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

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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.

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The 20 questions

  1. In the mathematical problem-solving cycle, which stage comes immediately after processing data?

    • Refining the model
    • Interpreting results
    • Specifying the problem
    • Collecting information

  2. What is the very first stage in the standard mathematical problem-solving cycle?

    • Interpret results
    • Specify the problem
    • Process information
    • Collect information

  3. What term describes removing irrelevant real-world details to reveal core mathematical structure?

    • Simplification
    • Modelling
    • Abstraction
    • Extrapolation

  4. Which sequence type best models a quantity that increases by 5% each year?

    • Fibonacci sequence
    • Geometric sequence
    • Arithmetic sequence
    • Quadratic sequence

  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. When a model's prediction differs greatly from reality, what step should be taken?

    • Discard the data
    • Refine the model
    • Publish the results
    • Ignore the error

  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