Maths exam papers

Sec 1 Maths exam paper

A free Secondary 1 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 1 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.

    A candle is 21 centimetres tall. It burns down 4 centimetres each hour. Which equation gives the candle's height h, in centimetres, after t hours?

    1. Ah = 21t − 4
    2. Bh = 17t
    3. Ch = 4t + 21
    4. Dh = −4t + 21
  2. 2.

    What are the prime factors of 30?

    1. A3² × 5
    2. B2 × 3 × 5
    3. C2 × 3² × 5
    4. D6 × 5
  3. 3.

    Find the value of x.
    6x + 17 = 4x + 27

    1. A1
    2. B10
    3. C22
    4. D5
  4. 4.

    How many diagonals does a 6-sided polygon have?

    1. A18
    2. B15
    3. C12
    4. D9
  5. 5.

    The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark?

    1. A120°
    2. B130°
    3. C50°
    4. D65°
  6. 6.

    A team's score changed from 20 points to 34 points. What is the percentage change?

    1. A26% increase
    2. B70% increase
    3. C70% decrease
    4. D14% increase
  7. 7.

    Find the value of x.
    6(x + 6) = 48

    1. A14
    2. B2
    3. C8
    4. D3
  8. 8.

    A cyclist rides 36 km in 45 minutes. What is its average speed?

    1. A1620 km/h
    2. B48 km/h
    3. C43 km/h
    4. D80 km/h
  9. 9.

    A sequence begins 11, 23, 35, 47, … and carries on in the same way. What is the 17th term?

    1. A203
    2. B215
    3. C187
    4. D204
  10. 10.

    A circle has a diameter of 42 cm. Taking π as 22/7, what is the distance all the way round it?

    1. A66 cm
    2. B1386 cm
    3. C264 cm
    4. D132 cm

Paper 1, Section B: short answers

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

  1. 11.

    What is the square root of 25 added to 3 squared?

    Answer: ______________

  2. 12.

    How many diagonals does a 6-sided polygon have?

    Answer: ______________

  3. 13.

    Look at this number pattern: 2, 6, 12, 20, 30. What number comes next?

    Answer: ______________

  4. 14.

    A charity's monthly donations rose from $300 to $1050 after an appeal. By what percentage did it go up? Give your answer as a percentage.

    Answer: ______________

  5. 15.

    What is the highest common factor of 40, 48?

    Answer: ______________

  6. 16.

    A bus travels at an average speed of 20 km/h for 30 minutes. How far does it go? Give your answer in km.

    Answer: ______________

  7. 17.

    Write 25,488 correct to 2 significant figures.

    Answer: ______________

  8. 18.

    A competitor is given the numbers 87 to 116 to hand out, one to each entrant. How many entrants can be given a number?

    Answer: ______________

  9. 19.

    6 batteries cost $22.50. What do 30 of the same batteries cost? Give your answer in dollars.

    Answer: ______________

  10. 20.

    In the drawing below, the two lines marked with arrows are parallel. What is the size of the angle marked x? Give your answer in degrees.

    Answer: ______________

  11. 21.

    A backpack costs $200. Its price is raised by 20% and the new price is then reduced by 20%. What is the final price? Give your answer in dollars.

    Answer: ______________

  12. 22.

    A map has a scale of 1 : 200,000. On the map, a beach and a lighthouse are 13.5 cm apart. How far apart are they in real life, in kilometres? Give your answer in km.

    Answer: ______________

  13. 23.

    A sequence begins 4, 12, 20, 28, … and carries on in the same way. What is the 9th term?

    Answer: ______________

  14. 24.

    One winter night in Thredbo the temperature dropped to −9 °C. The next afternoon it reached 3 °C. How many degrees warmer was the afternoon than the night?

    Answer: ______________

  15. 25.

    A circle with a radius of 14 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: ______________

Paper 1, Section C: longer problems

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

  1. 26.

    James sets off along a straight road walking at 5 km/h. 60 minutes later Aaron sets off from the same place along the same road, cycling at 15 km/h. How many minutes after Aaron sets off does Aaron catch up with James?

    Answer: ______________

  2. 27.

    Two taps working together fill the tank in 18 hours. Working on its own, the first tap would take 27 hours. How long would the second tap take on its own?

    Answer: ______________

  3. 28.

