Maths exam papers

Sec 2 Maths exam paper

A free Secondary 2 Mathematics paper in two parts: 51 questions for 160 marks, Paper 1 without a calculator and Paper 2 with one. Print it, then check every answer at the end.

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Secondary 2 Mathematics

51 questions · 160 marks · 165 minutes · no negative marking

Name ______________________ Date ____________

Paper 1, Section A: multiple choice (no calculator)

Questions 1 to 10, 2 marks each. Circle the letter of the best answer.

  1. 1.

    Find the missing number: 6, 18, ?, 162, 486, 1458

    1. A54
    2. B36
    3. C162
    4. D18
  2. 2.

    Dev uses the formula v = u + at. Given v = 33, u = 3 and a = 5, what is t?

    1. A30
    2. B36
    3. C7
    4. D6
  3. 3.

    Which of these is the same as 5(3x + 5y)?

    1. A15x + 25y
    2. B15x + 5y
    3. C40xy
    4. D8x + 10y
  4. 4.

    The shaded rectangle on this grid is enlarged by a scale factor of 2. Each square of the grid is 1 cm by 1 cm. What is the perimeter of the enlarged rectangle, in centimetres?

    1. A20
    2. B18
    3. C40
    4. D10
  5. 5.

    At the same time of day, a stick and a pole cast the shadows shown. How tall is the pole?

    1. A3 m
    2. B4.5 m
    3. C13.5 m
    4. D18 m
  6. 6.

    Which of these is (x + 5)² expanded?

    1. Ax² + 10x − 25
    2. Bx² + 5x + 25
    3. Cx² + 25
    4. Dx² + 10x + 25
  7. 7.

    7 pens and 2 rulers cost $100. 1 pen and 2 rulers cost $28. What does one pen cost?

    1. A$8
    2. B$15
    3. C$12
    4. D$9
  8. 8.

    Seven sunflowers were measured. Their heights, in centimetres, were 136, 108, 88, 143, 143, 156, 116. What is the median?

    1. A127
    2. B116
    3. C68
    4. D136
  9. 9.

    A right-angled triangle has a longest side of 10 cm and another side of 6 cm. What is its perimeter, in centimetres?

    1. A26
    2. B20
    3. C23
    4. D24
  10. 10.

    A fair coin has been tossed 12 times and landed heads 8 times. In the next 40 tosses, about how many heads would you expect?

    1. A18
    2. B40
    3. C20
    4. D10

Paper 1, Section B: short answers

Questions 11 to 25, 2 marks each. Write your answer on the line.

  1. 11.

    y is directly proportional to x. When x = 2, y = 12. Find y when x = 5.

    Answer: ______________

  2. 12.

    A pack holds 6 starred cards and 5 plain cards. Two cards are taken out one after the other, and the first is not put back. What is the chance that both are starred?

    Answer: ______________

  3. 13.

    Find the value of x.
    5x − 5 = 2x + 19

    Answer: ______________

  4. 14.

    In the triangle, the line across is parallel to the base. How long is the base, marked with a question mark? Give your answer in cm.

    Answer: ______________

  5. 15.

    Find the value of x.
    4x − 4 = 12

    Answer: ______________

  6. 16.

    The three faces that meet at one corner of a box have areas of 12 cm², 24 cm² and 8 cm². What is the volume of the box? Give your answer in cm³.

    Answer: ______________

  7. 17.

    The shaded rectangle on this grid is enlarged by a scale factor of 3. Each square of the grid is 1 cm by 1 cm. What is the area of the enlarged rectangle, in square centimetres?

    Answer: ______________

  8. 18.

    How many diagonals does a 8-sided polygon have?

    Answer: ______________

  9. 19.

    Find the missing number: 10, 20, 40, ?, 160, 320

    Answer: ______________

  10. 20.

    7 erasers and 3 notebooks cost $43. 5 erasers and 3 notebooks cost $35. What does one eraser cost? Give your answer in dollars.

