A-Level maths: facts to know cold
A-Level maths gives out a formula booklet, and it is a trap: the booklet only helps if you already know what to look for. The facts below have to be instant, because every exam question assumes them. Fold the sheet, write each from memory, and repeat weekly until writing them is boring.
Algebra
- Quadratic formula, and what the discriminant tells you
- Completing the square in the form a(x + p) squared + q
- Laws of indices, including negative and fractional powers
- Laws of logarithms: product, quotient, power, change of base
- Factor theorem and remainder theorem, stated precisely
- Binomial expansion for positive integer n
Trigonometry
- Exact values at 0, 30, 45, 60 and 90 degrees
- Sine rule, cosine rule and the area formula, half ab sin C
- sin squared + cos squared = 1, and the tan identity
- Small-angle approximations for sin, cos and tan
- Radians: converting, and arc length with theta
Calculus
- Derivatives of x to the n, sin x, cos x, e to the x and ln x
- Chain, product and quotient rules, stated from memory
- Derivative of a to the x and of trig in radians
- Standard integrals matching the derivatives above
- Integration by substitution and by parts, when each applies
- Differentiating from first principles, the definition
Tutor tip: This sheet is the floor, not the ceiling: once these are instant, past-paper volume does the rest. Weekly one-to-one sessions turn that fluency into full-method marks.