year 9 maths semester 1 exam revision booklet 2018

19
Year 9 Mathematics Semester 1, 2018 YEAR 9 MATHS – SEMESTER 1 EXAM REVISION BOOKLET 2018 Topics Examined ❖ Chapter 12 – Measurement (Exercises 12.2 – 12.7; 6.2-6.3) o Unit Conversions o Perimeter, Area, Total Surface Area, Volume and Capacity of squares, cylinders, circles (sectors), composite shapes o Pythagoras ❖ Chapter 3 – Algebra (Exercises 3.2 – 3.7) o Recognising coefficients, terms, linearity, trinomials o Expanding and simplifying algebraic expressions o Formulating expressions from worded situations ❖ Chapter 4 – Linear Equations o Substitution in equations o Solving Linear Equations o Rearranging equations to find the unknown pronumeral o Using linear equations to find area, perimeter of various polygons o Using linear equations to solve worded problems ❖ Chapter 6 – Trigonometry (6.4-6.5) o Knowing the TRIG RATIOs o Finding unknown side lengths using appropriate trigonometric ratios Exam Structure Reading Time: 10 minutes Writing Time: 90 minutes Section A: Vocabulary (5 minutes) Section B: Multiple Choice (25 minutes) Section C: Short Answer (45 minutes) Section D: Analysis (15 minutes) Exam Preparation The following options are suggestions that you might want to think about using to help you revise and study for your exam: ❖ Complete the Exam Revision questions on the following pages. ❖ Complete any practice work given by your teacher, including Mathspace and Education Perfect. ❖ Look over the topic tests and concentrate on the areas where you went wrong. ❖ Carefully read through sections of your textbook and class notes and worksheets. ❖ Go through Chapter Review Questions for the four topics listed above. ❖ Revise with a friend or in a group (such as Homework Club) – revising together may help you to better understand key concepts.

Upload: others

Post on 23-Mar-2022

2 views

Category:

Documents


0 download

TRANSCRIPT

Year 9 Mathematics Semester 1, 2018

YEAR 9 MATHS – SEMESTER 1 EXAM REVISION BOOKLET 2018

Topics Examined

❖ Chapter 12 – Measurement (Exercises 12.2 – 12.7; 6.2-6.3) o Unit Conversions o Perimeter, Area, Total Surface Area, Volume and Capacity of squares, cylinders,

circles (sectors), composite shapes o Pythagoras

❖ Chapter 3 – Algebra (Exercises 3.2 – 3.7) o Recognising coefficients, terms, linearity, trinomials o Expanding and simplifying algebraic expressions o Formulating expressions from worded situations

❖ Chapter 4 – Linear Equations o Substitution in equations o Solving Linear Equations o Rearranging equations to find the unknown pronumeral o Using linear equations to find area, perimeter of various polygons o Using linear equations to solve worded problems

❖ Chapter 6 – Trigonometry (6.4-6.5) o Knowing the TRIG RATIOs o Finding unknown side lengths using appropriate trigonometric ratios

Exam Structure

Reading Time: 10 minutes Writing Time: 90 minutes

Section A: Vocabulary (5 minutes) Section B: Multiple Choice (25 minutes) Section C: Short Answer (45 minutes) Section D: Analysis (15 minutes)

Exam Preparation

The following options are suggestions that you might want to think about using to help you

revise and study for your exam:

❖ Complete the Exam Revision questions on the following pages.

❖ Complete any practice work given by your teacher, including Mathspace and

Education Perfect.

❖ Look over the topic tests and concentrate on the areas where you went wrong.

❖ Carefully read through sections of your textbook and class notes and worksheets.

❖ Go through Chapter Review Questions for the four topics listed above.

❖ Revise with a friend or in a group (such as Homework Club) – revising together may

help you to better understand key concepts.

Year 9 Mathematics Semester 1, 2018

TOPIC 1: CHAPTER 12 – MEASUREMENT

Vocabulary:

Definition of perimeter, area, prism, volume, capacity

Multiple Choice Questions:

Q1. What is 0.045 m equivalent to?

