June 2024 Paper 2 Q14
14 \(P\) is the point on the graph \(\quad y = 3^{-x} \quad\) that has \(x\)-coordinate \(-2\)
\(Q\) is a point on the graph \(\quad y = 1152 \times \left(\dfrac{1}{2}\right)^x\)
\[y\text{-coordinate of } P = y\text{-coordinate of } Q\]Work out the \(x\)-coordinate of \(Q\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(3^2\) or 9 | M1 | oe value for \(y\) eg \(3^{--2}\) |
| \(\left(\dfrac{1}{2}\right)^x = \dfrac{\text{their } 9}{1152}\) or \(\dfrac{1}{2^x} = \dfrac{1}{128}\) | M1dep | oe equation with exponential term isolated eg \(2^{-x} =\) [0.0078, 0.007813] or \(2^x = 128\) |
| 7 | A1 |
Additional guidance
| M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Missing brackets must be recovered eg1 \(\dfrac{1}{2}^{x} = \dfrac{9}{1152}\) with no further correct work eg2 \(\dfrac{1}{2}^{x} = \dfrac{9}{1152}\) with answer 7 | M1M0A0 M2A1 |
| Logarithms may be seen eg \(\log\left(\dfrac{1}{2}\right)^x = \log\dfrac{9}{1152}\) or \((x =)\ \log_{0.5}\dfrac{1}{128}\) | M1M1 |