# Year 8 Key Objectives

- 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
*n*th 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.