Geometry and trigonometry

6.AEuclidean geometry

Geometrical properties of Euclidean space, as listed below In solving any problem or rider, students may use any knowledge they possess Solutions may be by traditional methods (e.g. congruent triangles), vectors, the use of transformations such as translation, reflection, rotation and enlargement, or a mixture of these Formal proofs of theorems will not be required

6.BGeometrical reasoning

Geometrical reasoning

6.CAngle properties

Angle properties of parallel lines, triangles and polygons, including regular polygons Angles on a straight line, angles around a point Angles measured anticlockwise will be taken as positive; clockwise as negative

6.DQuadrilaterals

Properties of the parallelogram, rectangle, square, rhombus, trapezium and kite

6.ESymmetry

Symmetry about a point, line or plane Recognise line and rotational symmetry Complete shapes with a given axis of symmetry and order of rotational symmetry

6.FPythagoras in 2D and 3D

Use of Pythagoras’ theorem in 2D and 3D Including its use in any acute–angled triangle where an altitude is given or constructed The angle bisector theorems are excluded

6.GSimilarity

Similarity: areas and volumes of similar figures Understanding how scale factors are related to area and volume

6.HTriangle similarity

Prove the similarity of two triangles

6.ICongruent shapes

Congruent shapes

6.JTriangle congruence

Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles

6.KCircle theorems

Chord, angle and tangent properties of circles To include knowledge of the intersecting chord properties (both internal and external) and the alternate segment theorem

6.LCyclic quadrilaterals

Properties of a cyclic quadrilateral

6.MLoci

Loci in two dimensions ‘Tracing paper’ methods will not be acceptable

6.NConstructions

Constructions of bisector of an angle and of perpendicular bisector (mediator) of a straight line Constructions using only ruler and compasses

Length, area, and volume

Mensuration of two-dimensional shapes, rectangle, parallelogram, trapezium, triangle, circle Straightforward calculations, where appropriate, of areas of the shapes mentioned and also of two-dimensional shapes that can be divided into a collection of such shapes (e.g. trapezia, polygons)

Mensuration of three-dimensional shapes, right circular cylinder, right circular cone and sphere, cuboid, pyramid, prism Straightforward calculations, where appropriate, of volumes of the shapes mentioned and also of three-dimensional shapes which can be divided into a collection of such shapes (e.g. cone, hemisphere)

Length of an arc, area of a sector of a circle Radian measure is excluded

Scalar and vector quantities Vectors will be in two dimensions only

Understand and use vector notation The notation for the vector from O to A, written OA with an arrow above it, and the bold vector a will be used, as will column vectors

Representation of a vector by a directed line segment

Parallel vectors, unit vectors and position vectors

Sum and difference of two vectors

Modulus (magnitude) of a vector

Multiplication of a vector by a scalar

Find the resultant of two or more vectors

Apply vector methods to simple geometrical problems The problems may involve colinearity, parallel lines and concurrency

Transformations of the plane Reflections in any line Rotations about any point Translations Enlargements

Combination of transformations

Multiplication of a vector by a matrix To include the finding of a matrix for a given transformation of the plane, using the column vectors (1, 0)ᵀ and (0, 1)ᵀ These transformations will be those for which the origin is unchanged

Use of sine, cosine and tangent of angles up to 180° Angles will be measured in degrees and decimals of a degree

Solution of problems in two and three dimensions by calculation and by drawing Use of the sine and cosine rule Area of a triangle = ¹⁄₂ab sin C Questions on latitude and longitude will not be set Calculations of the angle between two planes, or of the angle between a straight line and a plane will not be set

Angles of elevation and depression Angles will be given in degrees and decimals of a degree

Bearings The normal convention of bearings being measured clockwise will be adopted