‘Nice’ and ‘Interesting’ GCSE exam questions

I have spent some time collecting together maths GCSE exam style questions which I considered to be ‘nice’ or ‘interesting’. To be honest, it was more what you had to do to get the answer, that you could get the answer in different ways, or how that I considered the approach to solving the question was nice or interesting, rather than the question itself.

The questions are taken from sample papers, revision papers or actual examination papers. In some cases I have tweaked the question to make it a little more interesting or more useful for the classroom.

Today I going to share just four questions with you, say a little about what interested me about it, then leave you to have a go at them.

The first question is a practice question which I ‘helped’ my son with during his revision; he sat his GCSE this year. I say ‘helped’, as the first time I tried it I got the wrong answer!

The same dog food is on special offer in three different shops.

Shop A

Single tins are 80p each

But two tins and get the third one free

Shop B

Pack of 6 tins is £3.50 per pack. Buy two packs for £5

Shop C

Pack of 12 tins costs £5.50 per pack

Work out the cheapest way to buy 21 tins

I like this question as the answer is not apparent and the student needs to just start ‘doing some maths’ and see where it leads. I wonder whether the word ‘exactly’ should be added…buy exactly 21 tins? My answer comes to less than £10 and, I think, requires a little lateral thinking. I also like that, I think that my answer opens up a debate as to whether the mathematical answer is the same as the practical, real life answer.

The second question comes from a revision paper. The student I was helping was struggling to get started. They knew routines associated with fractions, percentages and ratios but could not see how any of these routines applied to this question which asked them to ‘show’ something rather than ‘find’ something. We ended up solving it together by drawing a series of diagrams, some discussion and whole load of mathematical reasoning.

A box contains red, yellow, blue and green bricks. 25% of the bricks are red. 12 bricks are yellow. The ratio yellow : blue : green is 2:3:1. Show that the box contains 48 bricks.

The third question I have tweaked to make it into a ‘show that’ question. The original question said find the area in the form a + b√c. I liked it as there are a number of different ways in which the answer could be found and I saw the route to the problem in a different way to the person I was helping, and I liked their way better than mine!

Four triangles are arranged as shown. Show that the area of the white square is 4(9 - 4√5) square units

Picture 1

Finally, a question which was shown to me by a participant on a CPD course I was running. He asked, how do we get students to answer this type of question? Our subsequent discussion highlighted the need for students to develop the ability to break down a question into a series of sub questions and the need for me in my teaching to present students with the opportunity to ask and devise their own questions in response to diagrams presented to them.

The area of the rectangle BCDE is equal to the area of the triangle ABE. Given that the length of BC is 2 units less than the length of BE, Find the length of BE.

Picture 2

 

Have a go at the questions, post you answers here and tell me what you think about the questions. I am collecting questions from a variety of sources to use in lessons throughout secondary school. If you have your own favourites please share them by replying to this post.

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Subject(s)Mathematics
Age11-14, 14-16
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