Pure Mathematics

Quadratics 28 Q

Completing the square

§1.1.1 · 9 questions (multi-part)

Practice

Discriminant and nature of roots

§1.1.2 · 5 questions

Practice

Solving quadratic equations and inequalities

§1.1.3 · 5 questions

Practice

Quadratic and linear simultaneous equations

§1.1.4 · 3 questions

Practice

Equations reducible to quadratic form

§1.1.5 · 6 questions

Practice

Functions 48 Q

Domain and range

§1.2.1 · 5 questions

Practice

Composite functions

§1.2.2 · 10 questions

Practice

Inverse functions

§1.2.3 · 14 questions (multi-part)

Practice

Transformations of graphs

§1.2.4 · 19 questions

Practice

Coordinate geometry 31 Q

Length, midpoint and gradient of a line segment

§1.3.1 · 2 questions

Practice

Equation of a straight line

§1.3.2 · 2 questions

Practice

Parallel and perpendicular lines

§1.3.3 · 3 questions

Practice

Equation of a circle

§1.3.4 · 16 questions (multi-part)

Practice

Intersection of a line and a curve

§1.3.5 · 8 questions (multi-part)

Practice

Circular measure 22 Q

Radian measure

§1.4.1 · 4 questions

Practice

Arc length

§1.4.2 · 5 questions

Practice

Area of a sector

§1.4.3 · 13 questions (multi-part)

Practice

Trigonometry 29 Q

Exact values and trigonometric graphs

§1.5.2 · 6 questions

Practice

Basic trigonometric identities

§1.5.3 · 5 questions

Practice

Solving trigonometric equations

§1.5.4 · 18 questions (multi-part)

Practice

Series 56 Q

Binomial expansion for positive integer n

§1.6.1 · 25 questions (multi-part)

Practice

Arithmetic progressions

§1.6.2 · 10 questions

Practice

Geometric progressions

§1.6.3 · 8 questions (multi-part)

Practice

Sum to infinity of a geometric series

§1.6.4 · 13 questions

Practice

Differentiation 47 Q

The derivative as a gradient function

§1.7.1 · 8 questions

Practice

Differentiating powers of x and the chain rule

§1.7.2 · 2 questions

Practice

Tangents and normals

§1.7.3 · 10 questions

Practice

Increasing/decreasing functions and stationary points

§1.7.4 · 20 questions (multi-part)

Practice

Connected rates of change

§1.7.5 · 7 questions

Practice

Integration 24 Q

Integration as the reverse of differentiation

§1.8.1 · 8 questions

Practice

Definite integrals

§1.8.2 · 2 questions

Practice

Area under a curve

§1.8.3 · 8 questions (multi-part)

Practice

Volume of revolution

§1.8.4 · 6 questions

Practice

Algebra 36 Q

Modulus function equations and inequalities

§3.1.1 · 10 questions

Practice

Polynomial division

§3.1.2 · 6 questions

Practice

Factor and remainder theorems

§3.1.3 · 5 questions

Practice

Partial fractions

§3.1.4 · 8 questions

Practice

Binomial expansion for any rational n

§3.1.5 · 7 questions

Practice

Logarithmic and exponential functions 22 Q

Laws of logarithms

§3.2.1 · 4 questions

Practice

Exponential and logarithmic equations

§3.2.2 · 8 questions

Practice

Graphs of e^x and ln x

§3.2.3 · 3 questions

Practice

Reducing a relation to linear form using logarithms

§3.2.4 · 7 questions

Practice

Trigonometry (further) 21 Q

Secant, cosecant and cotangent

§3.3.1 · 2 questions

Practice

Compound and double angle formulae

§3.3.2 · 6 questions

Practice

Expressing a cos x + b sin x in R sin(x + a) form

§3.3.3 · 5 questions

Practice

Proving identities and solving further trigonometric equations

§3.3.4 · 8 questions

Practice

Differentiation (further) 32 Q

Product and quotient rules

§3.4.1 · 11 questions

Practice

Differentiating exponential, logarithmic and trigonometric functions

§3.4.2 · 5 questions

Practice

Implicit differentiation

§3.4.3 · 7 questions

Practice

Parametric differentiation

§3.4.4 · 9 questions

Practice

Integration (further) 27 Q

Integrating exponential, trigonometric and 1/x functions

§3.5.1 · 3 questions

Practice

Integration using trigonometric identities

§3.5.2 · 4 questions

Practice

Integration by substitution

§3.5.3 · 7 questions

Practice

Integration by parts

§3.5.4 · 10 questions

Practice

Integration using partial fractions

§3.5.5 · 3 questions

Practice

Numerical solution of equations 31 Q

Locating roots by sign change

§3.6.1 · 16 questions

Practice

Iterative methods x = F(x)

§3.6.2 · 15 questions

Practice

Vectors 33 Q

Vector notation and magnitude

§3.7.1 · 5 questions

Practice

Scalar (dot) product and angles between vectors

§3.7.2 · 13 questions

Practice

Vector equation of a line

§3.7.3 · 7 questions

Practice

Intersecting, parallel and skew lines

§3.7.4 · 8 questions

Practice

Differential equations 16 Q

Forming differential equations

§3.8.1 · 7 questions

Practice

Separation of variables

§3.8.2 · 6 questions

Practice

General and particular solutions

§3.8.3 · 3 questions

Practice

Complex numbers 32 Q

Arithmetic of complex numbers

§3.9.1 · 9 questions

Practice

Conjugates and roots of polynomial equations

§3.9.2 · 3 questions

Practice

Argand diagram

§3.9.3 · 4 questions

Practice

Modulus-argument (polar) form

§3.9.4 · 5 questions

Practice

Loci in the complex plane

§3.9.5 · 11 questions

Practice