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10 Tough Problems for GCSE Maths Students

In this post I’m sharing a set of challenging problems for GCSE Maths students that I’ve put together with the aim of helping students to improve their problem-solving skills.

They’re aimed mainly at those doing the Higher Tier, but some of them can be solved using only Foundation skills.

Each problem is provided with a set of hints to set you on the right track if you’re struggling – but you should always try to get as far as you can on your own without peeking!

This is set 1 of a growing collection of problems for GCSE Maths students, and solutions, presented in this way. I don’t claim credit for creating the original problems, in most cases, but the hints and solutions are my own.

How will this help me in my GCSE?

You may be aware that there are three Assessment Objectives on a GCSE Maths exam:

  • AO1: Use and apply standard techniques – worth 50% of the total marks at Foundation and 40% at Higher
  • AO2: Reason, interpret and communicate mathematically – worth 25% of Foundation and 30% of Higher
  • AO3: Solve problems within mathematics and in other contexts – worth 25% of Foundation and 30% of Higher

A single question can include marks for all three AOs: AO3 is about working out what you need to do, AO1 is about carrying out the process, and AO2 is about communicating clearly. These problems for GCSE Maths students are focused on helping you develop the skills you need for those AO3 marks, but of course elements of the other AOs are there too.

How to approach these problems

Each problem is shown in the form of a video (though the set can also be downloaded as a PowerPoint – see here). You should keep the Pause button within easy reach at all times! All the content is presented visually so you don’t need to have the sound turned on, unless you enjoy a chirpy soundtrack!

First, reveal the problem and pause the video. If it involves a diagram then you might want to sketch it. Think about how you might approach the problem, and try to make a start:

  • What maths do you know that might help you to solve the problem?
  • What information are you given, and what can you work out from that?
  • Will it help you, or do you need to consider a different approach?

When you’ve done as much as you can on your own, reveal the hints, always pausing after each one and trying to get a bit further on your own before you reveal the next hint. If you’re revealing hints that prompt you to do something you’ve already done then that’s a good sign!

Problems for GCSE Maths students - try not to peek until you really need to!

Do as much as you can and then advance to the solution section.

Again, pause the video after each line is revealed. Compare each line with what you’ve done and see if you can take your own solution any further before you reveal the next line.

The more you manage to do by yourself, the more satisfying it will be when you reach the solution!

Problem 1: The repetitious number

This one requires only Foundation skills. It’ll be quicker if you use a calculator, but it’s doable without. The video also includes an introduction to the series.

Problem 2: Big powers

Only requires Foundation skills. No calculator needed (though you might find one helpful).

Problem 3: Missile collision

Again, only Foundation skills needed, and you should be able to do it without a calculator.

Problem 4: How many tests?

Another one requiring only Foundation skills and no calculator.

Problem 5: Camp dinner

Again, just Foundation skills and no calculator needed.

Problem 6: Square peg, round hole

A strong Foundation student might just about manage this one but it’s more suitable for those doing Higher Tier. No need for a calculator.

Problem 7: Farmer’s pens challenge

Higher skills are needed for this problem, and you will also need a calculator.

Problem 8: Circle in triangle

You’ll need to use some Higher skills for this one – and even then it’s quite challenging. Can be done without a calculator.

Problem 9: Surds challenge

Higher skills required. No calculator needed.

Problem 10: Shared area of two circles

This one’s really tricky! Higher skills and a calculator required.

Which problem was your favourite? Please comment below!

PowerPoint version

The full set of 10 problems is also available for free download in PowerPoint format from TES Resources. Each problem is over two slides, with the first slide giving hints and the second giving the solution. The hints and solutions are all animated so that they are only revealed a line/paragraph at a time, as in the videos. They could be used in class or uploaded onto a VLE for keen students to use for extra challenge.

Please also take a look at my other resources while you’re there!


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For more advice and resources on preparing for your exams, take a look at my blog posts on how to revise GCSE Maths and exam skills for GCSE Maths. Although the focus is on GCSE, a lot of the content is relevant for exams at any level.

To find out more about how B28 Maths Tutor can help you to achieve your goals, take a look at my Maths Help page.

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