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.