=−4 , x=−2 , x=0 , x=1 , x=3 , x=8

Page 126-129 &141- 145

229

x-2 -1 0 1 2 4 n

y 0.

5

1 2 128 2048


a) Draw a table to represent the above values of yb) Draw a graph to represent the answers in your table.


Learners prepare for the weekly assessment on Geometric and numeric patterns, functions, expressions and graphs

REFLECTION

230


Answers: Term 4 Grade 9 Week 6 Lesson 7 & 8

Class work

1.a) 36; 43; 50; 54b) Add 7 to the previous termc) 7(10) +1 = 71

d)

2.

x-2 -1 0 1 2 4 7 11 n

y 0.25 0.5 1 2 4 16 128 2048 2n

3.

x -4 -2 0 1 3 8

y 15 11 7 5 1 -9

231


232

x

y


Grade 9WEEKLY ASSESSMENTTerm 4Week6

QUESTION 11.1 Consider the following pattern:

1; 2; 4; 8; …1.1.1 Find the next 4 terms (3)1.1.2 Write in words how you obtained the next term. (2)1.1.3 Find the 10th term of the pattern (2)1.1.4 Write an algebraic expression for the pattern. (2)

[9]QUESTION 2Complete the following table of values

2.1 x -4 -2 -1 0 1 2 6 m

y -15 -

11

-7 -3 49

(6)

[6]TOTAL: 15

233


Grade 9WEEKLY ASSESSMENTMEMORANDUMTerm 4

QUESTION 11.11.1.1 16; 32; 64 ; (3)1.1.2 Double the previous term (2)1.1.3 512 (2)1.1.4 (2)

[9]QUESTION 2Complete the following table of values

2.1 x -4 -2 -1 0 1 2 6 14 m

y -23 -

15

-11 -7 -

3

1 17 49 4m-1

(6)

[6]TOTAL: 15

234


SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 7 LESSON 1 and 2

TOPIC: Constructions, Straight line Geometry and 2D shapes


construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides



How to construct angles and shapes The theory behind straight line geometry Triangles and quadrilaterals





10 min Revise the weekly assessment form the previous week

235



20min Learners work in groups and present their answers to the class. The educator emphasizes concepts and notation while answers are shared.

1.Refer to the diagram below and answer the questions that follow

a) Calculate the value ofx. Give a reason for your answerb) Determine the size of y. Give a reason for your answer


236

P

Q

A

C


2. In the diagram below,prove that ∆PTQ≡∆PTR. Give reasons for your answer.

3. Use a pair of compasses and ruler to make accurate constructions of the following angle:



REFLECTION

237


Answers: Term 4 Grade 9 Week 7 Lesson 1and 2Class work

1.a) 2 x+3 °+137°+ x+52 °=360° (Rev. ∠) 3 x=360°−192°

3 x=168 ° x=56°

b) y= x+52 ° (alt. ∠’s, AB∥CD) y=108°

2.STATEMENT REASON

PT¿PT CommonQT¿TR Given

Given

∴∆PTQ≡∆PTR S∠S

3. Step 1: Place the compass on one end point of the line segment (Point A).Draw an arc above and below the line.

238


Step 2: Without changing the compass width place the compass on point B. Draw an arc below and above the line so that the arcs cross the first two.

Step 3: Use a ruler to join the points where the arcs intersect. This line segment known as BD is the bisector of AB.

*the perpendicular is a line that meets another line at 90˚

239



TOPIC: Constructions, Straight line Geometry and 2D shapes





How to construct angles and shapes The theory behind straight line geometry Triangles and quadrilaterals





20min Learners must work individually and then present their answers to a partner across the room (make sure learners that share do not sit next to each other at first).

1. In the diagram below, A ¿ 70° quadrilateral ABCD is a rhombus extended to point E.


240


a) Calculate the value of A BC , give reasons for your answer.b) Determine the size of BC D , give a reason for your answerc) Determine the size of C B E , give a reason for your answer

2. In the diagram below, PQ∥ST, SR¿ST, Q PR=¿ 55° andPQ S=¿27°.

a) Determine the size of Q ST . Give a reason for your answer.b) Determine the size of T S R. Give a reason for your answer.c) Calculate the value of x . Give a reason for your answer.

3. Use a pair of compasses and ruler to make accurate constructions of the following angle

241



1. Choose the correct answers:

1.1

Calculate the value of A. B. C.D.

1.2 Refer to the figure in 1.1. Calculate the value of A.B.C.D.

242


1.3

Calculate the size of T

A.B.C.D.

1.4 Refer to the diagram in 1.3. Give a reason why ∆PQR /// ∆ TMSA. All angles are equalB. All sides are in proportionC. A;A;SD. S;A;S

REFLECTION

243


244



Classwork

1.a) is a rhombus A BC=18 00−700 ¿)¿1100

OR 2 A BC=3600−2¿ ¿)A BC=1100

b) BC D= A=700(opp .angles of arhombus)

c) C B E=700(corresponding angles AD ∥BC )

2.

a) (Alt. ∠s, QP∥TS )

b) (Cor. ∠s, QP∥TS¿

c) (sum of the ∠s ofa∆ ¿

x=180°−55°

2 ¿∠s opp. to equal sides)

x=¿ 62,5° 3. We know that:

So, to construct an angle of 30º, first construct a 60º angle and then bisect it. Often, we apply the following steps.Step 1: Draw the arm PQ.Step 2: Place the point of the compass at P and draw an arc that passes through Q.Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.

245


Step 4: With the point of the compass still at Q, draw an arc near T as shown.Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.

Step 6: Join T to P. The angle QPT is 30º.

246



TOPIC: Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability



RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, DVD Grade 9 Term 3 Disc 1; DVD Grade 9 Term 3 Disc 3; DVD Grade 9 Term 4 Disc 1


Formulae for area and perimeter and volume Properties of 3D shapes Mean; mode Range Graphical representation of data Probability definition Tree diagrams; two way tables


Use formulae to calculate the area, perimeter and volume of 3D shapes Find the measures of central tendency, given data Represent and interpret data on and off a graph Draw and interpret tree diagrams and two way tables



10min 1.1 A1.2 B1.3 B1.4 A

LESSON PRESENTATION/

20min Learners must attempt these questions individually and the educator must present solutions as the class completes each example.

CAPSTerm: T3 and

247


DEVELOPMENT/CLASSWORK 1. The area of a parallelogram below is 156 mm2, MR¿12 mm and

NR¿5 mm. Calculate the length of TS.

2. PQRS is a square with inscribed circle O where r ¿7 mm. Calculate the area of the shaded part

correct to one decimal place. Take. π=227

3. Complete the table below:

T4Page reference:146-148 and 149-153

248

12 mm

5 mm

M T

SN R

P Q

O

RS


Platonic Solid Shape of faces Number of facesOctahedronIcosahedron

4.

Name the above shapes.



REFLECTION


249


Class work

1.

2. Area of shaded part ¿ (Area PQRS – Area of circle) ÷4

¿ {14mm×14mm−¿(227×7mm2)} ÷4

¿ (196 mm2−¿ 154mm2) ÷4 ¿ 42 mm2÷4 ¿ 10,5 mm

3.

250


Platonic Solid Shape of faces Number of facesOctahedron Equilateral triangles 8Icosahedron Equilateral triangles 20

4.A- TetrahedronB- OctahedronC- Icosahedron

251



TOPIC: Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability



RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, DVD Grade 9 Term 3 Disc 1; DVD Grade 9 Term 3 Disc 3; DVD Grade 9 Term 4 Disc 1


Formulae for area and perimeter and volume Properties of 3D shapes Mean; mode Range Graphical representation of data Probability definition Tree diagrams; two way tables


Use formulae to calculate the area, perimeter and volume of 3D shapes Find the measures of central tendency, given data Represent and interpret data on and off a graph Draw and interpret tree diagrams and two way tables

252




25min 1. Given the circle below with right-angled triangle BCD. BD is 7cm and

DC is 5cm.

a) Find the diameter of the circle.b) Find the area of triangle BCD.c) Find the area in the circle that is not covered by ∆BCD.d) Find the circumference of the circle

2. If the perimeter of hexagon is 24 cm. The shape in Figure 2 is made of the hexagons of the same size as in Figure 1. What is the perimeter of the shape drawn in Figure 2?

