Solve linear equations in one unknown algebraically.

e.g. Solve \(3x - 1 = 5\)

Set up and solve linear equations in mathematical and non-mathematical contexts, including those with the unknown on both sides of the equation.

e.g. Solve \(5(x-1) = 4-x\)

Interpret solutions in context.

[Examples may include manipulation of algebraic fractions, 6.01g]

Solve quadratic equations with coefficient of \(x^2\) equal to 1 by factorising.

e.g. Solve \(x^2 - 5x + 6 = 0\)

Find \(x\) for an \(x\) cm by \((x + 3)\) cm rectangle of area 40 cm².

Know the quadratic formula.

Rearrange and solve quadratic equations by factorising, completing the square or using the quadratic formula.

e.g. \(2x^2 = 3x+5\)

\(\dfrac{2}{x} - \dfrac{2}{x+1} = 1\)

Set up and solve two linear simultaneous equations in two variables algebraically.

e.g. Solve simultaneously \(2x+3y=18\) and \(y=3x-5\)

Set up and solve two simultaneous equations (one linear and one quadratic) in two variables algebraically.

e.g. Solve simultaneously \(x^2+y^2 = 50\) and \(2y=x+5\)

Use a graph to find the approximate solution of a linear equation.

Use graphs to find approximate roots of quadratic equations and the approximate solution of two linear simultaneous equations.

Know that the coordinates of the points of intersection of a curve and a straight line are the solutions to the simultaneous equations for the line and curve.

Find approximate solutions to equations using systematic sign-change methods (for example, decimal search or interval bisection) when there is no simple analytical method of solving them.

Specific methods will not be requested in the assessment.