CAIE P1 2020 June — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (straightforward integration + point)
DifficultyModerate -0.8 This is a straightforward integration question requiring only basic power rule application and using a boundary condition to find the constant. The integration is routine (increasing powers by 1, dividing by new power), and substituting a point to find C is standard procedure with no conceptual challenges.
Spec1.07i Differentiate x^n: for rational n and sums1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
2 The equation of a curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { \frac { 1 } { 2 } } - 3 x ^ { - \frac { 1 } { 2 } }\). It is given that the point (4,7) lies on the curve. Find the equation of the curve.
Question 2:
AnswerMarks Guidance
AnswerMark Guidance
\(y = \dfrac{3x^{\frac{3}{2}}}{\frac{3}{2}} - \dfrac{3x^{\frac{1}{2}}}{\frac{1}{2}} \ (+c)\)B1 B1
\(7 = 16 - 12 + c\)M1 M1 for substituting \(x=4,\ y=7\) into their integrated expression
\(y = 2x^{\frac{3}{2}} - 6x^{\frac{1}{2}} + 3\)A1
Total: 4 marks
**Question 2:**

| Answer | Mark | Guidance |
|--------|------|----------|
| $y = \dfrac{3x^{\frac{3}{2}}}{\frac{3}{2}} - \dfrac{3x^{\frac{1}{2}}}{\frac{1}{2}} \ (+c)$ | B1 B1 | |
| $7 = 16 - 12 + c$ | M1 | M1 for substituting $x=4,\ y=7$ into their integrated expression |
| $y = 2x^{\frac{3}{2}} - 6x^{\frac{1}{2}} + 3$ | A1 | |

**Total: 4 marks**
2 The equation of a curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { \frac { 1 } { 2 } } - 3 x ^ { - \frac { 1 } { 2 } }$. It is given that the point (4,7) lies on the curve. Find the equation of the curve.\\

\hfill \mbox{\textit{CAIE P1 2020 Q2 [4]}}
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Q1 4 Q2 4 Q3 4 Q4 4 Q5 6 Q6 7 Q7 8 Q8 9 Q9 9 Q10 9 Q11 11