Year 10 quadratic equations and graphs test to download as PDF

This Year 10 quadratic equations and graphs test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 14-15, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Solving by factorising
Non-calculator.
1. Solve \(x^2-3x-10=0\). (2 marks)
2. Solve \(x^2+4x=21\). (2 marks)
Question 2 – Graph features
Calculator allowed. The curve \(y=x^2-4x-5\) is drawn for \(-2\le x\le6\).
1. Find the coordinates of the points where the curve crosses the axes. (2 marks)
2. Find the equation of the line of symmetry and the coordinates of the turning point. (2 marks)
Question 3 – Problem: the rocket
A toy rocket is launched. Its height \(h\) metres after \(t\) seconds is \(h=30t-5t^2\).
1. Work out the height after 2 seconds. (1 mark)
2. Show that the rocket lands after 6 seconds. (2 marks)
3. Find the maximum height. (1 mark)
Question 4 – Problem: the rectangle
A rectangle has width \(x\) cm and length \((x+6)\) cm. The area is 55 cm².
1. Show that \(x^2+6x-55=0\). (1 mark)
2. Solve the equation by factorising. (2 marks)
3. Find the perimeter of the rectangle. (1 mark)
Question 5 – Higher: formula and completing the square
Higher tier. Give answers to 2 decimal places where needed.
1. Solve \(3x^2-2x-4=0\) using the quadratic formula. (2 marks)
2. Write \(x^2-8x+3\) in the form \((x+a)^2+b\). (1 mark)
3. Hence write down the minimum value of \(x^2-8x+3\). (1 mark)

How to use this Year 10 quadratic equations and graphs test

First, revise with the quadratic equations and graphs lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the quadratic equations and graphs test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 10 quadratic equations and graphs 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.