Section 1 Part 1: AS-level pure mathematics
| Topic | Spec | Bank | Real | Progress | |
|---|---|---|---|---|---|
| Indices and surds Laws of indices for rational exponents; simplifying surds and rationalising denominators. | MM1.1, MM1.2, M2.7, M2.11, M2.12 | 23 | 3 | notesquick-fire | |
| Quadratic functions Graphs, the discriminant, completing the square, solving quadratic equations, roots and turning points. | MM1.3, M4.5, M4.11-M4.14 | 26 | 18 | notesquick-fire | |
| Simultaneous equations and inequalities Linear/quadratic simultaneous equations by substitution; linear and quadratic inequalities. | MM1.4, MM1.5, M4.16, M4.17 | 19 | 12 | notesquick-fire | |
| Polynomials, factor and remainder theorems Expanding, factorising, algebraic division by linear and quadratic divisors, the Factor and Remainder Theorems. | MM1.6 | 17 | 12 | notesquick-fire | |
| Functions and transformations One-to-one and many-to-one mappings, square-root and modulus functions, af(x), f(x)+a, f(x+a), f(ax) and compositions. | MM1.7, MM8.2, MM8.3, MM8.4 | 18 | 11 | notesquick-fire | |
| Sequences and series nth-term and recurrence sequences; arithmetic series; finite and infinite geometric series. | MM2.1, MM2.2, MM2.3, M4.19 | 23 | 24 | notesquick-fire | |
| Binomial expansion Expanding (1+x)^n and (a+f(x))^n for positive integer n; n! and nCr notation. | MM2.4 | 16 | 12 | notesquick-fire | |
| Straight lines Equations of lines, gradients, parallel and perpendicular lines, distances and midpoints. | MM3.1, M4.9, M4.10 | 15 | 7 | notesquick-fire | |
| Circles and circle theorems Equation of a circle in both forms, tangents and chords, and the seven circle theorems. | MM3.2, MM3.3, M5.8, M5.9 | 17 | 13 | notesquick-fire | |
| Triangles, radians and sectors Sine and cosine rules (including the ambiguous case), area = 1/2 ab sin C, radians, arc length, sector and segment area. | MM4.1, MM4.2, M5.16 | 17 | 8 | notesquick-fire | |
| Trigonometric functions and equations Exact values, graphs and periodicity of sin, cos, tan; tan = sin/cos and sin^2 + cos^2 = 1; solving equations in an interval. | MM4.3-MM4.6 | 19 | 33 | notesquick-fire | |
| Exponentials and logarithms y = a^x, the laws of logarithms, and solving a^x = b and equations that reduce to it. | MM5.1-MM5.3 | 21 | 25 | notesquick-fire | |
| Differentiation Derivatives of x^n, gradients, tangents and normals, stationary points, increasing and decreasing functions, second derivatives. | MM6.1-MM6.3, MM8.5 | 22 | 26 | notesquick-fire | |
| Integration Integrals of x^n, areas between curves and axes, the Fundamental Theorem of Calculus, combining integrals, the trapezium rule and dy/dx = f(x). | MM7.1-MM7.6 | 22 | 35 | notesquick-fire | |
| Graphs of functions Sketching lines, quadratics, cubics, trig, log, exponential, root and modulus graphs; intersections with axes; roots and intersections of graphs. | MM8.1, MM8.5-MM8.7, M4.15 | 18 | 24 | notesquick-fire |
Section 1 Part 2: Higher GCSE mathematics
| Topic | Spec | Bank | Real | Progress | |
|---|---|---|---|---|---|
| Number, units and estimation Units and compound measures, primes, HCF/LCM, index laws, standard form, recurring decimals, bounds, rounding and estimation, systematic counting. | M1.1, M1.2, M2.1-M2.14 | 21 | 4 | notesquick-fire | |
| Ratio, proportion and percentages Ratio and scale, percentage change and reverse percentages, direct and inverse proportion, growth and decay, similarity of lengths, areas and volumes. | M3.1-M3.11 | 15 | 2 | notesquick-fire | |
| GCSE algebra Algebraic manipulation, rearranging formulae, identities, rational expressions, nth terms of linear and quadratic sequences, kinematics graphs. | M4.1-M4.8, M4.18, M4.19 | 15 | 1 | notesquick-fire | |
| Angles, polygons, congruence and vectors Angle facts, interior and exterior angles, special quadrilaterals, congruence criteria, similarity, transformations, bearings and vectors. | M5.1-M5.6, M5.10, M5.14, M5.18, M5.19 | 16 | 9 | notesquick-fire | |
| Pythagoras, mensuration and 3D Pythagoras in 2D and 3D, areas of composite shapes, volumes and surface areas of prisms, cylinders, cones, spheres and pyramids, trig ratios in right-angled triangles. | M5.7, M5.11-M5.13, M5.15-M5.17 | 17 | 3 | notesquick-fire | |
| Statistics Mean, median, mode and range (including grouped estimates), histograms and frequency density, cumulative frequency, quartiles, scatter graphs. | M6.1-M6.4 | 11 | 3 | notesquick-fire | |
| Probability Possibility spaces, tree diagrams, Venn diagrams, mutually exclusive and independent events, conditional probability, expected frequency. | M7.1-M7.7 | 13 | 3 | notesquick-fire |
Section 2: Mathematical reasoning (Paper 2 only)
| Topic | Spec | Bank | Real | Progress | |
|---|---|---|---|---|---|
| The logic of arguments If/then, A if B, A only if B, if and only if; converse and contrapositive; necessary and sufficient; for all / for some / there exists; negating statements. | Arg1-Arg4 | 25 | 24 | notesquick-fire | |
| Mathematical proof Direct proof, proof by cases, proof by contradiction, disproof by counterexample; deducing implications; conjectures from small cases; ordering the steps of a proof. | Prf1-Prf4 | 21 | 12 | notesquick-fire | |
| Chains of reasoning Problems needing a sophisticated chain of reasoning: which statements must / could be true, extremal arguments, pigeonhole-style counting, working systematically. | Prf2, Prf3, Prf5 | 23 | 18 | notesquick-fire | |
| Identifying errors in proofs Spotting the first wrong line in a purported proof; the classic invalid deductions (x^2 = y^2 so x = y, sin a = sin b so a = b, dividing by zero, squaring inequalities). | Err1, Err2 | 19 | 18 | notesquick-fire |