Operations with numbers in the form a × 10k where 1 ≤ a < 10 and k is an integer.

Arithmetic sequences and series. Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for sums of arithmetic sequences. Applications. Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.

Different forms of the equation of a straight line. Gradient; intercepts. Lines with gradients m1 and m2 Parallel lines m1 = m2. Perpendicular lines m1 × m2 = − 1.

Concept of a function, domain, range and graph. Function notation, for example f (x), v(t), C(n). The concept of a function as a mathematical model. Informal concept that an inverse function reverses or undoes the effect of a function. Inverse function as a reflection in the line y = x, and the notation f −1(x).

The distance between two points in three-dimensional space, and their midpoint. Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids. The size of an angle between two intersecting lines or between a line and a plane.

Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles. a The sine rule: = sinA sinB sinC The cosine rule: c2 = a2 + b2 − 2abcosC; a2 + b2 − c2 cosC = 2ab Area of a triangle as absinC.

Concepts of population, sample, random sample, discrete and continuous data. Reliability of data sources and bias in sampling. Interpretation of outliers. Sampling techniques and their effectiveness.

Presentation of data (discrete and continuous): frequency distributions (tables). Histograms. Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR). Production and understanding of box and whisker diagrams.

Introduction to the concept of a limit. Derivative interpreted as gradient function and as rate of change.

Increasing and decreasing functions. Graphical interpretation of f ′(x) > 0, f ′(x) = 0, f ′(x) < 0.