    A courier adds a service charge to every order: nothing on the first $40, 10% on the next $120, and 20% on anything above $160. What is the service charge on an order of $200? Give your answer in dollars.

    Answer: ______________

  4. 29.

    A hose fills a fish tank that holds 195 L. In the first minute it pours in 24 L, and each minute after that it pours in 1 L less than the minute before. The fish tank becomes full exactly at the end of a minute. How many minutes does it take to fill? Give your answer in minutes.

    Answer: ______________

  5. 30.

    A family of 1 adult and 2 children pays $126 for tickets to a theme park. A child ticket costs $9 less than an adult ticket. How much does one adult ticket cost? Give your answer in dollars.

    Answer: ______________

  6. 31.

    2 potters make 90 bowls in 5 days. They all work at the same rate. How many days would 7 potters take to make 756 bowls? Give your answer in days.

    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 train travels at an average speed of 60 km/h for 90 minutes. How far does it go? Give your answer in km.

    Answer: ______________

  2. 2.

    Look at this number pattern: 23, 39, 64, 100, 149. What number comes next?

    Answer: ______________

  3. 3.

    A map has a scale of 1 : 25,000. On the map, two caves are 12.5 cm apart. How far apart are they in real life, in kilometres? Give your answer in km.

    Answer: ______________

  4. 4.

    A box measures 11 cm long, 3 cm wide and 4 cm high. What is its volume? Give your answer in cm³.

    Answer: ______________

  5. 5.

    Lucas buys pens in boxes of 15. Anh buys pens in boxes of 12. What is the smallest number of pens each of them can buy so that they end up with the same number?

    Answer: ______________

  6. 6.

    A market stall's takings went up from $480 to $1080 in a month. By what percentage did it go up? Give your answer as a percentage.

    Answer: ______________

  7. 7.

    How many multiples of 4 are there from 40 to 92, counting both ends?

    Answer: ______________

  8. 8.

    6 batteries cost $9.00. What do 24 of the same batteries cost? Give your answer in dollars.

    Answer: ______________

  9. 9.

    What is the value of −22 − (−6) × 5?

    Answer: ______________

  10. 10.

    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, Section B: longer problems

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

  1. 11.

    A box measures 4 cm long, 11 cm wide and 3 cm high. What is its volume? Give your answer in cm³.

    Answer: ______________

  2. 12.

    A scout hall had 300 students. Then the number of boys rose by 40%, the number of girls fell by 10%, and the total number of students rose by 10%. How many girls were there at first?

    Answer: ______________

  3. 13.

    5 carpenters make 400 chairs in 20 days. They all work at the same rate. How many days would 2 carpenters take to make the same 400 chairs? Give your answer in days.

    Answer: ______________

  4. 14.

    A circle has a diameter of 56 cm. Taking π as 22/7, what is the distance all the way round it? Give your answer in cm.

    Answer: ______________

  5. 15.

    A family of 2 adults and 2 children pays $198 for tickets to the science museum. A child ticket costs $11 less than an adult ticket. How much does one child ticket cost? Give your answer in dollars.

    Answer: ______________

  6. 16.

    A hose fills a trough that holds 153 L. In the first minute it pours in 21 L, and each minute after that it pours in 1 L less than the minute before. The trough becomes full exactly at the end of a minute. How many minutes does it take to fill? Give your answer in minutes.

    Answer: ______________

  7. 17.

    7 pens and 5 folders cost $79. 4 pens and 5 folders cost $73. What does one folder cost? Give your answer in dollars.

    Answer: ______________

  8. 18.

    A rectangular deck measures 11 m by 8 m. Paving costs $15 per square metre. What is the total cost of covering the deck? Give your answer in dollars.

    Answer: ______________

  9. 19.

    A shop sells muffins, pies and rolls. 2 muffins and 5 pies cost $39.50. 2 muffins and 2 pies cost $23. 2 muffins and 2 rolls cost $26. How much does 1 roll cost? Give your answer in dollars.

    Answer: ______________

  10. 20.

    Two printers working together print the whole job in 6 minutes. Working on its own, the first printer would take 10 minutes. How long would the second printer take on its own?

