3.3.1 Parametric equations of curves Quiz: Pearson Edexcel Maths, Unit 3

The 20 questions

1. What variable is most commonly used as the parameter in parametric equations?

   • theta
   • y
   • x
   • t

2. How do you eliminate the parameter t from x = t^2 and y = 2t?

   • Factorise
   • Substitute
   • Differentiate
   • Integrate

3. What is the Cartesian equation for x = 3t and y = 6t?

   • y = 6x
   • y = x
   • y = 3x
   • y = 2x

4. What curve is represented by the parametric equations x = cos(t) and y = sin(t)?

   • Ellipse
   • Parabola
   • Circle
   • Hyperbola

5. What is the Cartesian equation of the curve given by x = t^2 and y = t?

   • y = x^2
   • x = y^2
   • x + y = 1
   • xy = 1

6. Which trigonometric identity is most useful for eliminating the parameter in x = 2 cos(t) and y = 2 sin(t)?

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

7. What are the parametric equations for a circle with radius 5 centred at the origin?

   • x = cos(5t), y = sin(5t)
   • x = 5 cos(t), y = 5 sin(t)
   • x = 5t, y = 5t
   • x = 25 cos(t), y = 25 sin(t)

8. What is the Cartesian form of x = e^t and y = e^{2t}?

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

9. Find the y-coordinate on the curve x = t + 1, y = t^2 when t = 3.

   • 9
   • 3
   • 6
   • 4

10. Find the x-coordinate on the curve x = 2t^3, y = t - 1 when t = 2.

    • 6
    • 16
    • 8
    • 12

11. Determine the value of the parameter t at the point (4, 2) on the curve x = t^2, y = t.

    • 4
    • 16
    • 2
    • 1

12. Find the Cartesian equation for x = 1/t and y = t.

    • x + y = 1
    • xy = 1
    • y = 1/x^2
    • y = x

13. What is the starting point restriction if t represents time and must be non-negative?

    • t >= 0
    • t = 0
    • t <= 0
    • t > 0

14. Find the Cartesian equation for x = 3 + t and y = 2 - t.

    • y = x + 1
    • x - y = 1
    • xy = 6
    • x + y = 5

15. What is the gradient dy/dx in terms of derivatives with respect to t?

    • (dx/dt) / (dy/dt)
    • (dy/dt) / (dx/dt)
    • (dx/dt)(dy/dt)
    • (dy/dx) / dt

16. Find dx/dt given the parametric equation x = 4t^3 - 2t.

    • 12t^2 - 2t
    • 4t^2 - 2
    • 12t^2 - 2
    • 12t - 2

17. Find dy/dt given the parametric equation y = 5 sin(t) + 3.

    • 5 cos(t)
    • -5 cos(t)
    • 5 sin(t)
    • -5 sin(t)

18. What is the Cartesian equation for x = 2 cos(t) and y = 3 sin(t)?

    • 3x^2 + 2y^2 = 1
    • x^2/2 + y^2/3 = 1
    • x^2/4 + y^2/9 = 1
    • x^2 + y^2 = 36

19. Find the gradient dy/dx at t = 1 for x = t^2 and y = t^3.

    • 3
    • 2
    • 1
    • 1.5

20. What is the range of values for x given x = 4 sin(t)?

    • -4 <= x <= 4
    • x >= 4
    • all real numbers
    • 0 <= x <= 4

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