Additional Maths or Further Pure Maths: what they are and who takes them

Cambridge O Level Additional Mathematics (4037) and Edexcel International GCSE Further Pure Mathematics (4PM1) are both extra maths subjects. Both go beyond a main maths course into harder algebra, logarithms, trigonometry, series and calculus.

They are not the same qualification under two names. 4037 comes from Cambridge and 4PM1 from Pearson Edexcel. The papers, the marks and the calculator rules are different, so the practice has to match the code.

4PM1 is usually taken alongside Edexcel Mathematics A or Mathematics B. For 4037, ask the school how it fits with the main maths course. Either way, the school decides what it offers and enters students for, so start there.

Additional Mathematics 4037

The syllabus has 14 topics: functions; quadratic functions; factors of polynomials; equations, inequalities and graphs; simultaneous equations; logarithmic and exponential functions; straight-line graphs; coordinate geometry of the circle; circular measure; trigonometry; permutations and combinations; series; vectors in two dimensions; and calculus.

Further Pure Mathematics 4PM1

The specification covers logarithms, indices and surds; the quadratic function and the roots of a quadratic; identities and inequalities, with the factor and remainder theorems; graphs; arithmetic and geometric series; the binomial series; vectors; coordinate geometry; calculus, including kinematics, areas, volumes and rates of change; and trigonometry, from radians to the addition formulae and trigonometric equations.

The two lists overlap a good deal, but the topics are arranged and weighted differently. Read the full content of each syllabus before choosing, not just the topic names.

Neither has multiple choice. In both, the working earns marks, so a clearly set-out solution counts.

This is the clearest difference. Since the 2025 exams, 4037 Paper 1 is sat without a calculator. So half of the 4037 marks depend on working by hand: simplifying surds, using the laws of logarithms, knowing exact trigonometric values and handling fractions and algebra without a machine to check them.

4PM1 allows a calculator on both papers. That does not make it easy. The working still has to be shown, and a calculator cannot set out a proof or choose a method. But the arithmetic on the day is lighter.

Anyone sitting 4037 should practise Paper 1 questions without a calculator from the start, not only in the final weeks.

An extra maths subject suits a student who is secure in their main maths course and enjoys it. Both build on the algebra of the main course, so that algebra needs to be fluent. If the main course still feels hard, it usually makes more sense to get that secure first.

It is also a real workload: two more 2-hour papers, on top of the main maths papers and every other subject. Before starting, be honest about how many hours a week it will take and what else would have to give.

Whether it helps with later study, such as A Level Mathematics, depends on the school or college the student moves on to. Ask them directly.

• Which extra maths does the school offer and enter students for?
• Which board is my child's main maths course with? Knowing the code, such as 4024, 4MA1 or 4MB1, tells you which side you are on.
• Will it be taught in school hours, or prepared for alone?
• Does the sixth form or college being aimed for ask for it? Ask them rather than relying on what others have heard.
• For 4037: is working without a calculator comfortable? A few non-calculator questions will show you quickly.

Eudika Learn has a recorded course for each.

• Additional Mathematics 4037 teaches all 14 syllabus topics in Cambridge's order, with the methods worked by hand for the non-calculator Paper 1 and a short check at the end of each topic. See Cambridge O Level courses.
• Further Pure Mathematics 4PM1 teaches the specification in Pearson's order, then gives real 4PM1 past-paper questions by topic. You write the working, then tick each method and accuracy mark against the mark scheme. See Edexcel International GCSE courses.

Both courses are recorded, with no live teacher. If you need someone to talk a method through, keep a teacher or tutor for that. You can also look at Mathematics B past papers to see how the main Edexcel course asks its questions.