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Reference: Pearson Edexcel International A Level Pure Mathematics 3 Student Book. This chapter is about finding approximate answers when exact solving is difficult.
Main skills from this lesson
A root is where f(x)=0. If f(a) and f(b) have opposite signs, there is at least one root between a and b, provided the function is continuous there.
Make a small table of values and narrow the interval step by step.
f(a) < 0 and f(b) > 0 -> root between a and b
Sign change shows a root in the interval, but not always exactly one root.
Rewrite an equation as x = g(x), then use:
x_(n+1) = g(x_n)
Start with x_0, calculate x_1, x_2, x_3, and continue until values settle to the required accuracy.
x0 -> x1 -> x2 -> x3
If the iteration values get closer to a number, the method is converging. If they jump away or cycle, it may not be a useful rearrangement.
Study tip: keep extra decimal places during working, then round at the end.
Rounding too early can move the final answer outside the required accuracy.
Numerical methods questions reward clear working.
Continue with quizzes, flashcards, or games when you are ready.