Question 2 - A-Level Maths

CAIE P2 Specimen — Question 2 5 marks

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Session	Specimen
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Product & Quotient Rules
Type	Points with specific gradient
Difficulty	Standard +0.3 This is a straightforward application of the quotient rule followed by solving a simple equation. Students must differentiate the rational function, set dy/dx = -4, and solve for x-coordinates. While it requires multiple steps (differentiation, equation setup, algebraic manipulation), each step is routine and the question follows a standard template with no conceptual surprises.
Spec	1.07m Tangents and normals: gradient and equations

2 A curve has equation $$y = \frac { 3 x + 1 } { x - 5 }$$ Find the coordinates of the points on the curve at which the gradient is - 4 .

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Question 2:

Answer	Marks	Guidance
Answer	Marks	Guidance
Use quotient rule or, after adjustment, product rule	M1*
Obtain $\frac{3x-15-3x-1}{(x-5)^2}$ or equivalent	A1
Equate first derivative to $-4$ and solve for $x$	DM1
Obtain $x$-coordinates $3$ and $7$ or one correct pair of coordinates	A1
Obtain $y$-coordinates $-5$ and $11$ respectively or other correct pair of coordinates	A1
Total: 5

## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use quotient rule or, after adjustment, product rule | M1* | |
| Obtain $\frac{3x-15-3x-1}{(x-5)^2}$ or equivalent | A1 | |
| Equate first derivative to $-4$ and solve for $x$ | DM1 | |
| Obtain $x$-coordinates $3$ and $7$ or one correct pair of coordinates | A1 | |
| Obtain $y$-coordinates $-5$ and $11$ respectively or other correct pair of coordinates | A1 | |
| **Total: 5** | | |

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2 A curve has equation

$$y = \frac { 3 x + 1 } { x - 5 }$$

Find the coordinates of the points on the curve at which the gradient is - 4 .\\

\hfill \mbox{\textit{CAIE P2  Q2 [5]}}

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Q1 4 Q2 5 Q3 7 Q4 7 Q6 9 Q7 11