    Answer: ______________

  11. 21.

    What is 4 squared, take away the square root of 36?

    Answer: ______________

  12. 22.

    A right-angled triangle has a longest side of 10 cm and another side of 6 cm. What is its perimeter, in centimetres?

    Answer: ______________

  13. 23.

    Nine players each kept a tally of their points over a season. The totals were 56, 58, 58, 33, 27, 24, 28, 99, 84. What is the difference between the median and the mode?

    Answer: ______________

  14. 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: ______________

  15. 25.

    Isla has a right-angled ramp. The longest side is 25 cm and one shorter side is 24 cm. How long is the other shorter side, in centimetres?

    Answer: ______________

Paper 1, Section C: longer problems

Questions 26 to 31, 5 marks each. Write your answer on the line.

  1. 26.

    A market stall adds a service charge to every order: nothing on the first $100, 5% on the next $120, and 25% on anything above $220. What is the service charge on an order of $260? Give your answer in dollars.

    Answer: ______________

  2. 27.

    3 markers and 4 pens cost $62. 1 marker and 4 pens cost $50. What does one pen cost? Give your answer in dollars.

    Answer: ______________

  3. 28.

    A rectangular deck measures 15 m by 9 m. Turf costs $20 per square metre. What is the total cost of covering the deck? Give your answer in dollars.

    Answer: ______________

  4. 29.

    A scout hall had 260 students. Then the number of boys rose by 40%, the number of girls fell by 20%, and the total number of students fell by 5%. How many boys were there at first?

    Answer: ______________

  5. 30.

    Chloe sets off along a straight road walking at 6 km/h. 30 minutes later Ruby sets off from the same place along the same road, cycling at 15 km/h. How many minutes after Ruby sets off does Ruby catch up with Chloe?

    Answer: ______________

  6. 31.

    A hose fills a water tank that holds 99 L. In the first minute it pours in 15 L, and each minute after that it pours in 1 L less than the minute before. The water 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, Section A: short answers (calculator allowed)

Questions 1 to 10, 3 marks each. Write your answer on the line.

  1. 1.

    A cone has a base of diameter 18 cm and a height of 8 cm. Find its volume, correct to 3 significant figures. Use the π button on your calculator. Give your answer in cm³.

    Answer: ______________

  2. 2.

    Two tent ends are the same shape: the large tent end is an enlargement of the small one. How long is the side marked with a question mark? Give your answer in cm.

    Answer: ______________

  3. 3.

    y is directly proportional to x². When x = 2, y = 12. Find y when x = 4.

    Answer: ______________

  4. 4.

    A sphere has diameter 4 cm. Find its surface area, correct to 3 significant figures. Use the π button on your calculator. Give your answer in cm².

    Answer: ______________

  5. 5.

    The shaded rectangle on this grid is enlarged by a scale factor of 3. Each square of the grid is 1 cm by 1 cm. What is the perimeter of the enlarged rectangle, in centimetres?

    Answer: ______________

  6. 6.

    Finn has a right-angled path. The longest side is 10 cm and one shorter side is 6 cm. How long is the other shorter side, in centimetres?

    Answer: ______________

  7. 7.

    The shaded rectangle on this grid is enlarged by a scale factor of 4. Each square of the grid is 1 cm by 1 cm. What is the area of the enlarged rectangle, in square centimetres?

    Answer: ______________

  8. 8.

    A pack holds 5 starred cards and 6 plain cards. Two cards are taken out one after the other, and the first is not put back. What is the chance that both are starred?

    Answer: ______________

  9. 9.

    Write 0.0045999 correct to 3 significant figures.

    Answer: ______________

  10. 10.

    In triangle ABC, angle ABC = 90°, angle ACB = 46° and AB = 8.2 cm. Find x, the length of AC, correct to 3 significant figures. Give your answer in cm.

    Answer: ______________

Paper 2, Section B: longer problems

Questions 11 to 20, 5 marks each. Write your answer on the line.

  1. 11.

