ESAT Mathematics 1
MATHEMATICS 1 WORKED EXAMPLES.
4 worked ESAT Mathematics 1 questions, each with a route line before the working, numbered steps, and the specific mistake every wrong option was built to catch. Written from scratch to the published content specification.
- How do you find the total surface area of a square-based pyramid? Find the slant height first, from the right triangle whose legs are the perpendicular height and half the base. The perpendicular height is not the slant height, and using it as one is the single most common way to lose this question. M1.7 · MENSURATION
- What is the coefficient of x³ in the expansion of (2 − x/2)⁶? The coefficient is −20. The powers of 2 and of ½ cancel exactly, so the whole term collapses to −C(6,3), and the minus sign survives because the x term is being raised to an odd power. M1.3 · BINOMIAL EXPANSION
- How do you solve 3^(2x) − 10 × 3^x + 9 = 0? Substitute u = 3^x. The equation becomes u² − 10u + 9 = 0, which factorises to (u − 1)(u − 9) = 0, giving 3^x = 1 and 3^x = 9, so x = 0 and x = 2 and the two solutions sum to 2. M1.2 · INDICES AND LOGARITHMS
- How many solutions does sin 2x = ½ have between 0° and 360°? There are four solutions. Doubling the angle doubles the interval the angle travels through, so 2x runs from 0° to 720° — two complete turns — and sin θ = ½ has two solutions in every turn. M1.5 · TRIGONOMETRY
SIT A WHOLE PAPER, NOT A QUESTION.
A complete ESAT Mathematics 1 mock paper with every worked solution, free.