    Answer: ______________

Answers and working

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

  1. 1.D (h = −4t + 21). The candle's height starts at 21 and goes down by 4 each hour: h = −4t + 21.
  2. 2.B (2 × 3 × 5). Keep dividing by the smallest prime that will go in. 30 comes apart into 2 × 3 × 5, and multiplying those back together gives 30 again.
  3. 3.D (5). Take 4x from both sides: 2x + 17 = 27. Take off 17: 2x = 10. Divide by 2: x = 5.
  4. 4.D (9). From each of 6 vertices a diagonal can run to 3 others. That counts each diagonal twice, so there are 6 × 3 ÷ 2 = 9.
  5. 5.B (130°). The marked angle and the one asked for are in the same position at the two crossings, so they are equal and the answer is 130°.
  6. 6.B (70% increase). The change is 14, and 14 out of the starting 20 is 70%. So the answer is 70% increase.
  7. 7.B (2). Divide both sides by 6 to get x + 6 = 8, then take 6 off: x = 2.
  8. 8.B (48 km/h). Speed is how far it would go in one whole hour. In 45 minutes it covers 36 km, so in 60 minutes it covers 36 × 60 ÷ 45 = 48 km. Its speed is 48 km/h.
  9. 9.A (203). Each term is 12 more than the last, so the nth term is 11 + (n − 1) × 12. For n = 17: 11 + 16 × 12 = 203.
  10. 10.D (132 cm). The radius is half the diameter, so it is 21 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.

Paper 1, Section B: short answers

  1. 11.14. The square root of 25 is 5, because 5 × 5 = 25. 3 squared is 9, because 3 × 3 = 9. 5 + 9 = 14.
  2. 12.9. From each of 6 vertices a diagonal can run to 3 others. That counts each diagonal twice, so there are 6 × 3 ÷ 2 = 9.
  3. 13.42. 42 - each number is the position times the next whole number.
  4. 14.250. The rise is $1050 − $300 = $750. A percentage rise is always measured against what you started with, so compare 750 with 300: 750 ÷ 300 = 2.5, which is 250%.
  5. 15.8. 40 = 2 × 2 × 2 × 5, 48 = 2 × 2 × 2 × 2 × 3. The primes they all share multiply to 8.
  6. 16.10. In one hour it covers 20 km, so in one minute it covers 20 ÷ 60 km. Over 30 minutes that is 20 × 30 ÷ 60 = 10 km.
  7. 17.25000. Count 2 significant figures from the first non-zero digit of 25,488, then look at the next digit to round. The answer is 25,000.
  8. 18.30. Subtracting gives the gap rather than the count: (116 − 87) ÷ 1 = 29. Both ends are included, and there is always one more than the number of gaps, so it is 29 + 1 = 30.
  9. 19.112.50. One costs $22.50 ÷ 6 = $3.75. So 30 of them cost $3.75 × 30 = $112.50.
  10. 20.65. The top triangle's angle at E is 180° − 53° − 62°, and x is vertically opposite it: 65°.
  11. 21.192. The rise takes $200 to $240. The reduction comes off THAT price, not the first one: 20% of $240 is $48, leaving $192. Adding the rates would have given $200, which is not the same thing.
  12. 22.27. 13.5 cm on the map is 13.5 × 200,000 = 2,700,000 cm in real life, and 100,000 cm make a kilometre. So the answer is 27 km.
  13. 23.68. Each term is 8 more than the last, so the nth term is 4 + (n − 1) × 8. For n = 9: 4 + 8 × 8 = 68.
  14. 24.12. From −9 °C up to 0 °C is 9 degrees, and from 0 °C up to 3 °C is 3 more: 12 degrees.
  15. 25.168. The circle touches all four sides, so the square's side is twice the radius, 28 cm, and its area is 784 cm². The circle covers 22/7 × 14 × 14 = 616 cm². What is left is 784 − 616 = 168 cm².

Paper 1, Section C: longer problems

  1. 26.30. In 60 minutes James covers 5 km. Aaron gains 15 − 5 = 10 km every hour, so closing that gap takes 5 ÷ 10 of an hour = 30 minutes.
  2. 27.54. Count in one hour: together they do 1/18 of the job, and the first does 1/27. Taking one from the other leaves 1/18 − 1/27 = 1/54, so the second tap alone takes 54 hours.
  3. 28.20. Nothing on the first $40. The next $120 is charged at 10%, which is $12. That leaves $40 above $160, charged at 20%, which is $8. Altogether $12 + $8 = $20.
  4. 29.10. The hose pours 24 L, then 23 L, then 22 L, and the minutes add up to 195 L at the end of minute 10. So the answer is 10 minutes.
  5. 30.48. All 3 tickets at the adult price would cost $144, so an adult ticket is $48 and a child ticket is $39. So the answer is $48.
  6. 31.12. Each potter does 90 ÷ 2 ÷ 5 = 9 a day, so 7 potters do 63 a day. So the answer is 12 days.

