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A-Level Maths — Year 1 / AS Topic Tracker

AQA · Edexcel · OCR · Pure · Statistics · Mechanics

 
 
 
How to use: Shade each box honestly. Red Can't do it yet  ·  Amber Getting there  ·  Green Confident under exam pressure
Pure Mathematics
Algebra and Functions Red Amber Green
Index laws — positive, negative and fractional indices
Surds — simplifying, rationalising the denominator
Expanding brackets and collecting like terms
Factorising — common factors, difference of two squares, trinomials
Algebraic fractions — simplifying, adding, multiplying
Completing the square
Functions — domain, range, notation f(x)
Composite functions — fg(x)
Inverse functions — f⁻¹(x)
Quadratics Red Amber Green
Solving quadratics — factorising, formula, completing the square
Discriminant — b²−4ac and number of roots
Sketching quadratic graphs — vertex, intercepts
Quadratic inequalities
Simultaneous equations — one linear, one quadratic
Coordinate Geometry Red Amber Green
Straight lines — gradient, y = mx + c, ax + by + c = 0
Parallel and perpendicular lines
Midpoint and distance between two points
Equation of a circle — (x−a)² + (y−b)² = r²
Tangents and normals to a circle
Intersection of a line and a circle
Graphs and Transformations Red Amber Green
Sketching standard curves — y = xⁿ, y = 1/x, y = aˣ
Translations — y = f(x ± a), y = f(x) ± a
Reflections — y = −f(x), y = f(−x)
Stretches — y = af(x), y = f(ax)
Combining transformations
Binomial Expansion Red Amber Green
Pascal's triangle and nCr notation
Expanding (a + b)ⁿ for positive integer n
Finding specific terms in an expansion
Trigonometry Red Amber Green
SOHCAHTOA — in right-angled triangles
Sine rule and cosine rule
Area of a triangle — ½ab sin C
Exact trig values — 30°, 45°, 60°
Graphs of sin, cos, tan — shape, period, amplitude
Trig identities — sin²θ + cos²θ = 1, tan θ = sin θ/cos θ
Solving trig equations in a given interval
Transformations of trig graphs
Differentiation Red Amber Green
Differentiation from first principles
Differentiating polynomials — d/dx(xⁿ) = nxⁿ⁻¹
Second derivative — f''(x) and concavity
Stationary points — finding and classifying
Tangents and normals to a curve
Increasing and decreasing functions
Optimisation problems using differentiation
Integration Red Amber Green
Integrating polynomials — reverse of differentiation
Definite integrals — computing numerical values
Area under a curve — interpreting definite integrals
Area between two curves
Exponentials and Logarithms Red Amber Green
Exponential functions — y = aˣ and y = eˣ
The natural logarithm — ln x and its graph
Laws of logarithms — log(ab), log(a/b), log(aⁿ)
Solving equations with exponentials and logs
Linearising data — log graphs for y = axⁿ and y = abˣ
Vectors in 2D Red Amber Green
Vector notation — column vectors, i and j unit vectors
Adding, subtracting and scaling vectors
Magnitude of a vector
Unit vectors and position vectors
Geometric problems using vectors
Statistics
Statistical Sampling Red Amber Green
Population vs sample — advantages of sampling
Sampling methods — simple random, stratified, systematic, opportunity, quota
Data Presentation and Interpretation Red Amber Green
Histograms — frequency density, comparing distributions
Box plots — interpreting median, quartiles, outliers
Cumulative frequency diagrams
Scatter diagrams — correlation, outliers, interpolation vs extrapolation
Measures of Location and Spread Red Amber Green
Mean, median, mode from raw data and frequency tables
Variance and standard deviation — from data and coded data
Outliers — 1.5 × IQR rule and standard deviation rule
Coding data — effect on mean and standard deviation
Probability Red Amber Green
Probability basics — sample space, mutually exclusive, exhaustive
Addition rule — P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Conditional probability — P(A|B) = P(A ∩ B) / P(B)
Tree diagrams and Venn diagrams
Independent events — P(A ∩ B) = P(A) × P(B)
Statistical Distributions Red Amber Green
Binomial distribution — conditions for use
Calculating binomial probabilities — tables and formula
Mean and variance of binomial — np and np(1−p)
Hypothesis Testing (Binomial) Red Amber Green
Null and alternative hypotheses — H₀ and H₁
One-tailed and two-tailed tests
Critical regions and significance levels
Interpreting results — concluding in context
Mechanics
Kinematics Red Amber Green
Quantities — displacement, velocity, acceleration, time
SUVAT equations — selecting and applying correctly
Displacement-time and velocity-time graphs
Vertical motion under gravity — g = 9.8 m s⁻²
Forces and Newton's Laws Red Amber Green
Newton's first law — equilibrium, resultant force
Newton's second law — F = ma in one direction
Newton's third law — pairs of forces
Weight, normal reaction, tension and friction
Connected particles — strings over pulleys
Variable Acceleration (Calculus) Red Amber Green
Velocity as derivative of displacement — v = ds/dt
Acceleration as derivative of velocity — a = dv/dt
Finding displacement from velocity by integration