CAPSTerm: T3 and T4Page reference:146-148 and 149-153

253


3. Complete the table beow:Platonic Solid Shape of faces Number of facesOctahedron Equilateral triangles

Equilateral triangles 20Hexahedron 4


Prepare for the weekly assessment on :Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability

REFLECTION

254



Classwork Homework

1.a) BC2=B D2+C D2

BC2=(7 )2+ (5 )2

BC2=49+25

BC2=74

BC=√74

BC=8.6

b) Area=12b×h

Area=12×5×7

Area=17.5 cm2

c) Area of Circle ¿ π r2

¿ π (4.3 )2

¿58.09 c m2

Area not covered by ∆BCD = 58.09 – 17.5

= 40.59 cm2

d) Circumference ¿2πr

Prepare for the weekly assessment on :Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability

255


¿2π ( 4.3 )

¿27.02 cm

2.

1 side = 24cm

6

¿ 4 cm P¿ 4 cm × 12 ¿ 48 cm

3.Platonic Solid Shape of faces Number of facesOctahedron Equilateral triangles 8Icosahedron Equilateral triangles 20Hexahedron Square 4

256


Grade 9WEEKLY ASSESSMENT 15 minTerm 4 Week 7

QUESTION 11.1 Study the diagram belown and answer the questions:

Determine, with reasons the sizes of the following:1.1.1 (2)

1.1.2 (2)

1.1.3 (2)

1.1.4 (2)

1.1.5 (2)

[10]QUESTION 2

2.1 A triangular prism is shown in the figure below. The base is a right-angled triangle with DF= 8 cm, FE = 6 cm and the height 15 cm. A B C

15cm F

8 cm 6 cm

D E

2.1.1 Calculate the area of ΔDEF. (2)

2.1.2 Calculate the volume of the prism.(3)

[5]

TOTAL: 15

257


Grade 9WEEKLY ASSESSMENT 15 minTerm 4

QUESTION 11.1

1.1.1

(2)

1.1.2 (2)

1.1.3

(2)

1.1.4

(2)

1.1.5

(2)

[10]QUESTION 2

2.1.1

Area ΔDEF =1

2×8cm×6cm

=24 cm2

(2)

2.1.2 V =Area of base×height =24 cm2×15 cm

=360cm3 (3)

[5]TOTAL: 15

258



TOPIC: Transformations and Straight Line Graphs


transform co-ordinates and shapes across quadrants draw and interpret straight line graphs



plotting points in the four quadrants transformations across the quadrants how to draw and interpret straight line graphs


plot points in the four quadrants transform points and shapes across the quadrants, using reflections, rotations,

enlargements and reductions how to draw and interpret straight line graphs



10 min

Revise the weekly assessment form the previous week

259



20min

1. Draw the enlarged or reduced image of the following figure according to

the scale factor given. Scale factor =



260


3.Find the equation of the graph given below;



REFLECTION

261


Answers: Term 4 Grade 9 Week 8 Lesson 1and 2

Class work1.

262


2.

3. y=mx+c0=m (1.5 )−3m=2

y=2x−3

263



TOPIC: Transformations and Straight Line Graphs



RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 2; Grade 9 Term 4 Disc 1.


plotting points in the four quadrants transformations across the quadrants how to draw and interpret straight line graphs


plot points in the four quadrants transform points and shapes across the quadrants, using reflections, rotations, enlargements and reductions how to draw and interpret straight line graphs

264




20min Learners work in pairs and individuals are called to present answers with guidance of the educator.

1.

Translate PQR 5 units to the right and 3 units downTranslate PQR 5 units to the right and 3 units downAre all the triangles congruent?

2. Determine the equations of the straight lines passing through the following points:

a)

1 2 3 4 55 4 3 2 1


265


b)-4 -2 0 2 42 0 -2 -4 -6

3. Draw the graphs of the following graphs on the same system of axes:

and

1.

1.3 Yes

266


2.a)

b)

267


3.


1. Draw the graphs of on the same system of axes.

268


a) State the rule for the transformation from A to B in the form b) Describe in words the transformations from G to Hc) Which of the transformations are:

i) Reflectionsii) Rotations

REFLECTION

269


Answers: Term 4 Grade 9 Week 8 Lesson 3 and 4Class work

1.

1.3 Yes

2.a)

b)

270


3.

271



TOPIC: Expressions and equations

272











10 min 1.

-2 0 22 0 -2

273


2.

a) b) reflection in the line c)

i)

ii)

274



20min Learners must be put in groups, they answer the exercise, then are shuffled around so that they can explain to other members of the class how to answer the questions. The educator facilitates the process by walking around and correcting misconceptions as they arise.

1. Simplify:

a)

b)

c)

d)

2. Solve for :

a)x2 = 25

b)


4. Multiply by




REFLECTION

275



Class work Homework

1.a)

b)

c)

d)

2.a)

2.

-2 0 22 0 -2

276


b)

3.

4.

2.

a) b) reflection in the line c)

i)

ii)

277



TOPIC: Expressions and equations










20min Learners must be put in groups, they answer the exercise, then are shuffled around so that they can explain to other members of the class how to answer the questions. The educator facilitates the process by walking around and correcting misconceptions as they arise.

1. Simplify:

a) 12x2 y−6 xy2

3 xy

b) (xa −¿3)(xa + 3)

c) √34 y6−9 y6


278


d) (2 x−3 )2−4 ( x−1 ) ( x+1 )

e)2(x+4)

2−2

f)p2q2×( p−2)2

p−2

2. Solve for :a)b) 3 ( x−1 )=2 x+5c) ( x−2 ) ( x−2 )=0

d)2x3

− x+14

=1

e) 2− x=64

3. If , then =…


1min Learners prepare for the weekly assessment on expressions and equations

REFLECTION

279



Class work Homework

1.a)

b) (xa - 3)(xa + 3)

c) √34 y6−9 y6

¿√25 y6

¿5 y3

d) (2 x−3 )2−4(x−1)(x+1)

¿4 x2−12x+9−4 (x2−1) ¿4 x2−12x+9−4 x2+4 ¿−12 x+5

Learners prepare for the weekly assessment on expressions and equations

280


e)2(x+4)

2−2

¿ x+4−2¿ x+2

f)p2q2×( p−2)2

p−2

¿ p2q2× p−4

p−2

¿ p2−4+2q2 ¿ p0q2

¿q2

2. a)

b)

281


c) ( x−2 ) ( x−2 )=0x=2

d)2x3

− x+14

=1

12×( 2 x3 )−12×( x+1

4 )=12×1

8 x−3 x−3=12 5 x=15x=3

e)2− x=642− x=26

x=−6

282


Grade 9WEEKLY ASSESSMENT 15 minTerm 4Week 8

QUESTION 11.1 How many values of satisfy the equation ?

