King's College School

Coeducational Independent Prep school in Cambridge

KCS

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 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.