Lesson 3.4.1

3.4.1 Parametric equations in modelling Quiz: Pearson Edexcel Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3.4.1, Parametric equations in modelling: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 3: Coordinate geometry in the (x, y) plane, written with Revision Ninja.

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The 20 questions

  1. What variable is most commonly used as the parameter when modelling motion with time?

    • y
    • theta
    • t
    • x

  2. What parameter is most commonly used when modelling circular motion or projectiles using angles?

    • x
    • p
    • t
    • theta

  3. Which algebraic technique is used to convert parametric equations into a Cartesian equation?

    • Differentiation
    • Substitution
    • Factorisation
    • Integration

  4. What geometric shape is typically modelled by the parametric equations x = r cos(theta) and y = r sin(theta)?

    • Circle
    • Ellipse
    • Hyperbola
    • Parabola

  5. When modelling the horizontal motion of a projectile, what is generally assumed about horizontal acceleration?

    • Increasing
    • Zero
    • Constant
    • Gravity

  6. What vertical acceleration is typically applied in UK A-Level mechanics models involving gravity?

    • 9.81 m/s^2
    • 9.8 m/s^2
    • 10 m/s^2
    • 0 m/s^2

  7. If x = 3t and y = 4t, what is the Cartesian equation of the path?

    • y = 3x + 4
    • y = 4/3 x
    • 3x - 4y = 0
    • 4x - 3y = 0

  8. What does the parameter t usually represent in real-world kinematics models?

    • Time
    • Distance
    • Temperature
    • Tension

  9. Which trigonometric identity is most useful for eliminating theta from x = a cos(theta) and y = b sin(theta)?

    • cos(2theta) = 2cos^2 - 1
    • cos^2 + sin^2 = 1
    • sin(2theta) = 2sin(theta)cos(theta)
    • 1 + tan^2 = sec^2

  10. When finding the initial speed from parametric velocity components, which mathematical operation is used?

    • Integration
    • Scalar product
    • Pythagoras theorem
    • Division

  11. If x = t^2 and y = 2t, what is the Cartesian equation after eliminating t?

    • y^2 = 4x
    • y = 4x^2
    • y = 2x^2
    • y^2 = 2x

  12. What restriction must often be considered when substituting parameters in real-world models?

    • Gradient of tangent
    • Second derivative
    • Domain of t
    • Y-intercept

  13. What shape is modelled by parametric equations involving hyperbolic functions like sinh and cosh?

    • Hyperbola
    • Circle
    • Ellipse
    • Parabola

  14. How do you find velocity components from parametric position equations?

    • Substitute t equals 0
    • Integrate by t
    • Differentiate by t
    • Differentiate by x

  15. In projectile modelling, what trajectory shape is produced when air resistance is ignored?

    • Catenary
    • Parabola
    • Ellipse
    • Straight line

  16. If x = e^t and y = e^{2t}, what is the resulting Cartesian equation?

    • y = 2x
    • y = e^x
    • y = ln(x)
    • y = x^2

  17. What is a key advantage of using parametric equations in motion problems?

    • Removes need for calculus
    • Eliminates variables
    • Tracks motion over time
    • Always gives linear graphs

  18. If x = 2 cos(theta) and y = 3 sin(theta), what standard geometric curve is represented?

    • Hyperbola
    • Circle
    • Parabola
    • Ellipse

  19. How do you determine the maximum height in a projectile model defined parametrically for y?

    • Integrate y
    • Set dy/dt = 0
    • Set dx/dt = 0
    • Set y = 0

  20. When a model has a parameter restricted to t > 0, what does this usually signify physically?

    • Time after release
    • Terminal velocity
    • Negative velocity
    • Maximum range

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