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.

Applications of right and non-right angled trigonometry, including Pythagoras’s theorem. Angles of elevation and depression. Construction of labelled diagrams from written statements.

The circle: radian measure of angles; length of an arc; area of a sector.

Definition of cosθ, sinθ in terms of the unit circle. Definition of tanθ as Exact values of trigonometric ratios of 0, , , , and their multiples. Extension of the sine rule to the ambiguous case.

The Pythagorean identity cos2θ + sin2θ = 1. Double angle identities for sine and cosine. The relationship between trigonometric ratios.

The circular functions sinx, cosx, and tanx; amplitude, their periodic nature, and their graphs Composite functions of the form f (x) = asin(b(x + c)) + d. Transformations. Real-life contexts.

Solving trigonometric equations in a finite interval, both graphically and analytically. Equations leading to quadratic equations in sinx, cosx or tanx.

Definition of the reciprocal trigonometric ratios secθ, cosecθ and cotθ. Pythagorean identities: The inverse functions f (x) = arcsinx, f (x) = arccosx, f (x) = arctanx; their domains and ranges; their graphs.

Compound angle identities. Double angle identity for tan.

Relationships between trigonometric functions and sin(π the symmetry properties of their graphs.

Concept of a vector; position vectors; displacement vectors. Representation of vectors using directed line segments. Base vectors i, j, k. Components of a vector: v1 v = v2 = v1i + v2 j + v3k. v3 Algebraic and geometric approaches to the following: • the sum and difference of two vectors • the zero vector 0, the vector −v • multiplication by a scalar, kv, parallel vectors • magnitude of a vector, |v|; unit vectors, • position vectors OA = a, OB = b • displacement vector AB = b − a Proofs of geometrical properties using vectors.

The definition of the scalar product of two vectors. The angle between two vectors. Perpendicular vectors; parallel vectors.

Vector equation of a line in two and three dimensions: r = a + λb. The angle between two lines. Simple applications to kinematics.

Coincident, parallel, intersecting and skew lines, distinguishing between these cases. Points of intersection.

The definition of the vector product of two vectors. Properties of the vector product. Geometric interpretation of | v × w |

Vector equations of a plane: r = a + λb + μc, where b and c are non-parallel vectors within the plane. r · n = a · n, where n is a normal to the plane and a the position vector of a point on the plane. Cartesian equation of a plane ax + by + cz = d.

Intersections of: a line with a plane; two planes; three planes. Angle between: a line and a plane; two planes.