# Appendix: mathematical formulae

1. Students are expected to know the following formulae included in the
subject content; they will **not** be given in the exam. Refer to the Subject
content section to determine the tier at which these formulae could be used.

**The quadratic formula**

The solutions of , where

**Circumference and area of a circle**

Where is the radius and is the diameter:

Circumference of a circle = =

Area of a circle =

**Pythagoras’ theorem**

In any right-angled triangle where , and are lengths of the sides and is the hypotenuse:

**Trigonometry formulae**

In any right-angled triangle where , and are lengths of the sides and is the hypotenuse:

, ,

In **any** triangle
where
,
and
are lengths of the sides:

sine rule:

cosine rule:

Area =

2. Students are expected to know the following formulae or be able to
derive them; they will **not** be given in the exam. Refer to the Subject content
section to determine the tier at which these formulae could be used.

**Perimeter, area, surface area and volume formulae**

Where and are the lengths of the parallel sides and is their perpendicular separation:

Area of a trapezium =

Volume of a prism = area of cross section x length

**Compound interest**

Where is the principal amount, is the interest rate over a given period and is number of times that the interest is compounded:

Total accrued =

**Probability**

Where is the probability of outcome and is the probability of outcome :

3. Students are **not** expected to memorise the following formulae;
they will be given in the exam in the relevant question. Refer to the Subject
content section to determine the tier at which these formulae could be used.

**Perimeter, area, surface area and volume formulae**

Where is the radius of the sphere or cone, is the slant height of a cone and is the perpendicular height of a cone:

Curved surface area of a cone =

Surface area of a sphere =

Volume of a sphere =

Volume of a cone =

**Kinematics formulae**

Where is constant acceleration, is initial velocity, is final velocity, is displacement from the position when and is time taken: