Scholar Tests · Sample paper
Primary 5 Mathematics
45 questions · 100 marks · 150 minutes · no negative marking
Name ______________________ Date ____________
Paper 1, Booklet A (no calculator)
Questions 1 to 10, 1 mark each. Circle the letter of the best answer.
- 1.
What is the area of this shape?
- A50 cm²
- B36 cm²
- C60 cm²
- D30 cm²
- 2.
Three of the angles inside a quadrilateral are 54°, 86° and 114°. How big is the fourth angle?
- A106°
- B108°
- C254°
- D96°
- 3.
Each step Priya takes is 50 cm long. How many steps does it take to walk 12 metres?
- A417 steps
- B24 steps
- C600 steps
- D23 steps
- 4.
Aaron has $90.00. 4% of it is spent on a book. How much is spent on the book?
- A$2250.00
- B$0.36
- C$3.60
- D$36.00
- 5.
The average of 4 temperatures is 16 degrees. 3 of them are 7, 4 and 4. What is the last one?
- A49
- B54
- C21
- D64
- 6.
A leaking tank loses 3 litres of water in 8 hours, the same amount every hour. How much does it lose each hour?
- A0.38 L
- B0.0375 L
- C0.375 L
- D3.75 L
- 7.
In the diagram below, what is the size of the angle marked x?
- A55°
- B100°
- C45°
- D80°
- 8.
1/4 of the cars in a car park are white. Of those, 2/5 do not have a roof rack. What fraction of the cars in a car park are white and have a roof rack?
- A3/5
- B17/20
- C3/20
- D1/10
- 9.
The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark?
- A30°
- B80°
- C40°
- D50°
- 10.
This graph shows how far Ben and Dev walk for a given number of paces. Ben takes 360 paces to walk from school to the library. How many paces does Dev take to walk from school to the library?
- A480
- B270
- C360
- D90
Paper 1, Booklet A, continued
Questions 11 to 18, 2 marks each. Circle the letter of the best answer.
- 11.
What is 28/42 in its simplest form?
- A2/3
- B3/2
- C2/42
- D4/6
- 12.
A sequence begins 10, 19, 28, 37, … and carries on in the same way. What is the 17th term?
- A154
- B163
- C145
- D170
- 13.
What is a third of a half of an eighth of 192?
- A184
- B4
- C24
- D32
- 14.
In the triangle below, what is the size of the angle marked x?
- A71°
- B38°
- C40°
- D109°
- 15.
How many metres are there in 9 kilometres?
- A9000 metres
- B90000 metres
- C10000 metres
- D1 metre
- 16.
What is 2/7 multiplied by itself?
- A4/49
- B4/14
- C4/7
- D4/50
- 17.
What is 4/5 as a percentage?
- A85%
- B125%
- C80%
- D8%
- 18.
The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark?
- A65°
- B55°
- C58°
- D75°
Paper 1, Booklet B (no calculator)
Questions 19 to 30, 2 marks each. Write your answer on the line.
- 19.
What is 0.27 + 0.9?
Answer: ______________
- 20.
This graph shows how far Elena and Anika walk for a given number of paces. Elena takes 420 paces to walk from school to the library. How many paces does Anika take to walk from school to the library?
Answer: ______________
- 21.
The average of 9 numbers is 30. When 4 more are included, the average of all 13 becomes 31. What is the total of the 4 that were added?
Answer: ______________
- 22.
A rectangular storage box has a volume of 1008 cm³. Its base measures 9 cm by 8 cm. What is its height, in centimetres?
Answer: ______________
- 23.
What is 3/5 as a decimal?
Answer: ______________
- 24.
The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark? Give your answer in degrees.
Answer: ______________
- 25.
6 painters working together paint a hall in 48 hours. Every painter works at the same rate. How long would 4 of them take? Give your answer in hours.
Answer: ______________
- 26.
A sequence begins 13, 21, 29, 37, … and carries on in the same way. What is the 20th term?
Answer: ______________
- 27.
A foam cube has a volume of 729 cm³. What is the total area of its six faces? Give your answer in cm².
Answer: ______________
- 28.
What is the distance all the way round this shape? Give your answer in cm.
Answer: ______________
- 29.
What is the area of this triangle? Give your answer in cm².
Answer: ______________
- 30.
In the diagram below, what is the size of the angle marked x? Give your answer in degrees.
Answer: ______________
Paper 2: short answers (calculator allowed)
Questions 1 to 5, 2 marks each. Write your answer on the line.
- 1.
What is the distance all the way round this shape? Give your answer in cm.
Answer: ______________
- 2.
What is 29/50 as a percentage? Give your answer as a percentage.
Answer: ______________
- 3.
A sequence begins 11, 19, 27, 35, … and carries on in the same way. What is the 11th term?
Answer: ______________
- 4.
A wooden cube has a volume of 64 cubic centimetres. What is the total length of all its edges? Give your answer in cm.
Answer: ______________
- 5.
The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark? Give your answer in degrees.
Answer: ______________
Paper 2: longer problems at 3 marks
Questions 6 and 7, 3 marks each. Write your answer on the line.
