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(Draft2) Answers 2014 Exam

Pakuranga College

Year 9

Mathematics

2014 Examination

Time: 2 hours

Sections:

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

Paper for working will be provided.

Examination Date: 14th November 2014

Topic Suggested Time Score NZC Level

Number 30 mins

Algebra 30 mins

Statistics 20 mins

Measurement 20 mins

Geometry 20 mins

EOY Exam Year 9 Printed Monday, 17 November 2014 APN

Number Section Level 3 (10 minutes).

1. 3+15= 18

2. 1.5 + 0.5 = 2.0 = 2

3. 2003-47=1956

4. 3×40=120

5. 97-67=30

6. 15÷3=5

7. 4

50+

2

50=

𝟔

𝟓𝟎=

3

25

8. Reorder the numbers to make

addition easier, use tidy numbers.

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

9. List the prime factors of 12:

2 and 3

10. List the first 6 multiples of 8:

8, 16, 24, 32, 40, 48

11. What is the square root of 100? 10

12. Given 6 squared is 36, what is the

square root of 36? 6

13. (3+8)×(6-3)= 11×3=33

14. 3×(2+5)= 3×7=21

15. What comes next? 1,2,4,8,16,32

16. How many tens are in 7084? 8

17. Which is bigger ½ or ¼ ? ½

18. Which is smaller 1

13 or

1

12?

𝟏

𝟏𝟑

19. Write 50% as a fraction 𝟓𝟎

𝟏𝟎𝟎=

𝟏

𝟐

20. Write 0.25 as a percentage 25%

21. Write 2% as a decimal 0.02

22. 9

10 as a decimal is 0.9

23. 25% of $80 is $20

24. List all the factors of 26:

1,2,13,26

25. 4 to the power of 2 = 42 = 16

26. 3

4 -

1

2 =

𝟏

𝟒

27. The denominator of 8

5 is 5

28. The numerator of 6

8 is 6

29. Simplify 30

60 =

𝟏

𝟐

30. Write 10

40 as a percentage 25%

Level 3- Level 3 Level 3+

15-19 20-24 25-30



1. 2003-246= 1757

2. 32×5= 160

3. 9-31= -22

4. 2.4 - 2.6= -0.2

5. 3

5+

4

5=

𝟕

𝟓

6. List the prime factors of 81:

3

7. LCM of 15 and 25 is 75

8. HCF of 15 and 25 is 5

9. What is the cubed root of 8? 2

10. Given 3 cubed is 27, what is the

cubed root of 27? 3

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

root of b? a

12. (3-2)×(6+7)=1×13=13

13. What comes next? 9,7,5,3,1

14. How many tenths are in 768.47? 4

15. Which is bigger 5

8 or

4

7?

𝟓

𝟖

16. Which is smaller 7

8 or

1

13?

