AQA AS Paper 2 2021 June — Question 3 3 marks

Exam BoardAQA
ModuleAS Paper 2 (AS Paper 2)
Year2021
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind indefinite integral of polynomial/power
DifficultyEasy -1.8 This is a straightforward integration of a basic power function (x^{1/2}) requiring only recall of the standard power rule for integration and adding a constant. It's a routine AS-level question with minimal steps and no problem-solving required, making it significantly easier than average.
Spec1.08b Integrate x^n: where n != -1 and sums
3 It is given that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { x }$$ Find an expression for \(y\).
[0pt] [3 marks]
L
Question 3:
AnswerMarks Guidance
AnswerMark Guidance
Rewrites \(\sqrt{x}\) as \(x^{\frac{1}{2}}\)B1 AO1.1b
Integrates \(x^k\) for non-integer \(k\) to obtain \(x^{k+1}\)M1 AO1.1a
\(y = \dfrac{2}{3}x^{\frac{3}{2}} + c\)A1 AO1.1b — condone no constant of integration or numerical value for \(c\) used
Total: 3 marks
## Question 3:

| Answer | Mark | Guidance |
|--------|------|----------|
| Rewrites $\sqrt{x}$ as $x^{\frac{1}{2}}$ | B1 | AO1.1b |
| Integrates $x^k$ for non-integer $k$ to obtain $x^{k+1}$ | M1 | AO1.1a |
| $y = \dfrac{2}{3}x^{\frac{3}{2}} + c$ | A1 | AO1.1b — condone no constant of integration or numerical value for $c$ used |

**Total: 3 marks**
3 It is given that

$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { x }$$

Find an expression for $y$.\\[0pt]
[3 marks]\\
L\\

\hfill \mbox{\textit{AQA AS Paper 2 2021 Q3 [3]}}
This paper (18 questions)
View full paper
Q1 1 Q2 1 Q3 3 Q4 6 Q5 4 Q6 3 Q7 8 Q8 4 Q9 4 Q10 9 Q11 10 Q12 1 Q13 1 Q14 3 Q15 3 Q16 5 Q17 7 Q18 7