Number
Number is the first JCE Mathematics domain and tests accurate, flexible calculation rather than isolated rules. Expect integers, fractions, decimals, percentages, ratio, rate, proportion, indices and standard form, usually embedded in money, sharing, measurement or everyday contexts.
Core rules and concepts
- Directed numbers: adding a negative moves left; subtracting a negative moves right. For products and quotients, two like signs give a positive, two unlike signs give a negative.
- Fractions: convert to a common denominator before adding or subtracting; multiply numerators and denominators; divide by multiplying by the reciprocal.
- Percentages: percentage change = (change ÷ original) × 100. A percentage increase of 15% multiplies by 1.15; a decrease of 15% multiplies by 0.85.
- Ratio: add the parts to find the total number of parts, then divide the total quantity by this sum to get one part.
- Indices: a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n); a^0 = 1; a^(−n) = 1/a^n.
- Standard form: A × 10^n where 1 ≤ A < 10. Adjust the power when the decimal point moves.
- Estimation: round each value to one significant figure to check whether an answer is reasonable.
Worked example
P4 800 is shared in the ratio 2:3:5. Total parts = 2 + 3 + 5 = 10. One part = 4 800 ÷ 10 = P480. The largest share is 5 × 480 = P2 400. Check: 960 + 1 440 + 2 400 = 4 800.
Traps that cost marks
Adding denominators when adding fractions; dividing a percentage change by the new value instead of the original; forgetting that ratio shares must add to the total; writing 0.47 × 10^3 instead of 4.7 × 10^2 in standard form; and losing the sign when multiplying or dividing directed numbers.