Higher Maths formulae list: what is given and what to learn

Both papers print a short formulae list: the two forms of a circle's equation, the scalar product, the addition and double angle formulae, and the derivatives and integrals of sin ax and cos ax. Everything else must be learned.

Circle	x² + y² + 2gx + 2fy + c = 0 and (x - a)² + (y - b)² = r²
Scalar product	a.b = \|a\|\|b\| cos θ and a.b = a₁b₁ + a₂b₂ + a₃b₃
Trigonometry	sin (A ± B), cos (A ± B), sin 2A and the three forms of cos 2A
Calculus	Derivatives and integrals of sin ax and cos ax

Results you must learn

The laws of logarithms and indices, and that y = log_a x means a^y = x.
The discriminant conditions: real, equal or no real roots.
Gradient facts: m = tan θ, parallel lines share a gradient and perpendicular gradients multiply to -1.

Try 2 questions

Question 1Paper 1 style · no calculator

Find the centre and radius of the circle

x^2

{}+ y^2

{}- 6x

{}+ 4y

{}- 12

= 0

Question 2Paper 1 style · no calculator

ABC

is an equilateral triangle with sides of length

4

units.

\mathbf{p}

= \overrightarrow{AB}

and

\mathbf{q}

= \overrightarrow{BC}

, as shown. Find

\mathbf{p}.\mathbf{q}

Next step

Take the free test Start the circles lesson

Questions people ask

Is the chain rule on the formulae list?

No. Only the derivatives and integrals of sin ax and cos ax are listed; the chain rule and the power rules must be learned.

Is the wave function formula given?

No. The addition formulae are given, and you use them to expand k cos (x - α) or k sin (x + α) and compare coefficients.