GCSE Maths OCR J560

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. **