Maths exam papers

G2 Maths exam paper

A free SEC G2 Mathematics paper, the old N(A)-Level Maths, in SEAB's two-paper format: 36 questions for 140 marks, 2 hours a paper, calculator allowed in both. Section B of Paper 2 is a choice of one of two questions. Print it, then check every answer at the end.

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Scholar Tests · Sample paper

G2 Mathematics

36 questions · 140 marks · 240 minutes · no negative marking

Name ______________________ Date ____________

Paper 1: multiple choice (calculator allowed)

Questions 1 to 5, 2 marks each. Circle the letter of the best answer.

  1. 1.

    Find the equation of the straight line that passes through (3, −5) and (−1, −9).

    1. Ay = x − 10
    2. By = x + 8
    3. Cy = −x − 2
    4. Dy = x − 8
  2. 2.

    Write 510,000,000 in standard form.

    1. A51 × 10⁷
    2. B5.1 × 10⁹
    3. C5.1 × 10⁸
    4. D5.1 × 10⁻⁸
  3. 3.

    Solve the equation x² − 4x − 1 = 0, giving your answers correct to 2 decimal places.

    1. Ax = 4.24 or x = −0.24
    2. Bx = 0.24 or x = −4.24
    3. Cx = 3.73 or x = 0.27
    4. Dx = 6.24 or x = 1.76
  4. 4.

    Hugo uses the formula v = u + at. Given v = 62, u = 6 and a = 7, what is t?

    1. A9
    2. B56
    3. C68
    4. D8
  5. 5.

    $11,500 is put in a bank account that pays compound interest at 5% per year, compounded yearly. Find the interest earned after 4 years, correct to the nearest cent.

    1. A$13,978.32
    2. B$2300.00
    3. C$2478.32
    4. D$14,677.24

Paper 1: short answers at 3 marks

Questions 6 to 17, 3 marks each. Write your answer on the line.

  1. 6.

    y is inversely proportional to x. When x = 4, y = 56. Find y when x = 7.

    Answer: ______________

  2. 7.

    A map is drawn to a scale of 1 : 50,000. A nature reserve has an area of 2 cm² on the map. Find its actual area. Give your answer in km².

    Answer: ______________

  3. 8.

    A jar holds 12 counters numbered 1 to 12. Counters 1 to 5 are pink, 6 to 9 are brown and 10 to 12 are silver. One counter is taken out without looking. What is the chance that it is pink and its number is a multiple of 4?

    Answer: ______________

  4. 9.

    In triangle ABC, angle ABC = 90°, angle ACB = 33° and AC = 9 cm. Find x, the length of BC, correct to 3 significant figures. Give your answer in cm.

    Answer: ______________

  5. 10.

    Solve 6/(x + 3) = 2/(x + 5).

    Answer: ______________

  6. 11.

    A sofa costs $3700 in cash. On hire purchase, a buyer pays a deposit of 25% of the cash price, then 18 monthly instalments of $168.04. Find how much more is paid on hire purchase than in cash. Give your answer in dollars.

    Answer: ______________

  7. 12.

    Write 0.18686 correct to 3 significant figures.

    Answer: ______________

  8. 13.

    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: ______________

  9. 14.

    Solve 2/(x − 3) = 4/(x − 4).

    Answer: ______________

  10. 15.

    A ferry sails at an average speed of 90 km/h for 50 minutes. How far does it go? Give your answer in km.

    Answer: ______________

  11. 16.

    Chloe, James and Zara share $150 in the ratio 5 : 3 : 2. How much more does James get than Zara? Give your answer in dollars.

    Answer: ______________

  12. 17.

    A sphere has radius 9 cm. Find its volume, correct to 3 significant figures. Use the π button on your calculator. Give your answer in cm³.

    Answer: ______________

Paper 1: short answers at 4 marks

Questions 18 to 23, 4 marks each. Write your answer on the line.

  1. 18.

    A tub holds 15 balls numbered 1 to 15. Balls 1 to 3 are white, 4 to 8 are black and 9 to 15 are grey. One ball is taken out without looking. What is the chance that it is not grey and its number is not prime?

    Answer: ______________

  2. 19.

    Solve 9/(x + 4) = 7/(x + 6).

    Answer: ______________

  3. 20.

    A map is drawn to a scale of 1 : 100,000. A lake has an area of 12 cm² on the map. Find its actual area. Give your answer in km².

    Answer: ______________

  4. 21.

    y is directly proportional to x. When x = 8, y = 96. Find y when x = 6.

    Answer: ______________

  5. 22.

    By rounding each number to 1 significant figure, estimate the value of 82.7 × 69.7 ÷ 0.179.

    Answer: ______________

  6. 23.

    A cone has a base of radius 8 cm and a height of 10 cm. Find its volume, correct to 3 significant figures. Use the π button on your calculator. Give your answer in cm³.

    Answer: ______________

Paper 2, Section A: longer problems at 5 marks

Questions 1 to 4, 5 marks each. Write your answer on the line.

  1. 1.

