Algebra shortcuts

Get x on its own without losing marks on the way.

• The cover-up trickCover the x with your thumb and ask what number belongs there.
• Change the side, change the signMove a term across the equals sign and flip what it does.
• Two-step equations: the balanceUndo in reverse order — constants first, coefficient last.
• Inequalities: when to flip the signMultiply or divide by a negative, and the inequality turns around.
• Two equations: eliminationAdd or subtract the equations to make one letter disappear.

Break expressions apart by spotting the pattern.

• Factorise with sum and productFind two numbers that multiply to the last term and add to the middle one.
• Difference of two squaresSomething squared minus something squared factorises on sight.
• Squaring a bracketFirst squared, last squared, and twice the two multiplied in the middle.

Three rules cover almost every powers question.

• The three power rulesMultiplying adds the powers, dividing subtracts, a power of a power multiplies.
• Negative powers just flipA minus sign in the power means 'turn it upside down'.

Cross multiply, or find the value of one.

• Cross multiplyTwo fractions equal to each other? Multiply diagonally.
• The unitary methodFind the value of one, then multiply up to however many you need.

Read slope and distance straight off the points.

• Slope from two pointsRise over run — the change in y divided by the change in x.

The formula, the discriminant, and when to use each.

• The quadratic formulaWhen factorising fails, the formula never does.