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Date May 2016 Marks available 2 Reference code 16M.1.sl.TZ2.3
Level SL only Paper 1 Time zone TZ2
Command term Write Question number 3 Adapted from N/A

Question

Let \(x = \ln 3\) and \(y = \ln 5\). Write the following expressions in terms of \(x\) and \(y\).

\(\ln \left( {\frac{5}{3}} \right)\).

[2]
a.

\(\ln 45\).

[4]
b.

Markscheme

correct approach     (A1)

eg\(\,\,\,\,\,\)\(\ln 5 - \ln 3\)

\(\ln \left( {\frac{5}{3}} \right) = y - x\)    A1     N2

[2 marks]

a.

recognizing factors of 45 (may be seen in log expansion)     (M1)

eg\(\,\,\,\,\,\)\(\ln (9 \times 5),{\text{ }}3 \times 3 \times 5,{\text{ }}\log {3^2} \times \log 5\)

correct application of \(\log (ab) = \log a + \log b\)     (A1)

eg\(\,\,\,\,\,\)\(\ln 9 + \ln 5,{\text{ }}\ln 3 + \ln 3 + \ln 5,{\text{ }}\ln {3^2} + \ln 5\)

correct working     (A1)

eg\(\,\,\,\,\,\)\(2\ln 3 + \ln 5,{\text{ }}x + x + y\)

\(\ln 45 = 2x + y\)    A1     N3

[4 marks]

b.

Examiners report

Most candidates were able to earn some or all the marks on this question. Part (a) was answered correctly by nearly all candidates.

a.

Most candidates were able to earn some or all the marks on this question. In part (b), the majority of candidates knew they needed to factor 45, though some did not apply the log rules correctly to earn all the available marks here.

b.

Syllabus sections

Topic 1 - Algebra » 1.2 » Elementary treatment of exponents and logarithms.

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