A 0

B 1

C 2

D More than 2

[2]

QUESTION 22.1 The length of a rectangle is 4cm more than the width. If the perimeter is

32 cm, calculate the length and the width(5)

2.2 If I multiply a certain number by 5, I get the same answer as when I subtract the

number by 48. What is the number? (3)

[8]

QUESTION 2

2.1

Calculate if

(2)

2.2 Simplify the following expression

(3)

[5]TOTAL: 15

283


Grade 9WEEKLY ASSESSMENT MEMORANDUM15 minTerm 4

QUESTION 11.1 A (2)

[2]

QUESTION 22.1 Let the width be x, then length will be x +4

Let the width be then the length will be

Width is 6cm and the length is 10 cm. (5)

2.2

Let the number be

The number is 8. (3)

[8]

QUESTION 2

2.1

(2)

2.2

(3)

[5]TOTAL: 15

284


285


Grade 9Term 4Assessments

286


GRADE 9 CLASS TEST 1Functions and Relationships – Term 3MAX: 30TIME: 30 minutes

QUESTION 1

1.1 Determine the equations of the following graphs:

1.1.1 (2)

1.1.2 (2)

1.1.3 y

x

(2)

287

y

x


1.1.4 y(2)

1.1.5 (2)

[10]

QUESTION 2

2.1 Determine the x-intercept and gradient of the following graph:

(3)

288

x


2.2 Determine the gradient of the function passing through (2 ;2) and (−4 ;3). (3)

2.3 Determine equation of the straight line passing through (2 ;1) and perpendicular to y=3 x−5.

(4)

[10]

QUESTION 3

3.1 y=−x+33.1.1 Complete the table using the equation y=−x+3

x -3 -1 0 2 4y

(2)

3.1.2 Plot the graph on a Cartesian plane. (2)

3.2 Given: y=2x−13.2.1 Determine the x- and y−¿intercepts of the function. (4)

3.2.2 Plot the function on a Cartesian plane. (2)

[10]

TOTAL: 30

289


GRADE 9 CLASS TEST – MemorandumFunctions and Relationships – Term 3MAX: 30TIME: 30min

QUESTION 1

1.1 Determine the equations of the following graphs:

1.1.1

y=x

(2)

1.1.2

x=3

(2)

1.1.3

y=−4

(2)

290

y

x

x

y


1.1.4

x=−2

(2)

1.1.5

y=−x

(2)

[10]

QUESTION 2

2.1

x−int ercept : Let y=0x−2=0x=2(2 ;0)

(3)

291x

y

y

x


m=y2− y1

x2−x1

=(0−(−2 )(2−0 )

=22

=1

2.2m=

y2− y1

x2−x1

=(3−2)(−4−2)

=1−6

(3)

2.3m=−1

3; P(2 ;1)

y=mx+c

1=−13

(2)+c

c=53

y=−13x+5

3

(4)

[10]

QUESTION 3

3.1 y=−x+33.1.1 x -3 -1 0 2 4

y 6 4 3 1 -1(2)

3.1.2 (2)

292

xy


3.2

3.2.1x−int ercept : Let y=02x−1=02x=1

x=12

(12 ;0)y− int ercept : Let x=0y=2(0)−1y=−1(0 ;−1 )

(4)

3.2.2 (2)

[10]

TOTAL: 30

293

xy


GRADE 9 CLASS TEST 2GEOMETRY OF 2D SHAPESMAX: 20TIME: 30min

QUESTION 1

1.1 Name 2 properties of a parallelogram. (2)

1.2

Determine with reasons, without using a protractor, the size of:

1.2.1 x (3)

1.2.2 y (2)

1.2.3 z (2)

[9]

QUESTION 2Ín ∆ABC and ∆PQR is B = P = 90°; AB = PQ = 9cm and AC = QR = 34cm

2.1 Determine if the above pair of triangles is congruent. Give reasons. (4)2.2 Calculate the size of R with reasons if A=35° . (3)

2.3 Calculate the length of BC. (4)[11]

TOTAL: 20

294


GRADE 9 CLASS TEST – MemorandumGEOMETRY OF 2D SHAPESMAX: 20TIME: 30min

QUESTION 1

1.1 The opposite angles are equal The diagonals bisect each other The opposite sides are equal The opposite sides are parallel (any two)

(2)

1.2

1.2.1 3 x=58 °+ x ext. <s of ê 3 x−x=58 ° 2 x=58 ° x=29 °

(3)

1.2.2 y = 180°- (58° + 𝑥) sum of int. <s ∆ ¿180 °−87° = 93°

(2)

1.2.3 𝑧 = 𝑥 = 29° alt. <s (AE//DC) (2)

[9]QUESTION 2

2.1 ¿∆ ABC∧∆ PQRB=P=90 ° given AB = PQ given AC = QR given ∴∆ ABC≡∆PQR (RHS)

(4)

295


2.2 A=P ≡∆R=180°−( P+Q ) sum int < ∆¿180 °−(90 °+35° )¿180 °−125 °¿55 °

(3)

2.3 BC2 = AC2 – AB2

= 342 - 92

=1156 – 81BC = √1075 = 32,78719.... = 32,79cm

(4)

[11]TOTAL: 20

296


GRADE 9 CLASS TEST 3GEOMETRY OF 3D OBJECTSMAX: 20TIME: 30 min

QUESTION 1

1.1 Complete the table below:

Name Shape of faces

No of faces

No of vertices

No of edges

Triangles 4

6

Triangles 12

[10]

QUESTION 2

Draw the net shapes for the following 3D objects:

2.1 (2)

297


2.2 (2)

2.3 (2)

2.4 (2)

2.5 (2)

[10]

TOTAL: 20

298


GRADE 9 CLASS TEST – MemorandumGEOMETRY OF 3D OBJECTSMAX: 20TIME: 30min

QUESTION 1

1.1

Name Shape of faces

No of faces

No of vertices

No of edges

Tetrahedron Triangles 4 4 6

Octahedron Triangles 8 6 12

Icosahedron Triangles 20 12 30

Cube/hexahedron

Squares 6 8 12

Dodecahedron Pentagons 12 20 30

[10]

QUESTION 2

2.1 (2)

299


2.2 (2)

2.3 (2)

2.4 (2)

2.5 (2)

(2)

[10]

TOTAL: 20

300


GRADE 9 CLASS TEST 4GEOMETRY OF STRAIGHT LINESMAX: 20TIME: 30 min

QUESTION 11.1 Find the value of b in each of the following:1.1.1 a)

b)

(2)

1.1.2 (2)

301


1.1.3

(2)

1.2 Name the angle relationships between the following:

1.2.1 C and F (2)

1.2.2 F and D (2)

[10]QUESTION 22.1 Find the value of x in the following:

If AB // CD, A4=A3 and O2=60 °(6)

[6]

302


QUESTION 3Find the value of x in each of the following:

3.1 (2)

3.2 (2)

[4]TOTAL: 20

303


GRADE 9 CLASS TESTGEOMETRY OF STRAIGHT LINESMemorandumMAX: 20TIME: 30 min

QUESTION 11.11.1.1 b=180 °−50 °

=130° angles on a straight line

(2)

b=360 °−(209 °+96 ° )=55° angles around a point/revolution

1.1.2 b=43 ° vertically opposite angles (2)1.1.3 b=90 °−63 °

=27 ° complementary angles

(2)

1.21.2.1 C and F

alternate angles

(2)

1.2.2 F and DCo-interior angles

(2)

[10]QUESTION 22.1

AB // CD, A4=A3 and O2=60 ° (6)

304


O4=O2=60 ° (Vertically opposite angles)O4+ A4+ A3=180 ° ( Angles of triangle )

A4+ A3=180° −60 °=120 °

but : A4= A3 ( given )

A4= A3=120°2

=60 °

B2=A4 (alternate angles )B2=60 °

60 °+ { B 2

=180 ° ( straight line ) ¿ B2=180°−60 ° ¿ x=120° ¿¿

[6]QUESTION 33.1

2 x−50 °= x−30 °2 x−x=−30 °+50 °x=20 ° (vertically opposite angles)

(2)

3.2 x+44 °+107 °=180 ° (co−int erior angles)x=180 °−(44 °+107 )° }¿ =29 °

(2)

[4]TOTAL: 20

305


GRADE 9 CLASS TEST 5TRANSFORMATION GEOMETRYMAX: 20TIME: 30 min

QUESTION 11.1 ∆ABC with A(3;0), B(2;4) and C(0;2) is enlarged using the rule

(x ; y ¿→ (2x ;2 y ). The resulting image is A’B’C’ Draw ∆ABC and its image on the given grid.

