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Date November 2017 Marks available 7 Reference code 17N.1.sl.TZ0.7
Level SL only Paper 1 Time zone TZ0
Command term Find Question number 7 Adapted from N/A

Question

Consider f(x)=logk(6x3x2), for 0<x<2, where k>0.

The equation f(x)=2 has exactly one solution. Find the value of k.

Markscheme

METHOD 1 – using discriminant

correct equation without logs     (A1)

eg6x3x2=k2

valid approach     (M1)

eg3x2+6xk2=0, 3x26x+k2=0

recognizing discriminant must be zero (seen anywhere)     M1

egΔ=0

correct discriminant     (A1)

eg624(3)(k2), 3612k2=0

correct working     (A1)

eg12k2=36, k2=3

k=3     A2     N2

METHOD 2 – completing the square

correct equation without logs     (A1)

eg6x3x2=k2

valid approach to complete the square     (M1)

eg3(x22x+1)=k2+3, x22x+11+k23=0

correct working     (A1)

eg3(x1)2=k2+3, (x1)21+k23=0

recognizing conditions for one solution     M1

eg(x1)2=0, 1+k23=0

correct working     (A1)

egk23=1, k2=3

k=3     A2     N2

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 6 - Calculus » 6.3 » Optimization.

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