Number and Algebra
This domain carries a substantial share of the SEC Mathematics papers and underpins every other topic. It tests fluent calculation, confident manipulation of fractions, percentages, ratio and standard form, and the ability to form, rearrange and solve equations and inequalities. Algebra questions usually appear as short structured parts, so method marks are available even when the final answer is wrong.
Core rules
- Fractions: cancel factors, not terms; a/b + c/d needs a common denominator.
- Percentages: increase by 15% means ×1.15; a decrease means ×0.85. Reverse problems divide by the multiplier.
- Standard form: write A × 10^n with 1 ≤ A < 10.
- Indices: a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n); (a^m)^n = a^(mn); a^0 = 1; a^(−n) = 1/a^n.
- Expanding: every term in the first bracket multiplies every term in the second.
- Factorising: take out the highest common factor first; for x² + bx + c find two numbers multiplying to c and adding to b.
- Linear equations: do the same operation to both sides and keep equals signs aligned.
- Simultaneous equations: elimination by matching coefficients, or substitution.
- Rearranging formulae: use inverse operations on both sides.
- Sequences: find the common difference d, then nth term = dn + (first term − d).
Worked example
Solve 3x + 2y = 16 and x − y = 2. From the second equation x = y + 2. Substitute: 3(y + 2) + 2y = 16, so 3y + 6 + 2y = 16, giving 5y = 10 and y = 2. Then x = 2 + 2 = 4. Check in the first equation: 3(4) + 2(2) = 12 + 4 = 16. ✔
Traps
- Dropping a sign when subtracting a bracket: −(x − 3) = −x + 3.
- Cancelling across a plus sign, such as writing (x + 4)/4 = x.
- Rounding intermediate values; keep full accuracy until the final line.
- Forgetting to multiply every term when clearing a denominator.