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Date	November Example questions	Marks available	6	Reference code	EXN.1.SL.TZ0.1
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 0
Command term	Find	Question number	1	Adapted from	N/A

Question

The derivative of a function $f$ is given by $f' (x) = 3 \sqrt{x}$ .

Given that $f (1) = 3$ , find the value of $f (4)$ .

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

correct working (A1)

eg −5 + (8 − 1)(3)

u₈ = 16 A1 N2

[2 marks]

METHOD 1

$f (x) = \int 3 \sqrt{x} d x$ (A1)

attempts to integrate (M1)

$f (x) = 2 x^{\frac{3}{2}} + C (= 2 x \sqrt{x} + C)$ A1

uses $f (1) = 3$ to obtain $3 = 2 {(1)}^{\frac{3}{2}} + C$ and so $C = 1$ M1

substitutes $x = 4$ into their expression for $f (x)$ (M1)

so $f (4) = 17$ A1

METHOD 2

$\int_{1}^{4} f' (x) d x = \int_{1}^{4} 3 \sqrt{x} d x$ (A1)

attempts to integrate both sides (M1)

${[f (x)]}_{1}^{4} = {[2 x^{\frac{3}{2}}]}_{1}^{4}$ A1

$f (4) - f (1) = 16 - 2$ M1

uses $f (1) = 3$ to find their value of $f (4)$ (M1)

$f (4) - 3 = 16 - 2$

so $f (4) = 17$ A1

[6 marks]

Examiners report

[N/A]

Syllabus sections

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

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Topic 5 —Calculus