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Date	November 2020	Marks available	3	Reference code	20N.1.SL.TZ0.S_4
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 0
Command term	Find	Question number	S_4	Adapted from	N/A

Question

Let $f (x) = a \log_{3} (x - 4)$ , for $x > 4$ , where $a > 0$ .

Point $A (13, 7)$ lies on the graph of $f$ .

Find the value of $a$ .

[3]

The $x$ -intercept of the graph of $f$ is $(5, 0)$ .

On the following grid, sketch the graph of $f$ .

[3]

Markscheme

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

attempt to substitute coordinates (in any order) into $f$ (M1)

eg $a \log_{3} (13 - 4) = 7, a \log_{3} (7 - 4) = 13, a \log 9 = 7$

finding $\log_{3} 9 = 2$ (seen anywhere) (A1)

eg $\log_{3} 9 = 2, 2 a = 7$

$a = \frac{7}{2}$ A1 N2

[3 marks]

A1A1A1 N3

Note: Award A1 for correct shape of logarithmic function (must be increasing and concave down).
Only if the shape is correct, award the following:
A1 for being asymptotic to $x = 4$
A1 for curve including both points in circles.

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » SL 2.9—Exponential and logarithmic functions

20N.1.SL.TZ0.S_4b:
The $x$ -intercept of the graph of $f$ is $(5, 0)$ .

On the following grid, sketch the graph of $f$ .
EXN.2.SL.TZ0.9a:
Show that $T_{0} = 100$ .
EXN.2.SL.TZ0.9c:
Find the temperature of the water when $t = 15$ .
21M.1.SL.TZ1.8d:
Solve $f (x) > 0$ for $x > 0$ .
21M.2.SL.TZ2.6a:
Show that $A_{0} = 100$ .
21N.2.SL.TZ0.2b:
Sketch the graph of $f$ on the following grid.
21M.1.SL.TZ2.5a:
Find the exact value of $a$ .
21M.2.SL.TZ2.6c:
Find, correct to the nearest $10$ years, the time taken after the plant’s death for $25 %$ of the carbon-14 to decay.
21N.1.SL.TZ0.8b:
Write down an expression for $f^{- 1} (x)$ .
21N.2.SL.TZ0.2a:
Find the values of $x$ for which $f (x) = 0$ .
21N.1.SL.TZ0.8c:
Find the value of $f^{- 1} (\sqrt{32})$ .
EXN.2.SL.TZ0.9b:
Show that $k = \frac{1}{10} \ln \frac{10}{7}$ .
21M.2.SL.TZ2.6b:
Show that $k = \frac{\ln 2}{5730}$ .
20N.1.SL.TZ0.T_12b:
In the context of the model, state what the horizontal asymptote represents.
20N.1.SL.TZ0.T_12a:
Find the value of $K$ .
20N.1.SL.TZ0.T_12c:
Find Jean-Pierre’s vertical speed after $10$ seconds. Give your answer in $km h^{- 1}$ .
21N.1.AHL.TZ0.3:
Solve the equation $\log_{3} \sqrt{x} = \frac{1}{2 \log_{2} 3} + \log_{3} (4 x^{3})$ , where $x > 0$ .
21N.1.SL.TZ0.8a:
Show that $a = 8$ .
21N.1.SL.TZ0.8d.ii:
Find the value of $p$ and the value of $q$ .
21N.1.SL.TZ0.8d.i:
Show that $27, p, q$ and $125$ are four consecutive terms in a geometric sequence.

Topic 2—Functions » SL 2.11—Transformation of functions

Topic 2—Functions

Question

Markscheme

Examiners report

Syllabus sections

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