The Number section covers arithmetic fundamentals: fractions, percentages, ratio, indices, and standard form — skills needed across all other topic areas.
HCF and LCM using prime factorisation. Fraction operations: +, −, ×, ÷. Converting between fractions, decimals, and percentages. Percentage increase/decrease: new = original × (1 ± r/100). Reverse percentage: original = new / (1 ± r/100). Compound interest: A = P(1 + r/100)ⁿ. Ratio: sharing in a given ratio, scaling. Direct proportion: y = kx. Inverse proportion: y = k/x.
Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ/aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ. Negative indices: a⁻ⁿ = 1/aⁿ. Fractional indices: a^(1/n) = ⁿ√a, a^(m/n) = (ⁿ√a)ᵐ. Standard form: a × 10ⁿ where 1 ≤ a < 10. Surds: simplify √50 = 5√2. Rationalise denominator: multiply by conjugate. Upper and lower bounds for errors in measurement.
To remove a surd from the denominator: if the denominator is a single surd like √5, multiply top and bottom by √5 (e.g., 3/√5 = 3√5/5). If it\'s a binomial like (2+√3), multiply by the conjugate (2−√3): the denominator becomes (2+√3)(2−√3) = 4−3 = 1 — the surds cancel because of the difference of squares pattern. This technique is required because irrational denominators are not considered simplified form. Exam tip: always check if the result can be simplified further.
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →