Number and Quantity
Core concepts
This domain tests number sense: operations with rational and irrational numbers, exponent and radical laws, scientific notation, percentages, ratio and proportion, and approximation. You should be able to simplify expressions such as (2³ × 2⁻⁵) and rationalise a denominator, and to judge whether a result is reasonable in magnitude.
Traps to watch
- Adding exponents when multiplying bases that differ, e.g. treating 2³ × 3² as 6⁵.
- Forgetting that a negative exponent gives a reciprocal, not a negative value.
- Confusing percentage increase with percentage of, and applying successive percentages additively rather than multiplicatively.
- Rounding too early in a multi-step calculation.
- Assuming the product of two irrational numbers is always irrational; √2 × √2 = 2 is rational.
Worked example
Simplify (2³ × 2⁻⁵) ÷ 2⁻¹. Combine the numerator: 2^(3−5) = 2⁻². Divide: 2^(−2 − (−1)) = 2⁻¹ = 1/2.
Rule of thumb
Keep exact values (fractions, radicals) until the final step, and only then round-usually to the precision the question specifies.