A-level · Coordinate geometry

Converting to Cartesian formExam-style questions

Eliminating the parameter to find the Cartesian equation of a parametric curve, by substitution or rearrangement, and carrying the domain restriction from the parameter through to the Cartesian equation.

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23 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    A curve has parametric equations x=t+1, y=t2x = t + 1,\ y = t^2. Find a Cartesian equation of the curve.
    Level 2 · 2 marksTry it
  2. 2
    A curve has parametric equations x=2t, y=t2−3x = 2t,\ y = t^2 - 3. Find a Cartesian equation of the curve.
    Level 2 · 2 marksTry it
  3. 3
    A curve has parametric equations x=t−3,  y=2t+1x = t - 3, \; y = 2t + 1.

    Find a Cartesian equation of the curve, and state what kind of curve it is. (3 marks)
    Level 2 · 3 marksTry it
  4. 4
    A curve has parametric equations x=3t,  y=t2x = 3t, \; y = t^{2}.

    Find a Cartesian equation of the curve. (3 marks)
    Level 2 · 3 marksTry it