pakuranga college year 9. 2 mathematics assessments ... statistics project 7 reflection: topic...

1

Student Name:

Pakuranga College

Year 9

Mathematics Assessments

The five Platonic Solids are:

2015

2


Term One

Topic Assessment Page Level

Statistics Quiz 1 4

Statistics Quiz 2 5

Statistics Quiz 3 6

Statistics Project 7

Reflection:


Number Diagnostic 8 & 9

Number Quiz 1 10

Number Quiz 2 11

Number Quiz 3 12

Number Test 13 to 15

Reflection:

Term Two


Measurement Quiz 1 16



Measurement Project 19

Reflection:


Geometry Quiz 1 20

Geometry Quiz 2 21

Geometry Quiz 3 22

Geometry Test 23 to 25

Reflection:

3


Term Three


Algebra Quiz 1 26

Algebra Quiz 2 27

Algebra Quiz 3 28

Algebra Poster 29

Reflection:

Complete the more detailed reflection on page 30.


Algebra Graphs Quiz 1 31



Algebra Graphs Test 34 to 37

Reflection:


Probability Quiz 1 38



Probability Simulation 41 to 42

Reflection:

Term Four


Number Exam 44, 45 & 46

Algebra Exam 47 & 48

Statistics Exam 49 & 50

Measurement Exam 51 & 52

Geometry Exam 53 & 54

Probability Exam 55 & 56

Reflection:

4

Pakuranga College Junior Mathematics Award

Statistics – Quiz 1 Overview

Answer ALL questions and show all working in the space provided.

You have 15 minutes (1.5 minutes per question) to complete this quiz.

Formal test conditions must be present during this quiz.

Calculators are allowed but are no advantage in this quiz.

Question 1

Explain Univariate

Question 2

Explain Bivariate

Question 3

Explain Multivariate

Question 4

Explain time series

Question 5

Give an example of measurement data.

Question 6

Give an example of a categorical

variable.

Question 7

Give an example of a counting variable.

Question 8

Give an example of a time series

investigation.

Question 9

What does the PPDAC cycle stand for?

Question 10

What does Variable mean?

Mark out of 10:

Reflection:

5


Statistics – Quiz 2 Calculations





Question 1

Calculate the mean of 5,6,7,8,9

Question 2

Calculate the median of 5,6,7,8,9

Question 3

Calculate the mean of 5,6,7,8,20

Question 4

Calculate the median of 5,6,7,8,20

Question 5

Compare the mean and median of

question 1&2; then 3&4. Explain.

Question 6

Calculate the lower quartile (LQ) of

5,6,7,8,9

Question 7

Calculate the upper quartile (UQ)

of 5,6,7,8,9

Question 8

Calculate the range of 5,6,7,8,9

Question 9

Calculate the interquartile range

(IQR) of 5,6,7,8,9

Question 10

Which measure of central

tendency is best? The median or

the mean? Why?

Mark out of 10:

Reflection:

6


Statistics – Quiz 3 Boxplots





gender height

gender height

gender height female 170

female 160

male 170

female 165

female 166

male 182 male 167

female 173

male 147

male 165

female 139

male 152

1. Draw the Males Dotplot and Boxplot here: (4 marks)

2. Draw the Females Dotplot and Boxplot here: (4 marks)

3. The data is from census at school, the students are all from Auckland. Do you

think they are in year 9 or a mixture of year levels? (1 mark)

4. Justify your answer to question 3 (1 mark)

Mark out of 10:

Reflection:

7


Statistics – Project

Marking Grid

Level 2

Analysis Calculate two statistics

Conclusion Answer the question.

Level 3

Analysis Describe one feature of the data

Conclusion Answer question in context

Level 4

Analysis

Calculate one measure of centre

and one of spread

Describe two features using

statistical terms

Level 5

Analysis

Describe three features using

statistical terms in context

Calculate IQR

Level 6

Analysis Describe and justify four features

in context, using statistical terms

Conclusion

Informal inference

Statistical insight

Mark out of 70:

Reflection:

8

Pakuranga College Mathematics Department

Year 9 Number Diagnostic Test

Time allowed: 50 Minutes NO Calculators allowed

Find the answer to each of these questions:

1. 342 + 289 =

2. 983 − 276 =

3. 591 × 6 =

4. 3641 × 28 =

5. 392 ÷ 4 =

6. Find the next three numbers

in this sequence:

3, −5, 7, −9, ___,___,___

7. List all the factors of 24:

8. √16 =

9. 33 =

10. List the first five prime

numbers:

11. Use < or > to make this true:

−3__−5

12. −3 + 2 =

13. 4−−2 =

14. −3 × −5 =

15. 18 ÷− 9 =

16. Put these fractions in order

from smallest to largest:

1

2,

3

5,

1

4,

2

3,

2

5,

4

5,

3

4

17. 1

5+

3

5= 18.

3

4−

1

3=

19. 3 ×2

5= 20.

3

5×

2

7=

9

21. Complete this table of conversions:

Decimal Fraction Percentage

1

2

0.25

15%

3

8

22. 3.42 + 6.1 =

23. 1.4 × 3 =

24. 0.49 × 3.1 =

25. 1.428 ÷ 0.7 =

26. Round 3.4961 to two decimal

places:

27. Round 0.010249 to three

significant figures:

28. Write 3.42 × 10−3 in ordinary

form:

29. What is 30% of 50?

30. Increase 300 by 15%:

31. Decrease 150 by 60%:

32. If it takes three people five hours to cut some firewood, how long

would it have taken 4 people?

33. A car is travelling at 60km/h. How many hours will it take the car

to travel 150km?

How did you find this diagnostic test? (Please circle all that apply)

It was way too hard It was way too easy It was just right

Some of it was too easy Some of it was too hard

I ran out of time I finished really early

10


Number – Quiz 1 Whole Numbers




No calculators allowed in this quiz.