- 6.
A father is 70 years old. His daughter is 3/7 of his age. What will the gap between their ages be in 18 years?
Answer: ______________
- 7.
An empty tank holds 57 L. A tap fills it at 14 L each minute. In the first minute a leak lets out 2 L, and each minute after that the leak lets out 1 L more than the minute before. The tank becomes full exactly at the end of a minute. How many minutes does it take to fill? Give your answer in minutes.
Answer: ______________
Paper 2: longer problems at 4 marks
Questions 8 to 13, 4 marks each. Write your answer on the line.
- 8.
A shopper buys 5 novels at $13 each and 5 bookmarks at $9 each, and pays with $150. How much change is there? Give your answer in dollars.
Answer: ______________
- 9.
Zara is standing 15th from the front of a queue. Exactly one quarter of the people in the queue are standing behind Zara. How many people are in the queue altogether?
Answer: ______________
- 10.
The average of 4 temperatures is 39 degrees. 3 of them are 34, 18 and 30. What is the last one?
Answer: ______________
- 11.
A teacher has some apples to give out to a group of children. If she gives each child 8 apples, she is 53 short. If she gives each child 6 apples, she has 7 left over. How many children are there?
Answer: ______________
- 12.
Aaron is 4 years older than Tom. Tom is 12 years younger than Priya. If the total of their ages is 52 years, how old is Aaron?
Answer: ______________
- 13.
At a school, 1/3 of the members are boys. There are 125 more girls than boys. How many members are there altogether?
Answer: ______________
Paper 2: longer problems at 5 marks
Questions 14 and 15, 5 marks each. Write your answer on the line.
- 14.
Grace and Priya have marbles in the ratio 8 : 5. Grace gives 108 marbles to Priya. Now they have marbles in the ratio 1 : 4. How many marbles did Priya have at first?
Answer: ______________
- 15.
Tickets to the aquarium cost $16 for an adult and $13 for a child. A group of 31 people paid $445 altogether. How many adults were in the group?
Answer: ______________
Answers and working
Paper 1, Booklet A (no calculator)
- 1.C (60 cm²). Split it along the step. The upper rectangle is 6 by 5, which is 30 cm², and the lower one is 10 by 3, which is 30 cm². Together 60 cm². (Taking the 4 by 5 bite out of the whole 10 by 8 rectangle gives the same thing.)
- 2.A (106°). One diagonal cuts a quadrilateral into two triangles, so its four angles come to 2 × 180 = 360° — not 180°. The three given ones use 54 + 86 + 114 = 254°, so the fourth is 360 − 254 = 106°.
- 3.B (24 steps). 12 metres is 12 × 100 = 1200 cm. Each step covers 50 cm, so it takes 1200 ÷ 50 = 24 steps.
- 4.C ($3.60). 4% means 4 out of every 100. So the amount is $90.00 × 4 ÷ 100 = $3.60.
- 5.A (49). An average of 16 across 4 temperatures means they come to 4 × 16 = 64 altogether. The 3 printed ones come to 15, so the last one is 64 − 15 = 49.
- 6.C (0.375 L). Each part is 3 ÷ 8 = 3/8, and 3/8 = 375/1,000, which is 0.375 L.
- 7.C (45°). OA and OD lie in a straight line, so the angles between them come to 180°. The ones printed on the diagram take up 80° + 55° = 135°, which leaves 180° − 135° = 45°, so x = 45°.
- 8.C (3/20). 1/4 × 3/5 = 3/20, which is 3/20 of the whole.
- 9.C (40°). The marked angle and the one asked for are vertically opposite at the same crossing, so they are equal and the answer is 40°.
- 10.B (270). 360 paces puts Ben at 90 metres. Reading 90 metres back down Dev's line gives 270 paces.
Paper 1, Booklet A, continued
- 11.A (2/3). The highest common factor of 28 and 42 is 14. Dividing the top and the bottom by 14 gives 2/3.
- 12.A (154). Each term is 9 more than the last, so the nth term is 10 + (n − 1) × 9. For n = 17: 10 + 16 × 9 = 154.
- 13.B (4). Take the fractions one at a time, starting with an eighth: 192 → 24, then 24 → 12, then 12 → 4. The answer is 4.
- 14.B (38°). The two ticked sides are the same length, so the two angles at the ends of the third side are equal. Each of them is 71°, and the three angles come to 180°, so x = 180° − 71° − 71° = 38°.
- 15.A (9000 metres). There are 1000 metres in one of the kilometres, so 9 kilometres is 9 × 1000 = 9000 metres.
- 16.A (4/49). Both parts get squared, not doubled. The top is 2 × 2 = 4 and the bottom is 7 × 7 = 49, so the answer is 4/49. Note it is SMALLER than 2/7, because multiplying by a fraction below 1 always shrinks a number.
- 17.C (80%). 5 goes into 100 20 times, so 4/5 is the same as 80/100, and that is 80%.
- 18.A (65°). The marked angle and the one asked for are on the same side of the crossing line, outside the parallel pair, so they add to 180°, and 180 − 115 = 65°.
