Lesson OT3.1-OT3.5

OT3.1-OT3.5 Mathematical modelling Quiz: AQA Further Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson OT3.1-OT3.5, Mathematical modelling: 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. What term describes a simplifying statement made to make a complex system mathematically manageable?

    • Modelling assumption
    • Empirical observation
    • Mathematical proof
    • Theoretical conclusion

  2. What primary evidence indicates that a mathematical model needs to be refined?

    • Complex calculations
    • Inaccurate predictions
    • Large datasets
    • Negative solutions

  3. In the exponential model P = P0 e^(kt), what quantity does P0 represent?

    • Initial value
    • Growth rate
    • Time period
    • Final value

  4. What stage follows comparing a model's predicted outputs with real observed data?

    • Data collection
    • Problem formulation
    • Initial assumption
    • Model refinement

  5. What standard assumption treats a moving object as having mass concentrated at a single point?

    • Light string
    • Smooth surface
    • Particle model
    • Rigid body model

  6. A population is P = 200 x 1.1^t. What is the minimum whole year t where P exceeds 400?

    • 9 years
    • 7 years
    • 6 years
    • 8 years

  7. In the cost model C = 500 + 12n for making n items, what does 500 represent?

    • Unit price
    • Total profit
    • Fixed cost
    • Variable cost

  8. A particle's velocity is modelled by v = 20 - 4t for 0 <= t <= 5. What is its velocity at t = 5 according to the model?

    • -4
    • 20
    • 5
    • 0

  9. A model predicts T = 2t + 15. Observed T = 33 at t = 10. How is the model described?

    • Overestimates by 5
    • Underestimates by 2
    • Overestimates by 2
    • Underestimates by 5

  10. A cooling model is T = 20 + 60e^(-0.1t). What is the long-run temperature as t tends to infinity?

    • 20 degrees
    • 60 degrees
    • 0 degrees
    • 80 degrees

  11. What parameter is assumed to remain unchanged in a constant growth rate population model?

    • Zero mortality
    • Unlimited resources
    • Constant rate parameter
    • Constant population

  12. A car moves at a constant speed of 25 m/s according to the model distance = speed x time. How far does it travel in 12 seconds?

    • 37 m
    • 250 m
    • 300 m
    • 312 m

  13. Why is a model incorporating air resistance considered superior to a simple model without it?

    • Simpler calculation
    • Improved physical realism
    • Guaranteed linear fit
    • Higher predicted output

  14. A model N = 1000 e^(0.4t) describes bacteria. Using ln 10 = 2.303, roughly when does N reach 10000?

    • About 2.3 time units
    • About 5.8 time units
    • About 25 time units
    • About 10 time units

  15. A population model predicts negative output values for some t. What action is required?

    • Data collection
    • Parameter extrapolation
    • Model refinement
    • Model validation

  16. A probability model assumes a fair die, but test data shows the die is loaded. What is compromised?

    • Model validity
    • Algebraic accuracy
    • Mathematical proof
    • Sample space

  17. A tank's depth is modelled by h(t) = 2 + 0.5t for 0 <= t <= 8. What is the largest depth the model can validly predict?

    • 10
    • 8
    • 2
    • 6

  18. A logistic model N(t) = 500 / (1 + 4e^(-0.5t)) describes growth. What is the limiting value of N?

    • 2000
    • 4
    • 500
    • 125

  19. A sample decays to half its mass in 10 years under the model M = M0 e^(-kt). What is k?

    • k = 0.5
    • k = 10 / ln 2, about 14.4
    • k = 0.1
    • k = ln 2 / 10, about 0.0693

  20. What key real-world constraint limits the long-term validity of quadratic population models?

    • Variable definition
    • Initial conditions
    • Resource limitations
    • Rounding errors

All AQA Further Maths quizzes