Year 10 surds and exact values test to download as PDF

This Year 10 surds and exact values 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 – Exact circle answers
Non-calculator. Leave answers in terms of \(\pi\).
1. A circle has diameter 10 cm. Find its area and circumference. (2 marks)
2. A sector has radius 6 cm and angle \(60^\circ\). Find its area. (2 marks)
Question 2 – Pythagoras and surds
A right-angled triangle has shorter sides 5 cm and 10 cm. Give exact answers.
1. Find the hypotenuse in simplest surd form. (2 marks)
2. Find the area. (1 mark)
3. Find the perimeter in the form \(15+k\sqrt5\). (1 mark)
Question 3 – Higher: simplifying surds
Higher tier. Do not use a calculator.
1. Simplify \(\sqrt{75}+\sqrt{27}\). (2 marks)
2. Expand and simplify \((4+\sqrt3)(4-\sqrt3)\). (1 mark)
3. Expand and simplify \((2+\sqrt5)^2\). (1 mark)
Question 4 – Higher: rationalising
Higher tier. Rationalise the denominator.
1. \(\dfrac{14}{\sqrt7}\) (2 marks)
2. \(\dfrac{6}{3-\sqrt3}\), giving your answer in the form \(a+b\sqrt3\). (2 marks)
Question 5 – Problem: the cone
A cone has base radius 5 cm and vertical height 12 cm. Give answers in terms of \(\pi\).
1. Find the slant height. (1 mark)
2. Find the volume. (1 mark)
3. Find the curved surface area. (1 mark)
4. Find the total surface area. (1 mark)

How to use this Year 10 surds and exact values test

First, revise with the surds and exact values 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 surds and exact values test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 10 surds and exact values 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.