CAIE P1 2021 June — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (straightforward integration + point)
DifficultyModerate -0.8 This is a straightforward integration question requiring only standard power rule integration (including negative powers) and using a given point to find the constant of integration. It's a routine textbook exercise with no problem-solving or conceptual challenges, making it easier than average.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
1 A curve with equation \(y = \mathrm { f } ( x )\) is such that \(\mathrm { f } ^ { \prime } ( x ) = 6 x ^ { 2 } - \frac { 8 } { x ^ { 2 } }\). It is given that the curve passes through the point \(( 2,7 )\). Find \(\mathrm { f } ( x )\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\([f(x) =]\ 2x^3 + \frac{8}{x}\ [+c]\)B1 Allow any correct form
\(7 = 16 + 4 + c\)M1 Substitute \(f(2) = 7\) into an integral. \(c\) must be present. Expect \(c = -13\)
\(f(x) = 2x^3 + \frac{8}{x} - 13\)A1 Allow \(y =\ \), \(f(x)\) or \(y\) can appear earlier in answer
3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $[f(x) =]\ 2x^3 + \frac{8}{x}\ [+c]$ | **B1** | Allow any correct form |
| $7 = 16 + 4 + c$ | **M1** | Substitute $f(2) = 7$ into an integral. $c$ must be present. Expect $c = -13$ |
| $f(x) = 2x^3 + \frac{8}{x} - 13$ | **A1** | Allow $y =\ $, $f(x)$ or $y$ can appear earlier in answer |
| | **3** | |

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1 A curve with equation $y = \mathrm { f } ( x )$ is such that $\mathrm { f } ^ { \prime } ( x ) = 6 x ^ { 2 } - \frac { 8 } { x ^ { 2 } }$. It is given that the curve passes through the point $( 2,7 )$.

Find $\mathrm { f } ( x )$.\\

\hfill \mbox{\textit{CAIE P1 2021 Q1 [3]}}
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