Read this alongside the official syllabus.
This is Mentora revision material, not an official examination insert. “Not on the official list” does not say whether a relationship will be supplied within a question, or whether it is best memorised rather than understood or derived.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Published by Mentora · Published 12 Sept 2026 · Sources checked 12 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.