Algebra
Algebra tests manipulation and solution of equations, formulae, inequalities, sequences and graphs. The exam rewards showing equivalent stages; a correct final answer without a valid intermediate step may still lose method marks in “show that” questions.
Core skills
- Expand brackets fully, including negative signs: −3(x−4) = −3x+12.
- Factorise by taking the highest common factor; a quadratic x²+bx+c needs two numbers with product c and sum b.
- Solve linear equations by doing the same operation to both sides; for inequalities, reverse the sign when multiplying or dividing by a negative.
- Rearrange formulae by inverse operations, keeping the subject on one side.
- Sequences: linear sequences have a constant difference; quadratic sequences have a constant second difference.
Worked example
Solve 2x²−5x−3=0. Product ac = 2×(−3) = −6; find two numbers with product −6 and sum −5: −6 and +1. Split the middle term: 2x²−6x+x−3=0. Factorise pairs: 2x(x−3)+1(x−3)=0, so (2x+1)(x−3)=0. Hence x = −1/2 or x = 3. Check by substitution.
Traps
Sign errors when expanding; cancelling terms across a plus; forgetting the second solution of a quadratic; treating x²=9 as x=3 only; plotting a line from only two points without checking a third; using the wrong inequality direction after multiplying by a negative.