    Aaron sets off along a straight road walking at 4 km/h. 60 minutes later Zara sets off from the same place along the same road, cycling at 20 km/h. How many minutes after Zara sets off does Zara catch up with Aaron?

    Answer: ______________

  2. 12.

    A holiday camp had 440 students. Then the number of boys rose by 50%, the number of girls fell by 5%, and the total number of students rose by 15%. How many girls were there at first?

    Answer: ______________

  3. 13.

    One printer would print the whole job on its own in 30 minutes. A second printer would print it on its own in 45 minutes. If both work at the same time, how long do they take together?

    Answer: ______________

  4. 14.

    A tap fills a water tank that holds 160 L. The tap adds 16 L each minute, but a leak lets out 8 L each minute. How many minutes does it take to fill? Give your answer in minutes.

    Answer: ______________

  5. 15.

    A rectangular path measures 14 m by 9 m. Rubber matting costs $50 per square metre. What is the total cost of covering the path? Give your answer in dollars.

    Answer: ______________

  6. 16.

    A semicircle of cork has a slice cut away from its centre, as shown. The slice is 1/5 of the semicircle. What is the angle x at the centre of the piece that is left? Give your answer in degrees.

    Answer: ______________

  7. 17.

    3 erasers and 2 markers cost $17. 1 eraser and 2 markers cost $11. What does one marker cost? Give your answer in dollars.

    Answer: ______________

  8. 18.

    Isla works at a pet shop for $24 an hour on weekdays. At the weekend the pay is double. Isla worked 19 hours on weekdays and some hours at the weekend, and earned $1032 in all. How many hours did Isla work at the weekend?

    Answer: ______________

  9. 19.

    A cone has a base radius of 7 cm and a height of 24 cm. Find its curved surface area, correct to 3 significant figures. Use the π button on your calculator. Give your answer in cm².

    Answer: ______________

  10. 20.

    In triangle ABC, angle ABC = 90°, angle ACB = 32° and AB = 15.2 cm. Find x, the length of AC, correct to 3 significant figures. Give your answer in cm.

    Answer: ______________

Answers and working

Paper 1, Section A: multiple choice (no calculator)

  1. 1.A (54). Each term is 3 times the one before, not a fixed amount more. The term before the gap is 18, so the missing one is 18 × 3 = 54, and 54 × 3 = 162 checks it against the term after the gap.
  2. 2.D (6). v − u = at, so 33 − 3 = 30. Then t = 30 ÷ 5 = 6.
  3. 3.A (15x + 25y). The 5 multiplies both terms inside the bracket: 5 × 3x and 5 × 5y. So it is 15x + 25y.
  4. 4.A (20). Every length is multiplied by 2, so the 3 by 2 rectangle becomes 6 by 4 and its perimeter is 2 × (6 + 4) = 20 cm.
  5. 5.B (4.5 m). The rays are parallel, so the pole is to its shadow as the stick is to its shadow: 1.5 × 9 ÷ 3 = 4.5 m.
  6. 6.D (x² + 10x + 25). (x + 5)² = (x + 5)(x + 5) = x² + 10x + 25.
  7. 7.C ($12). Both orders hold the same 2 rulers, so the difference between them is pens alone: $100 − $28 = $72 buys 7 − 1 = 6 pens. One pen is therefore $72 ÷ 6 = $12.
  8. 8.D (136). In order the list is 88, 108, 116, 136, 143, 143, 156, and the middle one is 136.
  9. 9.D (24). By Pythagoras, the third side is √(102 − 62) = 8 cm. The perimeter is 6 + 8 + 10, which is 24.
  10. 10.C (20). The coin cannot remember the first 12 tosses, so the next 40 are still about half heads. So the answer is 20.