    In triangle ABC, angle ABC = 90°, angle ACB = 39° and AC = 16 cm. Find x, the length of BC, correct to 3 significant figures. Give your answer in cm.

    Answer: ______________

  2. 2.

    A solid hemisphere has diameter 8 cm. Find its volume, correct to 3 significant figures. Use the π button on your calculator. Give your answer in cm³.

    Answer: ______________

  3. 3.

    An empty tank holds 27 L. A tap fills it at 11 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: ______________

  4. 4.

    A semicircle is cut out of a square of side 8 m, as shown. What is the area of the shaded shape that is left? Use π = 3.14. Give your answer in m².

    Answer: ______________

Paper 2, Section A: longer problems at 6 marks

Questions 5 to 11, 6 marks each. Write your answer on the line.

  1. 5.

    One printer would print the whole job on its own in 6 minutes. A second printer would print it on its own in 12 minutes. If both work at the same time, how long do they take together?

    Answer: ______________

  2. 6.

    4 rulers and 2 erasers cost $68. 2 rulers and 2 erasers cost $44. What does one eraser cost? Give your answer in dollars.

    Answer: ______________

  3. 7.

    A sofa costs $2800 in cash. On hire purchase, a buyer pays a deposit of 10% of the cash price, then 18 monthly instalments of $152.60. Find how much more is paid on hire purchase than in cash. Give your answer in dollars.

    Answer: ______________

  4. 8.

    Ruby works at a pet shop. Ruby is paid a base wage of $210 a week plus 10% of everything Ruby sells. How much does Ruby earn in a week when Ruby sells $1100 of goods? Give your answer in dollars.

    Answer: ______________

  5. 9.

    A swimming club had 260 students. Then the number of boys rose by 132, the number of girls fell by 50%, and the total number of students rose by 20%. How many girls were there at first?

    Answer: ______________

  6. 10.

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

    Answer: ______________

  7. 11.

    A rectangular path measures 14 m by 7 m. Timber costs $15 per square metre. What is the total cost of covering the path? Give your answer in dollars.

    Answer: ______________

Paper 2, Section B: answer only one of these two

Questions 12 and 13, 8 marks each. Write your answer on the line.

  1. 12.

    In triangle ABC, AB = 4 cm, AC = 12 cm and BC = 13 cm. Find angle BAC, correct to 1 decimal place. Give your answer in degrees.

    Answer: ______________

  2. 13.

    The numbers of minutes 7 students took to walk to school were 10, 9, 11, 20, 3, 14, 30. Find the standard deviation, correct to 3 significant figures.

    Answer: ______________

Answers and working

Paper 1: multiple choice (calculator allowed)

  1. 1.D (y = x − 8). Gradient = (−9 − −5) / (−1 − 3) = 1. Put (3, −5) into y = mx + c to find c = −8. The answer is y = x − 8.
  2. 2.C (5.1 × 10⁸). Move the decimal point so one non-zero digit sits before it: 5.1. The point moved 8 places left, so the power is positive: 10⁸. The answer is 5.1 × 10⁸.
  3. 3.A (x = 4.24 or x = −0.24). Here a = 1, b = −4 and c = −1. x = (−b ± √(b² − 4ac)) / 2a = (4 ± √20) / 2. The answer is x = 4.24 or x = −0.24.
  4. 4.D (8). v − u = at, so 62 − 6 = 56. Then t = 56 ÷ 7 = 8.
  5. 5.C ($2478.32). Amount = P(1 + r/100)ⁿ. = 11500 × (1 + 5/100)^4 = $13,978.32. Interest = $13,978.32 − $11,500.00. The answer is $2478.32.

Paper 1: short answers at 3 marks

  1. 6.32. Write y = k/x, find k from x = 4, y = 56, then put in x = 7: y = 32.
  2. 7.0.5. On the map 1 cm stands for 0.5 km, so 1 cm² stands for 0.5 × 0.5 = 0.25 km². 2 × 0.25 = 0.5 km². The answer is 0.5 km².
  3. 8.1/12. Of the pink ones, 1 to 5, the ones whose number is a multiple of 4: 4. That is 1 of the 12: 1/12.
  4. 9.7.55. cos 33° = BC/AC, so BC = 9 × cos 33° = 7.55 cm.
  5. 10.−6. Cross-multiply: 6(x + 5) = 2(x + 3). Expand: 6x + 30 = 2x + 6. Collect: 4x = −24, so x = −6. The answer is −6.
  6. 11.249.72. Deposit = 25% of $3700.00 = $925.00. Instalments = 18 × $168.04 = $3024.72. Total paid = $3949.72. Extra = $3949.72 − $3700.00. The answer is $249.72.
  7. 12.0.187. Count 3 significant figures from the first non-zero digit of 0.18686, then look at the next digit to round. The answer is 0.187.
  8. 13.250. 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%.
  9. 14.2. Cross-multiply: 2(x − 4) = 4(x − 3). Expand: 2x − 8 = 4x − 12. Collect: −2x = −4, so x = 2. The answer is 2.
  10. 15.75. In one hour it covers 90 km, so in one minute it covers 90 ÷ 60 km. Over 50 minutes that is 90 × 50 ÷ 60 = 75 km.
  11. 16.15. One part is $150 ÷ 10 = $15, and James has 1 more parts than Zara: $15.
  12. 17.3050. Volume of a sphere = 4/3 πr³. = 4/3 × π × 9³. This is 3050 cm³.