(2)

1.2∆ABC is relfected in the y-axis. The reflection is A

} } B rSup { size 8{C} } } {¿ ¿¿. 1.2.1 Draw the image on the given grid A

} } B rSup { size 8{C} } } {¿ ¿¿ (2)

1.2.2What is the distance between A and A

} } } { ¿¿¿?(2)

[6]QUESTION 2

Give the coordinates of the following if:2.1 A ( -3 ;4 ) is reflected about the x−¿axis (2)

2.2 B ( 4 ; -12 ) is reflected about the line y=x (2)

2.3 C ( -2 ; 4 ) is translated 4 units down and 12 units to the left. (2)

2.4 D ( 3 ; -1 ) is reflected about the y−¿axis. (2)

2.5 E’ ( 16 ; 8 ) is enlarged by a factor of 4. (2)

2.6 F’ ( -2 ; 4 ) is translated 3 units up and 4 units to the right. (2)

[12]TOTAL: 18

306


QUESTION 1:

y

12

11

10

9

8

7

6

5

4

3

2

1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

-11

-12

307


GRADE 9 CLASS TEST - MEMORANDUMTRANSFORMATION GEOMETRYMAX: 20TIME: 30 min

QUESTION 11.1 and 1.2.1

(4)

1.2.2 6 (units) (2)

[6]QUESTION 22.1 A’ (-3 ; -4 ) (2)2.2 B’ (-12 ; 4 ) (2)2.3 C’ ( 0 ; -14 ) (2)2.4 D’ (-3 ; -1 ) (2)2.5 E ( 4 ; 2 ) (2)2.6 F (-3 ; 2 ) (2)

[12]TOTAL: 18

308


TEMPLATE TO MARK QUESTION 1

𝑦9 B’8

7

6

B” 5 C’ B4

3

C”

C

2

A” 1 A A’ 𝑥-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-1

-2

-3

-4

-5

-6

-7

-8

-9

309


Grade 9Term 4MathematicsProjects

310


Grade 9Project 1DATA HANDLING: FrequencyMax: 20

Conduct a survey at your nearest intersection for 1 hour.

Count the number of minibuses (taxis), buses, cars and vans that pass by in that interval that you observe.

1. Draw up a tally table for:

Minibuses (taxis)BusesCarsVans

2. Draw a bar graph to represent your information.

3. Answer the following questions:

3.1 Where is the intersection situated?3.2 Which are the most used type of vehicle?3.3 What could be the reason for this?

Use the following rubric to allocate marks for learners’ answers:

Criteria

Neatness (3)

Accuracy (4)

Bar graph (6)

Due date (2)

Answers (5)

Total [20]

311


Grade 9Project 2Financial MathsMax: 15

Find advertisements for 5 household items such as a fridge or a stove from a newspaper. (Do NOT use the internet!)Cut out and paste the adverts, then work out the interest you would pay on each item.

Answer the following questions:1. What other type of interest could be charged on the items you

chose?2. Which would be cheaper, to pay cash for the items or on hire

purchase?3. What do you think would be the most purchased item from the

items you chose?

Use the following rubric to allocate marks for learners’ answers:Criteria

Neatness (3)

Accuracy (4)

Due date ( 2 )

Answers (6 )

Total [15 ]

Note all learners’ answers will be unique to the advertisements they have chosen.

312


PROJECT 3 DATA COLLECTIONQuestionnaires

We can use different methods to collect data, for example questionnaires, face-to-face interviews or telephonic interviews. In this section, you will work with questionnaire questions that have multiple choice responses.

Here are two questions with multiple-choice responses from which a respondent will choose.

(A respondent is a person who responds to the questions)

How satisfied are you with our level of service? Not satisfied at all Fairly satisfied

Very satisfied

What is the colour of your eyes?

brown

green

blue

other

1. Write a suitable question with multiple-choice responses to find out the following information:

(a) What do teenagers spend their money on?

(b) How much time do Grade 8s spend on homework every day?

2. Choose one of the questions above. Write down what you think would be the best sample to use if you had to conduct this investigation.

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. Use the multiple-choice question that you chose in question 2 to collect the data. Keep the results for the next section.

313


Organising data

The way we organise and summarise data depends on the kind of data that we have. It also depends on what we want to find out from the data. Work in groups to explore this. Don’t worry about getting the answers right at this stage. You will learn about the different ways to organise and summarise data in this chapter.

Look at the following sets of data. For each one, discuss with your group and write down what we want to find out and what you think we need to do to the data.

1. Data collected to find out which day would be best to have a soccer club practice:Twenty-five learners’ preferred day for soccer practice

Tuesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Friday Friday Friday Tuesday Thursday Wednesday Wednesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Tuesday Wednesday Monday Thursday Tuesday

__________________________________________________________________________________________________________________________________________________________________________________

2. Data collected to find out whether 5-year-old children in a certain village have healthy body weights:Body weights of twenty-five children in kilograms, rounded off to the nearest 0,5 kg

17 kg 16,5 kg 13,5 kg 14 kg 18 kg 18 kg 14 kg 21 kg 13,5 kg 15 kg 15 kg 14,5 kg

15,5 kg 19,5 kg 17 kg 17,5 kg 14 kg 14 kg 20 kg 14,5 kg 16 kg 18 kg 12 kg 16 kg 19 kg

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. Data collected to find out how many learners answer a certain type of question in less than 20 seconds:Time taken (in seconds) by a group of learners to answer a question

20 25 24 33 13 26 10 19 39 31 11 16 21 17 11 34 14 15 21 18 17 38 16 21 25

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………..

314


4. Data collected to analyse the monthly salaries of employees of a small business:The monthly salaries of ten employees

R8 000 R2 500 R75 000 R6 000 R7 500 R5 200 R4 800 R10 300 R15 000 R9 500

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

315


PROJECT 3 MEMO – DATA

1. Write a suitable question with multiple-choice responses to find out the following information:(a) What do teenagers spend their money on?

(b) How much time do Grade 8s spend on homework every day?

Sample answers:

(a) On which of the following items do you spend most of your money?

food

clothing

air time

make-up or toiletries

entertainment

(b) How much time do you spend doing homework every day?

less than 1 hour

between 1 and 2 hours

between 2 and 3 hours

more than 3 hours

2. Choose one of the questions above. Write down what you think would be the best sample to use if you had to conduct this investigation.Sample answers:

(a) 50 teenagers from my school/50 teenagers from the local community

(b) All the Grade 8s in my school/20 Grade 8 learners from two schools in the area

3. Use the multiple-choice question that you chose in question 2 to collect the data. Keep the results for the next section.

Organising data

The way we organise and summarise data depends on the kind of data that we have. It also depends on what we want to find out from the data. Work in groups to explore this. Don’t worry about getting the answers right at this stage. You will learn about the different ways to organise and summarise data in this chapter.

Look at the following sets of data. For each one, discuss with your group and write down what we want to find out and what you think we need to do to the data.

1. Data collected to find out which day would be best to have a soccer club practice:Twenty-five learners’ preferred day for soccer practice

316


Tuesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Friday Friday Friday Tuesday Thursday Wednesday Wednesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Tuesday Wednesday Monday Thursday Tuesday

Sample answer: We want to know on which day the highest number of learners want to practise. We need to write down how many times each day appears.

