Mathematics

Year 9 core: the real number system (rational and irrational), the real number line, and scientific notation for very large and very small quantities.

Year 9 core: extend the index laws to zero, negative, and integer exponents applied to algebraic expressions, and connect to scientific notation.

Year 9 core: expand binomial products including perfect squares and difference of squares, factorise monic quadratics, and connect expanding and factorising as inverse operations.

Year 9 core: sketching linear graphs from y = mx + c and general form, gradient from two points, midpoint formula, distance formula, and parallel/perpendicular lines.

Year 9 core: graphing parabolas from y = ax^2 + bx + c, identifying key features, solving quadratic equations using the null factor law and factorisation.

Year 9 core: using linear functions to model real situations including simple interest, comparing plans, and interpreting gradient and y-intercept in context.

Year 9 core: how changing parameters in an equation shifts, stretches, compresses, or reflects its graph.

Year 9 core: surface area of right prisms and cylinders, volume of cylinders, and composite solids.

Year 9 core: sine, cosine, and tangent ratios in right-angled triangles, finding unknown sides and angles.

Year 9 core: applying Pythagoras' theorem in 2D and 3D contexts, trigonometric ratios for practical problems, angles of elevation and depression, bearings, and the distance formula on the Cartesian plane.

Year 9 core: absolute error, relative error, percentage error, upper and lower bounds of measurements, and how errors propagate through calculations.

Year 9 core: direct proportion (y = kx), recognising proportional relationships from tables and graphs, scale drawings and maps, rates in practical contexts, and modelling with proportion.

Year 9 core: enlargement transformations with scale factor k, properties preserved under enlargement, area and volume scaling, and using similarity to find unknown lengths.

Year 9 core: comparing data distributions using back-to-back stem-and-leaf plots and histograms, describing shape and spread, understanding sampling methods and bias, and planning statistical investigations.

Year 9 core: two-step experiments with and without replacement, tree diagrams, outcome tables, 'and' vs 'or' probabilities, relative frequency, and simulations.