𝟏

𝟏𝟑

17. 0.3 times 0.7 = 0.21

18. Write 65% as a fraction 𝟔𝟓

𝟏𝟎𝟎=

𝟏𝟑

𝟐𝟎

19. Write 0.1 as a percentage 10%

20. Write 5.7% as a decimal 0.057

21. What is 25% of $80? $20

22. 5/12 as a decimal is 0.4167

23. 65% as a fraction is 𝟔𝟓

𝟏𝟎𝟎=

𝟏𝟑

𝟐𝟎

24. 72% of $40 is $28.80

25. 5 to the power of 4 = 54= 625

26. -2 to the power of 2 =(-2)2 = 4

27. Round 3.09 to the nearest whole

number 3

28. Round 5.608 to the nearest tenth:

5.6

29. Simplify 30

80=

𝟑

𝟖

30. Decrease 150 by 70% 45


15-19 20-24 25-30



1. 305 in standard form= 3.05 × 102

2. 2918 in standard form = 2.918 × 103

3. -31+17+23-19= -10

4. 5(1

2−

1

3) = 5(

𝟑

𝟔−

𝟐

𝟔) =

𝟓

𝟔

5. Round 20.324 to 2 dp= 20.32

6. Round 20.356 to 4 sf = 20.36

7. 30×95%= 28.5

8. 22% of 20×52= 228.8

9. Increase $75 by 5%= $78.75

10. Decrease $87 by 15%= $73.95

11. 3% times 1%= 0.03%

12. 0.15 times 260= 39

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

many balls of wool do I need to have to

make 8 hats? 4

14. 32 – 28 = -247

15. 19

5−

14

5 =

𝟓

𝟓= 𝟏

16. 110−210

5=

−𝟏𝟎𝟎

𝟓= −𝟐𝟎

17. 5×4 – 5×9 = 5×(-5) = -25

18. Which is smaller 0.09 or 0.1? 0.09

19. LCM of 15 and 20 is 60

20. List the common prime factors of 36

and 42 CPFs are 2 and 3

21. What is the cubed root of 64? 4

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

root of 8000? 20

23. Given 5 cubed is 125, what is the

cubed root of 0.125? 0.5

24. 73 – 102 = 243

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

0.19, 0.193, 0.2, 0.29

26. 3 people take 12 hours to paint a

fence. How many people are needed to

paint the fence in 4 hours? 9 people

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

How many hours will it take to travel

150km? 3 hours

28. If three people take five hours to chop

up firewood, how many minutes would

it take 6 people? 150mins (2.5hrs)

29. 3

5 times

2

9 =

𝟔

𝟒𝟓=

𝟐

𝟏𝟓= 𝟎. 𝟏𝟑𝟑𝟑

30. Write 3.867 × 103 in decimal form

3867


15-19 20-24 25-30


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 5 7 9 11 13 15 21 2n+1

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

Add two lines.

4. Describe the rule for the

nth pattern: [1 mark] Double n plus one line.

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] Gradient is 2.

7. How does the gradient connect with the rule? [1 mark] Increase of pattern number by one means two more lines are added.


5-9 10-14 15-20


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]

They are always the same, expand and simplify the LHS to get the RHS.

3. Expand the following expressions: [5 marks]

a. 7(a+2b)=7a+14b

b. 5(x+2)=5x+10

c. 2a(a+3b)=2a2+6ab

d. 2x(3x-1)=6x2-2x

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

4x+2+4x+8=8x+10

4. Solve for x: [5 marks]

a. 10+x=15; x=5

b. 3x=21; x=7

c. 3(x+2)=18; x=4

d. 7x+7=28; x=3

e. 3+2x=6+x; x=3

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 (2,0) (0,1) -0.5 Y=-0.5x+1

LineB (1,0) (0,-1) 1 Y=x-1

CurveC (2,0)&(-2,0) (0,-4) Not constant Y=x2 - 4

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

LineA and LineB intersect? [2 Marks] Show all working.

-0.5x+1=x-1; 2=1.5x; x=1.33; y=1.33-1=0.33 So the point of intersection is (1.33,0.33).

3. What are the co-ordinates of the points where LineA and

CurveC intersect? [2 Marks] Show all working. -0.5x+1=x2-4; Reading the points from the graph. The points of intersection are (-2.5,2.25) & (2,0).

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

5-8 9-12 13-16 17-20 22-25 26-30

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


Statistics Section Level 3 (10 minutes).

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

P-P-D-A-C Short description (Examples of answers)

P is for Problem Clearly stated investigation question

P is for Plan Explanation of the sample method

D is for Data Collect enough data to answer the question

A is for Analysis What the data tells us: words and graphs.

C is for Conclusion Summary of findings

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

a. Which part of the

PPDAC cycle does

this image belong?

[1 Mark]

PPDAC

b. How many males were in this sample? [2 Marks] 5

c. How many females were in this sample? [2 Marks] 5

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

No,5 males and 5 females is not a large enough sample.

e. What is the population? [2 Marks]

New Zealand School Students.