2. Data collected to find out whether 5-year-old children in a certain village have healthy body weights:Body weights of twenty-five children in kilograms, rounded off to the nearest 0,5 kg

17 kg 16,5 kg 13,5 kg 14 kg 18 kg 18 kg 14 kg 21 kg 13,5 kg 15 kg 15 kg 14,5 kg

15,5 kg 19,5 kg 17 kg 17,5 kg 14 kg 14 kg 20 kg 14,5 kg 16 kg 18 kg 12 kg 16 kg 19 kg

Sample answer: We need to find out if these body weights are healthy compared to other children’s body weights. We could arrange the body weights in order and then summarise the whole set by using measures of central tendency and range. Grouping the data might be useful to show the number of body weights between 10 and 15 kg, 15 and 20 kg, and so on.

3. Data collected to find out how many learners answer a certain type of question in less than 20 seconds:Time taken (in seconds) by a group of learners to answer a question

20 25 24 33 13 26 10 19 39 31 11 16 21 17 11 34 14 15 21 18 17 38 16 21 25

Sample answer: We want to know how long different learners take to answer a question. We need to arrange the times in order and then look at a representation of the whole set. We could group the numbers to see how many are between 10 and 20 seconds, 20 and 30 seconds, etc. to answer the question.

4. Data collected to analyse the monthly salaries of employees of a small business:The monthly salaries of ten employees

R8 000 R2 500 R75 000 R6 000 R7 500 R5 200 R4 800 R10 300 R15 000 R9 500

Sample answer: This is a small data set of only ten values. We could arrange the data in order and then summarise it using measures of central tendency and range.

317


Grade 9 Project 4Geometry of 3D Objects Max: 48

1. Use the following nets to build 1.1 A rectangular prism1.2 A triangular prism1.3 A cylinder

2. Change all the dimensions by multiplying by 2 and build another rectangular prism in each – build again.

3. Work out the surface area and volume of both sets of prisms and compare them.

1.

2.

318


3.

Use the following rubric to allocate marks for learners’ objects:

1.3 A rectangular prism. Criteria

Neatness (3)


Materials used (2)

Due date (2)

Answers (5)

Total [16]

1.4 A triangular prismCriteria

Neatness (3)


Materials used (2)

Due date (2)

Answers (5)

Total [16]

319


2.2.1.2.2.2.3. A cylinder

Criteria

Neatness (3)

Accuracy (4)(original + enlarged)

Materials used(2)

Due date ( 2 )

Answers (5 )

Total [16 ]

320


Grade 9 Project 5Geometry of 3D Objects

Make a copy of the diagram below. Cut it out and fold it along the dotted lines. Attach the faces with sticky tape to make an open container with pentagonal faces.

Make another copy of the pentagon diagram, and make a second container.

321


Turn one of your containers upside down and put the two together to form a polyhedron.

Answer the following:

1. How many faces does your polyhedron have?2. Are the faces identical and what shape are they?3. Are the edges equally long, and how many edges are there?4. What is the common name for this polyhedron?

322


Grade 9 Project Geometry of 3D Objects Memorandum

ANSWERS1. 122. Identical regular pentagons3. 30 equally long edges4. Dodecahedron (5)

Use the following rubric to allocate marks for learners’ objects:Criteria

Neatness (3)

Accuracy (4)

Materials used (2)

Due date (2)

Answers (5)

Total [16]

323


GRADE 9TERM 4WORKSHEETS

324


Worksheet: Term 4 Grade 9 Week 1 Lesson 1Class workGive the learners the following exercise to complete in class:Complete the following table of real numbers:Numbe

r N N 0 Z Q Q’ Non-Real

Undefined

15 Yes Yes Yes Yes No No No

√3

0,14287

√ 14

−√1443√−1

√−1

325


Worksheet: Term 4 Grade 9 Week 1 Lesson 2Class work Homework

1. Divide R5 600 in the ratio 3: 4: 2.



4. Calculate the interest if R10 000 is invested at 10 % per annum compound interest for 3 years.

1. Simplify the ratio R250:R150:R1002. Divide 240g in the ratio 5 : 3 : 43. Calculate the interest if R6500 is invested for 3 years at 7,7% per

annum compound interest.4. Calculate the amount that will be in the bank after 5 years if R9500

was invested at 8% p.a. simple interest. 5. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange

rates are shown on the electronic notice board below.Currency Buy (R) Sell (R)US Dollar $ 1 8,1090 8,4586British Pound ￡ 1 12,7850 13,4767Euro €1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080


326



1. The weather forecast for the world on TV shows the following temperatures:

Minimum MaximumJohannesburg -4 0C 15 0CBloemfontein -10 0C -1 0CLondon -3 0C 14 0C

a) What is the difference between the minimum temperatures in Johannesburg and the minimum in Bloemfontein?

b) What is the rise in temperature from minimum to maximum in Johannesburg?

c) What is the rise in temperature from minimum to maximum in Bloemfontein?

2. Simplify:a) 4m5×3m7×−2m3

b) a7×a6

a8×a3

c) ¿

d) (−2 x2)¿

e) 2n8n+2

43n2−2n

1. Calculate:a)– 3(-11 + 5)

2. The minimum and maximum temperatures in Sutherland , Western Cape are shown in the table:

January August OctoberMin 0C 120 -160 50

Max 0C 290 00 220

a) What was the coldest temperature in Sutherland? b) What was the warmest temperature in

Sutherland? c) What is the difference between the two

temperatures?

3. Simplify:

a¿ 4 x2 y3

2x y5

b¿ 2 p8q4

8 p3qr÷ 16 p4

4 r

c ¿ 2x+1

3. 2x−1

327


Worksheet: Term 4 Grade 9 Week 1 Lesson 4Class work

1.In the figure, AB//ED, Determine the size of and

2. Calculate the values of and if

328



1. Determine whether the following are congruent, similar or neither:

a)

b)

329


c)

d)

330


2.Consider the triangles in the figure below. Prove∆ ABD≡∆CDB

3. Prove that ∆ ADE≡∆CFE

331



1. Use a pair of compass and a ruler to make accurate constructions of the following:

2.


332


Homework 1. Use a pair of compass and a ruler to make accurate constructions of the following:a) angle


b)

333


Worksheet: Term 4 Grade 9 Week 1 Lesson 7

Homework1. Simplify:

a) 2a2 (a−2)+2a(a2−3a )


4 x2+3 y2

3. Calculate the value of :; if

4. If and ,find the value of


6. If and y = -3, calculate the value of 2×−2xy


b)

c)

334


d)

e)

f)

335



1. Give the equation of the following:

2. Sketch the graph of y=−2

3. On the grid, draw the graphs defined by and . Label each graph and clearly mark the points where each graph cuts the axis and the axis.

336


337


4. Study the straight line graphs below and answer the questions that follow

Complete:a) The equation of line CD is… b) The equation of line AB is … c) The length of CE = …

338


Homework Revise for the weekly test: Topics:

1. Whole numbers i.e. number systems; financial maths; ratio and rate; integers2. Exponents3. Geometry of straight lines4. Geometry of 2D shapes5. Expression and equations

Functions and graphs

339


Grade 9 week 1 lesson 9

WEEKLY ASSESSMENT

QUESTION 1

In each of the questions below choose the correct answer.1.1 2a2 (a−2)+2a(a2−3a ) (2)

ABCD1.2 If x=5 and y=−4 , find the value of

4 x2+3 y2

(2)

A -148B 140C 148D -140

340


1.3 Solve for x: 3 x−1=−9

(2)

A.

B.

C.

D.

1.4 (2)

A.B.C.D.

341


1.5 Sketch the graph of (2)A.

B.

C.

342


D.

1.6

Calculate the value of .

(2)

ABCD

343


1.7

Choose a correct statement to describe the relationship between the above two triangles.

(2)

A

B

C They are not congruent

D They are neither congruent nor similar

1.8 Simplify : √ x8 + √ x16

A. x4+x8

B.C.D.

