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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 |
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 $B$. $[3]$