Question 5 - A-Level Maths

AQA AS Paper 2 2018 June — Question 5 4 marks

Exam Board	AQA
Module	AS Paper 2 (AS Paper 2)
Year	2018
Session	June
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Indefinite & Definite Integrals
Type	Find curve from gradient
Difficulty	Standard +0.3 This is a straightforward integration question requiring expansion of the bracket, term-by-term integration using standard power rules, and applying an initial condition to find the constant. While it involves multiple steps (expand, integrate, substitute), each step uses routine AS-level techniques with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
Spec	1.08b Integrate x^n: where n != -1 and sums

\(f'(x) = \left(2x - \frac{3}{x}\right)^2\) and \(f(3) = 2\) Find \(f(x)\). [4 marks]

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Question 5:

Answer	Marks	Guidance
5	Expands the bracket and obtains
any correct form (PI)	AO1.1b	B1

𝑓/(𝑥) = 4𝑥2 −12+

𝑥2

9 𝑓(𝑥) = ∫4𝑥2 −12+ 𝑑𝑥

𝑥2

4𝑥3 9

= −12𝑥 − +𝑐

3 𝑥

𝑓(3) = 36−36−3+𝑐 = 2

𝑐 = 5

4𝑥3 9

𝑓(𝑥) = −12𝑥 − +5

3 𝑥

Integrates at least one of ‘their’

Answer	Marks	Guidance
terms correctly	AO1.1a	M1

Substitutes x = 3 into ‘their’

integrated expression and equates

Answer	Marks	Guidance
to 2	AO1.1a	M1

Obtains completely correct

expression, must be explicitly

Answer	Marks	Guidance
stated CAO (ACF)	AO1.1b	A1
Total	4
Q	Marking Instructions	AO

Question 5:
5 | Expands the bracket and obtains
any correct form (PI) | AO1.1b | B1 | 9
𝑓/(𝑥) = 4𝑥2 −12+
𝑥2
9
𝑓(𝑥) = ∫4𝑥2 −12+ 𝑑𝑥
𝑥2
4𝑥3 9
= −12𝑥 − +𝑐
3 𝑥
𝑓(3) = 36−36−3+𝑐 = 2
𝑐 = 5
4𝑥3 9
𝑓(𝑥) = −12𝑥 − +5
3 𝑥
Integrates at least one of ‘their’
terms correctly | AO1.1a | M1
Substitutes x = 3 into ‘their’
integrated expression and equates
to 2 | AO1.1a | M1
Obtains completely correct
expression, must be explicitly
stated CAO (ACF) | AO1.1b | A1
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution

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$f'(x) = \left(2x - \frac{3}{x}\right)^2$ and $f(3) = 2$

Find $f(x)$.

[4 marks]

\hfill \mbox{\textit{AQA AS Paper 2 2018 Q5 [4]}}

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Q1 1 Q2 1 Q3 2 Q4 4 Q5 4 Q6 6 Q7 6 Q8 4 Q9 3 Q10 5 Q11 9 Q12 8 Q13 1 Q14 1 Q15 6 Q16 4 Q17 2 Q18 6 Q19 7