(2)

[16]

344


QUESTION 2

2.1 Complete the following statements:

2.1.1 ABC is an acute-angled triangle because_______________ (1)

2.1.2 DEF is a _____angled triangle because it has a 90° angle. (1)

2.1.3 GHI is an obtuse-angled triangle because ______________ (1)[3]

QUESTION 3

3.1 Calculate the interest if R1250 is invested for 3 years at 9% per annum compound interest. (4)

3.2 Calculate the amount that will be in the bank after 4 years if R6500 was invested at 5% p.a. simple interest.

(4)

[8]TOTAL 27

345


Worksheet: Term 4 Grade 9 Week 2 Lesson 1Classwork

1. Factorise the following expressions:a) 2 x2−8 xb) mx−my+5x−5 yc) 3m−3d−4de+4med) tv−uv−tw+uw

2. Solve for

a)b)

346


Worksheet: Term 4 Grade 9 Week 2 Lesson 2Class work1. Use the following graph on the chalkboard. Ask learners for the dependant and independent variables and then ask

learners the questions to interpret the graphs.

The graph below represents the charge per day from two car rental companies. Company A charges an initial fee of R120 and then charges R25 per day. Company B charges no initial fee, but charges R75 a day. According to the graph...

A. Company A is cheaperB. Company B is cheaper C. Company B is cheaper if you hire the car for two days.D. Company A is cheaper if you hire the car for more than two days

347


2. A Businessman earns a basic salary of R1 000 plus R500 commission for every item he sells.2.1 Write a function for calculating the salesman’s salary (y) if he sells x items.2.2 Complete the table of values using your function from Question 1.

X 1 2 3 4 5Y

2.3 Draw a grid using a scale of 0 to 10 on the x-axis and 0 to 5 000 (with intervals of 500) on the y-axis, and plot a graph based on your table.

2.4 Use the graph to find out how much the salesman would be paid if he sold 7 items2.5 Use the function you wrote in Question 1 to check your answer to Question4 .

Homework

1. Draw the graph of 2. Find the equation of the graph passing through (2;3) and (-4;2)

348


Worksheet: Term 4 Grade 9 Week 2 Lesson 3Class work1. Calculate, without the use of a calculator:

a)b)c)

d)2. Write down any 5 rational numbers that will fit between the following integers:

a) -1 ; -2b) 2,3 ; 2,4

349



1.

a)

b)

c)

d)

2.Study the following table:A B C0,825 4,2367 3,45

2.1 Round off 0,825 to the nearest : a) unit b) tenth c) hundredth

2.3 What is the place value of 2 in 0,825? 2.3 What is the number value of 2 in 0,825?2.4 What is the number value of 6 in 4,2367?

1. Calculate the following, without the use of a calculator:

a)

b)c)d)

2. Calculate the following: (Round your answers off to 2 decimal places)

a)

b)c)

350


Worksheet: Term 4 Grade 9 Week 2 Lesson 5Class workHomework

1. If 1 of petrol weighs 0,6798 . What will of petrol weigh? (round off your answer to 3 decimal places.

2. Mashudu bought a cooldrink for R7,50 ; a chocolate for R5,75 and a packet of chips for R6,00. He paid with a R50 note.a) How much did he spend?b) How much change did he get?

3. The reading on a water meter at the beginning of the month was 322,573 . At the end of the month the reading is 332,523 . The municipality

charges R1,25 per 200a) How much water was used during this month?b) How much will be paid for this month’s water .

4. Water drips from a tap at a rate of 15 of water per minute. How many litres of water drips from the tap in a day?

351



1. a) Complete the table below described by the function , show only 2 calculations.

Input Value

-3 -2 -1 0 1 2

Output Value

b) draw a flow diagram to show the 2 calculations.

2. Find the output values in a flow diagram below for the rule

3. Use and to determine the corresponding output values ( values). Represent the input and output values in :

b) A flow diagram

1. Study the following diagram:



352


Worksheet: Term 4 Grade 9 Week 2 Lesson 7Class work HomeworkAllow learners to complete individually and give different learners opportunity to present to class.

1. Copy and complete the table:Input Value

1 2 3 4 5 6

Output Value

4 7 10 19

2. Determine the rule for the relationship between the inputs and output values of the table

3. Find the values of and respectively-2 -1 0 1 12-7 -5 -3 -1 27

1. Study the following diagram:



353



1. Determine the rule to describe the relationship between the input

and output values of the table below.-2 -1 0 1 2-3 -1 1 3 5

2.In each of the following terms you can determine the next term by applying a rule to the previous term. Describe the rule in words in each case:

a)

b)c)d)

3. Calculate the output values:

0 1 2 3 4-8

Prepare for the weekly assessment on expressions; equations; functions and graphs number systems; integers; common fractions;

decimal fractions; financial contexts including ratio and rate

geometric patterns; Numeric patterns

354


Worksheet: Term 4 Grade 9 Week 3 Lesson 1

QUESTION 11.1 Which of the following equations is equivalent to the equation (2)

ABCD1.2 Look at the first two patterns, how many sticks will Pattern 3 have? (2)

A 6B 9C 2D 151.3 Choose the function that represents the following graph: (2)

355


A.B.C.D.


2.12.2 (1)2.3 (2)2.4 (2)

[7]QUESTION 3

3.1 Complete the following pattern by drawing the next three terms: (3)

356


3.2 Complete the table :

x -2 -1 0 1 2 4 n

y 15 12 -9 -24

(8)

[11]

TOTAL 25

357



1. The given data set represents the weight to the nearest kg of a group of learners.

82 73 6542 55 6265 58 6851 65 7263 48 65

a) Draw a stem and leaf diagram for the datab) Determine the range of the datac) Determine the moded) Determine the meane) Determine the median

2. An 8-sided die has the numbers 1 to 8 on its faces. When thrown, it has as equal chance of landing on any one of its faces

a) How many possible outcomes are there?b) What is the probablility that it will land on a prime number?c) What is the probablility that it will land on a prime number?

358


Worksheet: Term 4 Grade 9 Week 3 Lesson 2Class work Homework1. A group of 14 learners measure their height and foot

sizes and tabulate their results.

Height

174

158

163

175

140

126

153

160

160

Foot 27 24 24 26 23 23 22 25 24

2.Height 131 156 165 158 120Foot 20 23 25 24 20

a) Draw a scatterplot for the data collected.b) According to the graph, do taller people have longer

feet lengths and why?

3. There are eight balls in a basket. 2 are green, 3 are blue and the rest are white.a) Calculate how many white balls there are.b) What is the probability of picking a blue ball?c) What is the probability of picking a green ball?

1. A survey was conducted to test the relationship between the hand and shoe size. The table below shows 10 measurements of different hand lengths and shoe sizes.

Hand length

5 7 2 9 6 7 4 9 8 5

Shoe size 12

13

10

15

12

15

11

16

15

11

a) Draw a scatter plot using the information in the table.b) Draw a line of best fit.c) What conclusion can you draw about the relationship

between a hand length and a shoe size?d) Find the mode for the shoe size.e) Calculate the mean for the shoe size.f) Determine the range for the hand size.

2. There are 25 learners in a class. If a learner is chosen at random, what is the probability that a girl is chosen if there are 11 boys?

359


360



1. Study the bar graph below taken from the 2009 South African Census@School results. It shows the modes of transport to school from home of the learners who participated in the Census@School.

a) What is the graph about?b) What information is shown on the axes?c) Is the scale clear and easy to read?d) What conclusions can the graph help you make?

361


2.Stem Leaf1 1 2 5 7 2 0 1 3 4 83 2 9 4 3 3 5 6 85 0 1 6

a) What is the range for the stem and leaf plot? b) What is the median value for the stem and leaf plot? c) What is the mode for the stem and leaf plot below? d) What is the mean value?