Paper 1, Section B: short answers

  1. 11.30. Write y = kx, find k from x = 2, y = 12, then put in x = 5: y = 30.
  2. 12.3/11. The first draw is 6 out of 11. One starred is now gone, so the second is 5 out of 10. Both must happen, so multiply: 6/11 × 5/10 = 3/11.
  3. 13.8. Take 2x from both sides: 3x − 5 = 19. Add 5: 3x = 24. Divide by 3: x = 8.
  4. 14.10. The top triangle and the whole triangle are the same shape, and the whole side is 6 ÷ 3 times the top part. So the base is 10 cm.
  5. 15.4. Add 4 to both sides to get 4x = 16, then divide by 4: x = 4.
  6. 16.48. 12 × 24 × 8 = 2304 = 48 × 48, so the volume is 48 cm³.
  7. 17.180. Every length is multiplied by 3, so the area is multiplied by 3 × 3 = 9. That makes 20 × 9 = 180 square centimetres.
  8. 18.20. From each of 8 vertices a diagonal can run to 5 others. That counts each diagonal twice, so there are 8 × 5 ÷ 2 = 20.
  9. 19.80. Each term is 2 times the one before, not a fixed amount more. The term before the gap is 40, so the missing one is 40 × 2 = 80, and 80 × 2 = 160 checks it against the term after the gap.
  10. 20.4. Both orders hold the same 3 notebooks, so the difference between them is erasers alone: $43 − $35 = $8 buys 7 − 5 = 2 erasers. One eraser is therefore $8 ÷ 2 = $4.
  11. 21.10. The square root of 36 is 6, because 6 × 6 = 36. 4 squared is 16, because 4 × 4 = 16. 16 − 6 = 10.
  12. 22.24. By Pythagoras, the third side is √(102 − 62) = 8 cm. The perimeter is 6 + 8 + 10, which is 24.
  13. 23.2. In order the middle number is 56, and 58 appears most often. The difference is 2.
  14. 24.120. The marked angle and the one asked for are on the same side of the crossing line, between the two parallel lines, so they add to 180°, and 180 − 60 = 120°.
  15. 25.7. 25² − 24² = 625 − 576 = 49, so the missing side is 7 cm.

Paper 1, Section C: longer problems

  1. 26.16. Nothing on the first $100. The next $120 is charged at 5%, which is $6. That leaves $40 above $220, charged at 25%, which is $10. Altogether $6 + $10 = $16.
  2. 27.11. Both orders hold the same 4 pens, so the difference between them is markers alone: $62 − $50 = $12 buys 3 − 1 = 2 markers. One marker is therefore $12 ÷ 2 = $6. Putting that back into the second order: 1 marker cost $6, leaving $50 − $6 = $44 for 4 pens, so one pen is $11.
  3. 28.2700. Area = 15 × 9 = 135 m². Cost = 135 × $20 = $2700.
  4. 29.65. Boys : girls = 1 : 3, so each of the 4 parts is 65. So the answer is 65.
  5. 30.20. In 30 minutes Chloe covers 3 km. Ruby gains 15 − 6 = 9 km every hour, so closing that gap takes 3 ÷ 9 of an hour = 20 minutes.
  6. 31.9. The hose pours 15 L, then 14 L, then 13 L, and the minutes add up to 99 L at the end of minute 9. So the answer is 9 minutes.

Paper 2, Section A: short answers (calculator allowed)

  1. 1.679. The radius is half the diameter: 9 cm. Volume of a cone = 1/3 πr²h. = 1/3 × π × 9² × 8. This is 679 cm³.
  2. 2.10. Bases match bases: the large base is 20 ÷ 12 times the small one, so the upright side is 6 × 20 ÷ 12 = 10 cm.
  3. 3.48. Write y = kx², find k from x = 2, y = 12, then put in x = 4: y = 48.
  4. 4.50.3. The radius is half the diameter: 2 cm. Surface area of a sphere = 4πr². = 4 × π × 2². This is 50.3 cm².
  5. 5.54. Every length is multiplied by 3, so the 5 by 4 rectangle becomes 15 by 12 and its perimeter is 2 × (15 + 12) = 54 cm.
  6. 6.8. 10² − 6² = 100 − 36 = 64, so the missing side is 8 cm.
  7. 7.96. Every length is multiplied by 4, so the area is multiplied by 4 × 4 = 16. That makes 6 × 16 = 96 square centimetres.
  8. 8.2/11. The first draw is 5 out of 11. One starred is now gone, so the second is 4 out of 10. Both must happen, so multiply: 5/11 × 4/10 = 2/11.
  9. 9.0.00460. Count 3 significant figures from the first non-zero digit of 0.0045999, then look at the next digit to round. The answer is 0.00460.
  10. 10.11.4. sin 46° = AB/AC, so AC = 8.2 ÷ sin 46° = 11.4 cm.

