Scholar Tests · Sample paper
Primary 6 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 0.05 × 0.3?
- A0.35
- B0.015
- C15
- D0.0015
- 2.
The average of 6 numbers is 10. When 2 more are included, the average of all 8 becomes 12. What is the total of the 2 that were added?
- A24
- B37
- C36
- D4
- 3.
A circle has a radius of 21 cm. Taking π as 22/7, what is its area?
- A66 cm²
- B5544 cm²
- C1386 cm²
- D1392 cm²
- 4.
James has $115.00. 10% of it is spent on a book. How much is spent on the book?
- A$1150.00
- B$103.50
- C$11.50
- D$115.00
- 5.
In the diagram below, what is the size of the angle marked x?
- A105°
- B75°
- C40°
- D50°
- 6.
A box measures 6 cm long, 3 cm wide and 7 cm high. What is its volume?
- A16 cm³
- B126 cm³
- C81 cm³
- D162 cm³
- 7.
A train travels at an average speed of 60 km/h for 50 minutes. How far does it go?
- A50 km
- B72 km
- C25 km
- D52 km
- 8.
Three corners of a quadrilateral measure 47°, 90° and 130°. How big is the fourth angle?
- A83°
- B93°
- C91°
- D273°
- 9.
What is 95% as a fraction in its simplest form?
- A20/19
- B95/100
- C19/20
- D19/21
- 10.
2/3 of the students in a class have a pet. Of those, 1/4 do not have a dog. What fraction of the students in a class have a pet and have a dog?
- A2/3
- B1/2
- C5/12
- D1/6
Paper 1, Booklet A, continued
Questions 11 to 18, 2 marks each. Circle the letter of the best answer.
- 11.
The average of 8 parcel masses in kilograms is 18. When 4 more are included, the average of all 12 becomes 22. What is the total of the 4 that were added?
- A121
- B120
- C16
- D88
- 12.
What is the distance all the way round this shape?
- A79 cm
- B26 cm
- C12 cm
- D40 cm
- 13.
A circle has a radius of 21 cm. Taking π as 22/7, what is the distance all the way round it?
- A132 cm
- B135 cm
- C66 cm
- D264 cm
- 14.
What is 84% as a fraction in its simplest form?
- A22/25
- B21/26
- C21/25
- D25/21
- 15.
In the triangle below, what is the size of the angle marked x?
- A117°
- B27°
- C54°
- D63°
- 16.
A box measures 2 cm long, 10 cm wide and 4 cm high. What is its volume?
- A80 cm³
- B16 cm³
- C136 cm³
- D64 cm³
- 17.
This graph shows how far Dev and Jonah walk for a given number of paces. Dev takes 480 paces to walk from school to the local shops. How many paces does Jonah take to walk from school to the local shops?
- A360
- B200
- C120
- D480
- 18.
What is a tenth of an eighth of a half of 480?
- A24
- B240
- C348
- D3
Paper 1, Booklet B (no calculator)
Questions 19 to 30, 2 marks each. Write your answer on the line.
- 19.
The average of 6 test scores is 29. When 3 more are included, the average of all 9 becomes 30. What is the total of the 3 that were added?
Answer: ______________
- 20.
What is 0.8 × 0.8?
Answer: ______________
- 21.
Three of the angles inside a quadrilateral are 132°, 133° and 50°. How big is the fourth angle? Give your answer in degrees.
Answer: ______________
- 22.
What is the area of this shape? Give your answer in cm².
Answer: ______________
- 23.
James and Ethan share $100 in the ratio 3 : 1. How much does Ethan get? Give your answer in dollars.
Answer: ______________
- 24.
A sequence begins 3, 7, 11, 15, … and carries on in the same way. What is the 10th term?
Answer: ______________
- 25.
In the triangle below, what is the size of the angle marked x? Give your answer in degrees.
Answer: ______________
- 26.
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: ______________
- 27.
In the diagram below, every angle marked x is the same size. What is the size of one of them? Give your answer in degrees.
Answer: ______________
- 28.
What is the area of this triangle? Give your answer in cm².
Answer: ______________
- 29.
A rectangular tank has a volume of 294 cm³. Its base measures 7 cm by 6 cm. What is its height, in centimetres?
Answer: ______________
- 30.
5 boxes of tiles weigh 35 kg altogether. All of them weigh the same. What do 10 of them weigh? Give your answer in kg.
Answer: ______________
Paper 2: short answers (calculator allowed)
Questions 1 to 5, 2 marks each. Write your answer on the line.
- 1.
This graph shows how far Hugo and Chloe walk for a given number of paces. Hugo takes 240 paces to walk from school to the swimming pool. How many paces does Chloe take to walk from school to the swimming pool?
Answer: ______________
- 2.
Two of the angles inside a quadrilateral are 80° and 126°. The other two angles are equal to each other. How big is each of them? Give your answer in degrees.
Answer: ______________
- 3.
James, Lucas and Priya share $105 in the ratio 1 : 4 : 2. How much more does Lucas get than Priya? Give your answer in dollars.
