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Pure Mathematics (Papers 1 and 2)
1.2 Algebra and functions
P1.2.1 - Laws of indices for rational exponentsIndex laws are the rules that let you simplify powers without expanding long strings of multiplication. In A-level algebra the indices can be fractions or negative numbers as well as positive integers, so the same rules become a compact language for roots, reciprocals and powers. This lesson buil...
P1.2.2 - Surds and rationalising denominatorsSurds let you keep exact answers instead of replacing them with rounded decimals. In this lesson you will simplify, multiply, and collect square-root expressions, then use rationalising to rewrite fractions so the denominator is rational. The key idea is simple: choose a form of 1 that changes th...
P1.2.3 - Quadratic functions and graphsA quadratic function is one of the first places where algebra and graph shape become the same story. In this lesson you will connect the expression ax^2+bx+c with the parabola it draws, use completing the square to find the turning point, use the discriminant to decide how many real roots exist,...
P1.2.4 - Simultaneous equations by elimination and substitutionSimultaneous equations ask for values that satisfy two equations at the same time. In this lesson you will learn when elimination is the efficient move, when substitution is the safer move, and how to handle the Edexcel case where one equation is linear and the other contains squared terms. The f...
P1.2.5 - Linear and quadratic inequalitiesAn inequality asks for all values that make a statement true, not just a single value that balances two sides. In this lesson you will solve linear and quadratic inequalities in one variable, express answers with correct and, or, or set notation, and interpret inequalities using graphs. The centr...
P1.2.6 - Algebraic manipulation of polynomialsPolynomial manipulation is the art of changing the form of an expression without changing its value. In this lesson you will expand, collect, factorise, divide by linear expressions, use the factor theorem, and simplify rational expressions. The thread running through all of it is structure: look...
P1.2.7 - Graphs of functions and the modulus graphA graph is a picture of how a function behaves. In this lesson you will learn how to read the important features of polynomial, modulus, reciprocal, and proportional graphs, then use those features to solve equations and inequalities. The aim is not to draw perfect artwork: it is to produce sketc...
P1.2.8 - Composite and inverse functionsFunctions let us describe a process that takes an input and produces exactly one output. This lesson builds the language Edexcel uses for functions, then shows how to combine functions, reverse them, and understand the graph of an inverse. The main thread is simple: keep track of the direction of...
P1.2.9 - Transformations of y = f(x)A transformation changes the position, size, or orientation of a graph without asking you to rebuild the whole graph from scratch. In this lesson, y=f(x) is the original graph, and the aim is to predict what happens to its key points, shape, roots, asymptotes, and familiar function features. This...
P1.2.10 - Partial fractionsPartial fractions take one algebraic fraction and split it into simpler fractions. This is the reverse of adding fractions over a common denominator. The skill matters because the simpler pieces are much easier to use later in integration, differentiation, and series expansions.
P1.2.11 - Functions in modellingA function model turns a real situation into an equation that can be used for prediction and interpretation. In this lesson you will learn how to choose and use common function models, including trigonometric, exponential, and reciprocal models. You will also learn the Edexcel habit that matters...
1.3 Coordinate geometry in the (x, y) plane
P1.3.1 - Equation of a straight lineA straight-line equation is a compact way of describing every point on one line. In this lesson you will connect the graph, the gradient, the intercept, and the algebraic forms Edexcel expects. You will also use straight-line equations in geometry problems and simple modelling contexts, where the...
P1.3.2 - Coordinate geometry of the circleA circle is the set of all points a fixed distance from one centre. Coordinate geometry turns that idea into algebra, so you can move between an equation, a centre, a radius, a tangent, and a circumcircle. The key skill is not memorising several disconnected tricks: it is recognising when distanc...
P1.3.3 - Parametric equations and Cartesian formA Cartesian equation links x and y directly, such as y=x^2 or (x-2)^2+(y+4)^2=25. Parametric equations describe a curve differently: they give x and y separately in terms of a shared parameter, usually t or theta. In this lesson you will learn how to read a parametric curve, convert it to Cartesi...
P1.3.4 - Parametric equations in modellingParametric equations describe a point by giving both coordinates in terms of a third quantity, called a parameter. In modelling, that parameter often means something real, such as time, angle, or distance travelled. This lesson is about choosing and using parametric equations so that the mathemat...
1.4 Sequences and series
P1.4.1 - Binomial expansion of (a + bx)^nThe binomial expansion is a controlled way to expand a bracket with two terms. For positive integer powers it gives an exact finite polynomial. For rational powers, such as square roots or reciprocal powers, it gives an infinite series that can be used for approximation, but only inside a stated...
P1.4.2 - SequencesA sequence is an ordered list of terms, and the subscript tells you the position of a term in that list. In this lesson you will work with sequences given directly by a formula for the nth term and sequences generated recursively from an earlier term. The goal is not just to make terms, but to de...
P1.4.3 - Sigma notationSigma notation is a compact way to write a sum whose terms follow a rule. Instead of writing a long line such as 5 + 8 + 11 + 14, you can state the rule, the starting value, and the finishing value in one expression. In this lesson you will learn how to read, expand, evaluate, and write sigma not...
P1.4.4 - Arithmetic sequences and seriesArithmetic sequences are built by adding the same amount each time. This lesson shows how to move between the terms, the nth term, and the sum of the first n terms, including the proof of the arithmetic-series sum formula that Edexcel expects you to know.
P1.4.5 - Geometric sequences and seriesA geometric sequence is built by multiplying by the same number each time. That simple repeated multiplication gives you powerful formulae for terms, finite sums, and, when the ratio is small enough, a sum to infinity. In this lesson you will learn how to use those formulae, prove the finite sum...
P1.4.6 - Sequences and series in modellingSequences and series become useful when a repeated real-world change has a clear pattern. In this lesson you will learn how to translate a context into an arithmetic model, a geometric model, or a relation-defined model, then use the model to calculate and interpret terms or totals. The main skil...
1.5 Trigonometry
1.6 Exponentials and logarithms
1.7 Differentiation
1.8 Integration
1.9 Numerical methods
1.10 Vectors
Statistics (Paper 3, Section A)
Large Data Set
3.1 Statistical sampling
3.2 Data presentation and interpretation
3.3 Probability
3.4 Statistical distributions
3.5 Statistical hypothesis testing
Mechanics (Paper 3, Section B)
3.6 Quantities and units in mechanics
3.7 Kinematics
3.8 Forces and Newton's laws
3.9 Moments