CAIE P1 2015 June — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyEasy -1.2 This is a straightforward integration question requiring only the power rule and using a point to find the constant of integration. It's a routine 3-mark question with no problem-solving element—purely mechanical application of basic integration techniques, making it easier than average.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation

The function f is such that \(\mathrm{f}'(x) = 5 - 2x^2\) and \((3, 5)\) is a point on the curve \(y = \mathrm{f}(x)\). Find \(\mathrm{f}(x)\). [3]

Question 1:
AnswerMarks
1f′(x)=5−2x2
and (3, 5)
2x3
f(x) = 5x − (+c)
3
Uses (3, 5)
AnswerMarks
→ c = 8B1
M1
A1
AnswerMarks
[3]For integral
Uses the point in an integral
co
Question 1:
1 | f′(x)=5−2x2
and (3, 5)
2x3
f(x) = 5x − (+c)
3
Uses (3, 5)
→ c = 8 | B1
M1
A1
[3] | For integral
Uses the point in an integral
co
The function f is such that $\mathrm{f}'(x) = 5 - 2x^2$ and $(3, 5)$ is a point on the curve $y = \mathrm{f}(x)$. Find $\mathrm{f}(x)$. [3]

\hfill \mbox{\textit{CAIE P1 2015 Q1 [3]}}