A 4.5 mm

B 4.5 cm

C 450 mm

D 45 cm

E 450 cm

Q2: What is 5 litres equivalent to?

A 50 cm3

B 500 cm3

C 5000 cm3

D 50 000 cm3

E 500 000 cm3

Q3: The circumference of a circle with a diameter of 12.25 cm is:

A 471.44 cm

B 384.85 mm

C 76.97 cm

D 117.86 cm

Q4: The figure below represents the sector of a circle. Its angle is 45o. If the radius is 2 cm, then the area (in cm2) is:

A 2

B 2

C 4

D

E

Year 9 Mathematics Semester 1, 2018

Q5: If the total surface area of a cube is 200 cm2, then the length of an edge is closest to:

A 17 cm

B 10 cm

C 8 cm

D 6 cm

E 4 cm

Short Answer Questions:

Q1: Convert 0.0345 km to m, cm and mm.

Q2: Convert the following measurements to the units indicated. (a) 2.05 km to m

(b) 0.036 m to mm

Q3: Convert the following measures of volume to the units specified.

(a) 5.6 litres = __________ cm3

(b) 3.1 m3 = ___________ litres

(c) 0.0045 m3 = ___________ mm3

Q4. Convert 1 000 000 mm2 to:

(a) cm2

(b) m2

(c) ha

Q4: A rectangle has a width of 14 cm and a perimeter of 120 cm. Find the length of the rectangle.

Year 9 Mathematics Semester 1, 2018

Q5: Calculate the area of each of the following shapes. (Where appropriate, give your answer

correct to 2 decimal places.)

Q6: Find the area of the figures drawn below.

11 cm

15 cm

5 cm

8 cm

14 mm

8 cm

7 cm

Year 9 Mathematics Semester 1, 2018

Q7: A circular garden bed has a perimeter of 54 m. What is the area of the garden bed?

Q8: A satellite orbits the Earth at an altitude of 12 000 km. If the radius of the Earth is 6400 km, find

the circumference of the orbit. (Answer in scientific notation to the nearest 100 km.)

Q9: Find the perimeter of this shape.

6.2 cm

28.3 cm

Year 9 Mathematics Semester 1, 2018

Q10: Find the area of a circle with a diameter of 56 cm. Give answer correct to 2 decimal places.

Q11: Find the area of the sector of a circle shown in the figure below. The radius of the circle is 2 cm.

Give answer correct to 2 decimal places.

Q12: A cylinder has a radius of 4.7 cm and a height of 8.9 cm. Find the total surface area. Answer correct to 1 decimal place. Q13: Find the total surface area (TSA) of a cube whose edges are 3.53 cm long. Give the answer correct to 2 decimal places.

Q14: Show that a square of perimeter 4x + 20 has an area of x2 + 10x + 25.

Year 9 Mathematics Semester 1, 2018

Q15: Consider the cylinder to the right. In the space below calculate the: a) Surface area of the cylinder. b) The volume of the cylinder. Q16: Nina decides to invite some friends for a sleepover. She plans to have her guests sleep on inflatable mattresses with dimensions 60 cm by 170 cm. A plan of Nina’s bedroom is shown below.

a) Write an expression for the perimeter of Nina’s bedroom.

b) Write expressions for the area of Nina’s bed, Chest of Drawers and Door.

c) Write an expression for the area of the floor space that is available.

Year 9 Mathematics Semester 1, 2018

TOPIC 3: CHAPTER 3 – ALGEBRA

Vocabulary

Definition of pronumeral, variable, expression, term, trinomial Inverse Operations. Multiple Choice

Q1: In the following expression, what is the coefficient of π‘₯3 : βˆ’3π‘₯2 +π‘₯

4βˆ’

2π‘₯

3

3?

A -3

B π‘₯

4

C 2

3

D βˆ’2

3

E 3 Q2: Which of the following is not a linear equation? A 3 βˆ’ π‘₯ = 8

B 4π‘₯ = 3 +8π‘₯

9

C 2π‘₯ = 5π‘₯2 + 5

D π‘₯

5=

6

7

E 10𝑦 + 3 = 5𝑦 Q3: What is βˆ’2π‘₯𝑦2 + 23π‘₯𝑦2simplified? A 25π‘₯𝑦2 B π‘₯𝑦2 C 21π‘₯𝑦2 D βˆ’21π‘₯𝑦2 E βˆ’π‘₯𝑦2

Q4: What is the equivalent of 6 βˆ’ 4x(x + 2) + 3x?

