Roadmap
Pure Mathematics (Papers 1 and 2)
1 Proof
Pure 1.1 - Structure of mathematical proof
2 Algebra and functions
Pure 2.1 - Laws of indices for rational exponents
Pure 2.2 - Surds and rationalising denominators
Pure 2.3 - Quadratic functions and graphs
Pure 2.4 - Simultaneous equations by elimination and substitution
Pure 2.5 - Linear and quadratic inequalities
Pure 2.6 - Algebraic manipulation of polynomials
Pure 2.7 - Graphs of functions and the modulus graph
Pure 2.8 - Composite and inverse functions
Pure 2.9 - Transformations of functions
Pure 2.10 - Partial fractions
Pure 2.11 - Functions in modelling
3 Coordinate geometry in the (x, y) plane
Pure 3.1 - Equation of a straight line
Pure 3.2 - Coordinate geometry of the circle
Pure 3.3 - Parametric equations and Cartesian form
Pure 3.4 - Parametric equations in modelling
4 Sequences and series
Pure 4.1 - Binomial expansion
Pure 4.2 - Sequences
Pure 4.3 - Sigma notation
Pure 4.4 - Arithmetic sequences and series
Pure 4.5 - Geometric sequences and series
Pure 4.6 - Sequences and series in modelling
5 Trigonometry
Pure 5.1 - Unit-circle trigonometry, triangle rules and radians
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Pure 5.2 - Small angle approximations
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Pure 5.3 - Sine, cosine and tangent functions
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Pure 5.4 - Reciprocal and inverse trigonometric functions
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Pure 5.5 - Trigonometric identities
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Pure 5.6 - Compound and double angles, half-angles and R-form
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Pure 5.7 - Simple trigonometric equations
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Pure 5.8 - Proofs with trigonometric identities
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Pure 5.9 - Trigonometric functions in context
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6 Exponentials and logarithms
Pure 6.1 - Exponential functions and graphs
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Pure 6.2 - Gradients of exponential functions
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Pure 6.3 - Logarithms and natural logarithms
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Pure 6.4 - Laws of logarithms
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Pure 6.5 - Solving exponential equations
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Pure 6.6 - Logarithmic graphs for estimating parameters
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Pure 6.7 - Exponential growth and decay in modelling
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7 Differentiation
Pure 7.1 - Derivatives, tangents and second derivatives
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Pure 7.2 - Derivatives of standard functions
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Pure 7.3 - Gradients, tangents, normals, maxima and minima
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Pure 7.4 - Product, quotient and chain rules
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Pure 7.5 - Implicit and parametric differentiation
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Pure 7.6 - Constructing simple differential equations
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8 Integration
Pure 8.1 - Fundamental Theorem of Calculus
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Pure 8.2 - Integrating standard functions
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Pure 8.3 - Definite integrals and area under a curve
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Pure 8.4 - Integration as the limit of a sum
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Pure 8.5 - Integration by substitution and by parts
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Pure 8.6 - Integration using partial fractions
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Pure 8.7 - Separable first-order differential equations
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Pure 8.8 - Interpreting solutions of differential equations
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9 Numerical methods
Pure 9.1 - Locating roots by sign changes
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Pure 9.2 - Iteration, cobweb and staircase diagrams
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Pure 9.3 - Newton-Raphson and recurrence relations
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Pure 9.4 - Numerical integration and the trapezium rule
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Pure 9.5 - Numerical methods in context
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10 Vectors
Pure 10.1 - Vectors in two and three dimensions
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Pure 10.2 - Magnitude, direction and component form
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Pure 10.3 - Vector addition and scalar multiplication
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Pure 10.4 - Position vectors and distance between points
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Pure 10.5 - Vectors in pure mathematics and context
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Statistics (Paper 3, Section A)
Large Data Set
Use of data in statistics - Large Data Set weather data
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1 Statistical sampling
Statistics 1.1 - Populations, samples and sampling techniques
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2 Data presentation and interpretation
Statistics 2.1 - Single-variable data diagrams
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Statistics 2.2 - Scatter diagrams and regression lines
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Statistics 2.3 - Measures of central tendency and variation
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Statistics 2.4 - Outliers in data sets
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3 Probability
Statistics 3.1 - Mutually exclusive and independent events
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Statistics 3.2 - Conditional probability with diagrams and tables
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Statistics 3.3 - Probability modelling and assumptions
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4 Statistical distributions
Statistics 4.1 - Discrete and binomial probability distributions
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Statistics 4.2 - Normal distribution as a model
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Statistics 4.3 - Choosing an appropriate probability distribution
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5 Statistical hypothesis testing
Statistics 5.1 - Language of statistical hypothesis testing
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Statistics 5.2 - Hypothesis test for a binomial proportion
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Statistics 5.3 - Hypothesis test for a normal mean
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Mechanics (Paper 3, Section B)
6 Quantities and units in mechanics
Mechanics 6.1 - Fundamental and derived SI units
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7 Kinematics
Mechanics 7.1 - The language of kinematics
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Mechanics 7.2 - Kinematics graphs in straight-line motion
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Mechanics 7.3 - Constant acceleration formulae
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Mechanics 7.4 - Calculus in kinematics
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Mechanics 7.5 - Motion under gravity using vectors
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8 Forces and Newton's laws
Mechanics 8.1 - Force and Newton's first law
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Mechanics 8.2 - Newton's second law and resolving forces
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Mechanics 8.3 - Weight and motion under gravity
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Mechanics 8.4 - Newton's third law and equilibrium
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Mechanics 8.5 - Addition and resultant forces in dynamics
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Mechanics 8.6 - Friction, limiting friction and static friction
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9 Moments
Mechanics 9.1 - Moments in simple static contexts
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