Lesson OT2.1-OT2.7

OT2.1-OT2.7 Mathematical problem solving Quiz: AQA Further Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson OT2.1-OT2.7, Mathematical problem solving: 20 multiple choice questions for the AQA Further Maths (7367), Unit 1: Overarching themes, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. In the problem solving cycle, which stage comes immediately after processing and representing information?

    • Checking the original units
    • Interpreting results
    • Specifying the problem
    • Collecting information

  2. Which is the correct order of the first two stages of the problem solving cycle?

    • Process information, then collect information
    • Specify the problem, then collect information
    • Interpret results, then specify the problem
    • Collect information, then specify the problem

  3. Which description best matches abstraction in problem solving?

    • Adding extra variables and conditions so that the problem becomes harder to read
    • Memorising a worked answer to a standard problem so it can be repeated without reasoning
    • Removing irrelevant detail to reveal the underlying mathematical structure
    • Checking the final answer on a calculator without any reasoning about the structure

  4. The phrase the cost rises by 5% each year is best modelled by which structure?

    • A geometric sequence with common ratio 0.05
    • A geometric sequence with common ratio 1.05
    • An arithmetic sequence with common difference 5
    • An arithmetic sequence with common difference 1.05

  5. A rectangle has a perimeter of 36 cm and its length is twice its width. What is its area?

    • 144 cm^2
    • 48 cm^2
    • 36 cm^2
    • 72 cm^2

  6. A town's population is modelled by P(t) = 5000 x 1.03^t. Approximately what is P(10)?

    • About 6720
    • About 5300
    • About 5150
    • About 8000

  7. Solve the simultaneous equations x + y = 10 and x - y = 4. What is x?

    • x = 6
    • x = 5
    • x = 3
    • x = 7

  8. A right-angled triangle has legs of 5 cm and 12 cm. What is the length of its hypotenuse?

    • 17 cm
    • 15 cm
    • 13 cm
    • 119 cm

  9. Two trains start 300 km apart and travel towards each other at 60 km/h and 90 km/h. How long until they meet?

    • 2 hours
    • 3 hours
    • 2.5 hours
    • 5 hours

  10. Find the sum of the first 20 terms of the arithmetic series 3 + 7 + 11 + ...

    • 780
    • 820
    • 860
    • 410

  11. For which value of k do the equations x + ky = 2 and 2x + 4y = 4 have infinitely many solutions?

    • k = 1/2
    • k = 2
    • k = 4
    • k = -2

  12. Find the sum to infinity of the geometric series 12 + 6 + 3 + ...

    • 12
    • 18
    • 36
    • 24

  13. A cylinder has radius r and height h with volume 100 pi cm^3. Which expression gives its surface area in terms of r alone?

    • pi r^2 + 200 pi / r
    • 2 pi r^2 + 100 pi / r
    • 2 pi r^2 + 200 pi / r
    • 2 pi r^2 + 400 pi / r

  14. A bag holds 3 red and 2 blue balls. Two are drawn without replacement. What is the probability both are red?

    • 9/25
    • 3/5
    • 1/5
    • 3/10

  15. A model predicts a profit of 4.2 million pounds but the actual result is 1.1 million pounds. Which is the most appropriate next step in the problem solving cycle?

    • Accept the model because it was carefully constructed
    • Revisit the assumptions and refine the model
    • Treat the difference as random noise and stop
    • Round the profit to the nearest million and stop

  16. How many solutions in non-negative integers (x, y) satisfy 2x + 3y = 12?

    • 2
    • 5
    • 4
    • 3

  17. The number of handshakes among n people, each shaking hands once with every other person, is n(n-1)/2. For how many people does the number first exceed 100?

    • 20 people
    • 16 people
    • 15 people
    • 14 people

  18. What is the largest integer n such that 2^n is less than 1000?

    • 8
    • 9
    • 500
    • 10

  19. A price of 40 pounds is reduced by 25%, then the new price is reduced by a further 20%. What is the final price?

    • 30 pounds
    • 25 pounds
    • 24 pounds
    • 22 pounds

  20. A 5 m ladder leans against a wall with its foot 3 m from the wall. The foot then moves to 4 m from the wall. By how much does the top of the ladder drop?

    • 0.5 m
    • 3 m
    • 2 m
    • 1 m

All AQA Further Maths quizzes