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Programme Of Study For Key Stage 4 Mathematics

These are the statements, each one preceeded with the words "Pupils should be taught to:"

- simplify and manipulate algebraic ex
pressions (including those involving surds {and algebraic fractions}) by: factorising quadratic ex pressions of the form x ^{2}+ bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax ^{2}+ bx + c} and by simplifying expressions involving sums, products and powers, including the laws of indices - know the difference between an equation and an identity; argue mathematically to show algebraic ex
pressions are equivalent, and use algebra to support and construct arguments {and proofs} - where appropriate, interpret simple ex
pressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of 2 functions as a ‘composite function’} - use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through 2 given points, or through 1 point with a given gradient
- identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}
- recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = with x not equal to 0, {the exponential function y = k
^{x}for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size} - {sketch translations and reflections of the graph of a given function}
- plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
- {calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts}
- {recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point}
- solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph
- solve 2 simultaneous equations in 2 variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph
- {find approximate solutions to equations numerically using iteration}
- translate simple situations or procedures into algebraic ex
pressions or formulae; derive an equation (or 2 simultaneous equations), solve the equation(s) and interpret the solution - solve linear inequalities in 1 {or 2} variable {s}, {and quadratic inequalities in 1 variable}; represent the solution set on a number line, {using set notation and on a graph}
- recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r
^{n}where n is an integer, and r is a positive rational number {or a surd}) {and other sequences} - deduce ex
pressions to calculate the nth term of linear {and quadratic} sequences.

Statements in curly brackets {} are additional mathematical content to be taught to more highly attaining pupils.

Click on a statement above for suggested resources and activities from Transum.