Year 8

Add, subtract, multiply and divide integers.
Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease.
Divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.
Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.
Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
Substitute integers into simple formulae.
Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c correspond to straight-line graphs.
Identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a quadrilateral is 360°.
Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor.
The names angles (interior and exterior) and symmetric properties of polygons up to and including decagons.
Use straight edge and compasses to do standard constructions.
Deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid; calculate volumes and surface areas of cuboids. The area and circumference of a circle.
Construct, on paper and using ICT, a range of graphs and charts; identify which are most useful in the context of a problem. Range and measures of average .
Find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way.
Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic, geometric or graphical form.
Use logical argument to establish the truth of a statement.

Year 8 Scholarship (in addition to the above)

Add, subtract, multiply and divide fractions.
Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole.
Make and justify estimates and approximations of calculations.
Construct and solve linear equations with integer coefficients, using an appropriate method.
Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence; write an expression to describe the nth term of an arithmetic sequence.
Given values for m and c, find the gradient of lines given by equations of the form

y = mx + c.

Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations.
Solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons.
Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems.
Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text.
Know and use the index laws for multiplication and division of positive integer powers.
Understand and use proportionality and calculate the result of any proportional change using multiplicative methods.
Square a linear expression and expand the product of two linear expressions of the form x ± n; establish identities.
Solve a pair of simultaneous linear equations by eliminating one variable; link a graphical representation of an equation or a pair of equations to the algebraic solution.
Change the subject of a formula.
Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio.
Understand and apply Pythagoras' theorem.
Use measures of speed and other compound measures to solve problems.

F.M. Wareham