Question 1

342+198

Question 2

457×3

Question 3

What are the next 3 terms of this

sequence?

1, 4, 7, 10, ___, ___, ___

Question 4

How many 10s are there in 4520?

Question 5

Find the LCM for 4 and 6:

Question 6

What is the highest common factor of 12

and 18?

Question 7

What is the prime factorisation of 18?

Question 8

What is the value of 4 cubed?

Question 9

What is the value of √81?

Question 10

What is the value of

3(23 − 4) ÷ √4

Mark out of 10:

Reflection:

11


Number – Quiz 2 Integers and Fractions





Question 1

Use <, > or = to make this true:

-5 -6

Question 2

3+−5 =

Question 3

6− −−3 =

Question 4

14 ÷− 7 =

Question 5

4− ×− 5 =

Question 6

3

5−

2

5=

Question 7

2

3+

1

4=

Question 8

2

3× 4 =

Question 9

4

7÷

2

3=

Question 10

Put these fractions in order from smallest

to largest:

1

5,2

3,1

2,3

4,1

4,3

5

Mark out of 10:

Reflection:

12


Number – Quiz 3 Decimals and Percentages





Question 1

Write these decimals in order from

smallest to largest:

0.215, 0.209, 0.099, 0.22, 0.21

Question 2

0.215 + 1.24 − 0.034 =

Question 3

0.259 × 1.4 =

Question 4

1.2 ÷ 0.03 =

Question 5

Write the test score of 20 out of 25 as a

percentage:

Question 6

What is 30% of 140?

Question 7

Add G.S.T. to $120

Question 8

Convert 0.125 to a percentage.

Question 9

Convert 0.8 to a fraction in its simplest

form.

Question 10

Convert 3

4 into a decimal.

Mark out of 10:

Reflection:

13


Number Topic Test


You have 55 minutes to complete this test.

Formal test conditions must be present during this test.

No calculators allowed in this test.

Total marks available = 54

Question 1

Solve these questions:

a) 3 ×− 1

2=

b) 0.25 + 1.923 =

c) 3−−6 =

d) 12 ÷− 0.4 =

Question 2

The temperature in London one winter’s

day was -2oC.

(a) What is the temperature in

Vancouver that day if it is 5 degrees

colder than in London?

(b) A New Zealander boasted “to get

our temperature, take the London

temperature number and multiply by -12.” What is the temperature in New

Zealand that day?

Question 3

Describe how this pattern is generated

in enough detail so someone could

follow the instructions and produce the

next 3 terms:

3, -4, 7, -11, 18, -29, …

Question 4

Find the highest common factor of 36

and 96.

Question 5

Write down the prime factorisation of

420.

Question 6

Rowena is losing her marbles!

She bought a bag with 48 marbles in it.

She traded ¼ of them to get 4 new ones

that she really wanted.

Keeping the new ones separate, she

plays with the ones she has left and loses

1/3 of them.

(a) How many marbles did she trade to

get her 4 new ones?

(b) How many does she still have at the

end of her game (including the 4

new ones).

(c) What percentage of her original

marbles does she have left?

14

Question 7

Hinerangi wants to buy a new bike. The

bike costs $1300. She earns $15/week at

a part time job. There are several

options for how she might buy this:

A: Her parents give the bike shop a $200

deposit and then she pays $15/week for

80 weeks (the shop will collect extra

money this way).

B: Save up for 10 weeks. The bike will

then be on sale for 30% discount. Her

parents pay what she can’t afford and

she pays them back at $15/week.

C: Save until she can afford the full

price, but her parents will give her $1 for

every $10 she saves.

Work out the cost and time to pay off

the bike for each option.

Question 8

What two numbers does √28 lie

between?

Question 9

Round 35.05483 to 4 significant figures

(s.f.)

Question 10

Evaluate 0.25×4

5− (32+−7) =

Question 11

Complete this table:

Fraction Decimal Percentage 3

5

33. 3̇%

1.25

Question 12

Split 350 into the ratio 5:2

Question 13

If a car is driving at 50kmh-1, how far

does it travel in 2.25 hours?

Question 14

A farmer and 5 helpers took 12 hours to

put up 100m of fence. Two of the

helpers had to leave, how long will it

now take to put up the next 100m of

fence?

15

Question 15

What is 13% of 250?

Question 16

A shirt was in a 30% off sale. If its normal

price was $55, how much is it now?

Question 17

Put these numbers in order from smallest

to largest:

0.1, 1%, 1

50, 0.05, 50%

Question 18

John and Sione were doing some

landscaping. John is paid $20 per hour

and Sione is paid $25 per hour. They

both decided this was a little unfair and

felt it would be fairer if they split the total

amount earned by the number of hours

worked. If John worked 60 hours and

Sione worked 40 hours, using their new

fair scheme, how much will they each

get paid?

Question 19

The 110 m hurdles race has 10 hurdles

that are evenly-spaced from each

other. The first hurdle is placed 13.72 m

from the starting line. The distance from

last hurdle to the finish line is 14.02 m.

How far apart are the hurdles placed?

Question 20

If the large square is worth 1, give the

shaded portion as:

(a) A decimal

(b) A percentage

(c) A fraction in its simplest form

Mark out of 54:

Reflection:

16


Measurement – Quiz 1 Length, Time, Weight, Volume


You have 20 minutes (2 minutes per question) to complete this quiz.

Calculators are allowed, and students need a ruler or measuring tape.

Question 1

What is the width of this booklet in cm?

Question 2

What is the length of this booklet in m?

Question 3

What is the perimeter of this booklet in

cm?

Question 4

Convert 3 hours and 15 minutes to a

decimal with hours as the unit.

Question 5

Convert 5 hours and 30 minutes to a

decimal with minutes as the unit.

Question 6

Convert 36 mls to cm3

Question 7

Convert 5 cm3 to mls.

Question 8

What is the difference between

capacity and volume?

Question 9

Calculate the volume of a cuboid with

length 3cm, width 2cm and height 5cm.

