Algebra: expressions, equations and inequalities
What the Algebra strand tests
Algebra tests whether you can use letters for numbers, simplify expressions, substitute values, rearrange formulae, solve linear equations and inequalities, solve simultaneous linear equations and handle simple quadratics. Foundation questions reward clear, line-by-line method; a correct answer with no working may still lose marks.
Core rules
- Collect like terms only: 3x + 5x = 8x, but 3x + 5x² cannot be simplified.
- Multiply out brackets by distributing each term: a(b + c) = ab + ac. Watch negative signs.
- To solve an equation, do the same operation to both sides until the variable is isolated.
- When multiplying or dividing an inequality by a negative number, reverse the inequality sign.
- Check a solution by substituting it back into the original equation.
Worked example
Solve 3(x - 2) = 2x + 5. Expand: 3x - 6 = 2x + 5. Subtract 2x from both sides: x - 6 = 5. Add 6: x = 11. Check: left side = 3(11 - 2) = 3 × 9 = 27; right side = 2(11) + 5 = 27. Both sides are equal, so x = 11.
Traps that cost marks
- Sign errors when expanding -(x - 4): it becomes -x + 4, not -x - 4.
- Dividing only one side of an equation by a number.
- Forgetting to reverse an inequality when dividing by a negative.
- Treating x² and 2x as like terms.