The Additional Mathematics syllabus divides into algebra, geometry and trigonometry, and calculus. Calculus carries the largest share of marks in most papers, but algebra is the foundation every calculus question is wrapped in. Algebra rarely dominates a paper on its own but appears inside almost every calculus and trigonometry question.
This is a topic map of Additional Mathematics for parents who want to understand what their child is actually working through, and which parts carry the most weight.
It is written for parents who want to see the shape of the subject rather than to teach it. Knowing roughly what sits where makes two things possible: judging whether a reported difficulty is local or structural, and having a more useful conversation with the subject teacher than “how is she doing”.
Weightings vary by paper and are published by SEAB, so treat the emphasis below as our teaching experience rather than an official allocation.
Algebra
Quadratic functions and equations, surds and indices, polynomials and partial fractions, binomial expansions, exponential and logarithmic functions, simultaneous equations involving one quadratic.
The reason algebra is listed first despite rarely dominating a paper is that it is load-bearing. It appears inside the calculus questions, inside the trigonometry questions, and inside the coordinate geometry questions. A student who is slow here loses marks in topics they genuinely understand, which is both the most common and the most fixable pattern in the whole subject.
Weight: moderate directly, very high indirectly. Algebra rarely dominates a paper on its own, but it appears inside almost every other question.
Geometry and trigonometry
Trigonometric functions, identities and equations, coordinate geometry including circles, and proofs in plane geometry.
Weight: substantial. Trigonometric identities are the most common single source of difficulty, usually because students memorise rather than derive.
Calculus
Differentiation including product, quotient and chain rules; applications to gradients, tangents and normals, rates of change, and maxima and minima; integration including definite integrals, areas under curves, and kinematics.
Weight: the largest share in most papers, and the part most students find genuinely new.
Free practice material. Our past-year exam papers are free to download, with worked video solutions. No sign-up required.
Priority order when time is limited
If revision time is limited, in this order:
- Algebraic fluency — because it gates everything else
- Differentiation and its applications — highest mark density
- Trigonometric identities — learn two, derive the rest
- Integration and areas — procedurally reliable once the technique is secure
- Coordinate geometry of circles — self-contained and readily recoverable
Our A-Math programme follows roughly this priority, and the Sec 4 A-Math online course lets students work specific topics in isolation.
Prefer to learn at home? The online course for this level follows the same syllabus and the same sequence we teach in class, with worked video solutions your child can replay as often as they need. There is a free sample video for every level from Secondary 1 to JC2 if you would like to see the teaching first. There is a free sample video for every level from Secondary 1 to JC2 if you would like to see the teaching first. You can also join us in person at our Eunos centre.
A-Math calculus is the starting point for H2
Directly and substantially. H2 Mathematics in junior college assumes A-Math calculus as a starting point and extends it considerably. Students who finish A-Math with shaky differentiation find JC1 unforgiving.
This is worth knowing during Secondary 4 rather than discovering in JC1: the calculus done now is not merely for the O-Level. The junior college pages set out what follows.
The identities are taught as a list, and lists go blank
Because they are usually presented as a list to memorise. A list of nine results is a heavy load, and under examination pressure lists go blank.
Almost all of them derive from two: the Pythagorean identity and the addition formulae. A student who can derive rather than recall carries far less into the hall and, crucially, can rebuild an identity they have forgotten instead of losing the question.
This single change in approach accounts for a large share of the improvement we see in Secondary 3 students who arrive struggling with trigonometry.
How much practice it actually needs
More than E-Math, and the reason is worth understanding. A-Math rewards fluency built through varied repetition — seeing the same technique in enough different disguises that recognition becomes automatic.
For most students that means around two to three focused hours weekly, spread across sessions rather than concentrated. Fluency responds to spacing; it does not respond well to one long session at the weekend.
Read next
For why students find this subject difficult, see O-Level A-Math and why it feels different. For the choice that led to it, E-Math versus A-Math. For the year it starts, Secondary 3, and for where the calculus leads, H2 Mathematics. If you are still choosing a school, our list of secondary schools in Singapore covers each school’s programmes, streams and strengths.
Frequently asked questions
Which A-Math topic carries the most marks?
Calculus generally carries the largest share across the papers, particularly differentiation and its applications. Exact weightings vary by paper and are published by SEAB.
Is A-Math useful if my child will not study mathematics later?
It develops abstraction and sustained reasoning that transfer reasonably well. But if the pathway does not need it and it is displacing effort from subjects that do, that trade-off is worth weighing honestly.
Which A-Math topics should we prioritise with limited time?
Algebraic fluency first, because it gates everything else. Then differentiation and its applications, which carry the highest mark density. Then trigonometric identities, integration and areas, and finally coordinate geometry of circles, which is self-contained and readily recoverable.
Can a student pass A-Math with weak algebra?
It is difficult. Algebra appears inside most calculus and trigonometry questions, so a student slow at manipulation loses marks in topics they otherwise understand. Rebuilding algebra usually lifts several topics at once, which is why it comes first in any recovery plan.
How does A-Math prepare a student for H2 Mathematics?
Directly. H2 Mathematics assumes A-Math calculus as a starting point and extends it considerably. Students who finish A-Math with shaky differentiation find JC1 unforgiving, which is worth knowing during Secondary 4 rather than discovering afterwards.
Are there topics that rarely appear in the examination?
Weightings vary by paper and are published by SEAB, so it is worth checking their documents rather than relying on informal advice about what to skip. In practice, students who gamble on omitting a topic tend to meet it in the one year it appears prominently.
A note on what we can and cannot promise: the patterns described here come from what we have seen in our own classes over the years. They are not a forecast for any individual student. Progress in mathematics is produced jointly — our teachers work hard for a student who is willing to put in the effort, with support at home. No tuition centre can promise a grade, and we do not.
Last reviewed July 2026. Syllabus details follow the Ministry of Education and SEAB published documents.