Answer: ______________
- 4.
A circle with a diameter of 42 cm fits exactly inside a square, touching all four sides. Taking π as 22/7, how much of the square is NOT covered by the circle? Give your answer in cm².
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.
Tickets to the zoo cost $18 for an adult and $5 for a child. A group of 25 people paid $294 altogether. How many adults were in the group?
Answer: ______________
- 7.
An empty tank holds 81 L. A tap fills it at 20 L each minute. In the first minute a leak lets out 4 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.
The average of 6 readings is 11 millimetres. 5 of them are 15, 4, 6, 3 and 17. What is the last one?
Answer: ______________
- 9.
Ella works at a garden centre. Ella is paid a base wage of $350 a week plus 8% of everything Ella sells. How much does Ella earn in a week when Ella sells $6500 of goods? Give your answer in dollars.
Answer: ______________
- 10.
A group of 78 people is made up of adults, teenagers and children. There are 2 more teenagers than adults. There are twice as many children as teenagers. How many more children than adults are there?
Answer: ______________
- 11.
What is an eighth of five sixths of a third of 288?
Answer: ______________
- 12.
A mother is 32 years old. Her son is 3/8 of her age. What will the gap between their ages be in 16 years?
Answer: ______________
- 13.
A market stall adds a service charge to every order: nothing on the first $50, 5% on the next $200, and 15% on anything above $250. What is the service charge on an order of $270? Give your answer in dollars.
Answer: ______________
Paper 2: longer problems at 5 marks
Questions 14 and 15, 5 marks each. Write your answer on the line.
- 14.
Lucas is standing 8th from the front of a queue. Exactly one third of the people in the queue are standing behind Lucas. How many people are in the queue altogether?
Answer: ______________
- 15.
Leo, Harry and Ben share a prize. Leo gets $12. Harry gets $4 for every $2 that Leo gets, and Harry gets twice as much as Ben. Then Leo gives $3 to Harry. How much more than Ben does Harry have now? Give your answer in dollars.
Answer: ______________
Answers and working
Paper 1, Booklet A (no calculator)
- 1.B (0.015). 5 × 3 = 15, and the two numbers have 3 figures after the point between them, so the answer is 0.015.
- 2.C (36). The first 6 total 6 × 10 = 60. All 8 total 8 × 12 = 96. The difference, 96 − 60 = 36, is the total of the new ones.
- 3.C (1386 cm²). The area of a circle is π × r × r. That is 22/7 × 21 × 21, and the 7 cancels into one of the 21s, so it comes to 1386 cm².
- 4.C ($11.50). 10% means 10 out of every 100. So the amount is $115.00 × 10 ÷ 100 = $11.50.
- 5.C (40°). OA and OD lie in a straight line, so the angles between them come to 180°. The ones printed on the diagram take up 75° + 65° = 140°, which leaves 180° − 140° = 40°, so x = 40°.
- 6.B (126 cm³). Volume multiplies all three edges: 6 × 3 × 7 = 126 cm³.
- 7.A (50 km). In one hour it covers 60 km, so in one minute it covers 60 ÷ 60 km. Over 50 minutes that is 60 × 50 ÷ 60 = 50 km.
- 8.B (93°). One diagonal cuts a quadrilateral into two triangles, so its four angles come to 2 × 180 = 360° — not 180°. The three given ones use 47 + 90 + 130 = 267°, so the fourth is 360 − 267 = 93°.
- 9.C (19/20). Per cent means "out of a hundred", so 95% is 95/100 to start with. Cancelling that down as far as it goes gives 19/20.
- 10.B (1/2). 2/3 × 3/4 = 6/12, which is 1/2 of the whole.
Paper 1, Booklet A, continued
- 11.B (120). The first 8 total 8 × 18 = 144. All 12 total 12 × 22 = 264. The difference, 264 − 144 = 120, is the total of the new ones.
- 12.D (40 cm). Two sides carry no size: the step across the top is 10 − 3 = 7 cm and the side below it is 10 − 3 = 7 cm. Adding all six gives 40 cm — the same as going round the whole 10 by 10 rectangle, because a bite out of a corner moves the edges without adding to their total.
- 13.A (132 cm). The distance round a circle is 2 × π × r. That is 2 × 22/7 × 21, and the 7 cancels into the 21, so it comes to 132 cm.
- 14.C (21/25). Per cent means "out of a hundred", so 84% is 84/100 to start with. Cancelling that down as far as it goes gives 21/25.
- 15.B (27°). The two ticked sides are the same length, so the two angles at the ends of the third side are equal. Between them they take up 180° − 126° = 54°, so x = 54° ÷ 2 = 27°.
- 16.A (80 cm³). Volume multiplies all three edges: 2 × 10 × 4 = 80 cm³.
- 17.A (360). 480 paces puts Dev at 120 metres. Reading 120 metres back down Jonah's line gives 360 paces.
- 18.D (3). Take the fractions one at a time, starting with a half: 480 → 240, then 240 → 30, then 30 → 3. The answer is 3.
