Roadmap
Pure Mathematics (Papers 1 and 2)
1.1 Proof
P1.1.1 - Structure of mathematical proof
1.2 Algebra and functions
P1.2.1 - Laws of indices for rational exponents
P1.2.2 - Surds and rationalising denominators
P1.2.3 - Quadratic functions and graphs
P1.2.4 - Simultaneous equations by elimination and substitution
P1.2.5 - Linear and quadratic inequalities
P1.2.6 - Algebraic manipulation of polynomials
P1.2.7 - Graphs of functions and the modulus graph
P1.2.8 - Composite and inverse functions
P1.2.9 - Transformations of y = f(x)
P1.2.10 - Partial fractions
P1.2.11 - Functions in modelling
1.3 Coordinate geometry in the (x, y) plane
P1.3.1 - Equation of a straight line
P1.3.2 - Coordinate geometry of the circle
P1.3.3 - Parametric equations and Cartesian form
P1.3.4 - Parametric equations in modelling
1.4 Sequences and series
P1.4.1 - Binomial expansion of (a + bx)^n
P1.4.2 - Sequences
P1.4.3 - Sigma notation
P1.4.4 - Arithmetic sequences and series
P1.4.5 - Geometric sequences and series
P1.4.6 - Sequences and series in modelling
1.5 Trigonometry
P1.5.1 - Unit-circle trigonometry, triangle rules and radians
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P1.5.2 - Small angle approximations
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P1.5.3 - Sine, cosine and tangent functions
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P1.5.4 - Secant, cosecant, cotangent and inverse trig functions
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P1.5.5 - Trigonometric identities
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P1.5.6 - Compound and double angles, half-angles and R-form
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P1.5.7 - Simple trigonometric equations
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P1.5.8 - Proofs with trigonometric identities
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P1.5.9 - Trigonometric functions in context
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1.6 Exponentials and logarithms
P1.6.1 - Exponential functions and graphs
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P1.6.2 - Gradient of e^{kx}
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P1.6.3 - Logarithms and natural logarithms
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P1.6.4 - Laws of logarithms
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P1.6.5 - Equations of the form a^x = b
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P1.6.6 - Logarithmic graphs for estimating parameters
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P1.6.7 - Exponential growth and decay in modelling
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1.7 Differentiation
P1.7.1 - Derivatives, tangents and second derivatives
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P1.7.2 - Differentiating powers, exponentials, logarithms and trigonometric functions
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P1.7.3 - Gradients, tangents, normals, maxima and minima
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P1.7.4 - Product, quotient and chain rules
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P1.7.5 - Implicit and parametric differentiation
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P1.7.6 - Constructing simple differential equations
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1.8 Integration
P1.8.1 - Fundamental Theorem of Calculus
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P1.8.2 - Integrating powers, rational functions and standard forms
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P1.8.3 - Definite integrals and area under a curve
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P1.8.4 - Integration as the limit of a sum
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P1.8.5 - Integration by substitution and by parts
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P1.8.6 - Integration using partial fractions
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P1.8.7 - First order differential equations with separable variables
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P1.8.8 - Interpreting differential equation solutions in context
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1.9 Numerical methods
P1.9.1 - Locating roots by sign changes
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P1.9.2 - Iteration, cobweb and staircase diagrams
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P1.9.3 - Newton-Raphson and recurrence relations
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P1.9.4 - Numerical integration and the trapezium rule
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P1.9.5 - Numerical methods in context
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1.10 Vectors
P1.10.1 - Vectors in two and three dimensions
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P1.10.2 - Magnitude, direction and component form
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P1.10.3 - Vector addition and scalar multiplication
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P1.10.4 - Position vectors and distance between points
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P1.10.5 - Vectors in pure mathematics and context
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Statistics (Paper 3, Section A)
Large Data Set
S3.LDS - Pearson Large Data Set: weather variables and context
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3.1 Statistical sampling
S3.1.1 - Populations, samples and sampling techniques
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3.2 Data presentation and interpretation
S3.2.1 - Single-variable data diagrams
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S3.2.2 - Scatter diagrams and regression lines
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S3.2.3 - Measures of central tendency and variation
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S3.2.4 - Outliers in data sets
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3.3 Probability
S3.3.1 - Mutually exclusive and independent events
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S3.3.2 - Conditional probability with diagrams and tables
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S3.3.3 - Probability modelling and assumptions
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3.4 Statistical distributions
S3.4.1 - Discrete and binomial probability distributions
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S3.4.2 - Normal distribution as a model
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S3.4.3 - Choosing an appropriate probability distribution
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3.5 Statistical hypothesis testing
S3.5.1 - Language of statistical hypothesis testing
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S3.5.2 - Hypothesis test for a binomial proportion
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S3.5.3 - Hypothesis test for a normal mean
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Mechanics (Paper 3, Section B)
3.6 Quantities and units in mechanics
M3.6.1 - Fundamental and derived S.I. units
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3.7 Kinematics
M3.7.1 - Position, displacement, distance, velocity, speed and acceleration
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M3.7.2 - Kinematics graphs in straight-line motion
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M3.7.3 - Constant acceleration formulae
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M3.7.4 - Calculus in kinematics
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M3.7.5 - Motion under gravity using vectors
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3.8 Forces and Newton's laws
M3.8.1 - Force and Newton's first law
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M3.8.2 - Newton's second law in straight-line motion
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M3.8.3 - Weight and motion under gravity
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M3.8.4 - Newton's third law and equilibrium
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M3.8.5 - Addition and resultant forces in dynamics
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M3.8.6 - Friction, limiting friction and static friction
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3.9 Moments
M3.9.1 - Moments in simple static contexts
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