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

  1. 1.90. In one hour it covers 60 km, so in one minute it covers 60 ÷ 60 km. Over 90 minutes that is 60 × 90 ÷ 60 = 90 km.
  2. 2.213. 213 - the gaps grow by the same amount each time.
  3. 3.3.125. 12.5 cm on the map is 12.5 × 25,000 = 312,500 cm in real life, and 100,000 cm make a kilometre. So the answer is 3.125 km.
  4. 4.132. Volume multiplies all three edges: 11 × 3 × 4 = 132 cm³.
  5. 5.60. The lowest common multiple of 15 and 12 is 60, so the smallest equal number is 60.
  6. 6.125. The rise is $1080 − $480 = $600. A percentage rise is always measured against what you started with, so compare 600 with 480: 600 ÷ 480 = 1.25, which is 125%.
  7. 7.14. Subtracting gives the gap rather than the count: (92 − 40) ÷ 4 = 13. Both ends are included, and there is always one more than the number of gaps, so it is 13 + 1 = 14.
  8. 8.36.00. One costs $9.00 ÷ 6 = $1.50. So 24 of them cost $1.50 × 24 = $36.00.
  9. 9.8. Multiply first: (−6) × 5 = −30. Then −22 − (−30) = −22 + 30 = 8.
  10. 10.60. The marked angle and the one asked for are on opposite sides of the crossing line, between the two parallel lines, so they are equal — the answer is 60°.

Paper 2, Section B: longer problems

  1. 11.132. Volume multiplies all three edges: 4 × 11 × 3 = 132 cm³.
  2. 12.180. Boys : girls = 2 : 3, so each of the 5 parts is 60. So the answer is 180.
  3. 13.50. The job is 5 × 20 = 100 worker-days, and 2 carpenters share it. So the answer is 50 days.
  4. 14.176. The radius is half the diameter, so it is 28 cm. The distance round a circle is 2 × π × r. That is 2 × 22/7 × 28, and the 7 cancels into the 28, so it comes to 176 cm.
  5. 15.44. All 4 tickets at the adult price would cost $220, so an adult ticket is $55 and a child ticket is $44. So the answer is $44.
  6. 16.9. The hose pours 21 L, then 20 L, then 19 L, and the minutes add up to 153 L at the end of minute 9. So the answer is 9 minutes.
  7. 17.13. Both orders hold the same 5 folders, so the difference between them is pens alone: $79 − $73 = $6 buys 7 − 4 = 3 pens. One pen is therefore $6 ÷ 3 = $2. Putting that back into the second order: 4 pens cost $8, leaving $73 − $8 = $65 for 5 folders, so one folder is $13.
  8. 18.1320. Area = 11 × 8 = 88 m². Cost = 88 × $15 = $1320.
  9. 19.7.00. One pie is $5.50 and one muffin is $6, so 2 rolls cost $14. So the answer is $7.00.
  10. 20.15. Count in one minute: together they do 1/6 of the job, and the first does 1/10. Taking one from the other leaves 1/6 − 1/10 = 1/15, so the second printer alone takes 15 minutes.

Written by Scholar Tests to MOE's Secondary 1 Mathematics syllabus. Not a school paper. Scholar Tests is not connected with MOE, SEAB or any school.

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  • Secondary 1 Mathematics Paper 1

    31 questions · 75 minutes

    Secondary 1 work. Multiple choice, short answers, then longer problems. No calculator.

  • Secondary 1 Mathematics Paper 2

    20 questions · 90 minutes

    Secondary 1 work. Short answers, then longer problems. Calculator allowed.

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Questions parents ask

What does the Sec 1 paper cover?
The Secondary 1 Mathematics topics in MOE's syllabus: primes, HCF and LCM, negative numbers, approximation and significant figures, algebra and linear equations, ratio, rate, speed and percentage, angles and polygons, perimeter, area and volume, number patterns, gradient and straight-line graphs, 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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