Year 12 straight lines and circles test to download as PDF

This Year 12 straight lines and circles test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-17, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Lines
\(A(1,3)\) and \(B(5,11)\).
1. Find the equation of the line \(AB\) in the form \(y=mx+c\). (2 marks)
2. Find the equation of the perpendicular bisector of \(AB\). (2 marks)
Question 2 – Circle equation
A circle has equation \(x^2+y^2-10x+4y+13=0\).
1. Find the centre and the radius. (3 marks)
2. Determine whether \((1,-1)\) lies inside, outside or on the circle. (1 mark)
Question 3 – Tangent
The point \(P(7,1)\) lies on the circle \((x-3)^2+(y+2)^2=25\).
1. Show that \(P\) lies on the circle. (1 mark)
2. Find the equation of the tangent at \(P\). (3 marks)
Question 4 – Line and circle
The line \(y=x+k\) meets the circle \(x^2+y^2=8\). Find the values of \(k\) for which the line is a tangent.
Question 5 – Problem: a circular skate park
On a plan, the ends of a diameter of a circular skate park are \(A(2,3)\) and \(B(10,9)\) (metres). A kiosk is at \(C(9,10)\).
1. Find the centre and radius of the skate park and write down its equation. (3 marks)
2. Show that the kiosk lies on the boundary. (1 mark)
3. Show that angle \(ACB\) is \(90^\circ\). (1 mark)

How to use this Year 12 straight lines and circles test

First, revise with the straight lines and circles lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the straight lines and circles test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 straight lines and circles 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.