Paper 2, Section B: longer problems

  1. 11.15. In 60 minutes Aaron covers 4 km. Zara gains 20 − 4 = 16 km every hour, so closing that gap takes 4 ÷ 16 of an hour = 15 minutes.
  2. 12.280. Boys : girls = 4 : 7, so each of the 11 parts is 40. So the answer is 280.
  3. 13.18. Count what each does in one minute rather than in whole jobs: 1/30 and 1/45. Together that is 75/1350 of the job each minute, so the whole job takes 1350 ÷ 75 = 18 minutes.
  4. 14.20. Each minute 16 − 8 = 8 L stays in, and 160 ÷ 8 = 20. So the answer is 20 minutes.
  5. 15.6300. Area = 14 × 9 = 126 m². Cost = 126 × $50 = $6300.
  6. 16.144. 1/5 of 180° is 36°, so the angle left is 144°.
  7. 17.4. Both orders hold the same 2 markers, so the difference between them is erasers alone: $17 − $11 = $6 buys 3 − 1 = 2 erasers. One eraser is therefore $6 ÷ 2 = $3. Putting that back into the second order: 1 eraser cost $3, leaving $11 − $3 = $8 for 2 markers, so one marker is $4.
  8. 18.12. Weekday pay is $456. The weekend rate is $48 an hour, so the weekend pay is $576. So the answer is 12.
  9. 19.550. Find the slant height first: l = √(7² + 24²) = 25 cm. Curved surface area = πrl = π × 7 × 25. This is 550 cm².
  10. 20.28.7. sin 32° = AB/AC, so AC = 15.2 ÷ sin 32° = 28.7 cm.

Written by Scholar Tests to MOE's Secondary 2 Mathematics syllabus. Not a school paper. Scholar Tests is not connected with MOE, SEAB or any school.

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  • Secondary 2 Mathematics Paper 1

    31 questions · 75 minutes

    Secondary 2 work. Multiple choice, short answers, then longer problems. No calculator.

  • Secondary 2 Mathematics Paper 2

    20 questions · 90 minutes

    Secondary 2 work. Short answers, then longer problems. Calculator allowed.

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Questions parents ask

What does the Sec 2 paper cover?
The Secondary 2 Mathematics topics in MOE's syllabus: expanding and factorising quadratics, changing the subject, simultaneous equations, direct and inverse proportion, Pythagoras' theorem, trigonometry in right-angled triangles, similarity and scale, the volume and surface area of pyramids, cones and spheres, probability and statistics.
How is it marked?
In Paper 1 the multiple-choice questions and short answers are worth 2 marks and the 6 longer problems 5; in Paper 2 the short answers are worth 3 and the longer problems 5, for 160 in all. Schools set their own marks, so this is our scheme. We mark the final answer only, and an answer that is not exact must be correct to 3 significant figures (an angle to 1 decimal place), as the syllabus asks.
Can my child use a calculator?
In Paper 2 only. Paper 1 is done without one, as most schools set it.
Is it free?
A free account includes 3 practice tests. The Singapore pack (S$99 for 6 months) opens unlimited tests and shows the right answer and the working for every question.
Is this a real school exam paper?
No. Every question is written by us, and schools set their own papers in their own layouts. Scholar Tests is not connected with MOE, SEAB or any school.

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