NOTES · IP MATHS
IP Maths and H2: the A Math topics H2 Mathematics assumes
Method & Mark ·
Integrated Programme students go from Year 4 to junior college without sitting the O-Level. The H2 Mathematics syllabus (9758) does not start from zero, though. It states that knowledge of O-Level Mathematics is assumed, and it appends a list of O-Level Additional Mathematics content that is assumed too. For an IP student, that list is the nearest thing to an O-Level: the topics JC teachers will expect to be secure in the first term.
What H2 Mathematics assumes from A Math
| Topic | What is assumed |
|---|---|
| Quadratic functions; equations and inequalities | Completing the square for a maximum or minimum; conditions for two real, two equal or no real roots; when ax² + bx + c is always positive or negative; simultaneous equations with one linear |
| Surds | Four operations, rationalising the denominator, solving equations with surds |
| Polynomials and partial fractions | Multiplying and dividing polynomials; remainder and factor theorems; partial fractions with linear, repeated linear and quadratic factors |
| Exponential and logarithmic functions | aˣ, eˣ, logₐ x and ln x and their graphs; laws of logarithms; change of base; solving simple equations |
| Coordinate geometry | The equation of a circle, in both standard forms |
| Trigonometry | The six trigonometric functions; principal values of the inverses of sine, cosine and tangent; identities and equations; a cos θ + b sin θ as R sin(θ ± α) or R cos(θ ± α) |
| Differentiation and integration | Derivatives of xⁿ, sin x, cos x, tan x, eˣ and ln x; chain, product and quotient rules; stationary points and the second derivative test; connected rates of change; integration as the reverse of differentiation |
This is a summary of the list headed “Assumed knowledge: content from O-Level Additional Mathematics” in the 2026 syllabus. The full wording is in the syllabus itself.
What the list leaves out
The assumed list is not the whole of A Math. It does not include, for example, the binomial theorem or proofs in plane geometry. An IP scheme that spends less time on those is not leaving a gap for H2; one that skips partial fractions or the R-formula is.
Checking an IP scheme against it
- Ask for the Year 3 and Year 4 scheme of work. Each IP school writes its own, and the order varies.
- Tick each row above. Look for where each topic is taught, not only whether it appears.
- Watch the late topics. Items taught at the end of Year 4 get the least practice before JC. Those are the ones to revise over the holidays.
Source: the Content Outline and Assumed Knowledge sections of the SEAB A-Level H2 Mathematics 9758 syllabus (2026). For how we teach IP students, see IP Maths tuition.