9 Solve problems involving frustums of cones Find the area of a segment of a circle given the radius and length of the chord Solve problems for areas and volumes of similar shapes and solids Use trigonometry to solve 3-D problems Find the angle between a line and a plane Know the exact values of sin Ѳ and cos Ѳ for  Ѳ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan  Ѳ for  Ѳ = 0°, 30°, 45° and 60° Use the sine and cosine rules to solve 2-D and 3-D problems Apply vector methods for simple geometrical proofs Calculate the new volume of a shape after enlargement 8 Use the formulae for length of arcs and area of sectors of circles to solve problems Understand and use the fact that tangents from an external point are equal in length Prove lines are parallel or collinear Find points that divide a line in a given ratio, using the properties of similar triangles 7 Prove and use the alternate segment theorem Use Pythagoras’ theorem in 3-D problems Calculate the length of a diagonal of a cuboid Enlarge 2D shapes, given a negative, fractional scale factor Use the sine rule to find unknown lengths and angles Use the cosine rule to find unknown lengths Calculate the area of a triangle using 1/2 ab sin⁡C Work out the magnitude of a vector Calculate, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector Calculate the resultant of two vectors Solve geometrical problems in 2-D using vector methods Calculate the new area of a shape after enlargement 6 Use trigonometry to find the lengths of unknown sides, using more complex algebraic manipulation Find angles of elevation and angles of depression Prove and use the fact that the angle in a semicircle is a right angle Prove and use the fact that angles in the same segment are equal Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180° Prove and use facts about the angle subtended at the centre and at the circumference Know that the tangent at any point on a circle is perpendicular to the radius at that point Know that the perpendicular from the centre to the chord bisects the chord Complete a formal geometric proof of similarity of two given triangles 5 Find the surface area of prisms Find the surface area and volumes of compound solids Recognise the formulae for length of arcs in a circle and area of sectors in a circle. Use similarity to solve problems in 2D shapes Extend understanding of loci to include 3D problems Know the formula for Pythagoras’ theorem and use to find a shorter side Use Trigonometry to find lengths of unknown sides in a right-angled triangle Transform 2D shapes by a more complex combinations of rotations, reflections and translations Add and Subtract vectors Convert between compound measures (e.g. convert 2 m/s to km/h) Convert imperial units to imperial units Convert between metric and imperial measures Identify the scale factor of an enlargement 4 Use accurate drawing to solve bearings problems Calculate missing interior angles in polygons Calculate volumes of shapes made from cuboids Calculate the volume and surface area of right prisms Calculate the lengths, areas and volumes in cylinders Calculate the radius or diameter of a circle given the circumference or area Find the perimeters and areas of semicircles and quarter circles Use information to determine whether triangles are congruent or similar Construct the perpendicular from or to a point on a line segment Construct a triangle, given right angle, hypotenuse and side Construct loci Construct angles of 60°, 90°, 30°, 45° Know the formula for Pythagoras’ theorem and use to find the hypotenuse Use vector notation for translations Enlarge 2D shapes, given a fractional scale factor Find the centre of rotation Describe a transformation Describe reflections on a coordinate grid Express points as position vectors and understand and use vector notation Know that enlargements of 2D shapes produce similar shapes 3 Given the bearing of point A from point B, work out the bearing of B from A Identify co-interior angles and their values. Know that the sum of the exterior angles of any polygon is 360° Calculate the interior angles of regular polygons Deduce and use the formula for the area of a trapezium Calculate surface areas of shapes made from cuboids Know and use the formulae for the circumference and area of a circle Identify shapes which are similar Identify more complex nets of 3D shapes Draw plans and elevations of 3-D shapes Use straight edge and compasses to construct the bisector of an angle Use straight edge and compasses to construct a triangle given three sides (SSS) Construct an equilateral triangle and a regular hexagon inside a circle Use trigonometry to find the size of an angle in a right-angled triangle Know the names of parts of a circle Enlarge shapes, given a centre of enlargement and a positive integer scale factor Find the centre of enlargement Know rough metric equivalents of imperial measures in daily use Convert between area measures Convert between metric measures of volume and capacity 2 Identify alternate and corresponding angles on parallel lines and their values. Find the area of triangles by counting Know the formulae for the volume of cube and a cuboid Use a formula to calculate the area of parallelograms Use a formula to calculate the area of triangles Know that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not. Know that translations, rotations and reflections map objects on to congruent images Identify simple nets of 3D shapes Use straight edge and compasses to construct the midpoint and perpendicular bisector of a line Draw a circle given the radius or diameter Know that translations, rotations and reflections preserve length and angle Recognise that enlargements preserve angle but not length 1 Use a protractor to draw obtuse and reflex angles to the nearest degree Give a bearing between the points on a map or scaled plan Identify interior and exterior angles in a shape Find missing angles around a point Recognise and use vertically opposite angles Find missing angles in a quadrilateral Know that the sum of the interior angle and the exterior angle is 180° Calculate the perimeter and area of shapes made from rectangles Calculate the surface area of cubes and cuboids, without a net Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Use ruler and protractor to construct simple nets of 3D shapes Begin to use plans and elevations Identify regular and irregular polygons Draw or complete diagrams given information about rotational or line symmetry Plot coordinates to complete a shape Use properties of equilateral and isosceles triangles to solve problems Solve simple geometrical problems using properties of quadrilaterals Convert between simple metric units W3 Begin to estimate the size of angles Use a protractor to measure obtuse and reflex angles to the nearest degree Use a protractor to draw acute angles to the nearest degree Measure shapes to find perimeters and areas Use correct notation for labelling angles and triangles Distinguish between acute, obtuse and reflex angles Identify perpendicular lines Use the formula for the area of a rectangle/square Use nets to calculate the surface area of cubes and cuboids Calculate perimeter and area of compound shapes made from triangles, rectangles and other shapes Calculate missing angles in a triangle Identify simple angle, side and symmetry properties of triangles and quadrilaterals Recognise and visualise – rotation about a given point Draw lines and shapes to scale Use and interpret maps and scale drawings, using a variety of scales and units Estimate length using a scale diagram W2 Measure lines to the nearest millimetre Use a protractor to measure acute angles to the nearest degree Identify parallel lines Know the sum of angles around a point Understand that area is measured in square centimetres Choose suitable metric units to estimate length and area. Draw parallel lines and mark parallel lines on a diagram Recognise reflection symmetry Use correct notation for labelling lines Know the sum of angles in a triangle is 180° Recognise and visualise the reflection in a mirror line of a 2-D shape Translate a shape on a square/coordinate grid Understand and use the language associated with rotations Read and construct scale drawings W1 Know the sum of angles on a straight line Know how to tessellate polygons Find the perimeter of a square/rectangle by counting Identify the net of a cube Identify and name common solids Know the terms face, edge and vertex Suggest suitable units to measure length, mass and capacity Read and interpret scales on a range of measuring instruments Work out time intervals Draw sketches of shapes Recognise properties of squares and rectangles Understand and use the language associated with translations Understand and use the language associated with reflections Enlarge a shape on a grid (without a centre specified)