Year 13 parametric equations test to download as PDF

This Year 13 parametric equations test lasts 35 minutes and is marked out of 20. It covers the whole chapter for pupils aged 17-18, and the full answers are on a separate page.

⏱️ Duration : 35 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Table and Cartesian equation
A curve has parametric equations \(x=3t-1\), \(y=t^2+2\).
1. Find the value of \(t\) at the point \((8,11)\). [2 marks]
2. Find the Cartesian equation of the curve. [2 marks]
Question 2 – A circle
A curve has parametric equations \(x=1+3\cos t\), \(y=2+3\sin t\). Find its Cartesian equation, and state the centre and radius.
Question 3 – A restricted curve
A curve is given by \(x=\sin t\), \(y=\cos2t\).
1. Show that \(y=1-2x^2\). [2 marks]
2. State the range of \(x\) and of \(y\). [2 marks]
Question 4 – Intersection with a line
The curve \(x=t^2\), \(y=2t\) meets the line \(y=x-8\) at two points. Find their coordinates.
Question 5 – A thrown ball
A ball is thrown so that its path is \(x=12t\), \(y=2+10t-4.9t^2\) (metres, seconds).
1. Find the greatest height and the horizontal range. [3 marks]
2. State one assumption of the model. [1 mark]

How to use this Year 13 parametric equations test

First, revise with the parametric equations lesson and the worksheet. Then sit the test in one go, with a timer set to 35 minutes. After that, mark your work with the parametric equations test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 13 parametric equations test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.