Combined Mathematics Past Papers

Quadratic functions

1 question with a worked solution.

Polynomial functions

1 question with a worked solution.

Partial fractions

1 question with a worked solution.

Indices and logarithms

1 question with a worked solution.

Inequalities

1 question with a worked solution.

Circular (trigonometric) functions

1 question with a worked solution.

Sine rule and cosine rule

1 question with a worked solution.

Sine rule and cosine rule (Pure Maths)

1 question with a worked solution.

Limits of a function

2 questions with worked solutions.

Differentiation techniques

1 question with a worked solution.

The definite integral and the Fundamental Theorem

1 question with a worked solution.

Area bounded by curves

1 question with a worked solution.

Equation of a straight line

1 question with a worked solution.

Line through the intersection of two lines

1 question with a worked solution.

Position of two points relative to a line

1 question with a worked solution.

Cartesian coordinates and the straight line

1 question with a worked solution.

Perpendicular distance from a point to a line

1 question with a worked solution.

Cartesian equation of a circle

1 question with a worked solution.

Position of a straight line relative to a circle

1 question with a worked solution.

Tangents to a circle from an external point

1 question with a worked solution.

Circle through the intersection of two circles

1 question with a worked solution.

Position of two circles

1 question with a worked solution.

Condition for two circles to intersect orthogonally

1 question with a worked solution.

Mathematical induction

1 question with a worked solution.

Finite series

1 question with a worked solution.

Sums of elementary series

1 question with a worked solution.

Summation of series

1 question with a worked solution.

Convergence and divergence of series

1 question with a worked solution.

The complex number system

2 questions with worked solutions.

Algebra of complex numbers

1 question with a worked solution.

Complex conjugate

1 question with a worked solution.

Modulus of a complex number

1 question with a worked solution.

The Argand diagram

1 question with a worked solution.

De Moivre's theorem

1 question with a worked solution.

Loci and regions of a complex number

1 question with a worked solution.

Binomial expansion

1 question with a worked solution.

Binomial theorem

2 questions with worked solutions.

Factorials

2 questions with worked solutions.

Fundamental principle of counting

1 question with a worked solution.

Permutations

1 question with a worked solution.

Combinations

1 question with a worked solution.

Properties of matrices

1 question with a worked solution.

Special square matrices

1 question with a worked solution.

Transpose and inverse of a matrix

1 question with a worked solution.

Simultaneous equations by matrices

1 question with a worked solution.

Systems of coplanar forces

1 question with a worked solution.

Systems of coplanar forces (statics)

1 question with a worked solution.

Stresses in the rods of a framework

1 question with a worked solution.

Centre of mass of uniform bodies

1 question with a worked solution.

Centre of mass by integration

1 question with a worked solution.

Centre of mass of composite bodies

1 question with a worked solution.

Centre of gravity

1 question with a worked solution.

Stability of bodies in equilibrium

1 question with a worked solution.

Angle of inclination of suspended bodies

1 question with a worked solution.

Newtonian model of motion

1 question with a worked solution.

Velocity and acceleration in circular motion

1 question with a worked solution.

Motion in a horizontal circle

1 question with a worked solution.

Motion in a vertical circle

1 question with a worked solution.

Simple harmonic motion

1 question with a worked solution.

Simple harmonic motion on a horizontal line

1 question with a worked solution.

Simple harmonic motion on a vertical line

1 question with a worked solution.

Events of a random experiment

1 question with a worked solution.

Probability models for random events

1 question with a worked solution.

Conditional probability

1 question with a worked solution.

Bayes' theorem

1 question with a worked solution.

The nature of statistics

1 question with a worked solution.

Measures of central tendency

1 question with a worked solution.

Measures of relative position

1 question with a worked solution.

Measures of dispersion

1 question with a worked solution.