Paper 1, Booklet B (no calculator)
- 19.1.17. Write 0.9 as 0.90 so both have two figures after the point. Line the points up, not the last figures, and 0.27 + 0.90 = 1.17.
- 20.560. 420 paces puts Elena at 140 metres. Reading 140 metres back down Anika's line gives 560 paces.
- 21.133. The first 9 total 9 × 30 = 270. All 13 total 13 × 31 = 403. The difference, 403 − 270 = 133, is the total of the new ones.
- 22.14. Base area = 9 × 8 = 72 cm². Height = 1008 ÷ 72 = 14 cm.
- 23.0.6. 3/5 is the same as 60/100, and a hundredth is two places after the point, so the decimal is 0.6.
- 24.150. Two moves. The marked angle is 30°, and the angle opposite it at the same crossing is equal to it, so that one is 30° too. That angle and the one asked for lie between the parallel lines on the same side of the crossing line, so they add to 180°: 180 − 30 = 150°.
- 25.72. One painter on its own would take 6 × 48 = 288 hours. Sharing that between 4 of them takes 288 ÷ 4 = 72 hours.
- 26.165. Each term is 8 more than the last, so the nth term is 13 + (n − 1) × 8. For n = 20: 13 + 19 × 8 = 165.
- 27.486. 9 × 9 × 9 = 729, so each edge is 9 cm. Each face is 81 cm² and there are 6 of them: 486 cm².
- 28.30. Two sides carry no size: the step across the top is 9 − 3 = 6 cm and the side below it is 6 − 2 = 4 cm. Adding all six gives 30 cm — the same as going round the whole 9 by 6 rectangle, because a bite out of a corner moves the edges without adding to their total.
- 29.40. The dashed line meets the base at a right angle, so it is the height. Base × height = 16 × 5 = 80, and a triangle is half of that: 40 cm².
- 30.110. The angles at O go all the way round, so they come to 360°. The ones printed on the diagram take up 100° + 30° + 120° = 250°, which leaves 360° − 250° = 110°, so x = 110°.
Paper 2: short answers (calculator allowed)
- 1.30. Two sides carry no size: the step across the top is 6 − 4 = 2 cm and the side below it is 9 − 2 = 7 cm. Adding all six gives 30 cm — the same as going round the whole 6 by 9 rectangle, because a bite out of a corner moves the edges without adding to their total.
- 2.58. 50 goes into 100 2 times, so 29/50 is the same as 58/100, and that is 58%.
- 3.91. Each term is 8 more than the last, so the nth term is 11 + (n − 1) × 8. For n = 11: 11 + 10 × 8 = 91.
- 4.48. 4 × 4 × 4 = 64, so each edge is 4 cm. A cube has 12 edges, so they come to 48 cm.
- 5.120. Two moves. The marked angle is 60°, and the angle opposite it at the same crossing is equal to it, so that one is 60° too. That angle and the one asked for lie between the parallel lines on the same side of the crossing line, so they add to 180°: 180 − 60 = 120°.
Paper 2: longer problems at 3 marks
- 6.40. The daughter is 30 now, so the gap is 70 − 30 = 40. Both ages grow by the same 18 years, so the gap stays 40. So the answer is 40.
- 7.6. Each minute the tap adds 14 L and the leak takes 2 L, then 3 L, and so on, so 12 L, then 11 L stay in. Those add up to 57 L at the end of minute 6. So the answer is 6 minutes.
Paper 2: longer problems at 4 marks
- 8.40. The novels cost 5 × $13 = $65 and the bookmarks cost 5 × $9 = $45, which is $110 altogether. Change is what is handed over less what is owed: $150 − $110 = $40.
- 9.20. If one quarter are behind, the 15 people from the front through to Zara are the other 3/4. So 3/4 of the queue is 15, and the queue is 15 ÷ 3/4 = 20.
- 10.74. An average of 39 across 4 temperatures means they come to 4 × 39 = 156 altogether. The 3 printed ones come to 82, so the last one is 156 − 82 = 74.
- 11.30. The plans are 60 apart and each child accounts for 2 of that, so there are 30 children and 187 apples. So the answer is 30.
- 12.16. Let Tom = b. Then Aaron = b + 4 and Priya = b + 12, so 3b + 16 = 52 and b = 12. Aaron = 16.
- 13.375. If 1/3 are boys then 2/3 are girls, so the gap between them is 1/3 of everyone. That gap is 125, so one 3th is 125 and the whole group is 3 × 125 = 375.
Paper 2: longer problems at 5 marks
- 14.100. Passing 108 marbles across changes a share by 27/65 of the total, so the total is 260 marbles. At first Grace had 160 marbles and Priya had 100 marbles. So the answer is 100.
- 15.14. If all 31 paid the child price the total would be 31 × $13 = $403. The extra $42 comes from adults paying $3 more each, so there were 42 ÷ 3 = 14 adults.
Written by Scholar Tests to MOE's Primary 5 Mathematics syllabus. Not a school or PSLE paper. Scholar Tests is not connected with MOE, SEAB or any school.