| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find curve equation from derivative (straightforward integration + point) |
| Difficulty | Moderate -0.8 Part (a) is a straightforward integration of polynomial and power terms using standard rules. Part (b) adds one simple step of finding the constant of integration using the given point. This is a routine AS-level calculus question requiring only direct application of basic integration formulas with no problem-solving or conceptual challenges. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
| Answer | Marks | Guidance |
|---|---|---|
| 3(a) | Integrates with at least one term | |
| in x correct | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| ACF | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| increased by 1 | 1.1b | B1F |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 3(b) | Substitutes x = 2 and y = 0 into |
| Answer | Marks | Guidance |
|---|---|---|
| PI by their correct value of c | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| must have + c | 1.1b | A1F |
| Subtotal | 2 | |
| Question 3 Total | 5 | |
| Q | Marking instructions | AO |
Question 3:
--- 3(a) ---
3(a) | Integrates with at least one term
in x correct | 1.1a | M1 | 1 8
x4 – + c
2 x
Obtains correct integral
Condone omission of +c
Condone inclusion of integral
sign
ACF | 1.1b | A1
Includes + c
FT their integral
Must be some evidence of
integration e.g., a power
increased by 1 | 1.1b | B1F
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 3(b) ---
3(b) | Substitutes x = 2 and y = 0 into
their integral from part (a) to find
a value of c
PI by their correct value of c | 1.1a | M1 | 1 8
0 = 24 – + c
2 2
c = –4
1 8
y = x4 – – 4
2 x
Finds correct value of c for their
equation and states equation
FT their integral from (a) but
must have + c | 1.1b | A1F
Subtotal | 2
Question 3 Total | 5
Q | Marking instructions | AO | Marks | Typical solution\begin{enumerate}[label=(\alph*)]
\item Find $\int \left(2x^3 + \frac{8}{x^2}\right) dx$ [3 marks]
\item A curve has gradient function $\frac{dy}{dx} = 2x^3 + \frac{8}{x^2}$
The $x$-intercept of the curve is at the point $(2, 0)$
Find the equation of the curve. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2023 Q3 [5]}}