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] cm

Males Females

Lowest Armspan 152cm 157cm

Lower Quartile 160cm 158cm

Median 170cm 165cm

Upper Quartile 180cm 171cm

Highest Armspan 190cm 183cm


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


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?

Sample Answers Any valid reason The medians are closer together in the second

sample, compared to the first. The difference seen in the first sample may

not be real for all students. The overall range is greater in the second

sample, compared to the first. The sample of 10 was too small, so I would

trust the second sample more. The males IQR is smaller in this sample

compared with the first sample. More data gave a different result, a different

sample gives a different result. Largest median changed, from male in the first

sample to female in the second. Females having a greater median armspan

than males seems wrong. Both samples have a male with the smallest

and largest armspan. Males seem to have more variation compared

with females.

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]

Four decent comments gains 16 marks.

Examples of comments: This is a large random sample so it should be representative of the population. The median of the males’ armspan is slightly further up the scale than the females.

The females’ data is skewed to the left, compared to the males’ data which is more symmetrical. There is a male outlier, with an armspan of 100cm, which could be a very young child, small person, or input error. It is a long way from the next smallest male armspan.

The females have a smaller IQR than the males suggesting males armspans have more variation.

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

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


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

19 units

18 units

squared

Parallel-ogram

18 units

18 units squared

Rectangle

18 units

16units

squared Hexagon

Volume in units

cubed.

Surface Area

in units squared.

Total outside

edges in units.

12 units cubed 32 units

squared 28 units

18 units cubed 48 units squared

42 units


5-8 9-12 13-15



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]

Level 1 = 5×7 Level 2 = 3×5

Level 3 = 3×3 Level 4 = 3×2 Level 5 = 3×1

Total = 35+3(5+3+2+1)=35+33=68 There are 68 blocks

2. Explain any assumptions made. [5 Marks]

I assumed the shape was symmetrical, and solid. I assumed the line of symmetry was in the middle, and parallel to, the blue lines.

3. Calculate (or estimate) the surface area of the shape. [5 Marks] Bottom and top both have 5×7=35units2

Right side, and left side both have (7+5+3+2+1)=18 units2

Front and back both have (5+3×4)=17 units2 Total surface area = 2(35+18+17)= 140 units2


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

2. Calculate the volume of this 3D shape. [4 Marks] Radius = 5cm; Height=7cm V=𝝅𝒓𝟐𝒉 = 𝝅 × 𝟓𝟐 × 𝟕 = 549.78 cm3

3. Calculate the surface area of this 3D shape. [4 Marks] Radius = 5cm; Height=7cm

A=𝟐𝝅𝒓𝒉 + 𝟐𝝅𝒓𝟐 = 𝟑𝟕𝟔. 𝟗𝟗 cm2

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

𝐄𝐝𝐠𝐞 = 𝟐 × 𝟐𝛑𝐫 = 𝟒𝛑 × 𝟓 = 𝟔𝟐. 𝟖𝟑 𝐜𝐦

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


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 as much detail as you can.[2]

Reflection The mountain is reflected

through the shore line into the water. The mountain is the

object. The image is the reflection in the lake. The shore line is the mirror

line.

Rotation (360×2/32=22.5) The object is a capsule; it rotates around the centre

of the London eye, 22.5 degrees clockwise to reach the image.

Translation

Resizing

(enlargement)

The object is one pattern

repeat, it is translated to the right the same distance as the width of

the pattern. This pattern is approximately 2/3rds the

size, with three translations.

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


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

Cube (Regular

Hexahedron)

Faces= 6 Edges=12

Vertices=8

Tetrahedron

Faces= 4 Edges=6

Vertices=4

Octahedron

Faces= 8 Edges=12

Vertices=6

Dodecahedron

Faces= 12 Edges=30

Vertices=20

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]

Level 4- Level 4 Level 4+ Level 5- Level 5 Level 5+ 7-9 10-12 13-15 16-18 19-21 22-25

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