Roadmap
Pure Mathematics
Proof and mathematical argument
A1 - Deduction, exhaustion and counterexamples
A1 - Proof by contradiction
Algebra
B1, B2 - Indices and surds
B3 - Quadratic graphs and discriminants
B3 - Quadratic equations in unfamiliar forms
B4 - Simultaneous equations
B5 - Linear and quadratic inequalities
B5 - Regions defined by inequalities
B6 - Polynomials and the factor theorem
B6 - Rational expressions and algebraic division
Functions and graphs
B7 - Function graphs and intersections
B8 - Composite and inverse functions
B9 - Transforming function graphs
B10 - Partial fractions
B11 - Functions as models
Coordinate geometry
C1 - Straight lines and linear models
C2 - Circles, chords and tangents
C3 - Parametric and Cartesian equations
C4 - Parametric models
Sequences and series
D1 - Binomial expansions for integer powers
D1 - General binomial expansions and approximations
D2, D3 - Sequences, recurrence and sigma notation
D4 - Arithmetic sequences and series
D5 - Geometric sequences and series
D6 - Sequence and series models
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Trigonometry
E1 - Trigonometric ratios and triangle rules
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E1 - Radians, arcs and sectors
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E2 - Small-angle approximations
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E3 - Trigonometric graphs and exact values
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E4 - Reciprocal and inverse trigonometric functions
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E5, E8 - Trigonometric identities and proofs
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E6 - Compound and double-angle formulae
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E6 - Combining sine and cosine
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E7 - Solving trigonometric equations
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E9 - Trigonometric models and applications
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Exponentials and logarithms
F1, F3 - Exponential and logarithmic functions
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F4, F5 - Logarithm laws and equations
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F6 - Linearising exponential and power data
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F2, F7 - Exponential growth and decay models
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Differentiation
G1 - Derivatives from first principles
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G1 - First principles for sine and cosine
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G2 - Standard derivatives
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G3 - Tangents, normals and monotonicity
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G3 - Stationary points and optimisation
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G4 - Product and quotient rules
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G4 - Chain rule and composite derivatives
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G4 - Connected rates and inverse derivatives
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G5 - Implicit and parametric differentiation
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G6 - Constructing differential equations
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Integration and differential equations
H1, H2 - Antiderivatives and the fundamental theorem
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H2 - Standard exponential and trigonometric integrals
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H3 - Definite integrals and areas
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H4 - Integration as a limit of sums
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H5 - Integration by substitution
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H5 - Integration by parts
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H6 - Integration using partial fractions
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H7, H8 - Separable differential equations and models
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Numerical methods
I1 - Locating roots and sign-change limits
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I2 - Fixed-point iteration
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I2 - Newton-Raphson iteration
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I3, I4 - Trapezium rule and numerical models
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Vectors
J1, J2, J3 - Vector components and operations
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J4 - Position vectors and geometry
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J5 - Vector proofs and contextual problems
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Mechanics
Motion and modelling
P1, Q1 - Mechanical quantities and modelling
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Q2 - Displacement and velocity graphs
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Q3 - Constant-acceleration equations
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Q3 - Vector constant-acceleration motion
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Q4 - Calculus for straight-line motion
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Q4 - Calculus for vector motion
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Q5 - Projectile motion
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Forces and Newton's laws
R1, R3 - Forces, weight and Newton's first law
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R2, R5 - Resultant forces and Newton's second law
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R2, R4 - Resolving forces and equilibrium
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R3 - Vertical dynamics
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R4 - Newton's third law and connected particles
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R6 - Friction and limiting equilibrium
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R2, R4, R6 - Rough slopes and connected dynamics
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Moments and static equilibrium
S1 - Moments and equilibrium of rigid bodies
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S1 - Modelling supports and tipping
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Statistics
Sampling and the AQA large data set
K1, 3.21.1 - The AQA car data set and populations
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K1 - Sampling techniques and inference
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K1, L4, 3.21 - Using technology to investigate real data
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Presenting and interpreting data
L1 - Data displays and histograms
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L3 - Location, spread and standard deviation
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L4 - Outliers, missing values and data choices
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L2 - Scatter diagrams, regression and correlation
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Probability
M1 - Events, independence and probability
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M2 - Conditional probability
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M3 - Probability models and assumptions
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Statistical distributions
N1, N3 - Discrete and binomial distributions
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N2 - Normal distributions and probabilities
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N2, N3 - Choosing and checking distribution models
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Hypothesis testing
O1, O2 - Binomial hypothesis tests
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O1 - Correlation hypothesis tests
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O3 - Normal mean hypothesis tests
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