Question 10

If your desk was a cuboid, what would

its volume be? Show your working.

Mark out of 10:

Reflection:

17


Measurement – Quiz 2 Area: rectangles, parallelograms and triangles



Calculators are allowed, and students need a ruler or measuring tape.

Question 1

Draw a rectangle with an area of 6 cm2.

Question 2

Measure the perimeter of your

rectangle.

Question 3

Draw a triangle with an area of 4 cm2.

Question 4

Measure the perimeter of your triangle.

Question 5

Name this polygon.

Question 6

Measure the height of the polygon in

question 5. Give your answer to the

nearest mm.

Question 7

Measure the width of the polygon in

question 5. Give your answer to the

nearest mm.

Question 8

Measure the slant height of the polygon

in question 5. Give your answer to the

nearest mm.

Question 9

Calculate the perimeter of the polygon

in question 5 using your measurements.

Question 10

Calculate the area of the polygon in

question 5 using your measurements.

Mark out of 10:

Reflection:

18


Measurement – Quiz 3 Volume and surface area of cuboids and cylinders.



Calculators are allowed, and students need a ruler.

Question 1

The width, length and height of the

cuboid above are 4m, 3m and 2m.

Label the diagram (not drawn to scale).

Question 2

Calculate the volume of the cuboid in

question 1.

Question 3

Calculate the surface area of the

cuboid in question 1.

Question 4

Sketch a cuboid with a volume of 6 cm3.

Question 5

What is its surface area of the cuboid in

question 4?

Question 6

What is the volume of the cuboid in

question 1 in cm3?

Question 7


cuboid in question 1 in cm2?

Question 8

The cylinder has a diameter of 6 cm and

a height of 5 cm.

Label the diagram.

Question 9

Calculate the volume of the cylinder in

question 8.

Question 10


cylinder in question 8.

Mark out of 10:

Reflection:

19

Measurement Project: Marking Sheet.

Name: NZC

Level:

PPMCC Level 2 Level 3 Level 4 Level 5 L2 L3 L4 L5 Marks

25-29

level 3+ 40-44

level 4+ 55-59

level 5+

20-24 level 3

35-39 level 4

50-54 Level 5

15-19

level 3- 30-34

level 4- 45-49

level 5-

Total: 0 to 14 15 to 29 30 to 44 44 to 60

Problem Teacher provided question Write own question

8

Plan Information required is

listed 3 3

Plan Plan for collecting

measurements 3 3

Plan Units stated 4

Measure Collect and record several measurements 8 8 8 8

Calculate Setting out is clear. 6 8

Calculate cuboid Decimals Prisms and cylinders.

9 9 9

Calculate Explain what the

calculations are for 8 9

Conclusion Answer given

Answer question, state limitations, explain accuracy.

6 7 8 8

14 24 45 60

A very small number of students may be at Level 6 (Bringing the maximum to 70 marks)

Calculate measure at a level of precision appropriate to the task L6 2

Calculate apply the relationships between units in the metric system, including the units for measuring different

attributes and derived measures. L6 2

Calculate calculate volumes, including prisms, pyramids, cones,

and spheres, using formulae. L6 3

Calculate recognise similar shapes and use proportional

reasoning to find an unknown length. L6 3

Total Mark:

70

Mark out of 70:

Reflection:

20


Geometry – Quiz 1 Angles: Parallel lines and triangles.



Calculators are NOT allowed. Drawings are not to scale.

Give the value of the angle, and the reason for experts

.

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Mark out of 10:

Reflection:

21


Geometry – Quiz 2 Nets, 3, and 2 dimensional representations.




Question 1:

Sketch the top view.

Question 2: Sketch the net.

Question 3: Sketch the 3D shape

this net would make.

Question 4

Name the shape in question 3.

Question 5

List the platonic solids.

Question 6

Sketch the side views.

Question 7

Draw a triangular prism.

Question 8

Sketch the net of a triangular prism.

Question 9: Sketch the 3d shape

this net makes.

Question 10: Sketch the 3d shape

this net makes.

Mark out of 10:

Reflection:

22


Geometry – Quiz 3 Transformations: reflection, rotation, translation and resizing.




1. Rotate the object ABCDEF 180 degrees about point (0,0).

2. Reflect the object ABCDEFG through the y axis.

3. Enlarge the object ABCDEFG by a scale factor of 2 with the point of enlargement B.

4. Translate the object ABCDEFG by the vector (1,-6).

5. Label each of the images with the question number.

6. Label every point, on each image, the points ABCDEF.

7. Which of the images are congruent with the object?

8. Which of the images are similar to the object.

9. How many lines of symmetry does ABCDEF have?

10. Can you create a shape with one line of symmetry, by adding one square to ABCDEF?

Mark out of 10:

Reflection:

23


Geometry Common Test

Student Name:___________________ Points: ___ /70 NZC Level awarded: ___

1. (2 points) Sketch the 3D shape this net makes using the isometric dots provided.

2. Sketch the top view (pink) (1 point sketch, 1 point label)

3. Sketch the LHS view (green) (1 point sketch, 1 point label)

4. Sketch the FRONT view (yellow) (1 point sketch, 1 point label)

5. Sketch (4 points) and label (1 point) this 3D shape on isometric paper.

6. (10 points) Use a ruler to construct the net of a cuboid which is 2cm wide, 3cm long and 5cm high.

24

7. (5 points) Sketch the 3D object that this net would make:

8. (5 points) Sketch the 3D object that this net would make:

9. (10 points) Construct the net that makes this 3D object: Sketch in the space below and construct on the back of this sheet.

10. (14 points total) Deduce the values of the angles above, and give the reason.

(1 point) A= (1 point) Reason:

(1 point) B= (1 point) Reason:

(1 point) C= (1 point) Reason:

(1 point) D= (1 point) Reason:

(1 point) E= (1 point) Reason:

(1 point) F= (1 point) Reason:

(1 point) G= (1 point) Reason:

25

11. (2 points) Reflect the object in the y axis.

