Cambridge O Level Additional Mathematics (4037)
Calculus, logarithms, vectors and trigonometry a year or two early — Additional Maths is the bridge from O Level to A Level, and a favourite of future engineers, doctors and coders.
Checked against the official Cambridge syllabus for exams in 2025, 2026 and 2027 — and unchanged in substance for 2028–2030 · 18 October 2026
1.Quick facts
2.Why study Additional Mathematics?
Cambridge's aims for this course, in plain words. It helps you to:
- Build on the maths you already know and go further.
- Develop a mathematician's curiosity and use it flexibly.
- Tackle harder, multi-step problems with creativity and resilience.
- Become fluent and confident with techniques, with and without a calculator.
- Justify your reasoning with clear, structured arguments.
- Build a solid foundation for A Level Mathematics and other highly numerate subjects.
Based on the 'Aims' in the official syllabus.
3.Why these topics?
Functions and polynomials
Functions are machines that turn inputs into outputs; quadratics model the path of a ball; the factor theorem cracks open cubics. This is the algebra A Level is built on.
Logs and exponentials
Logarithms turn huge growth into straight lines — they measure earthquakes, sound and acidity, and they let you solve equations where the unknown is a power.
Geometry with algebra
Straight lines, circles, radians, trigonometric identities and vectors — the toolkit for engineering drawings, robotics and computer graphics.
Counting and series
How many passwords or team line-ups are possible? Permutations and combinations answer it. Series and the binomial expansion describe patterns that grow.
Calculus
The maths of change — finding the steepest point, the maximum profit, the speed of a moving object, and the area under a curve. Newton and Leibniz's idea that powers modern physics and economics.
4.Topic map
5.Maths → Add Maths → A Level
Additional Maths sits between O Level Mathematics (4024) and A Level Mathematics (9709). Much of it reappears in A Level Pure Mathematics 1.
| Idea | At O Level Mathematics (4024) | In Additional Mathematics (this course) |
|---|---|---|
| Algebra | Linear and quadratic equations | Polynomials, factor and remainder theorems, modulus functions |
| Graphs | Gradient of a straight line | Gradient of a curve by differentiation; area by integration |
| Trigonometry | Degrees, triangles | Radians, identities, trig equations and graphs |
| Growth | Exponential growth and decay | Laws of logarithms, solving exponential equations |
| Counting | Simple probability | Permutations, combinations, binomial expansion |
6.Exam pattern
Both papers are marked by Cambridge.
7.Types of questions
Examples are written by our teachers in Cambridge style to show the type of question — they are not copied from past papers.
8.Command words
| Word | Cambridge meaning | What to do |
|---|---|---|
| Show (that) | provide structured evidence that leads to a given result | Show every line; never skip to the given answer. |
| Verify | confirm a given statement/result is true | Substitute and check — conclude clearly. |
| Determine | establish with certainty | Justify fully (e.g. the nature of a stationary point). |
| Sketch | make a simple freehand drawing showing the key features | Intercepts, turning points, asymptotes. |
| Calculate | work out from given facts, figures or information | Clear working; exact or 3 s.f. as asked. |
| Write down | give an answer without significant working | One step — usually an easy mark. |
Meanings are quoted from the 'Command words' table in the official syllabus.
9.What examiners reward
About half the marks are for reasoning and problem-solving — learn methods, then practise mixed questions.
10.Grades
A*, A, B, C, D, E. 'Ungraded' means below E and is not shown on the certificate.
What it took in June 2026
| Grade | Marks out of 160 | Roughly |
|---|---|---|
| A* | 138–141 | about 86–88% |
| A | 117–122 | about 73–76% |
| B | 88–92 | about 55–57% |
| C | 59–62 | about 37–39% |
| D | 46–49 | about 29–31% |
| E | 33–36 | about 21–22% |
Minimum marks out of 160 in June 2026 (the range covers the different paper variants).
A good Additional Maths grade shows universities you can handle A Level-style mathematics early.
11.Exam toolkit
- Paper 1 has no calculator: practise exact values (surds, π, trig ratios of special angles) and log laws by hand.
- A List of formulas is printed in the papers — know where everything is so you don't waste time.
- Work in radians for calculus and circular measure unless told otherwise.
- Write each step on a new line; examiners award method marks for correct working.
- Check answers by substituting back — a great habit for 'verify' and 'show that'.
12.Books & resources
Cambridge's syllabus says textbooks endorsed for IGCSE Additional Mathematics are also suitable for this course.
13.Common mistakes
- Using degrees when the question is in radians.
- Breaking log laws — log(a + b) is not log a + log b.
- Forgetting the constant of integration, or the ± when square-rooting.
- Losing a solution when dividing both sides by an expression that could be zero.
- Not stating the nature (maximum or minimum) of a stationary point when asked.
Tips from our teachers.
14.Study plan
- StartMake sure O Level Maths algebra, indices and surds are secure — they are assumed.
- Block 1Functions, quadratics, polynomials, equations and inequalities (1–5).
- Block 2Logarithms and exponentials, straight lines and circles (6–8).
- Block 3Circular measure and trigonometry (9–10); permutations, combinations, series (11–12).
- Block 4Vectors (13) and calculus (14) — the largest and most rewarding topic.
- Final monthsTimed Paper 1 and Paper 2 practice every week; mixed-topic problems.
Cambridge designs the course for about 130 guided learning hours. Many students take it alongside O Level Mathematics.
15.Where it can take you
Additional Maths gives you a head start for the most maths-heavy degrees.
Typical subject requirements — always check each university's own entry rules.
16.Additional Mathematics in the real world
Al-Khwarizmi
His 9th-century book on solving equations gave us the word 'algebra' — Topics 2–5 are his legacy.
Logarithms in nature
Earthquake magnitude, sound in decibels and pH all use logarithmic scales — one step means ten times more.
Calculus in action
Engineers use differentiation to find maximum strength or minimum cost; integration gives areas and distances travelled.
Counting and security
Permutations tell you how many passwords are possible — and why longer passwords are so much safer.
17.Frequently asked questions
Do I need O Level Mathematics first?
Cambridge assumes you know the content of O Level / IGCSE Mathematics, including indices and surds. Many students take both together.
Is Additional Maths hard?
It's more demanding than O Level Maths — the A* boundary in June 2026 was about 86–88%. Regular practice makes the difference.
Do I need it for A Level Maths?
It isn't required, but students who have done it usually find AS Pure Mathematics much easier.
Calculator?
Not allowed in Paper 1; a scientific calculator is required for Paper 2.
Is the syllabus changing?
The 2028–2030 syllabus has no significant changes that affect teaching.
18.Study it with us
Live online classes with experienced Cambridge teachers, weekly quizzes and assignments in your portal, past-paper practice, and progress reports your parents can see.
19.Official sources
- Official syllabus 4037 for exams in 2025, 2026 and 2027 (PDF)
- Official syllabus 4037 for exams in 2028, 2029 and 2030 (PDF)
- Grade threshold table, June 2026 (PDF)
- Endorsed resources for 4037
Cambridge says its syllabuses and specimen materials are the final authority on the content and structure of its exams. Always check you are using the syllabus for the year you sit the exam.