A Level Mathematics

A Level Mathematics

Boards

Suitable for all examination boards.

Length of Course

Five full days, 40 hours total.

Easter Revision Course Dates 2025

Week 1: Monday 7 April – Friday 11 April
Week 2: Monday 14 April – Friday 18 April
Week 3: Monday 21 April – Friday 25 April

(Good Friday is 18 April; Easter Monday is 21 April 2025)

Topic 1 (AS) – Core Mathematics:
Proof, Algebra and Functions (Indices and surds, Simultaneous equations, Inequalities, Factor Theorem, Graphs Sketching, Transformations of Graphs) and Binomial Expansion.

Topic 2 (AS) – Core Mathematics:
Coordinate geometry (Straight Line, Circle), Trigonometry (Sine and Cosine Rules, Trigonometric graphs, Trigonometric Identities), Exponentials and Logarithms (Exponential and Logarithmic Graph, Exponential Growth and Decay, Law of Logarithms).

Topic 3 (AS) – Core Mathematics:
Differentiation (Differentiation from first principles, Tangents, Maximum and Minimum, Second derivatives), Integration (Fundamental Theorem of Calculus, Definite Integration).

Topic 4 (AS) – Mechanics:
Vectors (Vector algebra, Position Vectors), Quantities and Units, Kinematics (Motion Graphs, SUVAT, Calculus in Kinematics) and Forces.

Topic 5 (AS) – Statistics:
Sampling, Data Representation and Interpretation (Histograms, Scatter Diagrams, Regression line, Averages, Spread, Outliers), Probability, Binomial Distribution and Hypothesis Testing.

Topic 6 (2nd Year) – Core Mathematics:
Algebraic fractions and division, Partial fractions, the Binomial Expansion, Iterative Methods, Series and Sequences, Differentiation; including the chain, product and quotient rules, Implicit and Parametric differentiation.

Topic 7 (2nd Year) – Core Mathematics:
Radian measures including sectors and small angle approximation, Trigonometry including the Pythagorean Identities, the Addition formulae and the Double Angle formulae; Functions including domain and range, composite, inverse and modulus functions.

Topic 8 (2nd Year) – Core Mathematics:
Integration including methods by substitution, by partial fractions, by parts, by use of trigonometric identities and trapezium rule. Application to differential equations; Vectors in 3D and solving geometrical problems, Proof by contradiction.

Topic 9 (2nd Year) – Statistics:
Moments including tilting problems, Projectiles, Further kinematics including variable acceleration and using calculus, Statics of particles and rigid bodies, Equilibrium of a particle under the action of forces such as weight, normal reaction, tension and friction, coefficient of friction, Dynamics of a particle including motion of two connected particles.

Topic 10 (2nd Year) – Mechanics:
Probability including sum and products laws, conditional probabilities, independent and mutually exclusive events, Venn and tree diagrams; Correlation and Regression with Hypothesis testing, the Normal Distribution.