Structure and calculation Study Guide

A surd is an exact root that cannot be written as a rational number. Simplify surds by taking square factors outside the root, then collect like surd terms. To rationalise a denominator containing one square root, multiply the numerator and denominator by that root. For a denominator such as a + √b, use its conjugate a − √b, because the product removes the surd from the denominator. Keep answers exact rather than using decimal approximations.

The product rule counts outcomes formed by a sequence of choices. Multiply the number of available options at each stage, because every option at one stage can be paired with every option at the next stage. For example, choosing 3 starters, 4 main courses and 2 desserts gives 3 × 4 × 2 = 24 possible meals. The method assumes that each stated choice can be made in combination with the choices before it.