Year 11 problem solving and GCSE exam practice test to download as PDF

This Year 11 problem solving and GCSE exam practice test lasts 40 minutes and is marked out of 20. It covers the whole chapter for pupils aged 15-16, and the full answers are on a separate page.

⏱️ Duration : 40 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Ratio and percentage
£360 is shared in the ratio \(5:7\).
1. Work out each share. (2 marks)
2. Work out 12% of the larger share. (2 marks)
Question 2 – Solving equations
Solve these.
1. \(5(x-2)=3x+6\) (2 marks)
2. \(3x+2y=16\) and \(x-y=2\) (2 marks)
Question 3 – Trigonometry
A tower is 30 m tall. A point on the ground is 50 m from the base of the tower.
1. Work out the angle of elevation of the top from the point, to 1 decimal place. (3 marks)
2. Work out the distance from the point to the top. (1 mark)
Question 4 – Proof
Prove that the sum of two consecutive odd numbers is always a multiple of 4.
Question 5 – Problem: fencing a field
A rectangular field is 40 m by 25 m. A fence goes all the way round except for a 3 m gate. Fencing costs £14.50 per metre.
1. Work out the length of fence needed. (2 marks)
2. Work out the total cost. (2 marks)

How to use this Year 11 problem solving and GCSE exam practice test

First, revise with the problem solving and GCSE exam practice lesson and the worksheet. Then sit the test in one go, with a timer set to 40 minutes. After that, mark your work with the problem solving and GCSE exam practice test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 11 problem solving and GCSE exam practice 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.

Problem solving and GCSE exam practice – Year 11 GCSE maths test to download as PDF

Question 1 – Ratio and percentage

Question 2 – Solving equations

Question 3 – Trigonometry

Question 4 – Proof

Question 5 – Problem: fencing a field

How to use this Year 11 problem solving and GCSE exam practice test

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