Number and Numeration
What you must know
You need fluent, accurate work with integers, fractions, decimals and percentages, and the ability to move between them: 0.35 = 35% = 7/20. Revise the four operations on fractions (common denominators for addition and subtraction; cancel diagonally before multiplying), rounding to a given number of decimal places or significant figures, and estimation to check answers. Ratio and proportion run through the whole paper: sharing in a given ratio, direct proportion (both quantities grow together), inverse proportion (one grows as the other shrinks), and rates such as speed, density and exchange. Learn the index laws thoroughly: a^m x 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, and fractional indices such as a^(1/2) = sqrt(a). Standard form A x 10^n with 1 <= A < 10 must be handled with and without a calculator.
Traps
- Reverse percentages: after a 20% discount the price is 80% of the original, so divide by 0.8, not multiply by 1.2.
- Consecutive percentage changes do not simply add: +15% then -15% gives x1.15 x 0.85 = 0.9775, a 2.25% fall.
- In ratio sharing, check the total number of parts and what any remainder represents.
- Round only at the end; rounding mid-calculation often loses the mark.
- Negative indices give fractions, not negative numbers.
Rule of thumb
Of means multiply, and a percentage change is a single multiplier: increase by 12% means x1.12; decrease by 12% means x0.88. To reverse a change, divide by that multiplier.
Example: a coat costs P680 after a 15% discount. Original = 680 / 0.85 = P800.