·         vertically opposite angles, angles on a straight line and angles at a point

·         angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles

·         properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties

·         classifying special quadrilaterals on the basis of their properties

·         angle sum of interior and exterior angles of any convex polygon

·         properties of perpendicular bisectors of line segments and angle bisectors

·         construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate

·         properties of similar triangles and polygons:

*          corresponding angles are equal

*          corresponding sides are proportional

·         enlargement and reduction of a plane figure

·         scale drawings

·         determining whether two triangles are

*          congruent

*          similar

·         ratio of areas of similar plane figures

·         ratio of volumes of similar solids

·         solving simple problems involving similarity and congruence

*          equal chords are equidistant from the centre

*          the perpendicular bisector of a chord passes through the centre

*          tangents from an external point are equal in length

*      the line joining an external point to the centre of the circle bisects the angle between the tangents

·         angle properties of circles:

*          angle in a semicircle is a right angle

*          angle between tangent and radius of a circle is a right angle

*          angle at the centre is twice the angle at the circumference

*          angles in the same segment are equal

*          angles in opposite segments are supplementary

·         determining whether a triangle is right-angled given the lengths of three sides

·         use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles

·         extending sine and cosine to obtuse angles

·         use of the formula 1 ab sin C for the area of a triangle

2

·         use of sine rule and cosine rule for any triangle

·         problems in two and three dimensions including those involving angles of elevation and depression and bearings

·         problems involving perimeter and area of composite plane figures

·         volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere

·         conversion between cm² and m² , and between cm³ and m³

·         problems involving volume and surface area of composite solids

·         arc length, sector area and area of a segment of a circle

·         use of radian measure of angle (including conversion between radians and degrees)

·         finding the length of a line segment given the coordinates of its end points

·         interpreting and finding the equation of a straight line graph in the form

y = mx + c

·         geometric problems involving the use of coordinates

ç ÷

è y ø

·         representing a vector as a directed line segment

·         translation by a vector

·         position vectors

·         magnitude of a vector æ x ö as    x ² + y ²

ç ÷

è y ø

·         use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors

·         multiplication of a vector by a scalar

·         geometric problems involving the use of vectors

·         interpreting the solution in the context of the problem

*          tables

*          bar graphs

*          pictograms

*          line graphs

*          pie charts

*          dot diagrams

*          histograms with equal class intervals

*          stem-and-leaf diagrams

*          cumulative frequency diagrams

*          box-and-whisker plots

·         purposes and uses, advantages and disadvantages of the different forms of statistical representations

·         explaining why a given statistical diagram leads to misinterpretation of data

·         mean, mode and median as measures of central tendency for a set of data

·         purposes and use of mean, mode and median

·         calculation of the mean for grouped data

·         quartiles and percentiles

·         range, interquartile range and standard deviation as measures of spread for a set of data

·         calculation of the standard deviation for a set of data (grouped and ungrouped)

·         using the mean and standard deviation to compare two sets of data

·         probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)

·         probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)

·         addition and multiplication of probabilities (mutually exclusive events and independent events)