Algebra
What you must know
Be fluent in simplifying expressions by collecting like terms, multiplying out brackets (including double brackets), and factorising: common factors, difference of two squares (a^2 - b^2 = (a-b)(a+b)) and quadratic trinomials. Handle algebraic fractions by finding a common denominator and cancelling only factors, never terms. Solve linear equations, simultaneous equations (elimination is usually quickest when coefficients match; substitution when one equation is already solved for a variable) and quadratic equations by factorising or the formula x = [-b +/- sqrt(b^2 - 4ac)]/2a. Solve linear inequalities and show the solution on a number line. For sequences, find the nth term of arithmetic sequences (a + (n-1)d) and recognise simple geometric sequences. Know straight-line graphs: y = mx + c, gradient, intercepts, and the facts that parallel lines share m and perpendicular gradients multiply to -1.
Traps
- Sign errors when expanding a minus bracket: -(x - 3) = -x + 3.
- Multiplying an inequality by a negative number reverses the sign.
- Cancelling across a plus sign in algebraic fractions is invalid.
- In simultaneous equations, subtract when coefficients have the same sign, add when they differ.
- A quadratic may need rearranging to equal zero before factorising.
Rule of thumb
Whatever you do to one side, do to the other; then substitute your answer back into the original equation to check it.
Example: 3(x - 2) = 5x + 4 gives 3x - 6 = 5x + 4, so -10 = 2x and x = -5.