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(Draft) Answers / 2014 ExamPakuranga College
Year 9
Mathematics
2014 Examination
Time: 2 hours
Sections:
Topic
/Suggested Time
/Score
/NZC Level
Number
/ 30 minsAlgebra
/30 mins
/ /Statistics
/20 mins
/ /Measurement
/20 mins
/ /Geometry
/20 mins
/ /Students are advised to bring a Calculator, ruler, pen, pencil and eraser.
Paper for working will be provided.
Examination Date: 14th November 2014
Number Section Level 3 (10 minutes).
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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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. 450+ 250= 650= 325
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 113 or 112? 113
19. Write 50% as a fraction 50100=12
20. Write 0.25 as a percentage 25%
21. Write 2% as a decimal 0.02
22. 910 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. 34 - 12 = 14
27. The denominator of 85 is 5
28. The numerator of 68 is 6
29. Simplify 3060 = 12
30. Write 1040 as a percentage 25%
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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Level 3- / Level 3 / Level 3+15-19 / 20-24 / 25-30
Number Section Level 4 (10 minutes).
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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1. 2003-246= 1757
2. 32×5= 160
3. 9-31= -22
4. 2.4 - 2.6= -0.2
5. 35+ 45= 75
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 58 or 47?
16. Which is smaller 78 or 113? 113
17. 0.3 times 0.7 = 0.21
18. Write 65% as a fraction 65100= 1320
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 65100= 1320
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 = -8
27. Round 3.09 to the nearest whole number 3
28. Round 5.608 to the nearest tenth: 5.6
29. Simplify 3080= 38
30. Decrease 150 by 70% 105
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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Level 4- / Level 4 / Level 4+15-19 / 20-24 / 25-30
Number Section Level 5 (10 minutes).
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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1. 305 in standard form= 3.05 × 102
2. 2918 in standard form = 2.918 × 103
3. -31+17+23-19= -10
4. 5(12- 13) = 5(36- 26) = 16
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. 195- 145 = 55= 1
16. 110-2105=-1005= -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. 35 times 29 = 645= 215=0.1333
30. Write 3.867 × 103 in decimal form 3867
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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Level 5- / Level 5 / Level 5+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 / nNumber 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.
Level 3- / Level 3 / Level 3+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]
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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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
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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4. Solve for x: [5 marks]
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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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
EOY Exam Year 9 Printed Thursday, 6 November 2014 APN
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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 / EquationLineA / (-2,0) / (0,-1) / -0.5 / Y=-0.5x-1
LineB / (-0.67,0) / (0,2) / 3 / Y=3x+2
CurveC / (2,0)&(-2,0) / (0,-2) / Not constant / Y=x2 - 2
2. What are the exact co-ordinates of the point where LineA and LineB intersect? [2 Marks] Show all working.
-0.5x-1=3x+2; -3.5x=3; x=-0.86; y=-0.43-1=-0.57
So the point of intersection is (-0.86,-0.57).
3. What are the co-ordinates of the points where LineA and CurveC intersect? [2 Marks] Show all working.
-0.5x-1=x2-2; Reading the points from the graph.
The points of intersection are (-1.3,-0.4) & (0.8,-1.4).
Markers: Allow for an error of plus or minus 0.2
Level 4- / Level 4 / Level 4+ / Level 5- / Level 5 / Level 5+5-8 / 9-12 / 13-16 / 17-20 / 22-25 / 26-30
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]
Analysis
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.
Males / FemalesLowest Armspan / 152cm / 157cm
Lower Quartile / 160cm / 158cm
Median / 170cm / 165cm
Upper Quartile / 180cm / 171cm
Highest Armspan / 190cm / 183cm
g. What units is the arm-span measured in? [1 Mark] cm
Level 3- / Level 3 / Level 3+15-19 / 20-24 / 25-30
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
/ 14 units / 10 units squared / Rectangle
/ 30 units / 18units squared / Octagon
/ 16.3 units / 12units squared / Octagon
/ 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 / 32 units squared / 48 units
Level 3- / Level 3 / Level 3+
5-8 / 9-12 / 13-15
Measurement Section Level 4 (5 minutes).
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
Measurement Section Level 5 (5 minutes).
1. Name the 3D shape. [3 Marks]
Cylinder
2. Calculate the volume of this 3D shape. [4 Marks]
Radius = 5cm; Height=10cm