A 6 βˆ’ 4x2 βˆ’ 5x

B 6 + 4x2 + 5x

C 6 βˆ’ 4x2 + 5x

D 6 + 4x2 + 5x

Q5: The equivalent of (3 βˆ’ a)(3 + a) is: A 9 + a2

B 9 βˆ’ a2

C 3 + a2

D 3 βˆ’ a2

Year 9 Mathematics Semester 1, 2018

Q6: Expand and simplify the following expression: 5(π‘₯ + 2𝑦) + 6(π‘₯ βˆ’ 3𝑦): A 11π‘₯ βˆ’ 2𝑦 B 11π‘₯ + 8𝑦 C 11π‘₯ βˆ’ 8𝑦 D 11π‘₯ + 18𝑦 E 11π‘₯ + 28𝑦 Q7: Expand and simplify the following expression: (2π‘₯ + 3)(2π‘₯ βˆ’ 3): A 4π‘₯ βˆ’ 6 B 4π‘₯2 βˆ’ 9 C 4π‘₯2 + 6 D 4π‘₯2 + 9 E 4π‘₯2 + 6 Q8: Expand and simplify the following expression: (π‘₯ βˆ’ 2)2 : A π‘₯2 βˆ’ 4π‘₯ + 4 B π‘₯2 βˆ’ 2π‘₯ + 2 C π‘₯2 + 4π‘₯ βˆ’ 4 D π‘₯2 + 2π‘₯ βˆ’ 2 E 2π‘₯2 + 4 βˆ’ 4π‘₯ Q9: Expand and simplify the following expression: (π‘₯ βˆ’ 3)(π‘₯ + 4) βˆ’ 2(π‘₯ + 2) A π‘₯2 + 3π‘₯ + 8 B π‘₯2 βˆ’ π‘₯ βˆ’ 16 C π‘₯2 + π‘₯ + 16 D π‘₯2 + 5π‘₯ βˆ’ 16 Q10: If 𝑦 = 5π‘₯2 + 2π‘₯ βˆ’ 1, find y when π‘₯ = 5: A 134 B 59 C 56 D 24 E 119 Short Answer Questions

Q1: For the expression βˆ’8xy2 + 2x + 8y2 βˆ’ 5:

i state the number of terms

ii state the coefficient of the first term

iii state the constant term

iv state the term with the smallest coefficient

Q2: Simplify the following expressions by collecting like terms.

a) 5y2 + 2y βˆ’ 4y2

b) 11c2d βˆ’ 2cd + 5dc2

a) n2 βˆ’ p2q βˆ’ 3p2q + 6

Year 9 Mathematics Semester 1, 2018

Q3: Expand and simplify by collecting like terms.

a) πŸ‘(𝒙 βˆ’ 𝟐) + πŸ—

b) βˆ’πŸ(πŸ“π’Ž βˆ’ 𝟏) βˆ’ πŸ‘

c) 4m(m βˆ’ 3) + 3m βˆ’ 5

d) 7p βˆ’ 2 βˆ’ (3p + 4)

Q4. A rectangular rug has a length of 3x cm and a width of x cm.

a) Write an expression for its perimeter.

b) Write an expression for its area.

c)

i) f its side length is increased by y cm, write an expression for its new side length.

ii) Write an expression for its new perimeter and expand.

iii) Calculate the perimeter when x = 90 cm and y = 30 cm.

iv) Write an expression for its new area and expand.

v) Calculate the area when x = 90 cm and y = 30 cm.

Q5. A rectangular garden bed has a length of 15 m and a width of 8 m. It is surrounded by a path of width p m.

a) Write down the total area of the garden bed and path.

b) Expand the expression you found in a).

c) Find the area of the path in terms of p.

d) Write an equation that could be solved to find the width of the path if the area of the path is 200 m2.