12. (2 points) Rotate the object by 180 degrees anti clockwise through the point (0, 0).

13. (2 points) Translate the object by the vector (1,-5).

14. (2 points) Enlarge the object by a scale factor of 2 with a centre of enlargement being point C.

15. (1 point) Describe the invariant properties of reflection:

16. (1 point) Describe the invariant properties of rotation:

17. (1 point) Describe the invariant properties of translation.

18. (2 points) Write a reflection on your mindset within this unit of work. Did you have a growth mindset or a

fixed mindset and what habits did you develop in order to grow your brain?

19. Estimate your mark in this test.

20. Are you happy with your efforts?

70pnts: Q1: 2points; Q2: 2points; Q3: 2pts; Q4: 2pts; Q5: 5pts; Q6: 10pts; Q7: 5pnts; Q8: 5pnts; Q9: 10pnts; Q10: 14pnts; Q11: 2pnts; Q12: 2pnts; Q13: 2pnts; Q14: 2pnts; Q15: 1pnt; Q16: 1pnt; Q17: 1pnt; Q18: 2pnts.

Mark out of 70:

Reflection:

26


Algebra – Quiz 1 Manipulation





Question 1

Simplify 5𝑥 − 2𝑥

Question 2

Simplify 4𝑦 + 5𝑧 + 2𝑦 − 3𝑧

Question 3

Simplify 3 × 4𝑎

Question 4

Simplify 4𝑏 × 2𝑎𝑏𝑐

Question 5

Simplify 12𝑥

6𝑥

Question 6

Write this using algebra.

3 lots of a number plus 5.

Question 7

Expand 3(𝑓 − 2)

Question 8

Expand 3 + 4(𝑡 + 1)

Question 9

Factorise 4ℎ − 8

Question 10

Factorise 3𝑘 + 6𝑘2

Mark out of 10:

Reflection:

27


Algebra – Quiz 2 Substitution and Solving




Calculators allowed in this quiz.

Question 1

Expand and simplify 3a(2a+4)

Question 2

Factorise 4a + 8b

Question 3

Expand and simplify 3(5a+b)-2(a-3b)

Question 4

If 𝑓 = 4, 𝑔 = 3 find ℎ if ℎ =𝑓𝑔

𝑓+𝑔

Question 5

Find the value of 𝑥: 3𝑥 = 27

Question 6

Find the value of 𝑥: 𝑥 − 5 = 20

Question 7

Find the value of 𝑥: 𝑥

6= 3

Question 8

Find the value of 𝑥: 3𝑥 − 5 = 25

Question 9

Find the value of 𝑥: 3(1 + 𝑥) − 20 = 7

Question 10

Find the value of 𝑥: 3(𝑥 − 2) = 2(𝑥 + 4)

Mark out of 10:

Reflection:

28


Algebra – Quiz 3 Manipulation, Substitution and Solving





Question 1

Expand and simplify 3a(2a+4)

Question 2

Factorise 4a + 8b

Question 3

Expand and simplify 3(5a+b)-2(a-3b)

Question 4

If 𝑓 = 4, 𝑔 = 3 find ℎ if ℎ =𝑓𝑔

𝑓+𝑔

Question 5

Find the value of 𝑥: 3𝑥 = 27

Question 6

Find the value of 𝑥: 𝑥 − 5 = 20

Question 7

Find the value of 𝑥: 𝑥

6= 3

Question 8

Find the value of 𝑥: 3𝑥 − 5 = 25

Question 9

Find the value of 𝑥: 3(1 + 𝑥) − 20 = 7

Question 10

Find the value of 𝑥: 3(𝑥 − 2) = 2(𝑥 + 4)

Mark out of 10:

Reflection:

29

My Algebra Learning Poster

30

Reflection

Do I have a Growth Mindset?

Which Learning Habits do I most need to work on?

Thinking

Relating to Others

Understanding Language Symbols and Text

Managing Self.

Participating and Contributing.

Strive-Connect-Reflect-Respect.

31


Algebra Graphs – Quiz 1 Gradient.


You have 10 minutes (1 minute per question) to complete this quiz.



Gradient of segment AB = Gradient of segment KL =

Gradient of segment CD = Gradient of segment MN =

Gradient of segment EF = Gradient of segment OP =

Gradient of segment GH = Gradient of segment QR =

Gradient of segment IJ = Gradient of segment ST =

Mark out of 10:

Reflection:

32


Algebra Graphs – Quiz 2 Plotting points..


You have 10 minutes (1 minute per question) to complete this quiz.


Co-ordinates of point A are ( , ) Co-ordinates of point F are ( , )

Co-ordinates of point B are ( , ) Co-ordinates of point G are ( , )

Co-ordinates of point C are ( , ) Plot point H: (3,-2) and label it H

Co-ordinates of point D are ( , ) Plot point I: (-3,-2) and label it I

Co-ordinates of point E are ( , ) Plot point J: (-3,2) and label it J

Mark out of 10:

Reflection:

33


Algebra Graphs – Quiz 3 Patterns and Graphs





Question 1

Next three terms: 3, 5, 7, 9, …

Question 2


Question 3


Question 4

Next three terms: 9, 5, 1, -3, …

Question 5

Write the formula for the pattern in

Question 1:

Question 6

Write the formula for the pattern in

Question 4:

Question 7

Where does 𝑦 = 2𝑥 − 1 pass through the

𝑦-axis?

Question 8

Where does 𝑦 = 3𝑥 − 4 cut the 𝑦 -axis?

Question 9

What is the gradient of 𝑦 = 3𝑥 − 4?

Question 10

What is the equation of:

Mark out of 10:

Reflection:

-4

-2

0

2

4

6

-2 0 2 4

34


Year 9 Algebra Topic Test


You have 55 minutes to complete this test.

Formal test conditions must be present during this test.

Calculators allowed in this test.