Paper 1: short answers at 4 marks

  1. 18.4/15. Leaving out the grey ones and every one whose number is prime leaves 4 of the 15: 4/15.
  2. 19.−13. Cross-multiply: 9(x + 6) = 7(x + 4). Expand: 9x + 54 = 7x + 28. Collect: 2x = −26, so x = −13. The answer is −13.
  3. 20.12. On the map 1 cm stands for 1 km, so 1 cm² stands for 1 × 1 = 1 km². 12 × 1 = 12 km². The answer is 12 km².
  4. 21.72. Write y = kx, find k from x = 8, y = 96, then put in x = 6: y = 72.
  5. 22.28000. Round to 80 × 70 ÷ 0.2, which is 28,000.
  6. 23.670. Volume of a cone = 1/3 πr²h. = 1/3 × π × 8² × 10. This is 670 cm³.

Paper 2, Section A: longer problems at 5 marks

  1. 1.12.4. cos 39° = BC/AC, so BC = 16 × cos 39° = 12.4 cm.
  2. 2.134. The radius is half the diameter: 4 cm. A hemisphere is half a sphere: volume = 1/2 × 4/3 πr³ = 2/3 πr³. = 2/3 × π × 4³. This is 134 cm³.
  3. 3.6. Each minute the tap adds 11 L and the leak takes 4 L, then 5 L, and so on, so 7 L, then 6 L stay in. Those add up to 27 L at the end of minute 6. So the answer is 6 minutes.
  4. 4.38.88. The square is 64 and the semicircle half of π × 4², so the area is 38.88 m².

Paper 2, Section A: longer problems at 6 marks

  1. 5.4. Count what each does in one minute rather than in whole jobs: 1/6 and 1/12. Together that is 18/72 of the job each minute, so the whole job takes 72 ÷ 18 = 4 minutes.
  2. 6.10. Both orders hold the same 2 erasers, so the difference between them is rulers alone: $68 − $44 = $24 buys 4 − 2 = 2 rulers. One ruler is therefore $24 ÷ 2 = $12. Putting that back into the second order: 2 rulers cost $24, leaving $44 − $24 = $20 for 2 erasers, so one eraser is $10.
  3. 7.226.80. Deposit = 10% of $2800.00 = $280.00. Instalments = 18 × $152.60 = $2746.80. Total paid = $3026.80. Extra = $3026.80 − $2800.00. The answer is $226.80.
  4. 8.320. The commission is 10% of $1100 = $110, so the pay is $210 + $110. So the answer is $320.
  5. 9.160. The girls lost 80, which is 50% of them, so there were 160 girls and 100 boys at first. So the answer is 160.
  6. 10.20. In 30 minutes Aaron covers 3 km. Mia gains 15 − 6 = 9 km every hour, so closing that gap takes 3 ÷ 9 of an hour = 20 minutes.
  7. 11.1470. Area = 14 × 7 = 98 m². Cost = 98 × $15 = $1470.

Paper 2, Section B: answer only one of these two

  1. 12.95.4. Cosine rule: cos A = (4² + 12² − 13²) / (2 × 4 × 12) = 0.-9375. A = cos⁻¹(0.-9375). The answer is 95.4°.
  2. 13.8.13. Mean = 97/7 = 13.86. Standard deviation = √(Σ(x − mean)²/n) = √(462.9/7). The answer is 8.13.

Written by Scholar Tests to SEAB's G2 Mathematics syllabus (K210). Not an SEC paper. Scholar Tests is not connected with MOE, SEAB or any school.

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    G2 (was N(A)-Level) Mathematics, short answers. Calculator allowed.

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Questions parents ask

What does the G2 paper cover?
The topics in SEAB's G2 Mathematics syllabus: number, ratio and percentage, rates and speed, algebra, linear and quadratic equations, graphs, angles and polygons, congruence and similarity, Pythagoras' theorem and trigonometry, mensuration, coordinate geometry, statistics and probability; Paper 2 Section B adds circle properties, the sine and cosine rules, bearings, arcs and sectors in radians, quartiles and standard deviation, and combined events.
How is it marked?
Each paper is worth 70, as SEAB's are. In Paper 1 the 5 multiple-choice questions are worth 2 marks, the next 12 are worth 3 and the last 6 are worth 4. In Paper 2 Section A's longer problems are worth 5 or 6, and Section B's two questions 8 each, of which only the better one counts. SEAB gives marks for working; we mark the final answer only.
Can my child use a calculator?
Yes, in both papers, as in the SEC G2 Mathematics exam. Set it to degrees for angles, and use its π button.
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