Cambridge O Level Additional Maths Tutors Online

Cambridge O Level Additional Mathematics is syllabus 4037. This page works from the syllabus for exams in 2025, 2026 and 2027, version 1. Exams are available in the June and November series.

This is not a second version of O Level Mathematics. The syllabus states that knowledge of the content of Cambridge O Level Mathematics, or an equivalent syllabus, is assumed. So it is taken alongside or after the standard Mathematics course, and it assumes that course has already been done.

All candidates take two components, and all candidates are eligible for grades A* to E. The grade range stops at E, and anything below it is ungraded. There is no Core and Extended tier, because the whole syllabus is the demanding content. Every candidate studies all fourteen topics.

Paper 1 is the non-calculator paper. It lasts 2 hours, carries 80 marks and is worth 50% of the qualification, and it consists of structured and unstructured questions. Use of a calculator is not allowed.

Paper 2 is the calculator paper. It also lasts 2 hours and carries 80 marks and 50%, and it consists of structured and unstructured questions. Candidates should have a scientific calculator for this paper.

The two papers are identical in length and marks, and the only difference is the calculator. That makes the non-calculator paper a genuine skill in its own right rather than a formality, and at this level it means working fluently with logarithms, radians, surds and exact values by hand.

There is a piece of good news before revising: a List of formulas is provided on page 2 of the examination papers for candidates to refer to during the examination. The syllabus also confirms that proofs of results will not be required unless specifically mentioned, and that candidates are expected to be familiar with the scientific notation for compound units, such as metres per second written with a negative index.

There is also a subtle warning about assumed knowledge. The syllabus says that O Level material which is not included in this subject content, such as surds and indices, will not be tested directly, but that it may be required in response to questions on other topics. So a student cannot leave that material behind, even though it is not examined on its own.

The subject content is organised into fourteen 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.

The content inside those topics shows the level. Functions covers the terms function, domain and range, function notation, the relationship between a function and its inverse, explaining in words why a function does or does not have an inverse, finding the inverse of a one-one function with correct notation, forming and using composite functions with the order of functions understood, and sketch graphs showing the relationship between a function and its inverse. Quadratic functions covers maximum and minimum values, using them, the conditions for the equation to have particular kinds of roots through the discriminant, solving quadratic equations for real roots, and quadratic inequalities with solutions written in the correct form.

Factors of polynomials covers the remainder and factor theorems, finding factors, and solving cubic equations. Equations, inequalities and graphs covers solving equations of particular types, solving inequalities graphically or algebraically, substitution to form and solve a quadratic, sketching cubic polynomials, and cubic inequalities. Simultaneous equations covers solving them in two variables.

The logarithmic and exponential functions topic covers the properties and graphs, the laws of logarithms, and solving equations where a base is raised to an unknown power. The remaining topics take a student well beyond the standard O Level course: straight-line graphs, coordinate geometry of the circle, circular measure in radians, trigonometry, permutations and combinations, series, vectors in two dimensions, and calculus. Calculus is the clearest sign of the level here.

The syllabus notes that the subject content is organised by topic and is not presented in a teaching order, so schools plan their own sequence, and that learners are expected to use the listed techniques to solve problems with or without a calculator as appropriate. It also notes that this O Level syllabus shares content with other mathematics syllabuses, which is worth knowing if a student is moving between qualifications.

The assessment objectives are two. AO1 is knowledge and understanding of mathematical techniques, covering recalling and applying knowledge, carrying out routine procedures in mathematical and abstract situations, using notation and terminology, performing calculations with and without a calculator, organising and presenting information in written form, tables, graphs and diagrams, working to appropriate degrees of accuracy, and recognising and using spatial relationships in two and three dimensions. AO2 is analyse, interpret and communicate mathematically.

The weightings are given as ranges rather than fixed figures. AO1 is 45 to 55 per cent and AO2 is 45 to 55 per cent of the qualification, and the per component tables are the same for both papers. So the two objectives are deliberately balanced, and neither paper is weighted towards recall or towards problem solving.

The qualification is graded A*, A, B, C, D or E, with A* the highest and E the lowest. A candidate whose performance does not meet the standard required for grade E is ungraded, which is reported on the statement of results but not on the certificate.