The table lists several values for $y = x^2 - \frac{1}{2x}$, with $x \ne 0$.
The x-values are: -2, -1.5, -1, -0.5, -0.25, -0.2, 0.2, 0.25, 0.5, 1, 1.5, 2.
A few matching y-values are already shown.
(a)[4]
Finish completing the table of values.
(b)[5]
Use the grid to sketch the graph of $y = x^2 - \frac{1}{2x}$ for $-2 \le x \le -0.2$ and $0.2 \le x \le 2$.
(c)[3]
Draw a suitable line on your graph and use it to solve the equation $x^2 - \frac{1}{2x} = 2$.
(d)[2]
The equation $x^2 - \frac{1}{2x} = k$ has only one solution. State the range of values of $k$ for which this can happen.
(e)[3]
Use a suitable tangent to estimate the gradient of the curve at the point where $x = -1$.
Worked solution & mark scheme
This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The expected value is $1.5$.” …