Quelpr
3 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 4(a)(i)

Use the intermediate value theorem to prove that f(x) = 2x³ + x² + 9x - 5 has at least one root in the interval [0.2, 1].

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 4(a)(ii)Hence, use three iterations of the interval bisection method to estimate the root of f in the interval [0.2, 1].[5 marks]
  2. 4(b)(i)Write down an expression for the nᵗʰ term of the sequence.[4 marks]
  3. 4(b)(ii)Determine whether the sequence converges or diverges.[3 marks]
  4. 4(c)Calculate ∑(from r=0 to 27) r.[4 marks]
  5. 4(d)Use the sum of a series to calculate an equivalent fraction for the repeating decimal 0.2727272...[6 marks]

More practice: the rest of this paper · more Roots of Equations questions · all CAPE Pure Mathematics Unit 2 past papers