Lesson 7.6.1

7.6.1 Constructing simple differential equations Quiz: Pearson Edexcel Maths, Unit 7

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 7.6.1, Constructing simple differential equations: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 7: Differentiation, written with Revision Ninja.

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The 20 questions

  1. What does the rate of change of a variable with respect to time represent mathematically?

    • Second derivative
    • Function value
    • First derivative
    • Integral

  2. If a population grows at a rate proportional to its current size P, what is the proportionality constant?

    • Time period
    • Growth constant
    • Decay factor
    • Fixed capacity

  3. Which symbol represents time when modelling dynamic physical situations using calculus?

    • t
    • s
    • x
    • y

  4. What type of differential equation models radioactive decay where substance decreases proportionally to remaining mass?

    • First-order
    • Second-order
    • Quadratic
    • Linear algebraic

  5. How is 'proportional to' translated into an algebraic equation involving a constant k?

    • Multiplying by k
    • Dividing by k
    • Adding k
    • Raising to power k

  6. If liquid drains from a tank at a rate proportional to the square root of depth h, what term describes √h?

    • Inverse depth
    • Linear depth
    • Squared depth
    • Square root

  7. What does dV/dt represent when V is the volume of a expanding spherical balloon?

    • Surface area
    • Total volume
    • Radius length
    • Rate of inflation

  8. When setting up a model where quantity decreases over time, what sign must the proportionality constant take?

    • Zero
    • Negative
    • Positive
    • Undefined

  9. Translate 'the acceleration is proportional to displacement' into a differential equation.

    • d²x/dt² = kt
    • dx/dt = kx²
    • d²x/dt² = -kx²
    • dx/dt = -kx

  10. If bacteria population P triples every hour, which equation models this growth rate?

    • dP/dt = k + P
    • dP/dt = kP²
    • dP/dt = kt
    • dP/dt = kP

  11. A tank holds 500 litres and water flows in at 10 l/min. What is the inflow rate term?

    • 10t
    • 10
    • 500
    • 50

  12. Temperature T of a cooling object drops at a rate proportional to (T - 20). Write this differential equation.

    • dT/dt = k - 20
    • dT/dt = -kT
    • dT/dt = k(T - 20)²
    • dT/dt = -k(T - 20)

  13. If mass m decreases at a constant rate c, what differential equation represents this?

    • dm/dt = -cm²
    • dm/dt = c
    • dm/dt = -c
    • dm/dt = -cm

  14. An investment grows with continuous compounding at annual rate r. What is the differential equation for amount A?

    • dA/dt = rt
    • dA/dt = rA
    • dA/dt = r²A
    • dA/dt = A + r

  15. Raindrop mass increases at a rate proportional to its surface area A. Write the differential equation for mass m.

    • dm/dt = k/A
    • dm/dt = km
    • dm/dt = kA
    • dm/dt = km²

  16. If a chemical reaction speed is proportional to the product of remaining concentrations x and y, write the rate equation.

    • dx/dt = -k(x + y)
    • dx/dt = kxy
    • dx/dt = -kx²y
    • dx/dt = -kxy

  17. A patient absorbs medicine at rate a and excretes it at rate b times concentration c. Write dc/dt.

    • dc/dt = a - bc
    • dc/dt = ab - c
    • dc/dt = ac - b
    • dc/dt = a + bc

  18. If the rate of change of population P is inversely proportional to time t, what equation represents this?

    • dP/dt = t/k
    • dP/dt = k - t
    • dP/dt = k/t
    • dP/dt = kt

  19. What mathematical technique is required to solve the constructed differential equation after separation of variables?

    • Rationalisation
    • Integration
    • Factorisation
    • Differentiation

  20. When constructing a differential equation for a physical problem, what does the constant k typically ensure?

    • Dimensional consistency
    • Initial condition
    • Maximum value
    • Variable elimination

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