Number
The Number domain tests exact arithmetic and numerical reasoning: integers, fractions, decimals, percentages, powers and roots, standard form, rounding and bounds. O Level questions often combine two of these ideas, so keep the order of operations and the unit of the answer in view.
Rules to hold
- Work in the order brackets, indices, multiplication/division, addition/subtraction; a fraction bar acts as a bracket.
- To add or subtract fractions, use a common denominator; to divide, multiply by the reciprocal.
- Index laws: 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.
- Standard form is A × 10^n with 1 ≤ A < 10. Adjust the power when the coefficient moves.
- For a value rounded to a given unit, bounds are half a unit below and above. For calculations, combine lower with lower (or lower with upper for division) as appropriate.
Worked example
A rectangle measures 8.4 cm by 3.7 cm, each correct to 1 decimal place. Find the lower bound of its area. Each length is rounded to 0.1 cm, so the error is ±0.05 cm. Lower dimensions: 8.35 cm and 3.65 cm. Lower area = 8.35 × 3.65 = 30.4775 cm², so 30.5 cm² to 3 s.f. The upper bound would use 8.45 × 3.75. Keep the full product until the final rounding.
Marks lost
Rounding intermediate values, writing 240 (2 s.f.) bounds as 239.5 and 240.5 instead of 235 and 245, treating a negative power as a negative number, and dividing a percentage change by the new value rather than the original. In standard form, 0.6 × 10^4 is not in standard form.