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Geometry and trigonometry

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  1. 6 Geometry

    1. 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

    2. 6.BGeometrical reasoning

      Geometrical reasoning

    3. 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

    4. 6.DQuadrilaterals

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

    5. 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. 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

    7. 6.GSimilarity

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

    8. 6.HTriangle similarity

      Prove the similarity of two triangles

    9. 6.ICongruent shapes

      Congruent shapes

    10. 6.JTriangle congruence

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

    11. 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

    12. 6.LCyclic quadrilaterals

      Properties of a cyclic quadrilateral

    13. 6.MLoci

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

    14. 6.NConstructions

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

  2. 7 Mensuration

    1. 7.ALength, area and volume

      Length, area, and volume

    2. 7.B2D mensuration

      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)

    3. 7.C3D mensuration

      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)

    4. 7.DArcs and sectors

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

  3. 8 Vectors and transformation geometry

    1. 8.AScalars and vectors

      Scalar and vector quantities Vectors will be in two dimensions only

    2. 8.BVector notation

      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

    3. 8.CDirected line segments

      Representation of a vector by a directed line segment

    4. 8.DParallel, unit and position vectors

      Parallel vectors, unit vectors and position vectors

    5. 8.EVector sums and differences

      Sum and difference of two vectors

    6. 8.FVector magnitude

      Modulus (magnitude) of a vector

    7. 8.GScalar multiplication of vectors

      Multiplication of a vector by a scalar

    8. 8.HResultant vectors

      Find the resultant of two or more vectors

    9. 8.IVector geometry

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

    10. 8.JTransformations

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

    11. 8.KCombined transformations

      Combination of transformations

    12. 8.LVectors and matrices

      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

  4. 9 Trigonometry

    1. 9.ASine, cosine and tangent

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

    2. 9.B2D and 3D trigonometry

      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

    3. 9.CElevation and depression

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

    4. 9.DBearings

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