Algebra
Algebra tests whether you can generalise arithmetic using letters, manipulate expressions confidently, and solve equations and inequalities with a clear logical sequence. JCE questions often combine expansion, factorisation, substitution and linear equations, including simultaneous equations and formulae.
Core rules and concepts
- Like terms have identical letter parts; only their coefficients are added or subtracted.
- Expanding: multiply every term inside the bracket by the term outside. For (x + 3)(x − 5), use four products: x² − 5x + 3x − 15 = x² − 2x − 15.
- Factorising: always remove the highest common factor first. Check by expanding.
- Linear equations: do the same operation to both sides; aim to collect the unknown on one side and numbers on the other.
- Inequalities: solve like equations, but reverse the inequality sign when multiplying or dividing by a negative number.
- Simultaneous equations: elimination is efficient when coefficients match; substitution is useful when one equation is already solved for a variable.
- Formulae: rearrange by inverse operations, keeping the subject alone on one side.
Worked example
Solve 3(2x − 1) = 4x + 9. Expand: 6x − 3 = 4x + 9. Subtract 4x: 2x − 3 = 9. Add 3: 2x = 12. Divide by 2: x = 6. Check: left side 3(12 − 1) = 33; right side 24 + 9 = 33.
Traps that cost marks
Forgetting to multiply the second term inside a bracket by the outside factor; cancelling terms rather than factors; losing a negative sign when expanding; failing to reverse an inequality after dividing by a negative; and not substituting the answer back to check.