Free resource · O-Level and SEC (G3)

O-Level E-Math Formula Sheet (4052): Free PDF

The O-Level E-Math paper prints a short list of formulae: compound interest, the cone and sphere formulas, the area of a triangle using sine, arc length and sector area in radians, the sine and cosine rules, and the mean and standard deviation. Everything else, including the quadratic formula and Pythagoras' theorem, has to be memorised.

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

Printed in the paper

Formulae the O-Level E-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.

Compound interest

Total amount: $P (1 + \frac{r}{100})^{n}$

Mensuration

Curved surface area of a cone: $π r l$
Surface area of a sphere: $4 π r^{2}$

Volume of a cone: $\frac{1}{3} π r^{2} h$
Volume of a sphere: $\frac{4}{3} π r^{3}$
Area of triangle ABC: $\frac{1}{2} ab sin C$
Arc lengthwhere θ is in radians: $r θ$
Sector areawhere θ is in radians: $\frac{1}{2} r^{2} θ$

Trigonometry

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

a^{2} = b^{2} + c^{2} - 2 b c cos A

Statistics

Mean: $\frac{\sum f x}{\sum f}$

Standard deviation: $\frac{\sum f x ^{2}}{\sum f} - (\frac{\sum f x}{\sum f})^{2}$

Not printed, memorise

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

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

Number and algebra

Simple interest: $I = \frac{P R T}{100}$
Percentage change: $\frac{new - original}{original} \times 100%$

Quadratic formulanot printed in the E-Math paper: $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
Laws of indices: $a^{m} \times a^{n} = a^{m + n}, a^{m} \div a^{n} = a^{m - n}, (a^{m})^{n} = a^{mn}$
Zero, negative and fractional indices: $a^{0} = 1, a^{- n} = \frac{1}{a ^{n}}, a^{\frac{1}{n}} = n a$
Special products: $(a + b)^{2} = a^{2} + 2 ab + b^{2}, (a - b)^{2} = a^{2} - 2 ab + b^{2}, a^{2} - b^{2} = (a + b) (a - b)$
Direct and inverse proportion: $y = k x, y = \frac{k}{x}$
Average speed: $\frac{total distance}{total time}$
Speed-time graphs: $gradient = acceleration, area under the graph = distance travelled$

Geometry and measurement

Pythagoras' theorem: $a^{2} + b^{2} = c^{2}$

Trigonometric ratios: $sin θ = \frac{opp}{hyp}, cos θ = \frac{adj}{hyp}, tan θ = \frac{opp}{adj}$
Obtuse angles: $sin (18 0^{\circ} - A) = sin A, cos (18 0^{\circ} - A) = - cos A$
Area of a parallelogram and a trapezium: $bh, \frac{1}{2} (a + b) h$
Circle: $area = π r^{2}, circumference = 2 π r$
Volume of a prism or cylinder: $base area \times height, V = π r^{2} h$
Volume of a pyramid: $\frac{1}{3} \times base area \times height$
Surface area of a cylinder: $curved = 2 π r h, total = 2 π r^{2} + 2 π r h$
Total surface area of a cone: $π r l + π r^{2}$
Area of a segmentθ in radians: $\frac{1}{2} r^{2} θ - \frac{1}{2} r^{2} sin θ$
Radians and degrees: $π rad = 18 0^{\circ}$
Angles of an n-sided polygon: $interior sum = (n - 2) \times 18 0^{\circ}, exterior sum = 36 0^{\circ}$
Similar figures: $\frac{A _{1}}{A _{2}} = (\frac{l _{1}}{l _{2}})^{2}, \frac{V _{1}}{V _{2}} = (\frac{l _{1}}{l _{2}})^{3}$
Gradient and length of a line segment: $m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}, d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$
Equation of a straight line: $y = m x + c$
Magnitude of a vector: $(x y) = x^{2} + y^{2}$

Statistics and probability

Interquartile range: $Q_{3} - Q_{1}$

Probability: $P (A) = \frac{number of favourable outcomes}{total number of outcomes}, P (A^{'}) = 1 - P (A)$
Mutually exclusive events: $P (A or B) = P (A) + P (B)$
Independent events: $P (A and B) = P (A) \times P (B)$

Inside the PDF

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

Questions students ask

Is the quadratic formula given in the O-Level E-Math paper?

No. The E-Math list of formulae does not include the quadratic formula, so you must know x = (−b ± √(b² − 4ac)) ÷ 2a by heart. It is printed only in the A-Math paper.

Is the formula sheet the same for the 2027 SEC (G3) Mathematics paper?

Yes. The SEC G3 Mathematics syllabus K310 for 2027 prints the same list of formulae as the final O-Level syllabus 4052, so this sheet works for both.

Do I get the formula for the volume of a pyramid?

No. Only the cone and sphere formulas are printed. The volume of a pyramid, one third of the base area times the height, has to be memorised, together with the areas of a trapezium and a circle.

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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