CAIE P1 Specimen — Question 2 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
SessionSpecimen
Marks3
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TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (straightforward integration + point)
DifficultyEasy -1.2 This is a straightforward integration question requiring only basic polynomial integration and using an initial condition to find the constant. It's simpler than average A-level questions as it involves direct application of standard integration rules with no problem-solving or manipulation required.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
2 The function f is such that \(\mathrm { f } ^ { \prime } ( x ) = 3 x ^ { 2 } - 7\) and \(\mathrm { f } ( 3 ) = 5\). Find \(\mathrm { f } ( x )\).
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(f(x) = x^3 - 7x \ (+c)\)B1
\(5 = 27 - 21 + c\)M1 Sub \(x=3\), \(y=5\). Dep. on \(c\) present
\(c = -1 \rightarrow f(x) = x^3 - 7x - 1\)A1
Total: 3 
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $f(x) = x^3 - 7x \ (+c)$ | B1 | |
| $5 = 27 - 21 + c$ | M1 | Sub $x=3$, $y=5$. Dep. on $c$ present |
| $c = -1 \rightarrow f(x) = x^3 - 7x - 1$ | A1 | |
| **Total: 3** | | |

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2 The function f is such that $\mathrm { f } ^ { \prime } ( x ) = 3 x ^ { 2 } - 7$ and $\mathrm { f } ( 3 ) = 5$. Find $\mathrm { f } ( x )$.\\

\hfill \mbox{\textit{CAIE P1  Q2 [3]}}
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