Total marks available = 81

Question 1

Write these using algebra:

a) A number is multiplied by 4 and

then 3 is subtracted from the

result.

b) 4 more than double a number.

c) The result of 5 less than a number

is divided by 7.

Question 2

Simplify these expressions:

e) 𝑥 + 𝑥 + 𝑥 + 𝑥 =

f) 𝑦 × 𝑦 × 𝑦 × 𝑦 =

g) 4𝑥 + 3𝑥 − 𝑥 + 5𝑥 =

h) 3𝑥 + 5 − 5𝑥 + 1 =

Question 3


a) 3 × 𝑥 × 2 × 𝑦 =

b) 2𝑥 × 8𝑦 × 3𝑧 =

c) 3𝑥 × 5𝑥 =

d) (2𝑘2)3 =

Question 4


a) 2𝑎

4𝑏=

b) 3𝑟4

4𝑟=

Question 5

Write an algebraic expression for the

perimeter (the distance around the

outside) of this rectangle:

𝑥cm

𝑥 + 3cm

35

Question 6

Explain using your own words or

diagrams why the following statement is

true:

(𝑥3)4 = 𝑥12

Question 7

By using the distributive law, expand and

simplify these expressions:

a) 3(𝑑 − 2) =

b) 2 + 3(𝑒 + 1) =

c) 𝑡 − 2(𝑡 − 2) =

d) (𝑥 + 4)(𝑥 − 2) =

Question 8

Fully factorise the following expressions:

a) 3𝑓 − 6 =

b) 𝑥2 − 5𝑥 =

c) 8𝑎𝑏 + 4𝑏𝑐 =

d) 24𝑔4ℎ3 + 16𝑔ℎ6𝑘 =

Question 9

Given 𝑒 = 3, 𝑓 = −2 and 𝑔 = 1, find the

values of these expressions:

a) 𝑒 + 𝑓 + 𝑔 =

b) (𝑒−𝑓)

𝑔=

c) 𝑒(𝑓 − 𝑔) =

36

Question 10

Solve these equations to find the value

of the unknown:

a) 3𝑥 = 12

b) 𝑥 − 2 = 12

c) 2𝑥 − 5 = 10

d) 𝑥+3

4= 5

e) 3(2𝑥 − 1) = 11

f) 2𝑥 − 3 = 5𝑥 + 3

Question 11

Find the next 3 terms for this sequence:

3, 7, 11, 15, ___, ___, ___

Question 12

Write the formula for this number

pattern:

4, 1, -2, -5, …

Question 13

Write down the gradient and the y-

intercept for this equation of a straight

line. Then draw it on the grid provided. 𝑦 = 2𝑥 − 1

Gradient =____

Y-intercept=____

Question 14

What are the coordinates of point A and

B on the above grid?

A=(_____,_____)

B=(_____,_____)

A

B

37

Question 15

Write down the gradient and the y-

intercept for this equation of a straight

line.

𝑦 =2𝑥

3+ 2

Then draw it on the grid provided.

Question 16

Given the following graph shows the

graph of a swimmer in a 50m pool

where distance from the recorder is on

the y-axis and the time in seconds is on

the x-axis, answer the questions that

follow:

Question 16 Continued…

a) Did the swimmer start at the end

by the recorder?

How do you know?

b) What happened between 45 and

75 seconds?

How is this shown on the graph?

c) Did the swimmer travel faster in

the first 50m or the last 50m?

How is this shown on the graph?

Mark out of 70:

Reflection:

38


Probability – Quiz 1 Probability Experiments


You have 10 minutes (1 minute per Mark) to complete this quiz.



There is a bag of 10 Balls. Harry and Sam take turns picking a ball, without looking, recording

the colour and putting it back in the bag. They do this 100 times. Here are the results.

Colour Count Percentage Harry’s Guess Sam’s Guess

Blue 9 9% 1 1

Purple 35 35% 4 3

Yellow 21 21% 2 2

White 7 7% 1 1

Pink 28 28% 3 3

1. Who do you think is right? [1 Mark]

2. Explain why you think they are correct. [1 Mark]

3. Can you explain the error that the person who is wrong made? [2 Marks]

Assume there are 100 balls in this bag.

Polly and Dolly take turns picking out a ball from the bag, recording

the colour, and putting it back into the bag.

They do this 1000 times and here are the results.

Colour Count Percentage Guess1 Guess2

Blue 192

Purple 214

Yellow 415

White 94

Pink 85

4. Use the results of the experiment to make an educated guess about the number of each

coloured ball. Place your answer in Guess1 column. [3 marks]

5. Now, you are told that the colours come in multiples of 10. Change your guess in light of this

new information. Place you answer in Guess2 column. [3 marks]

Mark out of 10: Reflection:

39


Probability – Quiz 2 Probability Trees


You have 10 minutes (1 minute per Mark) to complete this quiz.



1. Draw a probability tree in order to calculate the probabilities when throwing a dice, then tossing

a coin. [3 Marks]

2. Make sure you have placed the probabilities on the branches. [2 Marks]

3. List the sample space to the right of the tree. [1 Mark]

4. Calculate the probability of getting a 6 followed by heads. [1 Mark]

5. Calculate the probability of getting a number more than 2 followed by tails. [1 Mark]

6. Imagine you throw a dice, and then toss a coin twice. What is the probability of getting a one on

the dice followed by heads, and then heads again? [2 Marks]

Mark out of 10:

Reflection:

40


Probability – Quiz 3 Randomness


You have 10 minutes (1 minute per mark) to complete this quiz.



1. You are the teacher. You have told students to toss a coin and record the results.You suspect

some of the students are just writing H (for heads) and T (for tails) without tossing the coin.

Mark beside each of the results is they are most likely real or fake. It is ok to be unsure.

[ 6 Marks]

HTHTHTHTHTHTHTHTHTHTHTH Real? Fake? Unsure? Reason?

