Number and Numeration
Number and numeration underpins every other topic on NSSCO 6131. Short-answer items test fluency with place value, fractions, percentages, ratio and standard form, while structured items embed the same skills in money and measurement contexts such as VAT, hire purchase, simple and compound interest, and rates.
Core rules
- Standard form: a × 10ⁿ with 1 ≤ a < 10; small numbers take a negative index (0.0043 = 4.3 × 10⁻³).
- Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1.
- Percentage change = (change ÷ original) × 100. A price marked with 15% VAT is 115% of the pre-VAT price.
- Compound interest: A = P(1 + r/100)ⁿ, where n is the number of periods.
- Direct proportion: quantities divide to the same constant. Inverse proportion: they multiply to the same constant.
- Round only at the final step, and state the accuracy asked for (decimal places or significant figures).
Worked example
A stove is priced at N$13 800 including 15% VAT. Find the price before VAT. Reasoning: N$13 800 represents 115% of the pre-VAT price, so the pre-VAT price is 13 800 ÷ 1.15 = N$12 000. The VAT component is 13 800 − 12 000 = N$1 800. Taking 15% of 13 800 (N$2 070) would be wrong, because VAT is calculated on the smaller amount.
Traps that cost marks
- Reversing a percentage by subtracting the rate instead of dividing by the multiplier.
- Using simple interest when the question specifies compound interest.
- Rounding a calculator display mid-way through a multi-step money problem.
- Confusing significant figures with decimal places (0.0452 to 2 sf is 0.045).