Algebra
Algebra
Candidates must manipulate algebraic expressions, solve linear and quadratic equations, rearrange formulas, solve inequalities and systems, and apply exponent laws. Know how to expand brackets, factor common factors and quadratics, and interpret solutions in context. Word problems often require defining a variable and translating conditions into an equation.
Traps: distributing a negative across a bracket; combining unlike terms such as 2x and 3; forgetting to reverse an inequality when multiplying or dividing by a negative; and losing solutions by dividing by a variable expression that could be zero. When solving rational or radical equations, check for extraneous roots. For systems, ensure the solution satisfies both equations. In quadratic problems, the zero-product property only works when one side is zero.
Rule of thumb: keep both sides balanced and perform the same operation on each side. For quadratics, try factoring first; if not factorable, use the quadratic formula. Always substitute back to check.
Worked example: solve 2(x − 3) + 4 = 3x − 5. Expand: 2x − 6 + 4 = 3x − 5, so 2x − 2 = 3x − 5. Subtract 2x: −2 = x − 5. Add 5: x = 3. Check: left side 2(0)+4=4; right side 9−5=4.