Edexcel A-level Maths Year 12 revision

Topic 1: Proof

It builds on what you learned at GCSE in Algebra: notation, manipulation and proof, and takes it further.

We will go through it step by step.

1. 1.1Proof by deduction, exhaustion and counter-exampleFree 36 questions

Topic 2: Algebra and functions

It builds on what you learned at GCSE in Algebra: notation, manipulation and proof and Algebra: solving equations and inequalities, and takes it further.

There are 6 parts: we start with algebra, functions and proof, and finish with graphs of functions and transformations; function notation, composite and inverse functions, proportional relationships.

1. 2.1Algebra, functions and proofFree 30 questions
2. 2.2Laws of indices and surds (rationalising denominators)34 questions
3. 2.3Quadratics: factorising, completing the square, quadratic formula and the discriminant17 questions
4. 2.4Polynomials: algebraic division, factor theorem and remainder theorem33 questions
5. 2.5Simultaneous equations (linear and quadratic) and inequalities, including graphical and set notation43 questions
6. 2.6Graphs of functions and transformations; function notation, composite and inverse functions, proportional relationships49 questions

Topic 3: Coordinate geometry in the (x, y) plane

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

There are 5 parts: we start with coordinate geometry and circles, and finish with circle geometry.

1. 3.1Coordinate geometry and circles49 questions
2. 3.2Straight lines: equations, gradients, parallel and perpendicular linesFree 37 questions
3. 3.3Distance between points, midpoints and intersection of lines70 questions
4. 3.4Equation of a circle and completing the square62 questions
5. 3.5Circle geometry: tangents, chords and circle theorems59 questions

Topic 4: Sequences and series: binomial expansion

It builds on what you learned at GCSE in Algebra: sequences, and takes it further.

We will go through it step by step.

1. 4.1Binomial expansion of (a + bx)^n for positive integer n using Pascal's triangle and nCr53 questions

Topic 5: Trigonometry

It builds on what you learned at GCSE in Geometry and measures, and takes it further.

There are 4 parts: we start with trigonometry, exponentials and logarithms, and finish with solving trigonometric equations in a given interval.

1. 5.1Trigonometry, exponentials and logarithms54 questions
2. 5.2Sine rule, cosine rule and area of a triangleFree 63 questions
3. 5.3Trigonometric graphs, exact values and the identities tan x = sin x / cos x and sin²x + cos²x = 149 questions
4. 5.4Solving trigonometric equations in a given interval46 questions

Topic 6: Exponentials and logarithms

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

There are 3 parts: we start with exponential functions y = a^x and e^x; gradient of e^kx, and finish with using logarithms to reduce y = ax^n and y = kb^x to linear form and modelling exponential growth and decay.

1. 6.1Exponential functions y = a^x and e^x; gradient of e^kx45 questions
2. 6.2Logarithms: laws of logarithms, ln x and solving a^x = b43 questions
3. 6.3Using logarithms to reduce y = ax^n and y = kb^x to linear form and modelling exponential growth and decay54 questions

Topic 7: Differentiation

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

There are 6 parts: we start with differentiation and integration, and finish with differentiating and integrating e^kx.

1. 7.1Differentiation and integration48 questions
2. 7.2Differentiation from first principles and the derivative of x^nFree 57 questions
3. 7.3Tangents, normals and gradient of a curve at a point53 questions
4. 7.4Increasing and decreasing functions, stationary points and the second derivative65 questions
5. 7.5Optimisation and rates of change in context; sketching gradient functions47 questions
6. 7.6Differentiating and integrating e^kx58 questions

Topic 8: Integration

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

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. 8.1Indefinite integration of x^n and finding constants of integration47 questions
2. 8.2Definite integrals, area under a curve and area between a curve and a line62 questions

Topic 9: Vectors

It builds on what you learned at GCSE in Geometry and measures, and takes it further.

There are 3 parts: we start with vectors and binomial expansion, and finish with vector geometry.

1. 9.1Vectors and binomial expansion49 questions
2. 9.2Two-dimensional vectors: components, magnitude, direction and position vectors51 questions
3. 9.3Vector geometry: proofs, parallel vectors and collinearity55 questions

Topic 10: Statistical sampling

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

There are 3 parts: we start with sampling, data and probability, and finish with working with the Large Data Set.

1. 10.1Sampling, data and probabilityFree 74 questions
2. 10.2Population, census and sampling methods (simple random, systematic, stratified, quota, opportunity)64 questions
3. 10.3Working with the Large Data Set: context, cleaning data and identifying outliers66 questions

Topic 11: Data presentation and interpretation

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

There are 3 parts: we start with measures of location and spread, and finish with bivariate data.

1. 11.1Measures of location and spread: mean, median, quartiles, variance, standard deviation and coding68 questions
2. 11.2Histograms, cumulative frequency graphs and box plots: drawing, interpreting and comparing distributions70 questions
3. 11.3Bivariate data: scatter diagrams, correlation and regression lines70 questions

Topic 12: Probability

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

There are 2 parts: we start with probability rules, and finish with Venn diagrams, tree diagrams, two-way tables and conditional probability.

1. 12.1Probability rules: mutually exclusive and independent eventsFree 68 questions
2. 12.2Venn diagrams, tree diagrams, two-way tables and conditional probability65 questions

Topic 13: Statistical distributions

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

There are 2 parts: we start with discrete random variables and probability distributions, and finish with the binomial distribution.

1. 13.1Discrete random variables and probability distributions67 questions
2. 13.2The binomial distribution: B(n, p), conditions and cumulative probabilities56 questions

Topic 14: Statistical hypothesis testing

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

There are 2 parts: we start with binomial distribution and hypothesis testing, and finish with hypothesis tests for a binomial proportion.

1. 14.1Binomial distribution and hypothesis testing62 questions
2. 14.2Hypothesis tests for a binomial proportion: critical regions, one- and two-tailed tests47 questions

Topic 15: Quantities and units in mechanics

It builds on what you learned at GCSE in Ratio, proportion and rates of change, and takes it further.

We will go through it step by step.

1. 15.1Quantities, SI units and modelling assumptions in mechanics69 questions

Topic 16: Kinematics

It builds on what you learned at GCSE in Algebra: graphs and Ratio, proportion and rates of change, and takes it further.

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

1. 16.1KinematicsFree 70 questions
2. 16.2Displacement-time and velocity-time graphs63 questions
3. 16.3Constant acceleration (suvat) equations and vertical motion under gravity47 questions
4. 16.4Variable acceleration: using differentiation and integration in kinematics63 questions

Topic 17: Forces and Newton's laws

It builds on what you learned at GCSE in Ratio, proportion and rates of change, and takes it further.

There are 3 parts: we start with forces and Newton's laws, and finish with connected particles.

1. 17.1Forces and Newton's laws70 questions
2. 17.2Resolving forces, equilibrium and forces as vectors64 questions
3. 17.3Connected particles: pulleys, towing and Newton's third law65 questions

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