O-Level A-Math Formula Sheet: What You're Given and What to Memorise

Every year, students lose marks in A-Math not because they can't do the question, but because they assumed a formula would be given. The formula list covers algebra and trigonometry only. Everything in calculus and coordinate geometry has to come from memory.

O-Level A-Math becomes SEC G3 A-Math in 2027

From 2027, SEAB says the GCE N(T), N(A) and O-Levels "will be combined and renamed as the Singapore-Cambridge Secondary Education Certificate (SEC)", with subjects taken at G1, G2 or G3. Additional Mathematics is a G3 subject with the new syllabus code K341, replacing 4049.

We compared SEAB's 2026 O-Level syllabus (4049) and its 2027 SEC syllabus (K341) line by line. The formula list, the exam format, the calculator rules and the topic content are identical. Only the names change. So if you are sitting the exam in 2027 and searching for the "O-Level A-Math formula sheet", everything below applies to you.

The formulae given in the exam

This is the full list printed under "Mathematical Formulae" in the syllabus and the exam paper.

Algebra

Trigonometry: identities

Trigonometry: formulae for triangle ABC

That's everything. There is nothing for calculus, logarithms, coordinate geometry, the R-formula or partial fractions.

What you must memorise

Each item below is named in the syllabus content but is not on the formula list. The topic codes match the K341 and 4049 syllabus.

Quadratic functions and inequalities (A1, A2)

• Completing the square to find the maximum or minimum value of a quadratic.
• The conditions for $y = ax^2 + bx + c$ to be always positive or always negative.
• The discriminant conditions for two real roots, two equal roots and no real roots, and for a line to intersect, touch or miss a curve. The formula list gives you the quadratic formula, but not these conditions.

Polynomials and partial fractions (A4)

• Sum and difference of cubes: $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$ and $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$.
• The remainder and factor theorems.
• The partial fraction forms for denominators $(ax+b)(cx+d)$, $(ax+b)(cx+d)^2$ and $(ax+b)(x^2+c^2)$.

Binomial expansions (A5)

• Using the general term $\binom{n}{r}a^{n-r}b^r$ to find a specific term. It appears inside the expansion on the formula list but isn't labelled, so know how to use it.

Exponential and logarithmic functions (A6)

• The laws of logarithms.
• The equivalence of $y = a^x$ and $x = \log_a y$.
• Change of base of logarithms.

Trigonometry (G1)

• The ratio identities $\tan A = \dfrac{\sin A}{\cos A}$ and $\cot A = \dfrac{\cos A}{\sin A}$.
• Exact values for 30°, 45° and 60° (or $\tfrac{\pi}{6}, \tfrac{\pi}{4}, \tfrac{\pi}{3}$).
• The R-formula: expressing $a\cos\theta + b\sin\theta$ as $R\cos(\theta \pm \alpha)$ or $R\sin(\theta \pm \alpha)$.
• Principal values of $\sin^{-1}x$, $\cos^{-1}x$ and $\tan^{-1}x$, and the amplitude, period and symmetries of sine and cosine graphs.

Coordinate geometry (G2)

• Conditions for two lines to be parallel or perpendicular, and the midpoint of a line segment.
• The area of a rectilinear figure.
• Both forms of the circle equation: $(x-a)^2 + (y-b)^2 = r^2$ and $x^2 + y^2 + 2gx + 2fy + c = 0$. You need to read off the centre and radius from each.
• Converting relationships such as $y = ax^n$ and $y = kb^x$ to linear form (linear law).

Proofs in plane geometry (G3)

• Properties of parallel lines, perpendicular and angle bisectors, triangles, special quadrilaterals and circles; congruent and similar triangles; the midpoint theorem; and the tangent-chord (alternate segment) theorem.

Differentiation and integration (C1)

None of calculus is on the formula list. The syllabus expects you to know:

Exam format

The syllabus also sets out a few rules worth knowing before the exam:

• An approved calculator is allowed in both papers.
• Omitting essential working loses marks. Show the method, not just the answer.
• Give non-exact answers to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
• Use your calculator's value of π, or 3.142, unless the answer is required in terms of π.
• G3 (or O-Level) Mathematics content is assumed knowledge. It isn't tested directly but may be needed inside A-Math questions.

Thinking ahead to JC

A-Math is the foundation for H2 Math, and H2 Math is a prerequisite for engineering, data science and several computing and business analytics courses. If you're weighing up JC subjects, our guide to JC subject combinations lists which university courses need it.

Get help with A-Math

You can also see MACRO's upper secondary A-Math programme.

FAQs

What formulas are given in the O-Level A-Math exam?

The quadratic formula, the binomial expansion and binomial coefficient, nine trigonometric identities (Pythagorean, addition and double angle), and three formulae for triangle ABC: the sine rule, the cosine rule and the area formula.

Are differentiation and integration formulas given?

No. None of the calculus content is on the formula list. You must memorise the standard derivatives and integrals, and the product, quotient and chain rules.

Is the R-formula given in A-Math?

No. The syllabus requires you to express a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α), but the method isn't on the formula list.

Is the formula sheet different for the 2027 SEC exam?

No. SEC G3 Additional Mathematics (K341) has the same formula list, exam format and content as O-Level Additional Mathematics (4049). Only the name and syllabus code change.

Can I use a calculator in both A-Math papers?

Yes. The syllabus says an approved calculator may be used in both Paper 1 and Paper 2.