CAIE P1 2018 November — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypePure definite integration
DifficultyModerate -0.8 This is a straightforward definite integration question requiring only basic power rule application (rewriting as x^(1/2) and x^(-1/2)), integration to get (2/3)x^(3/2) + 4x^(1/2), and substitution of limits. It's routine practice with no problem-solving element, making it easier than average but not trivial since it requires careful handling of fractional powers and arithmetic with surds.
Spec1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)

Showing all necessary working, find \(\int_1^4 \left(\sqrt{x} + \frac{2}{\sqrt{x}}\right) \text{d}x\). [4]

Question 2:
AnswerMarks
23 1
x2 x2
Integrate → + 2 (+C)
3 1
AnswerMarks Guidance
2 2B1 B1 B1 for each term correct – allow unsimplified. C not
required.
4
 3 1 
x2 x2  40 14
 + 2  → −
3 1 3 3
 
 2 2 
AnswerMarks Guidance
1M1 Evidence of 4 and 1 used correctly in their integrand ie at
least one power increased by 1.
26
= oe
AnswerMarks Guidance
3A1 Allow 8.67 awrt. No integrand implies use of integration
function on calculator 0/4. Beware a correct answer from
wrong working.
4
AnswerMarks Guidance
QuestionAnswer Marks
Question 2:
2 | 3 1
x2 x2
Integrate → + 2 (+C)
3 1
2 2 | B1 B1 | B1 for each term correct – allow unsimplified. C not
required.
4
 3 1 
x2 x2  40 14
 + 2  → −
3 1 3 3
 
 2 2 
1 | M1 | Evidence of 4 and 1 used correctly in their integrand ie at
least one power increased by 1.
26
= oe
3 | A1 | Allow 8.67 awrt. No integrand implies use of integration
function on calculator 0/4. Beware a correct answer from
wrong working.
4
Question | Answer | Marks | Guidance
Showing all necessary working, find $\int_1^4 \left(\sqrt{x} + \frac{2}{\sqrt{x}}\right) \text{d}x$. [4]

\hfill \mbox{\textit{CAIE P1 2018 Q2 [4]}}