June 2025 Paper 3 Q2
2
(a) The curve \(y = \dfrac{1}{x^3}\) is translated by 4 units in the positive \(x\)-direction.
Write down the equation of the curve after it has been translated. [2]
Write down the equation of the curve after it has been translated. [2]
(b) The curve \(y = 5x^2\) is stretched parallel to the \(y\)-axis with scale factor 4.
The point on the curve \(y = 5x^2\) with \(x\)-coordinate 3 is transformed to the point \(P\).
Write down the coordinates of \(P\). [2]
The point on the curve \(y = 5x^2\) with \(x\)-coordinate 3 is transformed to the point \(P\).
Write down the coordinates of \(P\). [2]
| Scheme | Marks | AO |
|---|---|---|
| M1 | 1.1 | |
| \(y = \dfrac{1}{(x - 4)^3}\) | A1 | 1.1 |
| [2] |
Notes
M1: M1 for \(\dfrac{1}{(x \pm 4)^3}\) only (so no misreads) - need not be an equation for this mark
oe e.g. \((x \pm 4)^{-3}\)
A1: Must be an equation of the form \(y = \ldots\) but A0 for only \(\mathrm{f}(x) = \ldots\)
ISW if expanded either correctly or incorrectly
| Scheme | Marks | AO |
|---|---|---|
| \((3, 180)\) | B1 B1 | 1.1 1.1 |
| [2] |
Notes
B1: B1 for correct explicit \(x\)-coordinate (so not embedded in a calculation for \(y\))
B1: B1 for correct explicit simplified \(y\)-coordinate (so must be 180)
B1 for \(x = 3\)
B1 for \(y = 180\)
Allow missing bracket round coordinates