$\require{\cancel}$ $\require{\stix[upint]}$

Qtn No.	1	2	3	4	5	6	Total
Marks	3	4	3	4	7	8	29
Score

Question 1

A line has equation $y=2 x-7$ and a curve has equation $y=x^{2}-4 x+c$, where $c$ is a constant. Find the set of possible values of $c$ for which the line does not intersect the curve. $[3]$

Question 2

$\text{(i)}$ Express $x^{2}+6 x+2$ in the form $(x+a)^{2}+b$, where $a$ and $b$ are constants. $[2]$

$\text{(ii)}$ Hence, or otherwise, find the set of values of $x$ for which $x^{2}+6 x+2>9$. $[2]$

Question 3

Showing all necessary working, solve the equation $4 x-11 x^{\frac{1}{2}}+6=0$. $[3]$

Question 4

$\text{(i)}$ Express $4 x^{2}-12 x$ in the form $(2 x+a)^{2}+b$. $[2]$

$\text{(ii)}$ Hence, or otherwise, find the set of values of $x$ satisfying $4 x^{2}-12 x>7$. $[2]$

Question 5

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 6

A curve for which $\displaystyle\frac{\mathrm{d} y}{\mathrm{~d} x}=7-x^{2}-6 x$ passes through the point $(3,-10)$.

$\text{(i)}$ Find the equation of the curve. $[3]$

$\text{(ii)}$ Express $7-x^{2}-6 x$ in the form $a-(x+b)^{2}$, where $a$ and $b$ are constants. $[2]$

$\text{(iii)}$ Find the set of values of $x$ for which the gradient of the curve is positive. $[3]$