O-Level G3 Math Formula Sheet and Reference

Read this alongside the official syllabus.

This source-checked reference separates formulae listed in the 2026 4052 and 2027 K310 documents from other useful relationships, then links each entry to a relevant guide. It is Mentora revision material, not an official examination insert.

Not sure which examination document applies? Check the 2027 K310 and 4052 examination-year transition.

Formulae on the official provided list

Compound interest

A=P(1+r100)ⁿ

Variables and conditions: P is the principal, r the percentage rate per period, and n the number of periods.
Use it when: Find a total amount after repeated percentage growth at a constant rate.
Common check: Match the rate and the number of periods; r is entered as a percentage here.

Study Ratio and proportion

Curved surface area of a cone

π rl

Variables and conditions: r is the base radius and l is the slant height.
Use it when: Find the curved surface only, without the circular base.
Common check: Use slant height l, not perpendicular height h.

Study Mensuration

Surface area of a sphere

4π r²

Variables and conditions: r is the radius.
Use it when: Find the outside area of a sphere.
Common check: Do not use diameter in place of radius.

Study Mensuration

Volume of a cone

13π r²h

Variables and conditions: r is the base radius and h is the perpendicular height.
Use it when: Find the space inside a cone.
Common check: Use perpendicular height, not slant height.

Study Mensuration

Volume of a sphere

43π r³

Variables and conditions: r is the radius.
Use it when: Find the space inside a sphere.
Common check: Cubing the radius matters; do not use the surface-area formula.

Study Mensuration

Area of triangle ABC

12absin C

Variables and conditions: a and b are the two sides enclosing angle C.
Use it when: Find an area when two sides and their included angle are known.
Common check: C must be the angle between a and b.

Study Trigonometry

Arc length

rθ

Variables and conditions: r is radius and θ is the central angle in radians.
Use it when: Find a circular arc length when the angle is in radians.
Common check: Do not substitute degrees for θ.

Study Mensuration

Sector area

12r²θ

Variables and conditions: r is radius and θ is the central angle in radians.
Use it when: Find a sector area when the angle is in radians.
Common check: Do not substitute degrees for θ.

Study Mensuration

Sine rule

asin A=bsin B=csin C

Variables and conditions: Each side is paired with its opposite angle.
Use it when: Work with a non-right-angled triangle when an opposite side-angle pair is known.
Common check: Do not pair a side with an adjacent angle.

Study Trigonometry

Cosine rule

a²=b²+c²-2bccos A

Variables and conditions: a is opposite angle A; b and c enclose A.
Use it when: Find a side from two sides and their included angle, or rearrange for an angle.
Common check: Keep the opposite side and its angle matched.

Study Trigonometry

Mean from a frequency table

bar{x}=∑ fx∑ f

Variables and conditions: x is a value (or class midpoint), f its frequency.
Use it when: Find the mean from frequency data.
Common check: Divide by total frequency, not the number of table rows.

Study Statistics

Standard deviation

sqrt{∑ fx²∑ f-(∑ fx∑ f)²}

Variables and conditions: x is a value and f its frequency.
Use it when: Calculate spread around the mean from a frequency table.
Common check: Use the same total frequency in both fractions.

Study Statistics

Other useful syllabus relationships for revision

Pythagoras' theorem

c²=a²+b²

Variables and conditions: c is the hypotenuse of a right triangle; a and b are perpendicular sides.
Use it when: Find a missing side in a right triangle or a coordinate distance.
Common check: The hypotenuse is opposite the right angle and is the longest side.

Study Trigonometry

Trigonometric ratios

sinθ=OH, cosθ=AH, tanθ=OA

Variables and conditions: O, A and H are opposite, adjacent and hypotenuse relative to θ.
Use it when: Find a side or an acute angle in a right triangle.
Common check: Opposite and adjacent change with the chosen angle; check degree mode when answering in degrees.

Study Trigonometry

Gradient

m=y_2-y_1x_2-x_1

Variables and conditions: (x₁, y₁) and (x₂, y₂) are two distinct points.
Use it when: Find the gradient of a straight line or its tangent estimate.
Common check: Subtract in the same order in numerator and denominator.

Study Coordinate geometry

Distance between two points

√(x_2-x_1)²+(y_2-y_1)²

Variables and conditions: (x₁, y₁) and (x₂, y₂) are two points.
Use it when: Find the length of a line segment on a coordinate grid.
Common check: Square both coordinate changes before adding.

Study Coordinate geometry

Trapezium area

12(a+b)h

Variables and conditions: a and b are parallel sides; h is their perpendicular separation.
Use it when: Find the area of a trapezium.
Common check: h is perpendicular to both parallel sides, not a slant side.

Study Mensuration

Probability complement

P(A')=1-P(A)

Variables and conditions: A′ is the event that A does not occur.
Use it when: Find a probability by counting the opposite event.
Common check: The complement is relative to the stated sample space.

Study Probability

Published by Mentora · Published 13 Sept 2026 · Sources checked 13 Sept 2026

Editorial and source details

Official formula pages were visually checked for both cohorts and the rendered formulae were checked with automated mathematical/content QA. No individual author, human reviewer or independent expert review is recorded.