Q6. Write expressions for the following, where x and y represent numbers:

a) number 8 more than y

b) the difference between x and y

c) the sum of x and y

d) 7 times the product of x and y

e) 2 times x is subtracted from 5 times y.

Q7: A father is 4 times the age of his son. In 4 years time, the father will be 3 times the age of his son. How old is the father now?

Year 9 Mathematics Semester 1, 2018

TOPIC 5: CHAPTER 4 – LINEAR EQUATIONS

Vocabulary

Definition of linear equation. How to find the solution to an equation. Inverse arithmetic operations. Factorisation methods Multiple Choice

Q1: The solution to the equation π‘₯+2

3= 6 is:

A π‘₯ = 12 B π‘₯ = 16 C π‘₯ = 20 D π‘₯ = 24 E π‘₯ = 6 Q2: The solution for π‘₯ in 2π‘₯ + 3 = 3π‘₯ βˆ’ 7 is: A π‘₯ = βˆ’10 B π‘₯ = 10

C π‘₯ =βˆ’4

5

D π‘₯ = βˆ’2 E π‘₯ = 2 Q3: The solution for 7(π‘₯ βˆ’ 5) = 28 is: A π‘₯ = βˆ’1 B π‘₯ = 9 C π‘₯ = βˆ’7 D π‘₯ = 7 E π‘₯ = 3.285 Q4: The solution for 3(π‘₯ + 1) = 14 βˆ’ 2π‘₯ is: A π‘₯ = 17

B π‘₯ =17

5

C π‘₯ =11

5

D π‘₯ = 55 E π‘₯ = 11 Q5: The solution for 2(π‘₯ + 3) = 3(π‘₯ + 7) is: A π‘₯ = 3 B π‘₯ = 15 C π‘₯ = 5 D π‘₯ = βˆ’15

E π‘₯ =27

5

Year 9 Mathematics Semester 1, 2018

Q6: Which equation matches the following statement? Dividing 7 times a certain number by βˆ’4 equals 9:

A π‘₯

βˆ’4= 9

B βˆ’4π‘₯

7= 9

C 7+π‘₯

βˆ’4= 9

D 7π‘₯

βˆ’4= 9

E βˆ’4

7π‘₯= 9

Q7: Rearrange this formula to make π‘₯ the subject: 𝑦 = π‘šπ‘₯ + 𝑐 A π‘₯ = π‘¦π‘š βˆ’ 𝑐

B π‘₯ =π‘¦βˆ’π‘

π‘š

C π‘₯ =𝑦+𝑐

π‘š

D π‘₯ =𝑦

π‘š+ 𝑐

E π‘₯ = π‘¦π‘š + 𝑐

Q8: Rearrange this formula to make 𝐺 the subject: 𝐹 =πΊπ‘€π‘š

π‘Ÿ2

A 𝐺 =πΉπ‘Ÿ2

π‘€π‘š

B 𝐺 =πΉπ‘Ÿ2βˆ’π‘€

π‘š

C 𝐺 =𝐹

π‘Ÿ2 βˆ’ π‘€π‘š

D 𝐺 =𝐹+π‘€π‘š

π‘Ÿ2

E 𝐺 =πΉπ‘€π‘š

π‘Ÿ2

Q9: Rearrange this formula to make 𝑏 the subject: 𝑦 = 6𝑏 βˆ’ 4π‘Ž A 𝑏 = 4π‘Ž βˆ’ 𝑦

B 𝑏 =𝑦+4π‘Ž

6

C 𝑏 = 𝑦 βˆ’ 4π‘Ž

D 𝑏 =π‘¦βˆ’4π‘Ž

6

E 𝑏 = 6𝑦 βˆ’ 4π‘Ž

Year 9 Mathematics Semester 1, 2018

Short Answer Questions:

Q1: The rectangular blocks of land drawn below have the same area. Find the dimensions of

each block, and the area.

Q2: A square pool is surrounded by a paved area that is 2 metres wide. If the area of the

paving is 72 m2, what is the length of the pool?

