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Date	November 2020	Marks available	7	Reference code	20N.1.SL.TZ0.S_6
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 0
Command term	Find	Question number	S_6	Adapted from	N/A

Question

The graph of a function $f$ passes through the point $(\ln 4, 20)$ .

Given that $f' (x) = 6 e^{2 x}$ , find $f (x)$ .

Markscheme

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

evidence of integration (M1)

eg $\int f' (x) d x, \int 6 e^{2 x}$

correct integration (accept missing $+ c$ ) (A1)

eg $\frac{1}{2} \times 6 e^{2 x}, 3 e^{2 x} + c$

substituting initial condition into their integrated expression (must have $+ c$ ) M1

eg $3 e^{2 \times \ln 4} + c = 20$

Note: Award M0 if candidate has substituted into $f'$ or $f''$ .

correct application of $\log (a^{b}) = b \log a$ rule (seen anywhere) (A1)

eg $2 \ln 4 = \ln 16, e^{\ln 16}, \ln 4^{2}$

correct application of $e^{\ln a} = a$ rule (seen anywhere) (A1)

eg $e^{\ln 16} = 16, {(e^{\ln 4})}^{2} = 4^{2}$

correct working (A1)

eg $3 \times 16 + c = 20, 3 \times {(4)}^{2} + c = 20, c = - 28$

$f (x) = 3 e^{2 x} - 28$ A1 N4

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5 —Calculus » SL 5.10—Indefinite integration, reverse chain, by substitution

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