Mathematics Topic Directory

Positive and negative integers, BIDMAS rules, and place value.

Adding, subtracting, multiplying and converting fractions and decimals.

Percentage change, reverse percentages, and simple/compound interest.

Sharing in ratios, direct and inverse proportion problems.

Laws of indices, fractional and negative powers.

Expressing large and small numbers in scientific standard form.

Simplifying, collecting like terms, and expanding single brackets.

Single brackets, double brackets, and difference of two squares.

Solving equations with unknowns on one side and both sides.

Solving by factorising, completing the square, and using the formula.

Elimination, substitution, and graphical intersection methods.

Arithmetic, geometric, quadratic, and Fibonacci-style sequences.

Domain, range, inverse functions f⁻¹(x) and composite functions gf(x).

Angles on straight lines, parallel lines, polygons and triangles.

Calculations for rectangles, triangles, parallelograms, and trapeziums.

Circumference, area of circle, arc length, and sector area.

Prisms, cylinders, pyramids, cones, and spheres.

Translation, reflection, rotation, and enlargement with scale factors.

Angles at centre, cyclic quadrilaterals, alternate segment theorem.

Finding missing sides and angles using sin, cos, and tan ratios.

Calculating hypotenuse and shorter sides in 2D and 3D shapes.

Solving non-right-angled triangles and calculating area using ½ab sin(C).

Graphs of sin x, cos x, tan x, transformations and exact values.

Using sin²θ + cos²θ = 1 and tanθ = sinθ/cosθ to prove identities.

Mean, median, mode, and range from raw data and frequency tables.

Drawing and interpreting histograms with unequal class widths.

Plotting cumulative curves, finding median and interquartile range (IQR).

Line of best fit, positive/negative correlation, and extrapolation.

Measures of spread, variance, standard deviation, and Z-scores.

Probability scale, expected frequency, and relative frequency.

Sample space diagrams, AND/OR rules for independent events.

Independent and dependent events without replacement.

Intersections ∩, unions ∪, complements, and conditional probability P(A|B).

First principles, power rule d/dx(xⁿ) = nxⁿ⁻¹, gradients of tangents.

Finding turning points, using second derivative d²y/dx² to classify.

Differentiating composite functions, products, and quotients.

Indefinite integration ∫xⁿ dx, constant of integration + C.

Evaluating limits, calculating area enclosed between curves and x-axis.

Vector addition, scalar multiplication, magnitude and direction.

Using vectors to prove parallel lines, collinear points, and ratios.

Constant acceleration equations v = u + at, s = ut + ½at².

Resolving forces, friction, F = ma, inclined planes, and pulleys.