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Date May 2018 Marks available 4 Reference code 18M.2.SL.TZ1.S_7
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find and Hence Question number S_7 Adapted from N/A

Question

Let f(x)=e2sin(πx2), for x > 0.

The k th maximum point on the graph of f has x-coordinate xk where kZ+.

Given that xk + 1 = xk + a, find a.

[4]
a.

Hence find the value of n such that nk=1xk=861.

[4]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach to find maxima     (M1)

eg  one correct value of xk, sketch of f

any two correct consecutive values of xk      (A1)(A1)

eg  x1 = 1, x2 = 5

a = 4      A1 N3

[4 marks]

a.

recognizing the sequence x1,  x2,  x3, …, xn is arithmetic  (M1)

eg  d = 4

correct expression for sum       (A1)

eg  n2(2(1)+4(n1))

valid attempt to solve for n      (M1)

eg  graph, 2n2n − 861 = 0

n = 21       A1 N2

[4 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 1—Number and algebra » SL 1.2—Arithmetic sequences and series
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Topic 2—Functions » SL 2.10—Solving equations graphically and analytically
Topic 1—Number and algebra
Topic 2—Functions

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