Cambridge A-level Maths Year 12 revision

Topic 1.1: Quadratics

It builds on what you learned at IGCSE in Algebra and graphs, and takes it further.

There are 2 parts: we start with quadratics, and finish with simultaneous equations (linear and quadratic) and inequalities, including graphical and set notation.

1. 1.1.1Quadratics: factorising, completing the square, quadratic formula and the discriminant17 questions
2. 1.1.2Simultaneous equations (linear and quadratic) and inequalities, including graphical and set notation43 questions

Topic 1.2: Functions

It builds on what you learned at IGCSE in Algebra and graphs, and takes it further.

We will go through it step by step.

1. 1.2.1Graphs of functions and transformations; function notation, composite and inverse functions, proportional relationships49 questions

Topic 1.3: Coordinate geometry

It builds on what you learned at IGCSE in Coordinate geometry, and takes it further.

There are 4 parts: we start with straight lines, and finish with coordinate geometry and circles.

1. 1.3.1Straight lines: equations, gradients, parallel and perpendicular linesFree 37 questions
2. 1.3.2Distance between points, midpoints and intersection of lines70 questions
3. 1.3.3Equation of a circle and completing the square62 questions
4. 1.3.4Coordinate geometry and circles49 questions

Topic 1.4: Circular measure

It builds on what you learned at IGCSE in Mensuration, and takes it further.

We will go through it step by step.

1. 1.4.1Radian measure, arc length and sector area61 questions

Topic 1.5: Trigonometry

It builds on what you learned at IGCSE in Trigonometry, and takes it further.

There are 3 parts: we start with trigonometric graphs, exact values and the identities tan x = sin x / cos x and sin²x + cos²x = 1, and finish with trigonometry, exponentials and logarithms.

1. 1.5.1Trigonometric graphs, exact values and the identities tan x = sin x / cos x and sin²x + cos²x = 149 questions
2. 1.5.2Solving trigonometric equations in a given interval46 questions
3. 1.5.3Trigonometry, exponentials and logarithms54 questions

Topic 1.6: Series

We will go through it step by step.

1. 1.6.1Binomial expansion of (a + bx)^n for positive integer n using Pascal's triangle and nCr53 questions

Topic 1.7: Differentiation

It builds on what you learned at IGCSE in Algebra and graphs, and takes it further.

There are 5 parts: we start with differentiation from first principles and the derivative of x^n, and finish with differentiation and integration.

1. 1.7.1Differentiation from first principles and the derivative of x^nFree 57 questions
2. 1.7.2Tangents, normals and gradient of a curve at a point53 questions
3. 1.7.3Increasing and decreasing functions, stationary points and the second derivative65 questions
4. 1.7.4Optimisation and rates of change in context; sketching gradient functions47 questions
5. 1.7.5Differentiation and integration48 questions

Topic 1.8: Integration

There are 2 parts: we start with indefinite integration of x^n and finding constants of integration, and finish with definite integrals, area under a curve and area between a curve and a line.

1. 1.8.1Indefinite integration of x^n and finding constants of integration47 questions
2. 1.8.2Definite integrals, area under a curve and area between a curve and a line62 questions

Topic 4.1: Forces and equilibrium

There are 2 parts: we start with quantities, SI units and modelling assumptions in mechanics, and finish with resolving forces, equilibrium and forces as vectors.

1. 4.1.1Quantities, SI units and modelling assumptions in mechanics69 questions
2. 4.1.2Resolving forces, equilibrium and forces as vectors64 questions

Topic 4.2: Kinematics of motion in a straight line

There are 4 parts: we start with kinematics, and finish with variable acceleration.

1. 4.2.1KinematicsFree 70 questions
2. 4.2.2Displacement-time and velocity-time graphs63 questions
3. 4.2.3Constant acceleration (suvat) equations and vertical motion under gravity47 questions
4. 4.2.4Variable acceleration: using differentiation and integration in kinematics63 questions

Topic 4.3: Momentum

We will go through it step by step.

1. 4.3.1Momentum: conservation of momentum and collisions in a straight line34 questions

Topic 4.4: Newton's laws of motion

There are 2 parts: we start with forces and Newton's laws, and finish with connected particles.

1. 4.4.1Forces and Newton's laws70 questions
2. 4.4.2Connected particles: pulleys, towing and Newton's third law65 questions

Topic 4.5: Energy, work and power

We will go through it step by step.

1. 4.5.1Work, energy and power: work done, kinetic and potential energy, and power56 questions

Topic 5.1: Representation of data

It builds on what you learned at IGCSE in Statistics, and takes it further.

There are 2 parts: we start with measures of location and spread, and finish with histograms, cumulative frequency graphs and box plots.

1. 5.1.1Measures of location and spread: mean, median, quartiles, variance, standard deviation and coding68 questions
2. 5.1.2Histograms, cumulative frequency graphs and box plots: drawing, interpreting and comparing distributions70 questions

Topic 5.2: Permutations and combinations

We will go through it step by step.

1. 5.2.1Permutations and combinations: arrangements, selections and restrictions53 questions

Topic 5.3: Probability

It builds on what you learned at IGCSE in Probability, and takes it further.

There are 3 parts: we start with probability rules, and finish with sampling, data and probability.

1. 5.3.1Probability rules: mutually exclusive and independent eventsFree 68 questions
2. 5.3.2Venn diagrams, tree diagrams, two-way tables and conditional probability65 questions
3. 5.3.3Sampling, data and probabilityFree 74 questions

Topic 5.4: Discrete random variables

There are 3 parts: we start with discrete random variables and probability distributions, and finish with binomial distribution and hypothesis testing.

1. 5.4.1Discrete random variables and probability distributions67 questions
2. 5.4.2The binomial distribution: B(n, p), conditions and cumulative probabilities56 questions
3. 5.4.3Binomial distribution and hypothesis testing62 questions

Topic 5.5: The normal distribution

We will go through it step by step.

1. 5.5.1The normal distribution: standardising, using tables and the normal approximation to the binomial44 questions

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