GCSE Intermediate

SHAPE, SPACE AND MEASURES

Angles at a point; on straight line; perpendicular lines; opposite angles
Distinguish between acute, obtuse, reflex and right angles
Estimate the size of an angle
Measure and draw an angle
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

Deduce the formulae for area of a parallelogram and a triangle from the formula for area of rectangle
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, 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

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
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.

Find area of rectangle; triangle; parallelogram; circles; surface area of shapes; volume of cuboids and prisms; Solve problems involving surface areas and volumes of prisms and cylinders
Convert between area measures inc. cm and m and volume measures including cm and m

Understand that rotation is specified by a centre and an angle; Reflection is specified by a mirror line;
Translations specified by a given distance and direction (or a vector); Enlargements specified by centre and positive scale factor
Recognise reflection symmetry in 2D and 3D shapes; rotation in 2D shapes; translations
Transform 2D shapes by translation, reflection, rotation, about any centre, and combinations of these
Distinguish properties that are preserved under particular transformations
Recognise and construct enlargements of shapes using positive whole number and fractional scale factors
Identify the scale factor of an enlargement as the ratio of the lengths of 2 corresponding sides
Understand the effect of enlargement on perimeter

Use and interpret maps and scale drawings
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

Convert from one unit to another; Know rough metric equivalents of pounds, feet, miles, pints and gallons
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 using ruler and protractor
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