GCSE Higher

SHAPE, SPACE AND MEASURES

Angles at a point; on straight line; perpendicular lines; opposite angles
Use parallel lines, alternate and corresponding angles
Understand the properties of parallelograms
Understand the proof of angle sum of a triangle is 180
Understand a proof that the exterior angle of a triangle = sum of interior angles at other 2 vertices
Distinguish between lines and line segments
Use angles properties of equilateral, isosceles and right angled triangles
Explain why the angle sum of a quadrilateral is 360 degrees

Recall properties of quadrilaterals and classify quadrilaterals by their geometric properties
Calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons
Calculate and use the angles of regular polygons
Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles

Understand, recall and use Pythagoras’ Theorem in 2D
Understand and use Similar Triangles and other shapes
Understand, recall and use Trigonometry;
Solve problems using these, including those involving bearings
Use these in 3D contexts, including finding the angle between a line and a plane
Use the Sine and Cosine Rules to solve 2D and 3D problems

Circles- know radius, chord, diameter, circumference, tangent, arc, sector, segment
Find Circumference of circles and areas enclosed by circles
Understand the tangent at any point is perpendicular to the radius at that point
Understand and use that tangents from an external point are equal in length
PROVE and Use the facts:
The angle subtended by an arc at the centre of a circle is twice the angle at any point on the circumference;
The angle on the circumference in a semicircle is a right angle; Angles in the same segment are equal;
Opposite angle in a cyclic quadrilateral = 180 degrees.
Prove and use the alternate segment theorem

Find area of rectangle; triangle; parallelogram; circles; surface area of shapes; volume of cuboids and prisms; Calculate the area of a triangle using ½ abSinC
Solve problems involving surface areas and volumes of prisms and cylinders; pyramids, cones and spheres, segments of circles, frustrums of cones.
Calculate the length of arcs and areas of sectors of a circle

Understand that rotation is specified by a centre and an angle; Reflection is specified by a mirror line;
Translations specified by a vector; Enlargements specified by a centre and positive scale factor
Recognise reflection symmetry in 2D and 3D shapes; rotation in 2D shapes; translations
Transform 2D shapes by combinations of translation, rotation and reflection
Distinguish properties that are preserved under particular transformations
Recognise and construct enlargements of shapes using positive whole number, fractional and negative S.F.
Identify the scale factor of an enlargement as the ratio of the lengths of 2 corresponding sides
Understand the effect of enlargement on perimeter, area and volume

Understand the difference between formulae for perimeter, area and volume by considering dimensions
Find the coordinates of the midpoint of a line AB given A and B; Calculate the length of AB
Understand and use vector notation; calculate the sum, difference and scalar multiple of 2 vectors
Solve simple geometric problems in 2D using vector methods

Understand and use speed and density
Recognise that measurements given to nearest unit are inaccurate by up to half in either direction
Construct triangles and other 2D shapes, cubes, square based pyramids and other 3D shapes
Construct the midpoint and perpendicular bisector of a line; perpendicular from a point to a line; bisector of an angle; perpendicular from a point on a line