3. Represent the following 2-way table on a tree diagram:

T-shirt JeansBlack Blue Red

Green Black/green Blue/green Red/greenWhite Black/white Blue/white Red/white

362




Platonic Solid Name of solid

Number of edges

Number of vertices

Number of faces

a) b) c) d)

2. In the figure below, AP= 5m; AS = SB = 2m, PT = 12m and PS ⊥ AB

Calculate the area of the figure correct to 2 decimal places.

1. a) Draw line segment PQ with P (2;3) and Q(5;5) on a Cartesian planeb) Translate line PQ 2 units to the right and 2 units upwards and

label the image P 'Q'c) Write down the coordinates of P'∧Q '

2. Which of the following polyhedral are prisms?

363


3. Refect ∆≝¿ in the x-axis; y−¿axis and in the line y=x .

364


Worksheet: Term 4 Grade 9 Week 3 Lesson 5Class work1.

a) Draw the Cartesian plane𝐛) Draw rectangle JKLM with the following coordinates: J (−5 ; 4) ,K (−3 ;4) , L(−3 ;1)∧M (−5;1)c) Shade half of the rectangled) Reflect the rectangle along the y-axis and label the image J ' ,K ' , L' , M ' and write down the coordinates of each vertexe) Reflect the rectangle J ' ,K ' , L' , M ' along the x-axis and label the image J K L M and write down the coordinates of each vertex.

2. What is a prism? 3. Calculate the volume of the following:

365


Worksheet: Term 4 Grade 9 Week 3 Lesson 6Class work Homework1.

a) Draw a Cartesian plane on the grid provided and label the axes

b) Draw the figure SAMP with vertices S(1 ;−2) , A (2 ;−1) and M (3 ;−2) and P(2 ;−5)

c) Reflect the figure along the y-axis and label it S' A 'M 'P 'd) Write down the coordinates of S' A 'M 'P '’ e) Compare the coordinates of SAMP and S' A 'M 'P 'f) What is the relationship between the coordinates of

the object and the coordinates of the image? g) Complete: (x ; y)→¿

2. Complete the table:

1. Calculate the volume of the following, use π=3,14

2. Describe the transformation if the coordinates of the original point and its image are:a) (−2 ;−3)→(−2 ;−5)

b) (4 ;−7)→(−6 ;0)

c) (3 ;11)→(16 ;20)

3.

a) Name the shapeb) What is the shape of its faces?c) How many faces does the shape have?d) How many edges does the shape have?e) How many vertices does the shape have?f) Draw the net of the shape.

366


3. Calculate the volume of the following object:

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1. Study the diagram below:

Complete the following:a) AB= 3cm A ' B' = 6cm therefore A ' B' = ------× ABb) BC= 2cm B' C ' = 4cm therefore B' C ' = ------× BCc) CD= 3cm C ' D ' = 6cm therefore C ' D ' = ------× CDd) AD= 2cm A ' B' = 4cm therefore A ' B' = ------× AD

2. Refer to question 1.a) Calculate the ratio of the area of figure B to the area of Figure A.b) Simplify the ratio in question 2.a) above.

368



Name Shape of faces

No of faces (F)

No of vertices (V)

No of edges (E)

F+V-E

4. The area of the base of a rectangular prism is and its height is 12mm. What is its volume?5. The volume of a cube is 216m3. What is the length of one of its edges?

369



1. Expand and simplify:a) 2 (x2+4 x+8 )b¿ (x+2)(x+5)

2. Factorise:

a) 25a2−9b) 1−16 x2

c) 2 x2−2d) ( x+ y )2−b2

e) 4 x6−19

f) −(x+ y )2+1g) x2+5x+6h) x2−5 x+6i) 2 x2+10 x+12j) −2b2+6b−4

3. Simplify:a)

x2−9x2+x−6

÷ x2−3 xx+1

b) 2x2+4 x−12

−1x−2

4. Solve the following equations:a) 4(2m – 5) = 5 – 2(m + 1)

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b) 3(x – 1) – 4x = 5 – 2(x+ 1)c) 2(x – 3) = x- 3(x+ 2)


1. Simplify:

a)

b)c) ( 4a2+2b ) ( 4a−2ab+9c )

d) 9 x2( 13x+2x3)−4 x(1

2x4−3 x2)

2. Solve the following equations:2.1 4 ( x+2 )−3=2 (3−x )

2.2

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Worksheet: Term 4 Grade 9 Week 4 Lesson 2Classwork Homework

1. Simplify:a)

2. Solve for :

a)b)

3. (See next page)

1. Solve for :

a)

2.

a) Write down the defining equation of each of the following straight line graphs.

b) What can you deduce about the lines AD and BC. Give a reason for your answer.

372


a) Use the graph to calculate the gradient of the straight line.b) Determine the equation of the straight line.c) Write down the gradient of any other straight line which can be drawn

parallel to the given line

373



1.Simplify the following expressions

a)

b)

2. Solve the following equations:a)

b)

3. Determine the gradient of the following straight line:, as well as the intercept and the intercept

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a)b)


a)



a)b)


a)

3. Find the equation of the graph

375

x

y



1. Simplify:a)b)c)

2. Factorisea)b)

3. Solve for :

a)

4. Study the graph :

a) What type of graph is this?b) Is it an increasing or decreasing function?c) Approximately what ℉ is freezing point?

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Worksheet: Term 4 Grade 9 Week 4 Lesson 6Classwork Homework

3. Simplify:a)b)

4. Solve for

a) x2 = 25

What is the equation of the following:

a) At how many minutes do both companies charge the same rate?

b) When is company T’s rates lower than

1. Simplify:a)

2. , calculate , when .

3. Complete the table below and draw the graph.-3 -2 -1 0 1 2 3

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that of Company S?

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1. Simplify:a)b)c)

2. Solve for

a)3. , calculate , when

4. Use the given coordinates to find the equation of the straight line graphs passing through them.

a) (16; 5) and (7; 2)b) (−1

2;8) and (-6; -3)

379



1. Simplifya)

b) 9 x2( 13x+2x3)−4 x( 1

2x4−3 x2)

c)12abc ( 14a2b

c+ 8ac3

b−22c3b3

a )2. Given that a=−1 ;b=7∧c=0 find the value for each of the following

expressions:

a) 17abcb) 3a+2b−7c

3. Solve for :

a) 4 ( x+2 )−3=2 (3−x )

b) 4 ( x−7 )+6 (2−3x )=5 (x−6 )

4. a) On the same Cartesian plane draw the graphs y = 4 and x = 4. b) What is the gradient for each graph? c) What do you notice about these two graphs?

Learners must prepare for weekly test on expressions, equations, functions and straight line graphs

380


Worksheet: Term 4 Grade 9 Week 5 Lesson 1 and 2Classwork1. Which of the following numbers belong to each group below?

−2 13

9π √20 1,23 .. . −3 √16

a) Integersb) Rational numbersc) Irrational numbers

2. List the following:a) The factors of 15b) The first four multiples of 6c) Find two rational numbers between -1,36 and -1,35

3. Calculate:a) 1 1

2−1

6+5

3

b) 3 56−3 1

3

c) -9 – (21 – 4)d) 3 + 3 - (-7) – 8e) (450-349) x 2 + (-101)

4.US Dollar $8,4916 R11,78British Pound £13,7697 R7,26Euro €8,9 R11,24

Jamie is travelling to Europe. She has R2 000 for spending. a) How much will Jamie get in Euros?b) Will it be cheaper for her to go to London and use the British pound?

381


Worksheet: Term 4 Grade 9 Week 5 Lessons 3 and 4Class work Homework

1. Simplify:a) (3 1

2+3 1

2 )÷1 34

b) 3 56−2 1

3

c) (-3)3

2. Calculate:a) 3 – (-9)b) -1 + 2 – 3 x 4c) 3 x 3 + 1 x 11 – 6d) √90−9

3. Don bought a music set for R199 and sold it to Tumi for R250. Thando bought a TV for R800 and sold it for R850.a) Calculate the profit that each one made.b) Calculate the percentage profit that each person

made. (correct to one decimal place)c) Who made the larger profit?d) Who made the larger percentage profit?

