CAIE P2 2013 June — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2013
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (exponential/logarithmic functions)
DifficultyModerate -0.8 This is a straightforward integration question requiring recognition of the standard integral form 1/(ax+b), followed by applying initial conditions to find the constant. It's simpler than average A-level questions as it involves only one direct integration step with no algebraic manipulation or problem-solving required.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits
1 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 } { 7 - 2 x }\). The point \(( 3,2 )\) lies on the curve. Find the equation of the curve.
AnswerMarks Guidance
Integrate and obtain term of the form \(k \ln(7 - 2x)\)M1
State \(y = -2 \ln(7 - 2x) + c\)A1
Evaluate \(c\)DM1
Obtain answer \(y = -2 \ln(7 - 2x) + 2\)A1✓ [4] 
Integrate and obtain term of the form $k \ln(7 - 2x)$ | M1 |
State $y = -2 \ln(7 - 2x) + c$ | A1 |
Evaluate $c$ | DM1 |
Obtain answer $y = -2 \ln(7 - 2x) + 2$ | A1✓ | [4]
1 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 } { 7 - 2 x }$. The point $( 3,2 )$ lies on the curve. Find the equation of the curve.

\hfill \mbox{\textit{CAIE P2 2013 Q1 [4]}}
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