HHTHTTTTHTHTHTHTHTHHHHH Real? Fake? Unsure? Reason?

HTTTTTHTHHTHTTTTTTTHTTTT Real? Fake? Unsure? Reason?

TTTTHHHHHHHHTHTTHTHTHTH Real? Fake? Unsure? Reason?

HHTTHHTTHHTTHHTTHHTTHHT Real? Fake? Unsure? Reason?

HHHHHHHHHHHHHHTHTTHTHT Real? Fake? Unsure? Reason?

2. Which of these images is random and which one if fake?

Explain you answer [4 Marks]

Mark out of 10:

Reflection:

41


Probability Common Test 2015

Simulation.

1. How many heads would you expect to get if you toss a coin 10 times? [1 mark]

2. How did you arrive at your answer to question 1? [2 marks]

3. Imagine someone tosses a coin 10 times, and records the number of heads. They repeat this 31

times. This means they would have tossed the coin 310 times to complete the simulation.

Do you think the results could look like this? [1 mark]

Why? [2 marks]

4. If the person repeated the simulation, would they get the exact same results? [1 mark]

5. Explain your reasoning in question 4. [2 marks]

6. Carry out your own simulation, aim to toss the coin (or use a virtual coin), 100 times, to get ten

dots on this number line. [12 marks]

42

7. In what way is your distribution similar to the given distribution? [2 marks]

8. In what way is your distribution different to the given distribution? [2 marks]

9. Do your think your distribution will look exactly the same as the other people in your class?

[2 marks]

10. I used Excel to toss a coin ten times, thousands of times. I then used Geogebra to show me the

distribution. Here it is:

What do you notice about this distribution, compared to yours? List the similarities [2 marks] and

differences [3 marks].

Mark out of 30: Reflection:

43

NAME:

TEACHER:

Pakuranga College

Year 9

Mathematics

2014 Examination

Time: 2 hours

Topic Suggested Time NZC Level

Number 30 mins

Algebra 30 mins

Statistics 20 mins

Measurement 20 mins

Geometry 20 mins

*Probability* *30 mins*

Students are advised to bring a Calculator, ruler, pen, pencil and eraser.

*Probability section was not in the 2014 Exam.* Ask your teacher about the 2015 format.

44

Number Section Level 3 (10 minutes).

1. 3+15= __

2. 1.5 + 0.5 = __=__

3. 2003-47=____

4. 3×40=__

5. 97-67=___

6. 15÷3=___

7. 4

50+

2

50=

8. Reorder the numbers to make addition

easier, use tidy numbers.

5+4+46+75=(__+__)+(__+__)

9. List the prime factors of 12:

_________________________

10. List the first 6 multiples of 8:

_________________________

11. What is the square root of 100? __

12. Given 6 squared is 36, what is the

square root of 36? __

13. (3+8)×(6-3)=__×__=__

14. 3×(2+5)=__×__=__

15. What comes next? 1,2,4,8,16,__

16. How many tens are in 7084? __

17. Which is bigger ½ or ¼ ? ___

18. Which is smaller 1

13 or

1

12? ___

19. Write 50% as a fraction _____

20. Write 0.25 as a percentage ____

21. Write 2% as a decimal ____

22. 9

10 as a decimal is ___

23. 25% of $80 is ____

24. List all the factors of 26:

__________________________

25. 4 to the power of 2 =42 = ___

26. 3

4 -

1

2 = ___

27. The denominator of 8

5 is __

28. The numerator of 6

8 is __

29. Simplify 30

60 =

30. Write 10

40 as a percentage ___%

Level 3- Level 3 Level 3+

15-19 20-24 25-30

45


1. 2003-246=____

2. 32×5=__

3. 9-31=___

4. 2.4 - 2.6=___

5. 3

5+

4

5=

6. List the prime factors of 81:

_________________________

7. LCM of 15 and 25___________

8. HCF of 15 and 25___________

9. What is the cubed root of 8? __

10. Given 3 cubed is 27, what is the cubed

root of 27? __

11. If a cubed is b, what is the cubed root of

b? __

12. (3-2)×(6+7)=__×__=__

13. What comes next? 9,7,5,3,__

14. How many tenths are in 768.47? __

15. Which is bigger 5

8 or

4

7?

16. Which is smaller 7

8 or

1

13?

17. 0.3 times 0.7 = ____

18. Write 65% as a fraction _____

19. Write 0.1 as a percentage ____

20. Write 5.7% as a decimal ____

21. What is 25% of $80? ____

22. 5/12 as a decimal is ___

23. 65% as a fraction is ___

24. 72% of $40 is ____

25. 5 to the power of 4 = 54= ___

26. -2 to the power of 2 =(-2)2 = ___

27. Round 3.09 to the nearest whole number

____

28. Round 5.608 to the nearest tenth: __

29. Simplify 30

80=

30. Decrease 150 by 70% _____


15-19 20-24 25-30

46


1. 305 in standard form= ___ × 102

2. 2918 in standard form = ____ × ____

3. -31+17+23-19=___

4. 5(1

2−

1

3) = 5( − ) =

5. Round 20.324 to 2 dp= _____

6. Round 20.356 to 4 sf = _____

7. 30×95%=__

8. 22% of 20×52=____

9. Increase $75 by 5%=______

10. Decrease $87 by 15%=_____

11. 3% times 1%=___

12. 0.15 times 260=___

13. If 4 hats takes two balls of wool, how

many balls of wool do I need to have to

mane 8 hats? __________

14. 32 – 28 =___

15. 19

5−

14

5 =

16. 110−210

5=

17. 5×4 – 5×9 = 5×___ = ___

18. Which is smaller 0.09 or 0.1? ___

19. LCM of 15 and 20___________

20. List the common prime factors of 36 and

42 _____________________

21. What is the cubed root of 64? __

22. Given 2 cubed is 8, what is the cubed root

of 8000? _____

23. Given 5 cubed is 125, what is the cubed

root of 0.125? _____

24. 73 – 102 = _____

25. Put in order 0.193, 0.2, 0.29, 0.19

__________________________

26. 3 people take 12 hours to paint a fence.

