Free resource · O-Level and SEC (G3)

O-Level A-Math Formula Sheet (4049): Free PDF

The O-Level A-Math paper prints the quadratic formula, the binomial expansion, the trigonometric identities including the addition and double angle formulae, and the sine rule, cosine rule and area of a triangle. It does not print any calculus results, laws of logarithms or circle equations, so those must be memorised.

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$First page of the O-Level A-Math Formula Sheet PDF$

Printed in the paper

Formulae the O-Level A-Math paper gives you

In the order SEAB prints them. You do not need to memorise these, but you do need to know when to use each one.

1. Algebra

Quadratic equationFor the equation ax² + bx + c = 0: $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$

Binomial expansion: $(a + b)^{n} = a^{n} + (1 n) a^{n - 1} b + (2 n) a^{n - 2} b^{2} + \dots + (r n) a^{n - r} b^{r} + \dots + b^{n}$
where n is a positive integer and: $(r n) = \frac{n !}{r ! ( n - r )!} = \frac{n ( n - 1 ) \dots ( n - r + 1 )}{r !}$

2. Trigonometry

Identities: $sin^{2} A + cos^{2} A = 1$; $sec^{2} A = 1 + tan^{2} A$

$cosec^{2} A = 1 + cot^{2} A$; $sin (A \pm B) = sin A cos B \pm cos A sin B$; $cos (A \pm B) = cos A cos B \mp sin A sin B$; $tan (A \pm B) = \frac{tan A \pm tan B}{1 \mp tan A tan B}$; $sin 2 A = 2 sin A cos A$; $cos 2 A = cos^{2} A - sin^{2} A = 2 cos^{2} A - 1 = 1 - 2 sin^{2} A$; $tan 2 A = \frac{2 tan A}{1 - tan ^{2} A}$
Formulae for △ABC: $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$; $a^{2} = b^{2} + c^{2} - 2 b c cos A$; $Δ = \frac{1}{2} b c sin A$

Not printed, memorise

Formulas the O-Level A-Math paper does not give you

The syllabus expects you to use these, but the paper does not print them.

Quadratics and polynomials

Nature of roots: $b^{2} - 4 a c > 0 two real distinct, = 0 equal, < 0 no real roots$

Line and curve: $substitute, then b^{2} - 4 a c > 0 meets at two points, = 0 tangent, < 0 no intersection$
Always positive: $a x^{2} + b x + c > 0 for all x ⟺ a > 0 and b^{2} - 4 a c < 0$
Remainder and factor theorems: $f (x) \div (x - a) leaves remainder f (a), f (a) = 0 ⟺ (x - a) is a factor$
Dividing by (ax − b): $remainder = f (\frac{b}{a})$
Sum and difference of cubes: $a^{3} \pm b^{3} = (a \pm b) (a^{2} \mp ab + b^{2})$
General term of a binomial expansion: $T_{r + 1} = (r n) a^{n - r} b^{r}$

Exponentials and logarithms

Definition: $a^{x} = b ⟺ x = lo g_{a} b$

Laws of logarithms: $lo g_{a} x y = lo g_{a} x + lo g_{a} y, lo g_{a} \frac{x}{y} = lo g_{a} x - lo g_{a} y, lo g_{a} x^{n} = n lo g_{a} x$
Change of base: $lo g_{a} b = \frac{lo g _{c} b}{lo g _{c} a}$

Coordinate geometry

Midpoint: $(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$
Parallel and perpendicular lines: $m_{1} = m_{2}, m_{1} m_{2} = - 1$

Equation of a circle: $(x - a)^{2} + (y - b)^{2} = r^{2}$
Area of a rectilinear figure (shoelace method)vertices taken in order around the figure: $\frac{1}{2} ∣ x_{1} y_{2} + x_{2} y_{3} + \dots + x_{n} y_{1} - y_{1} x_{2} - y_{2} x_{3} - \dots - y_{n} x_{1} ∣$
General form: $x^{2} + y^{2} + 2 g x + 2 f y + c = 0, centre (- g, - f), r = g^{2} + f^{2} - c$

