November 2021 Paper 1 Q13
13 Here is a sketch of \(\quad y = k^x \quad\) where \(\quad k \gt 0\)
\(A\left(2,\ 3\frac{1}{16}\right)\) is a point on the curve.
Not drawn accurately
(a) Work out the value of \(k\). [2 marks]
(b) \(B\) is a point on the curve with \(x\)-coordinate \(-1\)
Work out the \(y\)-coordinate of \(B\). [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(k^2 = \dfrac{49}{16}\) or \(k = \sqrt{\dfrac{49}{16}}\) | M1 | oe |
| \(\dfrac{7}{4}\) | A1 | oe |
Additional guidance
| \(-\dfrac{7}{4}\) or \(\pm\dfrac{7}{4}\) will not gain the A mark unless recovered | M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{4}{7}\) | B1ft | oe allow decimal rounded to 2dp or better ft their (a) but not if \(k = 0\) or 1 |
Additional guidance
| \(\dfrac{1}{\frac{4}{7}}\) | B0 |