CAIE A Level Mathematics 9709 · Numerical solution of equations

Numerical solution of equations: calculation question

2 marksStandard

The positive root of $x^4 = 1301$ lies between two consecutive integers. Find the lower integer $N$ .

(a)
State $N$ .
[2]

Work it out, then check it

Your working is checked step by step against the answer key, with method marks, units and carried-forward errors handled the way a mark scheme handles them.

Answer this and get it marked, free

Free account, no card. Three marked written answers a day on the free plan.

How this question is marked

2 marks. Method marks are awarded for correct working even if the final answer is wrong, and a later part can still score if it correctly uses an earlier wrong answer.

More Numerical solution of equations questions

3 marks · Use the iterative formula xn+1 = (2xn^3 + 8)/(3xn^2) with x0 = 1 to find the cube root of 8 correct to 3 decimal places.
2 marks · The iteration xn+1 = (2xn^3 + 512)/(3xn^2) converges to √[3]512. State the value it converges to.
2 marks · The equation x^2 - 11x + 10 = 0 has two positive roots. State the larger root.
2 marks · The root of 2^x = 7 lies between two consecutive integers. Find the lower integer N.
2 marks · The equation ln x = 6 - x has exactly one root. Find the integer N such that the root lies in [N, N+1].
2 marks · The equation x = 5 + (12)/(x) has a positive root. Find the integer N such that the root lies in [N, N+1].

All Numerical solution of equations questions

Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.