1

The line $y=x+k$ is a tangent to the curve $y=x^2$. Work out the value of $k$. [4]

2

A circle has equation $x^2+y^2=20$. The line $y=2x$ meets the circle at two points. Work out the coordinates of both points. [3]

3

A line has gradient $3$ and passes through the point $(0,-5)$. It intersects the curve $y=x^2-3$ at two points, $A$ and $B$. Work out the coordinates of $A$ and $B$, and the coordinates of the midpoint of $AB$. [5]

4

A straight line passes through the points $(0,1)$ and $(2,5)$. Work out the coordinates of the points where this line meets the curve $y=x^2+1$. [4]

5

The line $y=x+c$ is a tangent to the circle $x^2+y^2=8$. Work out the two possible values of $c$. [5]