CAIE P1 2017 November — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeEquation of tangent line
DifficultyModerate -0.8 This is a straightforward differentiation and tangent line question. It requires applying the power rule to differentiate (no chain rule actually needed despite the topic label), substituting x=4 to find the gradient, then using y-y₁=m(x-x₁). All steps are routine with no problem-solving required, making it easier than average but not trivial since it involves fractional powers and multiple terms.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations
1 A curve has equation \(y = 2 x ^ { \frac { 3 } { 2 } } - 3 x - 4 x ^ { \frac { 1 } { 2 } } + 4\). Find the equation of the tangent to the curve at the point \(( 4,0 )\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{dy}{dx} = 3x^{1/2} - 3 - 2x^{-1/2}\)B2,1,0
At \(x = 4\), \(\frac{dy}{dx} = 6 - 3 - 1 = 2\)M1
Equation of tangent is \(y = 2(x-4)\) OEA1FT Equation through \((4, 0)\) with *their* gradient
Total: 4 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{dy}{dx} = 3x^{1/2} - 3 - 2x^{-1/2}$ | B2,1,0 | |
| At $x = 4$, $\frac{dy}{dx} = 6 - 3 - 1 = 2$ | M1 | |
| Equation of tangent is $y = 2(x-4)$ OE | A1FT | Equation through $(4, 0)$ with *their* gradient |
| **Total: 4** | | |

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1 A curve has equation $y = 2 x ^ { \frac { 3 } { 2 } } - 3 x - 4 x ^ { \frac { 1 } { 2 } } + 4$. Find the equation of the tangent to the curve at the point $( 4,0 )$.\\

\hfill \mbox{\textit{CAIE P1 2017 Q1 [4]}}
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Q1 4 Q2 4 Q3 6 Q4 6 Q5 6 Q6 9 Q7 9 Q8 9 Q9 10 Q10 12