Paper 1, Booklet B (no calculator)
- 19.96. The first 6 total 6 × 29 = 174. All 9 total 9 × 30 = 270. The difference, 270 − 174 = 96, is the total of the new ones.
- 20.0.64. Ignore the points first: 8 × 8 = 64. Each number has one figure after the point, so the answer has two: 0.64. Multiplying by a number below 1 makes it SMALLER, which is why the answer is less than 0.8.
- 21.45. One diagonal cuts a quadrilateral into two triangles, so its four angles come to 2 × 180 = 360° — not 180°. The three given ones use 132 + 133 + 50 = 315°, so the fourth is 360 − 315 = 45°.
- 22.42. Split it along the step. The upper rectangle is 5 by 3, which is 15 cm², and the lower one is 9 by 3, which is 27 cm². Together 42 cm². (Taking the 4 by 3 bite out of the whole 9 by 6 rectangle gives the same thing.)
- 23.25. There are 4 equal parts, so one part is $100 ÷ 4 = $25. Ethan has 1 of them: $25.
- 24.39. Each term is 4 more than the last, so the nth term is 3 + (n − 1) × 4. For n = 10: 3 + 9 × 4 = 39.
- 25.67. The two ticked sides are the same length, so the two angles at the ends of the third side are equal. Between them they take up 180° − 46° = 134°, so x = 134° ÷ 2 = 67°.
- 26.135. Two moves. The marked angle is 45°, and the angle opposite it at the same crossing is equal to it, so that one is 45° 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 − 45 = 135°.
- 27.115. The angles at O go all the way round, so they come to 360°. The ones printed on the diagram take up 130°, which leaves 360° − 130° = 230° to share between the two angles marked x, so x = 230° ÷ 2 = 115°.
- 28.57. The dashed line meets the base at a right angle, so it is the height. Base × height = 19 × 6 = 114, and a triangle is half of that: 57 cm².
- 29.7. Base area = 7 × 6 = 42 cm². Height = 294 ÷ 42 = 7 cm.
- 30.70. One weighs 35 ÷ 5 = 7 kg. So 10 of them weigh 7 × 10 = 70 kg.
Paper 2: short answers (calculator allowed)
- 1.360. 240 paces puts Hugo at 120 metres. Reading 120 metres back down Chloe's line gives 360 paces.
- 2.77. A diagonal splits any quadrilateral into two triangles, so its angles come to 2 × 180 = 360°. The two given ones use 80 + 126 = 206°, leaving 360 − 206 = 154° for the pair — so each is 154 ÷ 2 = 77°.
- 3.30. One part is $105 ÷ 7 = $15, and Lucas has 2 more parts than Priya: $30.
- 4.378. The circle touches all four sides, so the square's side is the diameter itself, 42 cm, and its area is 1764 cm². The circle covers 22/7 × 21 × 21 = 1386 cm². What is left is 1764 − 1386 = 378 cm².
- 5.105. The marked angle and the one asked for are on opposite sides of the crossing line, outside the parallel pair, so they are equal and the answer is 105°.
Paper 2: longer problems at 3 marks
- 6.13. If all 25 paid the child price the total would be 25 × $5 = $125. The extra $169 comes from adults paying $13 more each, so there were 169 ÷ 13 = 13 adults.
- 7.6. Each minute the tap adds 20 L and the leak takes 4 L, then 5 L, and so on, so 16 L, then 15 L stay in. Those add up to 81 L at the end of minute 6. So the answer is 6 minutes.
Paper 2: longer problems at 4 marks
- 8.21. An average of 11 across 6 readings means they come to 6 × 11 = 66 altogether. The 5 printed ones come to 45, so the last one is 66 − 45 = 21.
- 9.870. The commission is 8% of $6500 = $520, so the pay is $350 + $520. So the answer is $870.
- 10.22. With adults as x, the three amounts are x, x + 2, 2x + 4. Together they make 4x + 6 = 78, so x = 18. So the answer is 22.
- 11.10. Take the fractions one at a time, starting with a third: 288 → 96, then 96 → 80, then 80 → 10. The answer is 10.
- 12.20. The son is 12 now, so the gap is 32 − 12 = 20. Both ages grow by the same 16 years, so the gap stays 20. So the answer is 20.
- 13.13. Nothing on the first $50. The next $200 is charged at 5%, which is $10. That leaves $20 above $250, charged at 15%, which is $3. Altogether $10 + $3 = $13.
Paper 2: longer problems at 5 marks
- 14.12. If one third are behind, the 8 people from the front through to Lucas are the other 2/3. So 2/3 of the queue is 8, and the queue is 8 ÷ 2/3 = 12.
- 15.15. Harry gets $24 and Ben gets $12. After the gift Leo has $9 and Harry has $27. So the answer is $15.
Written by Scholar Tests to MOE's Primary 6 Mathematics syllabus. Not a school or PSLE paper. Scholar Tests is not connected with MOE, SEAB or any school.