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Date May 2018 Marks available 4 Reference code 18M.1.SL.TZ1.S_5
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 1
Command term Find Question number S_5 Adapted from N/A

Question

Let f(x)=12x1, for x>12.

Find (f(x))2dx.

[3]
a.

Part of the graph of f is shown in the following diagram.

The shaded region R is enclosed by the graph of f, the x-axis, and the lines x = 1 and x = 9 . Find the volume of the solid formed when R is revolved 360° about the x-axis.

[4]
b.

Markscheme

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

correct working      (A1)

eg   12x1dx,(2x1)1,12x1,(1u)2du2

(f(x))2dx=12ln(2x1)+c      A2 N3

Note: Award A1 for 12ln(2x1).

[3 marks]

a.

attempt to substitute either limits or the function into formula involving f 2 (accept absence of π / dx)     (M1)

eg   91y2dx,π(12x1)2dx,[12ln(2x1)]91

substituting limits into their integral and subtracting (in any order)     (M1)

eg  π2(ln(17)ln(1)),π(012ln(2×91))

correct working involving calculating a log value or using log law     (A1)

eg  ln(1)=0,ln(171)

π2ln17(accept πln17)    A1 N3

Note: Full FT may be awarded as normal, from their incorrect answer in part (a), however, do not award the final two A marks unless they involve logarithms.

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 5 —Calculus » SL 5.5—Integration introduction, areas between curve and x axis
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