Is grade 5 on Foundation or Higher?

Both. Grade 5 is the highest grade on Foundation and the second-lowest on Higher, so these 34 topics can be examined on either paper. On Foundation they tend to be the last questions; on Higher they are the first third.

What is the difference between a grade 4 and a grade 5?

Mostly the number of steps. A grade 4 question usually asks for one method: find a percentage, solve an equation, find the hypotenuse. A grade 5 question chains two or three: a reverse percentage inside a ratio problem, a quadratic that has to be factorised and then solved, a trigonometry question that needs an angle rather than a side. The sheets here are built to practise the chains.

How many grade 5 topics do I need to be secure?

All of them, ideally, but the ones that come up most are reverse percentages, compound interest, expanding and factorising quadratics, simultaneous equations, trigonometry (both sides and angles) and tree diagrams. Get those eight green first, then fill in the rest.

Can I use these sheets for a resit?

Yes. Post-16 resit students sit the same Foundation paper, and grade 4 and grade 5 topics are exactly where resit marks are won. Start with the grade 4 weekly check to find the gaps, then work through the grade 5 topics on this page.

Free GCSE maths · grade 5

GCSE maths grade 5 worksheets

Free worksheets for every GCSE maths grade 5 topic: 34 sheets of original exam-style questions, each with an answers sheet and solutions written out by hand. Print them or answer online. No account needed.

Grade 5 is the "strong pass": the top of Foundation, the floor of Higher, and the grade many sixth forms and apprenticeships ask for. It is also the grade where the questions stop being one step. Reverse percentages, expanding double brackets, simultaneous equations and trigonometry all arrive at grade 5, and each needs a method held in the head for three or four lines. The 34 grade 5 topics from our GCSE maths library are listed below, every one with 10 original questions, an answers sheet and a hand-written solutions sheet.

Grade 5 topics are examined on both tiers, so this page is for a Foundation student aiming for the top of the paper and a Higher student making sure the base is solid.

All 34 grade 5 topics

The library's full grade 5 list, grouped by strand. Number and algebra are the biggest groups and carry the most marks.

Number

Algebra

Ratio, proportion and rates

Geometry

Probability and statistics

Open grade 5 in the library My RAG sheet

How to use the worksheets

Print it. Every topic has three PDFs: the worksheet, an answers sheet for quick marking, and a solutions sheet with every step written out by hand. Print the worksheet first and keep the solutions back until all the questions have been attempted.

Or answer online. Open the topic page, type each answer into the box and check it. The page marks it straight away and keeps your best score in this browser. Score 80% or more and the topic is ticked as done on the GCSE library; you can also tick a topic by hand once you are happy with it.

Use the solutions properly. The solutions are hand-written, one step per line, the way a tutor writes next to a student. If an answer is wrong, cover the solution, find the first line that differs from your working and redo the question from there. Forty of the topics also open with a short method guide before the questions.

Keep a RAG sheet. The GCSE RAG sheet colours each topic red, amber or green from your scores. Work through the reds first, then the ambers, then use a weekly check sheet to prove the grade holds up when the topics are mixed.

The grade 5 check sheet. Once most of the topics above are green, print the grade 5 weekly check: 20 mixed questions, about 50 marks, with an answers sheet and hand-written solutions. A score of 40 or more out of 50 means the grade is holding up when the topics are mixed, which is the real test.

Frequently asked questions

Is grade 5 on Foundation or Higher?: Both. Grade 5 is the highest grade on Foundation and the second-lowest on Higher, so these 34 topics can be examined on either paper. On Foundation they tend to be the last questions; on Higher they are the first third.
What is the difference between a grade 4 and a grade 5?: Mostly the number of steps. A grade 4 question usually asks for one method: find a percentage, solve an equation, find the hypotenuse. A grade 5 question chains two or three: a reverse percentage inside a ratio problem, a quadratic that has to be factorised and then solved, a trigonometry question that needs an angle rather than a side. The sheets here are built to practise the chains.
How many grade 5 topics do I need to be secure?: All of them, ideally, but the ones that come up most are reverse percentages, compound interest, expanding and factorising quadratics, simultaneous equations, trigonometry (both sides and angles) and tree diagrams. Get those eight green first, then fill in the rest.
Can I use these sheets for a resit?: Yes. Post-16 resit students sit the same Foundation paper, and grade 4 and grade 5 topics are exactly where resit marks are won. Start with the grade 4 weekly check to find the gaps, then work through the grade 5 topics on this page.