GCSEs

Test your knowledge with these 20 questions taken from real exam papers

A student in a maths lesson. Photograph: Peter Macdiarmid/Getty Images

If you haven’t done a maths exam for a while, or had anyone living with you who is studying for one, you might be curious about what goes into a GCSE maths paper these days. Here’s a chance to test yourself with these 20 questions taken from last year’s real papers.

We can’t replicate exam conditions. In the real world, pupils taking GCSE maths have to sit four-and-a-half hours of exams. Ninety minutes of that is a paper for which they aren’t allowed calculators.

And, unlike an online quiz, none of the papers are wholly multiple choice, and pupils have to show their working to earn full marks. But after taking this quiz you’ll have a feel for some of the kinds of maths questions students in England and Wales are expected to answer.

Good luck – and let us know how you get on in the comments.

OK. Here we go. No calculators allowed to start with. Which of these shapes has the most sides? Hexagon Octagon Yes, eight sides on an octagon, and a nice gentle start from foundation level paper one. If you only take the foundation papers, the highest grade you can score in the new system is a grade 5. Rhombus Trapezium Nadia has £5 to buy pencils and rulers. Pencils are 8p each. Rulers are 30p each. She says “I will buy 15 pencils. Then I will buy as many rulers as possible. With my change I will buy more pencils.” How many pencils and how many rulers does she buy? 17 pencils, 12 rulers Nadia spends £1.20 on the 15 pencils. She can then afford 12 rulers, costing £3.60. She has spent £4.80, so can afford two further pencils 18 pencils, 12 rulers 17 pencils, 10 rulers 12 pencils, 14 rulers Work out 25.68 divided by 12 2.14 It is 2.14. Three questions now from the higher level non-calculator paper. A fair spinner has five equal sections numbered 1, 2, 3, 4 and 5. A fair six-sided dice has five red faces and one green face. The spinner is spun. If the spinner shows an even number, the dice is thrown. Work out the probability of getting an even number and the colour green. 0.066 The chances are two in five, followed by one in six. So you multiply those fractions together to give you 2/30 or 0.066. Give the reason why these two triangles are congruent. ASA Triangles are congruent if any two angles and their included side are equal in both triangles – ASA. There are five ways in total to find if two triangles are congruent, others include: SSS (side, side, side), SAS (side, angle, side), AAS (angle, angle, side) and HL (hypotenuse, leg) Billy wants to buy these tickets for a show. 4 adult tickets at £15 each and 2 child tickets at £10 each. A 10% booking fee is added to the ticket price. 3% is then added for paying by credit card. Work out the total charge for these tickets when paying by credit card. £88.64 £90.64 The GCSE exam bravely preparing children for a future of being repeatedly scalped by online ticket retailers. £94.64 £98.64 Right, now you can make like Kraftwerk and get out your little pocket calculator for the rest of these questions, as they come from papers where pupils are allowed them. Choose the multiple of both 8 and 12 72 Shouldn’t have been too tricky. Lily goes on a car journey. For the first 30 minutes her average speed is 40 miles per hour. She then stops for 15 minutes. She then completes the journey at an average speed of 60 miles per hour. The total journey time is 1 hour. What is her overall average speed? 25 mph 30 mph 35 mph She’s travelled at 60 mph for 15 minutes, giving an overall average, including the stationary portion, of 35 mph 40 mph Eva thinks she can save water by showering instead of bathing. Her shower uses 10.8 litres per minute and lasts 8 minutes. Eva assumes the water in her bath is in the shape of a cuboid 110cm x 50cm x 35cm. How many litres of water does she save? 106.1 The shower uses 86.4 litres of water in 8 minutes. The bath holds 192.5 litres of water, so she saves 106.1 litres overall. A shop sells two brands of battery. Brand A powers a toy for 5 hours, and is sold in packs of 8 for £3.60. Brand B battery powers the same toy for 5-and-a-half hours, and sells in packs of 6 for £2.94. Which brand is better value? Brand A Brand B A pack of Brand B will give you 33 hours of life, working out at 8.9p per hour. Brand A gives you 40 hours of life, working out a 9p. To be honest, as a parent, the extra seven hours of children not moaning that their toys need new batteries is possibly priceless, but that’s not what GCSE examiners are looking for. Here’s a number machine. What is the output when the input is 4? 10 4 x 3 = 12, then subtract the two to get 10. Here’s that number machine again. What is the output if the input changes to -4? -14 It is -14. -4 x 3 is -12, then subtract a further 2. A is (2, 12) and B is (8, 2). What is the midpoint AB? (3, 5) (5, 7) That’s your midpoint. (4, 6) (6, 10) Here is a sequence: 90 82 74 66 58. What is the expression for the nth term of the sequence? 98 – 8n Remember your order of operations. You multiply the n by the 8 first, before taking it away from the 98. 8n + 82 8n – 98 Use trigonometry to work out the length x. 7.6 Be honest, you Googled how to do this, didn’t you? The method given in the mark scheme is sin 72 = x over 8, but there are alternative ways of working it out too. Children taking the exam are expected to show their working. The next five questions are from paper 3 of the higher level, a sample from the most difficult paper. In a class of 28 students the mean height of the 12 boys is 1.58 metres, and the mean height of all 28 students is 1.52 metres. Work out the mean height of the girls. 1.475 Because 23.6 ÷ 16 = 1.475. Solve this… A fair few of you guessed this, didn’t you? AB, CD and EF are straight lines. Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y? 110 Again, students are expected to work this out from scratch and have to show their working. They don’t get to just pick an option like you do in an online quiz version. Plot twist. The lines are NOT parallel as Ava assumed. The fool. Angle w is 60° – so what effect does this have on the size of angle y? y is bigger Pupils get no marks for saying “‘y is bigger” but not showing their working. Also, the genuine exam question doesn’t call Ava a fool. y is smaller y is the same The value of a new car is £18,000. The value of the car decreases by 25% in the first year and 12% in each of the next 4 years. Work out the value of the car after 5 years. £7,096 £8,096 Depreciation is brutal. £9,096 £10,096

You got…

Not a bad effort, but your school might worry about you dragging their league table place down

Back to school for you without a doubt.

Well done a really decent effort.

Excellent work. A 9 for you. Or an A* as it used to be.

Very good.

[Source for questions: AQA’s 2017 GCSE papers.]

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