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Date May 2016 Marks available 3 Reference code 16M.2.sl.TZ2.3
Level SL only Paper 2 Time zone TZ2
Command term Sketch Question number 3 Adapted from N/A

Question

Let \(f(x) = {{\text{e}}^{0.5x}} - 2\).

For the graph of f:

(i)     write down the \(y\)-intercept;

(ii)     find the \(x\)-intercept;

(iii)     write down the equation of the horizontal asymptote.

[4]
a.

On the following grid, sketch the graph of \(f\), for \( - 4 \leqslant x \leqslant 4\).

M16/5/MATME/SP2/ENG/TZ2/03.b

[3]
b.

Markscheme

(i)     \(y =  - 1\)     A1     N1

(ii)     valid attempt to find \(x\)-intercept     (M1)

eg\(\,\,\,\,\,\)\(f(x) = 0\)

1.38629     A1     N2

\(x = 2\ln 2{\text{ (exact), }}1.39\)

(iii)     \(y =  - 2\) (must be equation)     A1     N1

a.

M16/5/MATME/SP2/ENG/TZ2/03.b/M     A1A1A1     N3

[3 marks]

b.

Examiners report

In part a), most candidates were successful at finding the intercepts with the x and y axis, though many failed to write the horizontal asymptote as an equation. Some candidates gave the answer for the horizontal asymptote as \(y \ne  - 2\).

a.

For part b), a considerable number of candidates could sketch the exponential function providing an approximately correct shape, although many of them did not use the correct domain, making it go beyond \(x = 4\). Others plotted an incorrect value of \(y\) at \(x = 4\), resulting in the loss of a mark.

Considering that all the question requires from students is to copy the graph off the GDC, it is important to stress which are the features that cannot be missed.

b.

Syllabus sections

Topic 5 - Statistics and probability » 5.3 » Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles.
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