Maths a level questions

A-Level Mathematics Study Guide

1. Pure Mathematics

  • Algebra:

    • Quadratic equations

    • Polynomials

    • Factor theorem

    • Complex numbers

  • Functions:

    • Types of functions (linear, quadratic, exponential, logarithmic)

    • Transformations of functions

  • Calculus:

    • Differentiation (first principles, product and quotient rules)

    • Integration (definite and indefinite integrals, techniques of integration)

    • Applications of calculus (areas under curves, rates of change)

  • Trigonometry:

    • Trigonometric identities

    • Graphs of sine, cosine, and tangent functions

    • Solving trigonometric equations

2. Statistics

  • Data Representation:

    • Types of data (qualitative vs. quantitative)

    • Graphs and charts (histograms, box plots)

  • Probability:

    • Basic probability rules

    • Conditional probability

    • Independent events

  • Distributions:

    • Normal distribution

    • Binomial distribution

    • Poisson distribution

  • Statistical Tests:

    • Hypothesis testing

    • P-values and significance levels

3. Mechanics

  • Kinematics:

    • Motion in a straight line

    • SUVAT equations

  • Forces and Newton's Laws:

    • First, second, and third laws of motion

    • Friction, tension, and normal forces

  • Work and Energy:

    • Work done by a force

    • Conservation of energy

    • Power

4. Decision Mathematics

  • Graph Theory:

    • Terminology (vertices, edges, paths)

    • Eulerian and Hamiltonian paths

  • Algorithms:

    • Dijkstra’s algorithm

    • Prim’s and Kruskal’s algorithms (minimum spanning trees)

  • Linear Programming:

    • Graphical method

    • Simplex method