Q3: A rectangular swimming pool is surrounded by a path which is enclosed by a pool fence.

All measurements are in metres and are not to scale in the diagram shown.

a) Write an expression for the area of the entire fenced-off section.

b) Write an expression for the area of the path surrounding the pool.

c) If the area of the path surrounding the pool is 34m2, find the dimensions of the

swimming pool.

Year 9 Mathematics Semester 1, 2018

TOPIC 6: CHAPTER 6 – TRIGONOMETRY

Vocabulary

Definition of the sides of a right-angle triangle. Multiple Choice

Q1: For the triangle below, what trigonometric ratio would be suitable?

A sin 𝛼 =𝑖

β„Ž

B cos 𝛼 =β„Ž

𝑔

C tan 𝛼 =β„Ž

𝑖

D tan 𝛼 =𝑖

𝑔

E cos 𝛼 =𝑖

𝑔

Q2: What is the correct trigonometric ratio for the triangle below?

A tan(𝛾) =π‘Ž

𝑐

B sin(𝛾) =𝑐

π‘Ž

C cos(𝛾) =𝑐

𝑏

D sin(𝛾) =𝑐

𝑏

E tan(𝛾) =𝑏

π‘Ž

Year 9 Mathematics Semester 1, 2018

Q3: The value of length π‘š, correct to 2 decimal places is:

A π‘š = 18.76π‘π‘š B π‘š = 46.45π‘π‘š C π‘š = 18.77π‘π‘š D π‘š = 43.0665π‘π‘š E π‘š = 46.448π‘π‘š

Q4: What is the appropriate trigonometric ratio to use to solve for 𝑦?

A 𝑦 = cos(27) Γ— 7.9

B 𝑦 = tan(27) Γ— 7.9

C 𝑦 =tan(27)

7.9

D 𝑦 = sin(27) Γ— 7.9

E 𝑦 = sin(7.9) Γ— 27

Q5: The value of π‘₯ to 2 decimal places is?

A 59.65 B 23.31 C 64.80 D 27.51 E 48.65

Year 9 Mathematics Semester 1, 2018

Q6: The value of π‘₯ correct to 2 decimal places is?

A 99.24mm B 92.55mm C 185.55mm D 198.97mm E 208.95mm Q7: If cos(πœƒ) = 0.8572, the value of ΞΈ correct to 2 decimal places is: A 61.07Β° B 41.19Β° C 25.84Β° D 28.93Β° E 45.89Β° Q8: The value of ΞΈ in the triangle shown, correct to 2 decimal places, is:

A 41.30Β° B 28.55Β° C 48.70Β° D 61.45Β° E 36.87Β° Q9: A ladder 4 m long leans against a wall. The foot of the ladder is 130 cm from the wall. The size of the angle the ladder makes with the wall to the nearest degree is: A 19Β° B 71Β° C 18Β° D 70Β° E 58Β°

Year 9 Mathematics Semester 1, 2018

Q10: Which of the following could be used to find the value of angle a?

A sin π‘Ž =

7

26

B tan π‘Ž =7

26

C cos π‘Ž =7

13

D tan π‘Ž =7

13

E sin π‘Ž =7

13

Short Answer Questions Q1: Using Pythagoras’ theorem, calculate the missing length of the side in the following right-angled triangles. a) b)

Year 9 Mathematics Semester 1, 2018

Q2: A ship that was to travel due north veered off course and travelled N 80Β°E (or 080Β°T) for a distance of 280 km, as shown in the diagram.

a) How far east has the ship travelled? b) How far north has the ship travelled?

Q3: Calculate the unknown values in the figures below. Give your answers correct to 2 decimal places.

a)

b)

Year 9 Mathematics Semester 1, 2018

Q4: An ironwoman race involves 3 swim legs and a beach run back to the start as shown in the figure. What is the total distance covered in the race?

Q5: Two towers are 30 m apart. From the top of tower A, the angle of depression of the base of tower B is 60Β°, and the angle of depression of the top of tower B is 30Β°. What is the height of tower B? Round to the nearest metre.

Q5: Calculate the total height of the shape below: