Maths exam papers

Sec 3 Maths exam paper

A free Secondary 3 E-Math paper in the O-Level's two-paper shape: 41 questions for 180 marks, 2 hours 15 minutes a paper, calculator allowed in both. Print it, then check every answer at the end.

See the answersSit a new paper online

Scholar Tests · Sample paper

Secondary 3 Mathematics

41 questions · 180 marks · 270 minutes · no negative marking

Name ______________________ Date ____________

Paper 1: multiple choice (calculator allowed)

Questions 1 to 8, 3 marks each. Circle the letter of the best answer.

  1. 1.

    Solve 4/(x − 3) = 5/(x − 5).

    1. A35
    2. B−5
    3. C5
    4. D−4
  2. 2.

    A, B and C lie on a circle with centre O, and C is on the major arc. Angle AOB = 48°. Find angle ACB.

    1. A96°
    2. B24°
    3. C66°
    4. D132°
  3. 3.

    In a class, ξ is the set of all 28 students, A is the set who play a sport and B the set who play an instrument. n(A) = 17, n(B) = 10 and n(A ∩ B) = 5. Find n(A ∪ B).

    1. A28
    2. B5
    3. C22
    4. D27
  4. 4.

    Chloe uses the formula v = u + at. Given v = 26, u = 11 and a = 3, what is t?

    1. A37
    2. B5
    3. C15
    4. D9
  5. 5.

    The odds against a raffle ticket winning a prize are 4 : 7. What is the probability of a raffle ticket winning a prize?

    1. A4/11
    2. B1/11
    3. C7/4
    4. D7/11
  6. 6.

    Write 0.043 in standard form.

    1. A4.3 × 10⁻³
    2. B4.3 × 10²
    3. C43 × 10⁻³
    4. D4.3 × 10⁻²
  7. 7.

    A sector has radius 4 cm and angle 0.3 radians. Find its area, correct to 3 significant figures.

    1. A2.40 cm²
    2. B1.20 cm²
    3. C4.80 cm²
    4. D0.0419 cm²
  8. 8.

    Solve the equation 3x² + 5x − 6 = 0, giving your answers correct to 2 decimal places.

    1. Ax = 9.02 or x = −10.68
    2. Bx = 0.81 or x = −2.47
    3. Cx = 1.62 or x = −4.95
    4. Dx = 2.47 or x = −0.81

Paper 1: short answers at 3 marks

Questions 9 to 14, 3 marks each. Write your answer on the line.

  1. 9.

    Solve 4/(x + 3) = 2/(x + 6).

    Answer: ______________

  2. 10.

    A pack holds 7 starred cards and 3 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. 11.

    y is inversely proportional to x². When x = 2, y = 539. Find y when x = 7.

    Answer: ______________

  4. 12.

    In triangle PQR, PQ = 15 cm, PR = 12 cm and angle QPR = 86°. Find the area of the triangle, correct to 3 significant figures. Give your answer in cm².

    Answer: ______________

  5. 13.

    Solve 9/(x + 4) = 6/(x + 6).

    Answer: ______________

  6. 14.

    $21,000 is put in a bank account that pays compound interest at 3% per year, compounded yearly. Find the total amount in the account after 2 years, correct to the nearest cent. Give your answer in dollars.

    Answer: ______________

Paper 1: short answers at 4 marks

Questions 15 to 26, 4 marks each. Write your answer on the line.

  1. 15.

    A and B lie on a circle with centre O. Angle OAB = 36°. Find angle AOB. Give your answer in degrees.

    Answer: ______________

  2. 16.

    Write 6.105 correct to 1 decimal place.

    Answer: ______________

  3. 17.

    AB is a diameter of a circle, and C is a point on the circle. Angle CAB = 43°. Find angle CBA. Give your answer in degrees.

    Answer: ______________

  4. 18.

    A pyramid has a square base of side 7 cm and a height of 30 cm. Find its volume. Give your answer in cm³.

    Answer: ______________

  5. 19.

    Write 100° in radians, correct to 3 significant figures.

    Answer: ______________

  6. 20.

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

    Answer: ______________

  7. 21.

    A ship sails from port P to a buoy B, which is 6 km west and 14 km north of P. Find the bearing of B from P, correct to 1 decimal place where it is not exact. Give your answer in degrees.

    Answer: ______________

  8. 22.

    Two similar cones have heights 15 cm and 24 cm. The volume of the smaller cone is 500 cm³. Find the volume of the larger cone. Give your answer in cm³.

    Answer: ______________

  9. 23.

    y is inversely proportional to x². When x = 5, y = 1728. Find y when x = 12.

    Answer: ______________

  10. 24.

    In triangle ABC, angle ABC = 90°, AB = 15 cm and BC = 11 cm. Find angle θ, correct to 1 decimal place. Give your answer in degrees.

    Answer: ______________

  11. 25.

    In a class, ξ is the set of all 40 students, A is the set who play a sport and B the set who play an instrument. n(A) = 29, n(B) = 16 and n(A ∩ B) = 10. Find n(A ∩ B′).

    Answer: ______________

  12. 26.

    In triangle ABC, angle ABC = 44°, angle ACB = 36° and AC = 12 cm. Find the length of BC, correct to 3 significant figures. Give your answer in cm.

    Answer: ______________

Paper 2: longer problems (calculator allowed)

Questions 1 to 15, 6 marks each. Write your answer on the line.

  1. 1.

    A toy car wheel has a diameter of 42 cm. It rolls in a straight line for 18.48 m without slipping. How many complete turns does it make? Use π = 22/7.

    Answer: ______________

  2. 2.

    A rectangular path measures 10 m by 12 m. Rubber matting costs $20 per square metre. What is the total cost of covering the path? Give your answer in dollars.

    Answer: ______________

  3. 3.

    A chord AB cuts off a segment from a circle with centre O and radius 10 cm. Angle AOB is 1.9 radians. Find the area of the minor segment, correct to 3 significant figures. Give your answer in cm².

    Answer: ______________

  4. 4.

    7 pens and 2 notebooks cost $45. 2 pens and 2 notebooks cost $30. What does one notebook cost? Give your answer in dollars.

    Answer: ______________

  5. 5.

    Lily works at a bookshop for $38 an hour on weekdays. At the weekend the pay is double. Lily worked 27 hours on weekdays and some hours at the weekend, and earned $1786 in all. How many hours did Lily work at the weekend?

    Answer: ______________

  6. 6.

    In triangle PQR, PQ = 5 cm, PR = 5 cm and angle QPR = 37°. Find the area of the triangle, correct to 3 significant figures. Give your answer in cm².

    Answer: ______________

  7. 7.

    In triangle ABC, angle ABC = 90°, angle ACB = 41° and AB = 5.5 cm. Find x, the length of AC, correct to 3 significant figures. Give your answer in cm.

    Answer: ______________

  8. 8.

    A ship sails from port P to a buoy B, which is 11 km east and 15 km north of P. Find the bearing of B from P, correct to 1 decimal place where it is not exact. Give your answer in degrees.

    Answer: ______________

  9. 9.

    One painter would paint the fence on its own in 18 hours. A second painter would paint it on its own in 90 hours. If both work at the same time, how long do they take together?

    Answer: ______________

  10. 10.

    A scout hall had 480 students. Then the number of boys rose by 20%, the number of girls fell by 20%, and the total number of students fell by 5%. How many boys were there at first?

    Answer: ______________

  11. 11.

    Two similar rectangles have areas 16 cm² and 100 cm². The shorter side of the smaller rectangle is 8 cm. Find the shorter side of the larger rectangle. Give your answer in cm.

    Answer: ______________

  12. 12.

    $10,500 is put in a bank account that pays compound interest at 1.5% per year, compounded monthly. Find the total amount in the account after 6 years, correct to the nearest cent. Give your answer in dollars.

    Answer: ______________

  13. 13.

    Mia 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 Mia?

    Answer: ______________

  14. 14.

    An empty tank holds 171 L. A tap fills it at 24 L each minute. In the first minute a leak lets out 1 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: ______________

  15. 15.

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

    Answer: ______________

Answers and working

Paper 1: multiple choice (calculator allowed)

  1. 1.B (−5). Cross-multiply: 4(x − 5) = 5(x − 3). Expand: 4x − 20 = 5x − 15. Collect: −x = 5, so x = −5. The answer is −5.
  2. 2.B (24°). The angle at the centre is twice the angle at the circumference standing on the same arc. The answer is 24°.
  3. 3.C (22). Fill the Venn diagram from the middle: A ∩ B = 5, A only = 17 − 5 = 12, B only = 10 − 5 = 5, outside both = 28 − 22 = 6. Read off n(A ∪ B). The answer is 22.
  4. 4.B (5). v − u = at, so 26 − 11 = 15. Then t = 15 ÷ 3 = 5.
  5. 5.D (7/11). The odds make 4 + 7 = 11 ways in all, and 7 of them are what is asked. So the answer is 7/11.
  6. 6.D (4.3 × 10⁻²). Move the decimal point so one non-zero digit sits before it: 4.3. The point moved 2 places right, so the power is negative: 10⁻². The answer is 4.3 × 10⁻².
  7. 7.A (2.40 cm²). Area = ½r²θ = ½ × 4² × 0.3. The answer is 2.40 cm².
  8. 8.B (x = 0.81 or x = −2.47). Here a = 3, b = 5 and c = −6. x = (−b ± √(b² − 4ac)) / 2a = (−5 ± √97) / 6. The answer is x = 0.81 or x = −2.47.

Paper 1: short answers at 3 marks

  1. 9.−9. Cross-multiply: 4(x + 6) = 2(x + 3). Expand: 4x + 24 = 2x + 6. Collect: 2x = −18, so x = −9. The answer is −9.
  2. 10.7/15. The first draw is 7 out of 10. One starred is now gone, so the second is 6 out of 9. Both must happen, so multiply: 7/10 × 6/9 = 7/15.
  3. 11.44. Write y = k/x², find k from x = 2, y = 539, then put in x = 7: y = 44.
  4. 12.89.8. Area = ½ × PQ × PR × sin P = ½ × 15 × 12 × sin 86°. The answer is 89.8 cm².
  5. 13.−10. Cross-multiply: 9(x + 6) = 6(x + 4). Expand: 9x + 54 = 6x + 24. Collect: 3x = −30, so x = −10. The answer is −10.
  6. 14.22278.90. Amount = P(1 + r/100)ⁿ. = 21000 × (1 + 3/100)^2 = $22,278.90. The answer is $22,278.90.

Paper 1: short answers at 4 marks

  1. 15.108. OA and OB are both radii, so triangle OAB is isosceles and angle OBA = angle OAB. Angle AOB = 180° − 2 × 36°. The answer is 108°.
  2. 16.6.1. Keep 1 digit after the decimal point and look at the next one to round. The answer is 6.1.
  3. 17.47. The angle in a semicircle is 90°, so angle ACB = 90°. Angle CBA = 180° − 90° − 43°. The answer is 47°.
  4. 18.490. Volume of a pyramid = 1/3 × base area × height. = 1/3 × 7² × 30. This is 490 cm³.
  5. 19.1.75. 180° is π radians, so multiply by π/180: 100 × π/180. The answer is 1.75 radians.
  6. 20.7. 25² − 24² = 625 − 576 = 49, so the missing side is 7 cm.
  7. 21.336.8. The angle from the north–south line is tan⁻¹(6/14) = 23.2°. B is north-west of P, so measure clockwise from north to reach it. The answer is 336.8°.
  8. 22.2048. The length ratio is 5 : 8, so the volume ratio is 125 : 512. 500 × 512/125. The answer is 2048 cm³.
  9. 23.300. Write y = k/x², find k from x = 5, y = 1728, then put in x = 12: y = 300.
  10. 24.53.7. tan θ = opposite ÷ adjacent = 15 ÷ 11, so θ = 53.7°.
  11. 25.19. Fill the Venn diagram from the middle: A ∩ B = 10, A only = 29 − 10 = 19, B only = 16 − 10 = 6, outside both = 40 − 35 = 5. Read off n(A ∩ B′). The answer is 19.
  12. 26.17.0. Angle BAC = 180° − 44° − 36° = 100°. Sine rule: BC / sin 100° = 12 / sin 44°, so BC = 12 sin 100° / sin 44°. The answer is 17.0 cm.

Paper 2: longer problems (calculator allowed)

  1. 1.14. One turn rolls π × 42 = 132 cm, and 1848 ÷ 132 = 14.
  2. 2.2400. Area = 10 × 12 = 120 m². Cost = 120 × $20 = $2400.
  3. 3.47.7. Sector = ½ × 10² × 1.9. Triangle AOB = ½ × 10² × sin 1.9. Segment = sector minus triangle = ½r²(θ − sin θ). The answer is 47.7 cm².
  4. 4.12. Both orders hold the same 2 notebooks, so the difference between them is pens alone: $45 − $30 = $15 buys 7 − 2 = 5 pens. One pen is therefore $15 ÷ 5 = $3. Putting that back into the second order: 2 pens cost $6, leaving $30 − $6 = $24 for 2 notebooks, so one notebook is $12.
  5. 5.10. Weekday pay is $1026. The weekend rate is $76 an hour, so the weekend pay is $760. So the answer is 10.
  6. 6.7.52. Area = ½ × PQ × PR × sin P = ½ × 5 × 5 × sin 37°. The answer is 7.52 cm².
  7. 7.8.38. sin 41° = AB/AC, so AC = 5.5 ÷ sin 41° = 8.38 cm.
  8. 8.036.3. The angle from the north–south line is tan⁻¹(11/15) = 36.3°. B is north-east of P, so measure clockwise from north to reach it. The answer is 036.3°.
  9. 9.15. Count what each does in one hour rather than in whole jobs: 1/18 and 1/90. Together that is 108/1620 of the job each hour, so the whole job takes 1620 ÷ 108 = 15 hours.
  10. 10.180. Boys : girls = 3 : 5, so each of the 8 parts is 60. So the answer is 180.
  11. 11.20. The area ratio is 4 : 25, so the length ratio is √4 : √25 = 2 : 5. 8 × 5/2. The answer is 20 cm.
  12. 12.11488.18. Amount = P(1 + r/100)ⁿ, with r = 1.5/12 a month and n = 72 months. = 10500 × (1 + 1.5/1200)^72 = $11,488.18. The answer is $11,488.18.
  13. 13.15. In 60 minutes Mia covers 4 km. Zara gains 20 − 4 = 16 km every hour, so closing that gap takes 4 ÷ 16 of an hour = 15 minutes.
  14. 14.9. Each minute the tap adds 24 L and the leak takes 1 L, then 2 L, and so on, so 23 L, then 22 L stay in. Those add up to 171 L at the end of minute 9. So the answer is 9 minutes.
  15. 15.1880. Find the slant height first: l = √(24² + 7²) = 25 cm. Curved surface area = πrl = π × 24 × 25. This is 1880 cm².

Written by Scholar Tests to MOE's Secondary 3 Mathematics syllabus. Not a school paper. Scholar Tests is not connected with MOE, SEAB or any school.

Sit a new paper online

Every online paper is new, timed like an exam, and marked the moment it ends. Type each answer in the unit the question asks for, to 3 significant figures where it is not exact.

  • Secondary 3 Mathematics Paper 1

    26 questions · 135 minutes

    Secondary 3 E-Math in the O-Level Paper 1 shape. Calculator allowed.

  • Secondary 3 Mathematics Paper 2

    15 questions · 135 minutes

    Secondary 3 E-Math longer problems. Calculator allowed.

Pricing

Three free practice tests. Unlimited tests and answers are S$99.

A free account includes 3 practice tests. The pack opens unlimited tests and shows your child what they got right, the right answers and how to reach them, on every Singapore practice paper.

Singapore practice pack

S$99

for 6 months

  • Which questions your child got right, after every practice test
  • The right answer to every question
  • A worked solution for every question, step by step
  • PSLE-style Mathematics, Standard and Foundation, both papers, Science Booklets A and B, and English Papers 1 to 4: marked writing, grammar, vocabulary, editing, cloze, synthesis, comprehension, listening and oral
  • Primary 3, 4 and 5, and Secondary 1 to 4, Mathematics exam papers, with G3 (O-Level-style) E-Math and A-Math at Secondary 3 and 4, and G2 and G1 Mathematics at Secondary 4
  • AEIS-style Mathematics at every level, and English for SEC 1 to 3 with a marked composition
  • SASMO-style olympiad papers, Primary 1 to JC 2
  • RMO-style, APMOPS-style and NMOS-style primary olympiad papers
  • SMO-style Junior and Senior Round 1 papers and self-marked Round 2 proofs, Secondary 1 to 4
  • Maths Kangaroo-style competition papers, Primary 1 to Secondary 4, scored the SMKC way

One payment in Singapore dollars for 6 months of access. No auto-renewal: when the 6 months end, access stops unless you buy again.

Questions parents ask

What does the Sec 3 paper cover?
The Secondary 3 Mathematics topics in MOE's syllabus: standard form, compound interest, hire purchase and exchange rates, quadratic equations by the formula, algebraic fractions, sets, the equation of a line, the sine and cosine rules, bearings, angle properties of circles, arcs and sectors in radians, and areas and volumes of similar figures.
How is it marked?
As the O-Level papers are, each paper is worth 90: in Paper 1 the first 14 questions are worth 3 marks and the other 12 are worth 4; in Paper 2 each of the 15 longer problems is worth 6, for 180 in all. The real Paper 2 splits each question into parts and gives marks for method; we mark one final answer per problem, correct to 3 significant figures (an angle to 1 decimal place) where it is not exact. The parts a computer cannot mark, a graph to draw, a construction, a chart that misleads and an extended real-world task, are a separate written paper of 30 marks in the practice room, which you mark yourself against a model answer.
Is there practice for graphs, constructions and the extended task?
Yes, in the practice room: Paper 2's written questions, one graph to plot and read, one ruler-and-compass construction, one chart or statistic that misleads, and one extended real-world task, 30 marks in 45 minutes. They are done on paper, then marked against a model answer, one tick a mark.
Can my child use a calculator?
Yes, in both papers, as in the O-Level E-Math exam. Set it to degrees for angles, and use its π button.
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 O-Level paper?
No. It is written by us in the shape of SEAB's SEC G3 Mathematics papers. Past O-Level papers are copyright and are not used. Scholar Tests is not connected with MOE, SEAB or any school.

Papers for other levels

P3 MathsP4 MathsP5 MathsP6 MathsPSLE Foundation MathsSec 1 MathsSec 2 MathsSec 4 MathsG2 MathsG1 MathsSec 3 A-MathSec 4 A-Math