Trigonometry

Quotient identity: $tan A = \frac{sin A}{cos A}$

Exact values: $sin 3 0^{\circ} = \frac{1}{2}, cos 3 0^{\circ} = \frac{3}{2}, tan 3 0^{\circ} = \frac{1}{3}, sin 4 5^{\circ} = cos 4 5^{\circ} = \frac{1}{2}, tan 4 5^{\circ} = 1, sin 6 0^{\circ} = \frac{3}{2}, cos 6 0^{\circ} = \frac{1}{2}, tan 6 0^{\circ} = 3$
Reciprocal ratios: $sec x = \frac{1}{cos x}, cosec x = \frac{1}{sin x}, cot x = \frac{1}{tan x}$
R-formula: $a sin θ \pm b cos θ = R sin (θ \pm α), R = a^{2} + b^{2}, tan α = \frac{b}{a}$; $a cos θ \pm b sin θ = R cos (θ \mp α), R = a^{2} + b^{2}, tan α = \frac{b}{a}$

Calculus

Standard derivatives: $\frac{d}{d x} x^{n} = n x^{n - 1}, \frac{d}{d x} sin x = cos x, \frac{d}{d x} cos x = - sin x, \frac{d}{d x} tan x = sec^{2} x$

$\frac{d}{d x} e^{x} = e^{x}, \frac{d}{d x} ln x = \frac{1}{x}$
Chain, product and quotient rules: $\frac{d y}{d x} = \frac{d y}{d u} \cdot \frac{d u}{d x}, (uv)^{'} = u v^{'} + v u^{'}, (\frac{u}{v})^{'} = \frac{v u ^{'} - u v ^{'}}{v ^{2}}$
Stationary points: $\frac{d y}{d x} = 0, \frac{d ^{2} y}{d x ^{2}} > 0 minimum, \frac{d ^{2} y}{d x ^{2}} < 0 maximum$
Connected rates of change: $\frac{d y}{d t} = \frac{d y}{d x} \times \frac{d x}{d t}$
Standard integrals: $\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + c (n \neq = - 1), \int e^{x} d x = e^{x} + c$; $\int sin x d x = - cos x + c, \int cos x d x = sin x + c, \int sec^{2} x d x = tan x + c$
Integrals of (ax + b): $\int (a x + b)^{n} d x = \frac{( a x + b ) ^{n + 1}}{a ( n + 1 )} + c (n \neq = - 1), \int e^{a x + b} d x = \frac{1}{a} e^{a x + b} + c$; $\int sin (a x + b) d x = - \frac{1}{a} cos (a x + b) + c, \int cos (a x + b) d x = \frac{1}{a} sin (a x + b) + c$
Area under a curve: $Area = \int_{a}^{b} y d x$
Kinematics: $v = \frac{d s}{d t}, a = \frac{d v}{d t}, s = \int v d t$

Inside the PDF

4 A4 pages, ready to print. Tap a page to open the PDF there.

Questions students ask

Are differentiation and integration formulas given in O-Level A-Math?

No. The A-Math list of formulae covers algebra and trigonometry only. The derivatives and integrals of xⁿ, sin x, cos x, tan x, eˣ and ln x, and the chain, product and quotient rules, all have to be memorised.

Is the A-Math formula list the same for the 2027 SEC (G3) paper?

Yes. The SEC G3 Additional Mathematics syllabus K341 for 2027 prints the same list of formulae as the final O-Level syllabus 4049.

Do I need to memorise the double angle formulae?

No. sin 2A, cos 2A in all three forms, and tan 2A are printed in the paper, together with the addition formulae. What you must know is when to use them, for example rewriting cos 2A as 1 − 2sin²A to form a quadratic in sin A.

Keep revising

Source

The exam paper itself is what counts on the day. If anything here differs from the SEAB document, the SEAB document is right. Tell us and we will fix it.

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