How many people are needed to paint the

fence in 4 hours? _____

27. A car is travelling at 50 km per hour. How

many hours will it take to travel 150km?

_____

28. If three people take five hours to chop up

firewood, how many minutes would it take

6 people? _____

29. 3

5 times

2

9 = ___

30. Write 3.867 × 103 in decimal form

___________


15-19 20-24 25-30

47

Algebra Section Level 3 (10 minutes).

1. Continue the pattern, draw the next three terms. [3 marks]

2. Complete the table: [8 marks]

Term n 1 2 3 4 5 6 7 10 n

Number of

lines. 3

3. Describe the rule for the next pattern: [1 mark]

4. Describe the rule for the nth pattern: [1 mark]

5. Graph the pattern. The term or pattern

number (n) is on the x

axis.

The number of lines in the

pattern on the y axis.

[5 points, 0.5 for each

correctly plotted point]

6. If the dots were joined up with a line, (which we do NOT do because there are no patterns

between the patterns), what would the gradient of this line be? [1 mark]

7. How does the gradient connect with the rule? [1 mark]


5-9 10-14 15-20

48

Algebra Section Level 4 (10 minutes).

1. A function machine has an input and an output. The first function takes the number which is input and outputs that number multiplied by 3. The rule is 3n. Can you work out the rules for the

other 3 function machines and write the rule in the empty box. [3 marks: 1 marks per rule] NZMathsAnswersHere

2. What can you say about n + (n+1) + (n+2) compared with 3n + 3? [1 Mark]

3. Expand the following expressions: [5 marks]

a. 7(a+2b)=

b. 5(x+2)=

c. 2a(a+3b)=

d. 2x(3x-1)=

e. 2(2x+1)+4(x+2)=

4. Solve for x: [5 marks]

a. 10+x=15

b. 3x=21

c. 3(x+2)=18

d. 7x+7=28

e. 3+2x=6+x

Algebra Section Level 5 (10 minutes). 1. Fill out the table in relation to the graph below. [12 marks, 1 per answer]

Function X-intercept Y-intercept Gradient Equation

LineA

LineB

CurveC

2. What are the exact co-ordinates of the point where LineA and

LineB intersect? [2 Marks] Show all working.

3. What are the co-ordinates of the points where LineA and CurveC intersect? [2 Marks] Show all working.

Level 4- Level 4 Level 4+ Level 5- Level 5 Level 5+

7-10 11-14 15-18 19-22 23-26 27-30

http://www.nzmaths.co.nz/sites/default/files/curriculum/Level4NumberandAlgebraPatterns.pdf

49

Statistics Section Level 3 (10 minutes).

1. Explain each step of the PPDAC cycle: [10 Marks]

P-P-D-A-C Short description

P is for

P is for

D is for

A is for

C is for

2. This image is from new.censusatschool.org.nz. Data Viewer.

a. Which part of the

PPDAC cycle does this

image belong?

[1 Mark]

b. How many males were in this sample? [2 Marks]

c. How many females were in this sample? [2 Marks]

d. Is the sample large enough to give information about the population? [2 marks]

e. What is the population? [2 Marks]

f. What else do the Box Plots tell you about the sample? [10 Marks] Fill in the table below by estimating the values from the Box plot.

g. What units is the arm-span measured in? [1 Mark]

Males Females

Lowest Armspan

Lower Quartile

Median

Upper Quartile

Highest Armspan


15-19 20-24 25-30

http://new.censusatschool.org.nz/tools/data-viewer/index.php?switchBox=on&problem_wonder=&problem_variable=&database=cas2013&strat1a=gender&strat1b_l0=female&strat1b_l1=male&strat2a=&strat3a=&strat4a=&sample_size_n=10&sample_size_s0a=5&sample_size_s1a=5&gms=Get+data#bottom

50

Statistics Section Level 4 (5 minutes).

1. Discus the similarities and differences between this sample and the sample on the previous page (inset). [14 Marks]

Describe the Similarity or Difference It matters because?

Statistics Section Level 4&5 (5 minutes).

1. Discus this sample, using statistical

language. Words that might help you

include: representative, difference, variation, outliers, interquartile range, spread, central tendency. [ 16 Marks]

Level 4- Level 4 Level 4+ Level 5- Level 5 Level 5+

7-10 11-14 15-18 19-22 23-26 27-30

51

Measurement Section Level 3 (10 minutes).

1. Fill in the table below:[15 Marks, one per cell]

Perimeter Area Shape

4 units 1 unit squared Square

Volume in units

cubed.

Surface Area in

units squared.

Total outside

edges in units.


5-8 9-12 13-15

52


1. Estimate (or calculate) the number of blocks used to create this image. The clarity of your

working is worth more marks than the answer. [5 Marks]

2. Explain any assumptions made. [5 Marks]

3. Calculate (or estimate) the surface area of the shape. [5 Marks]


1. Name the 3D shape. [3 Marks]

2. Calculate the volume of this 3D shape. [4 Marks]

3. Calculate the surface area of this 3D shape. [4 Marks]

4. Calculate the edge length of this 3D shape. [4 Marks]

Level 4- Level 4 Level 4+ Level 5- Level 5 Level 5+ 7-10 11-14 15-18 19-22 23-26 27-30

53

Geometry Section Level 3 (10 minutes).

1. Fill in the table below.[15 Marks: 5 Marks per transformation]

Label the Object and Image. [1]

Label the transformations identifiers.[1]

Name of

transformation [1]

Give Details.[2]

is the object

We can keep building on the pattern:

2. Sketch and Name five polyhedra (platonic solids, prisms, pyramids) of your choice. [10 Marks- 1 Mark per sketch, 1 Mark for the correct name]


10-14 15-19 20-25

54

Geometry Section Level 4 (5 minutes). 1. Fill in the table with the missing information, the first row is done for you. [12 Marks]

Name 3D Net Faces; Edges;

Vertices.

