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MATHEMATICS 9709

Cambridge International AS and A Level

Name of student Date
Adm. number Year/grade Stream
Subject Pure Mathematics 1 (P1) Variant(s) P11, P12, P13
Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 3 7 7 9 9 35
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject.
Attempt all the 5 questions

Question 1 Code: 9709/13/O/N/16/1, Topic: Quadratics

Find the set of values of $k$ for which the curve $y=k x^{2}-3 x$ and the line $y=x-k$ do not meet. $[3]$

Question 2 Code: 9709/12/O/N/11/4, Topic: Quadratics

The equation of a curve is $y^{2}+2 x=13$ and the equation of a line is $2 y+x=k$, where $k$ is a constant.

$\text{(i)}$ In the case where $k=8$, find the coordinates of the points of intersection of the line and the curve. $[4]$

$\text{(ii)}$ Find the value of $k$ for which the line is a tangent to the curve. $[3]$

Question 3 Code: 9709/11/M/J/15/5, Topic: Quadratics

A piece of wire of length $24 \mathrm{~cm}$ is bent to form the perimeter of a sector of a circle of radius $r \mathrm{~cm}$.

$\text{(i)}$ Show that the area of the sector, $A \mathrm{~cm}^{2}$, is given by $A=12 r-r^{2}$. $[3]$

$\text{(ii)}$ Express $A$ in the form $a-(r-b)^{2}$, where $a$ and $b$ are constants. $[2]$

$\text{(iii)}$ Given that $r$ can vary, state the greatest value of $A$ and find the corresponding angle of the sector. $[2]$

Question 4 Code: 9709/11/O/N/11/9, Topic: Quadratics, Coordinate geometry, Differentiation

A line has equation $y=k x+6$ and a curve has equation $y=x^{2}+3 x+2 k$, where $k$ is a constant.

$\text{(i)}$ For the case where $k=2$, the line and the curve intersect at points $A$ and $B$. Find the distance $A B$ and the coordinates of the mid-point of $A B$. $[5]$

$\text{(ii)}$ Find the two values of $k$ for which the line is a tangent to the curve. $[4]$

Question 5 Code: 9709/12/O/N/18/10, Topic: Quadratics, Coordinate geometry

The equation of a curve is $\displaystyle y=2 x+\frac{12}{x}$ and the equation of a line is $y+x=k$, where $k$ is a constant.

$\text{(i)}$ Find the set of values of $k$ for which the line does not meet the curve. $[3]$

In the case where $k=15$, the curve intersects the line at points $A$ and $B$.

$\text{(ii)}$ Find the coordinates of $A$ and $B$. $[3]$

$\text{(iii)}$ Find the equation of the perpendicular bisector of the line joining $A$ and $B$. $[3]$

Worked solutions: P1, P3 & P6 (S1)

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