OCR MEI Further Pure Core 2020 November — Question 3 4 marks

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2020
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration using inverse trig and hyperbolic functions
TypeStandard integral of 1/√(a²-x²)
DifficultyStandard +0.3 This is a standard Further Maths integral requiring recognition of the inverse sine form 1/√(a²-x²). Students must manipulate 4-9x² into the form a²-(bx)², apply the standard result arcsin(x/a), and evaluate at the limits. While it requires careful algebraic manipulation and knowledge of a Further Maths formula, it's a direct application of a bookwork result with no novel problem-solving, making it slightly easier than average overall but typical for Further Pure.
Spec4.08h Integration: inverse trig/hyperbolic substitutions

3 In this question you must show detailed reasoning.
Find \(\int _ { 0 } ^ { \frac { 1 } { 3 } } \frac { 1 } { \sqrt { 4 - 9 x ^ { 2 } } } \mathrm {~d} x\), expressing your answer in terms of \(\pi\).

Question 3:
AnswerMarks
3DR
= 1(arcsin1[−arcsin0])
AnswerMarks
3 2M1
A1
M1
AnswerMarks
A13.1a
1.1
1.1
AnswerMarks
1.1must be in the form k
√4−x2
9
k=/ 1
k arcsin(3x/2)
AnswerMarks
​ ​​can award M1A1 if integral is
fully correct before limits
substituted
AnswerMarks
ORM1
A1
M1
A1
AnswerMarks
[4]for suitable substitution
an equivalent expression that
can be integrated
substitution of correct limits
of their variable
Question 3:
3 | DR
= 1(arcsin1[−arcsin0])
3 2 | M1
A1
M1
A1 | 3.1a
1.1
1.1
1.1 | must be in the form k
√4−x2
9
k=/ 1
k arcsin(3x/2)
​ ​​ | can award M1A1 if integral is
fully correct before limits
substituted
OR | M1
A1
M1
A1
[4] | for suitable substitution
an equivalent expression that
can be integrated
substitution of correct limits
of their variable
3 In this question you must show detailed reasoning.\\
Find $\int _ { 0 } ^ { \frac { 1 } { 3 } } \frac { 1 } { \sqrt { 4 - 9 x ^ { 2 } } } \mathrm {~d} x$, expressing your answer in terms of $\pi$.

\hfill \mbox{\textit{OCR MEI Further Pure Core 2020 Q3 [4]}}