GCSE Higher

ALGEBRA

Collecting like terms
Multiply out single and double brackets
Factorise expressions
Factorise quadratic expressions including difference of 2 squares
Cancel common factors in rational expressions
Substitute positive and negative numbers into expressions
Solving equations with integer or fractional coefficients - one unknown; unknown on both sides;
inc. brackets; negative solution
Substitute numbers into a formula
Change the subject of a formula inc. where the subject appears twice, or as a power.
Set up and use equations to solve word problems involving direct and inverse proportion
Relate algebraic solutions to graphical representation of the equations

Solve Simultaneous equations algebraically and graphically
Solve several linear inequalities in 2 variables and find the solution set
Solve quadratic equations by factorizing; completing the square and using the quadratic formula
Solve 2 simultaneous equations , one of which is linear in each unknown, and the other is linear in one unknown and quadratic in the other, or where the second is of the form x + y = r

Trial and Improvement

Generate integer sequences inc. squares; powers of 2; powers of 10; triangular numbers
Find the nth term of a sequence

Plot Coordinate in all 4 quadrants
Recognise y = mx+c correspond to straight line graphs
Plot graphs of functions in which y is give explicitly in terms of x
Construct linear functions from real life problems and plot corresponding graphs
Discuss and interpret graphs from real life situations
Find the gradient of lines in the form y = mx + c; understand that m = gradient and c = y intercept;
explore the gradient of parallel lines and lines perpendicular to these lines

Plot quadratic functions
Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function
Find the intersection points of the graphs of a linear and quadratic function, knowing that these are approximate solutions of corresponding simultaneous equations
Plot simple cubic functions
Plot the reciprocal function
Plot the exponential function; y = sin x and y = cos x
Recognise the shapes of all of these functions

Apply to the graph y = f(x) the transformations: y = f(x) + a, y = f(ax), y = f(x+a), y = af(x) for linear, quadratic, sine and cosine function

Construct the graphs of simple loci Including the circle x + y = r
Find graphically the intersection points of a given straight line with this circle and know that this corresponds to solving 2 simultaneous equations representing the line and circle