Algebra
Algebra
Algebra questions test manipulation and solving rather than memorised answers. You should simplify expressions by collecting like terms, expand single and double brackets, factorise by taking out a common factor, and recognise difference of two squares. Solving linear equations, inequalities, simultaneous equations and quadratic equations is central. Also practise substitution into formulae, changing the subject of a formula, simplifying algebraic fractions, and using algebraic expressions to model word problems.
Traps to watch include sign errors when moving terms across an equals sign, forgetting to reverse an inequality when multiplying or dividing by a negative number, and losing one solution of a quadratic. When expanding, multiply every term in the second bracket by every term in the first. When factorising, always check for a common factor before using other methods. A quadratic may have two, one or no real solutions, so do not stop at the first value. Avoid dividing by zero and check whether a denominator can be zero.
Worked example: solve 5(x - 2) = 3x + 4. Expand: 5x - 10 = 3x + 4. Subtract 3x: 2x - 10 = 4. Add 10: 2x = 14. Divide by 2: x = 7. Substitute back to verify: left side 5(5) = 25 and right side 21 + 4 = 25.
Rule of thumb: whatever operation you perform, do it to both sides, and show each line so that sign errors are easier to spot.