Icosahedron

Faces= 20

Edges=30 Vertices=12

Geometry Section Level 5 (5 minutes). 1. Label this diagram with everything you can, giving the geometrical reasons. The dotted lines are

parallel.[13 Marks: Find at least 8 Angles and give at least 5 reasons]


55

Probability Section Level 3 (10 minutes). 1. Harry was playing a dice game and got double sixes on

every single turn. He asked his friends to close their

eyes when he thre the dice. Do you think he was lucky

or cheating? Explain your reasoning. [5 Marks.]

2. Samuel completed a simulation. He threw a dice ten times and

recorded the number of heads. He repeated this ten times. His

results were: 5;5;5;5;5;5;5;5;5;5. So every single time he threw

the dice ten times, he got exactly 5 heads and 5 tails.

What do you think about his results? (Are they what would be

expected?) [4 marks]

Are Samuels results possible? [1 mark]

3. There is a bag of lollies, it contains 4 red, 3 yellow and 3

green jellybeans. Polly has her eyes closed, and reaches

into the bag to retrieve one lolly.

What is the likely hood that the lolly is black? [2 marks]

What is the likely hood that the lolly is red? [1 mark]

What is the likely hood that the lolly is green? [1 mark]

What is the likely hood that the lolly is yellow? [1 mark]

4. Is the spinner from maths playground fair? [1 marks]

Explain [2 marks]

How many times has it been spun so far? [1 mark]

What do the results suggest? [1 mark]


6-10 11-15 16-20

56

Probability Section Level 4 (10 minutes). 1. Complete this table for two dice.[3 marks]

1 2 3 4 5 6

1 1,1 1,2

2

3

4 4,5

5 5,4 5,6

6

2. What is the probability of getting double sixes with two fair dice? [1 mark]

3. Fred has got double sixes three times in a row. The dice he is using are fair dice. Does the fact

that he got double sixes three times in a row impact on his chances of getting double sixes in the

future? Explain. [2 marks]

4. There are an unknown number of lollies in a bag. We know the probability of getting a red one is

one half. The probability of getting a green one is one fifth. The only other colour in the bag is

pink. What is the probability of getting a pink lolly? [4 marks]

Probability Section Level 5(10 minutes). 5. What is the probability of getting an even number of a dice? [1 mark]

6. What is the probability of getting two even numbers when throwing two dice? [2 marks]

7. Draw a probability tree to calculate the probability of getting two heads when tossing two coins.

[6 marks]

8. These are the experimental results of a spinner.

How many times was it spun? [1 mark]

Compare the experimental results with

the expected probability. Assume the

spinner is fair.[5 marks]


57

My Glossary of Mathematical Language.

58

My Glossary of Mathematical Language.

59

Year 9 Mathematics Weekly Planner 2015

Week Date Unit of Work Assessment Event

2 Feb 2 - Feb 6 Growth mindset and BYOD set up Waitangi Day – 6th

3 Feb 9 - Feb 13 Statistics Quiz 1

4 Feb 16 - Feb 20 Statistics Quiz 2 Y9 Camp 18th

– 20th

5 Feb 23 - Feb 27 Statistics Quiz 3

6 Mar 2 - Mar 6 Statistics Project PPDAC poster or digital presentation School Athletics 4th

7 Mar 9 - Mar 13 Number Quiz 1 Primes LCM HCF Swim Sports 10th

& 12th

8 Mar 16 - Mar 20 Number Quiz 2 Place value, fractions, decimals, percentages

9 Mar 23 - Mar 27 Number Quiz 3 Integers, order of operations

10 Mar 30 - Apr 3 Number Common Test Good Friday – Apr 3rd

1 Apr 20 - Apr 24 Measurement Quiz 1

2 Apr 27 - May 1 Measurement Quiz 2 ANZAC – Apr 27

3 May 4 - May 8 Measurement Quiz 3

4 May 11 - May 15 Measurement PPMCC Project

5 May 18 - May 22 Measurement Project Presentations to class

6 May 25 - May 29 Geometry Quiz 1 TOD – 29th

May

7 Jun 1 - Jun 5 Geometry Quiz 2 Queen’s B’day – 1st

8 Jun 8 - Jun 12 Geometry Quiz 3

9 Jun 15 - Jun 19 Geometry Common Test

10 Jun 22 - Jun 26 Algebra Quiz 1

11 Jun 29 - Jul 3 Algebra Quiz 2

1 Jul 20 - Aug 2 Algebra Quiz 3

2 Jul 27 - Jul 31 Algebra Posters

3 Aug 3 - Aug 7 Algebra Graphs Quiz 1



6 Aug 24 - Aug 28 Algebra Common Test

7 Aug 31 - Sep 4 Probability Quiz 1 Tournament Week

8 Sep 7 - Sep 13 Probability Quiz 2 School Exams

9 Sep 14 - Sep 18 Probability Quiz 3 School Exams

10 Sep 21 - Sep 25 Probability Simulation

1 Oct 12 - Oct 16 Examination Preparation

2 Oct 19 - Oct 23 Examination Preparation

3 Oct 26 - Oct 30 Examination Preparation Labour Day 26th

4 Nov 2 - Nov 6 Examination Preparation Last Days Y11 - Y13

5 Nov 9 - Nov 13 Examination Preparation, study leave and Exam NCEA Exams

6 Nov 16 - Nov 20 Group Project based assessment – students decide on a problem NCEA Exams

7 Nov 23 - Nov 27 Students work towards presentation of their learning NCEA Exams

8 Nov 30 - Dec 4 Presentations and sharing of projects. NCEA Exams

9 Dec 7 - Dec 10 Mathematical Art

Junior Prizegivings – 9th

pakuranga college year 9. 2 mathematics assessments ... statistics project 7 reflection: topic...

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