ESAT Mathematics 2
MATHEMATICS 2 WORKED EXAMPLES.
3 worked ESAT Mathematics 2 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 coefficient of x⁶ in the derivative of (1 + 2x)⁷? Differentiate first, then pick the term. Doing it the other way round means expanding seven terms you will throw away, and in an ESAT Mathematics 2 module you have about 89 seconds. M2.3 · SERIES
- Why does plotting log y against log x give a straight line? A log-log plot is straight exactly when y and x obey a power law y = kxⁿ. Taking logs of both sides gives log y = n log x + log k, which is the equation of a line whose gradient is the power n and whose vertical intercept is log k, not k. M2.2 · LOGARITHMS
- How many distinct real roots does x⁴ + 3x² − 4 = 0 have? There are two distinct real roots, x = 1 and x = −1. Substituting u = x² gives u = 1 and u = −4, and only the non-negative value of u can come from a real x, so the pair of roots from u = −4 does not exist. M2.1 · ALGEBRA
SIT A WHOLE PAPER, NOT A QUESTION.
A complete ESAT Mathematics 1 mock paper with every worked solution, free.