382


Worksheet: Term 4 Grade 9 Week 5 Lessons 5 and 6Class work1. Simplify:

a) 3 37×(4 2

3−11

5 )b) 4

5+1 7

10c) -(3)2

d) 1,5 : 3

2. Calculate:

a) 80 – 0

b)c) 11 + 12 + 13 + 14 + 115

3. Jabu deposits R2 000 into a savings account where the interest is 15% p.a. compounded annually.a) How much interest did he receive?

4. You receive R500 for your birthday. You decide to invest it for 15%p.a for 3 years.a) Calculate the interest after 3 years.b) The final amount he will receive after 3 years.

383


Worksheet: Term 4 Grade 9 Week 5 Lesson 7 and 8Class work


Number N N 0 Z Q Q' Non-Real Undefined0

√0,910

−3111

2. Simplify:

a) 23× 9

10

b) 24+ 4

4

3. Calculate:a) 4 × - 5 = - 20 b) (-135) +145

c) 20 – (8)(0) ÷ 2(-10)(-1)

4. Johnny borrows R800 from his brother to buy a new i-pod. The agreement is that he will pay the money back together with 12% p.a. simple interest after two years. How much will he have to pay back?

5. A car costs R90 000. Calculate the value of the car after 10 years if the rate of depreciation is 12% p.a. on a reducing balance.6. 6. Your dad bought a laptop for R11000. It depreciates in value on a simple interest basis. Calculate the value of the new computer after 3 years.

384


Worksheet: Term 4 Grade 9 Week 6 Lesson 1 & 2Class work

1. Consider the following pattern:1; 4; 9; 16; ….

a) Find the next 3 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.

2. 7; 11; 15; 19; …a) Find the next 3 terms of the pattern

3.

a) Draw the next three patterns for the above.b) Describe in words the pattern.

4. If y=12 x−10 and x=−3 , x=−1 , x=0 , x=2 , x=4 , x=12. Draw a graph to represent the above information. HINT: Draw a table of values first.

385


386


Worksheet: Term 4 Grade 9 Week 6 Lesson 3 & 4Class work Homework

1. Study the pattern below:

a) Draw the next three patterns for the above.b) Write down in words what the pattern is.

2. Complete the following tables by filling in the missing input and output values and the formula for the pattern.

a)x -

2-1

0 1 2 7 n

y -7

-4

-1

26

44

b) Give the formula that defines the above table.c) Draw the graph of y=−3x+8.

1. Find the next two terms of the pattern: 1; 2 ; 4; 8;….2. Find the equations of the following:a)

b)

387


3.Find the value of b 2 -6 3 b 4 ×(−3) -12

4 a

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Worksheet: Term 4 Grade 9 Week 6 Lesson 5 & 6Class work

1. Consider the values in the following table. The rule for finding y is: divide x by −2 and subtract 4.

2 0 2 5-1 -3 -4 48

a) Use the rule to determine the missing values in the table, and write them in.

2. Sketch the graph of y=−x


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Worksheet: Term 4 Grade 9 Week 6 Lesson 7 & 8Class work Homework


2. Complete the following table of valuesx -

2-1 0 1 2 4 n

y 0.5

1 2 128

2048

3.If y=−2x+7 and x=−4 , x=−2 , x=0 , x=1 , x=3 , x=8

a) Draw a table to represent the above values of y b) Draw a graph to represent the answers in your table.

Learners prepare for the weekly assessment on Geometric and numeric patterns, functions, expressions and graphs

390


Worksheet: Term 4 Grade 9 Week 7 Lesson 1 and 2Classwork

1.Refer to the diagram below and answer the questions that follow

a) Calculate the value ofx. Give a reason for your answerb) Determine the size of ∠ y. Give a reason for your answer

2. In the diagram below,prove that ∆PTQ≡∆PTR. Give reasons for your answer.

391

P

Q

A

C


3. Use a pair of compasses and ruler to make accurate constructions of the following angle:

392

P

Q

T

T

R


Worksheet: Term 4 Grade 9 Week 7 Lesson 3 and 4Class work Homework

1.In the diagram below, A ¿ 70° and quadrilateral ABCD

is a rhombus.

a) Calculate the value of A BC , give reasons for your answer.

b) Determine the size of BC D , give a reason for your answer

c) Determine the size of C B E , give a reason for your answer

1. In the diagram below, PQ∥ST, SR¿ST, Q PR=¿ 55° andPQ S=¿27°.

1. Choose the correct answers:

1.1

Calculate the value of A. B. C.D.

1.2 Refer to the figure in 1.1. Calculate the value of A.B.C.D.

393

EBA

CD


a) Determine the size of Q ST . Give a reason for your answer.

b) Determine the size of T S R. Give a reason for your answer.

c) Calculate the value of x . Give a reason for your answer.

2. Use a pair of compasses and ruler to make accurate constructions of the following angle

1.3

Calculate the size of T

A.B.C.D.

1.4 Refer to the diagram in 1.3. Give a reason why ∆PQR /// ∆ TMS

A. All angles are equalB. All sides are in proportionC. A;A;SD. S;A;S

394

27°

55°P

Q R

S

T



1. The area of a parallelogram below is 156 mm2, MR¿12 mm and NR¿5 mm. Calculate the length of TS.

2. PQRS is a square with Circle O where r ¿7 mm. Calculate the area of the shaded part correct to one decimal place. N.B. π=22

7

395

12 mm

5 mm

M T

SN R

P Q

O

RS


3. Complete the table below:Platonic Solid Shape of faces Number of facesOctahedronIcosahedron

4.

Name the above shapes.

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1. Given the circle below with right-angled triangle BCD. BD is 7cm and DC is 5cm.

a) Find the diameter of the circle.b) Find the area of triangle BCD.c) Find the area in the circle that is not covered by ∆BCD.d) Find the circumference of the circle

397


2. If the perimeter of hexagon is 24 cm. The shape in Figure 2 is made of the hexagons of the same size as in Figure 1. What is the perimeter of the shape drawn in Figure 2?

3. Complete the table beow:

Platonic Solid Shape of faces Number of facesOctahedron Equilateral

trianglesEquilateral

triangles20

Hexahedron 4

398

Figure 1

Figure 2



1. Draw the enlarged or reduced image of the following figure according to the scale factor given. Scale factor =

399


2. Draw the graph of 3. Find the equation of the graph

400


Worksheet: Term 4 Grade 9 Week 8 Lesson 3 and 4Class work1.

Translate PQR 5 units to the right and 3 units downTranslate PQR 5 units to the right and 3 units downAre all the triangles congruent?

401


2. Determine the equations of the straight lines passing through the following points:

c)

1 2 3 4 55 4 3 2 1

d)-4 -2 0 2 42 0 -2 -4 -6

3. Draw the graphs of the following graphs on the same system of axes: and

402


Homework

1. Draw the graphs of on the same system of axes.

a) State the rule for the transformation from A to B in the form

b) Describe in words the transformations from G to Hc) Which of the transformations are:

i) Reflectionsii) Rotations

403



1. Simplify:a)b)c)d)

2. Solve for :

a) x2 = 25

b)


4. Multiply by

404



1. Simplify:a) 12x2 y−6 xy2

3 xy

b) (xa - 3)(xa + 3)

c) √34 y6−9 y6

d) (2 x−3 )2−4(x−1)(x+1)

e) 2(x+4)2

−2

f) p2q2×( p−2)2

p−2

2. Solve for :

a)b) 3 ( x−1 )=2 x+5c) ( x−2 ) ( x−2 )=0

d) 2x3

− x+14

=1

e) 2− x=64

3. Complete the following ,if then x=…

405


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