June 2025 Paper 1 Q1
1 Express each of the following in the form \(px^q\), where \(p\) and \(q\) are constants.
| Scheme | Marks | AO |
|---|---|---|
| \(2x^{-\frac{1}{4}}\) | B1 | 1.1 |
| [1] |
Notes
B1: Correct expression. Or \(2x^{-0.25}\). Could be implied by \(p = 2\), \(q = -0.25\)
| Scheme | Marks | AO |
|---|---|---|
| \(125\ldots\) | B1 | 1.1 |
| \(\ldots x^{\frac{9}{2}}\) | B1 | 1.1 |
| [2] |
Notes
B1: Obtain 125. Could be implied by \(p = 125\)
B1: Obtain \(x^{\frac{9}{2}}\). Allow \(4\tfrac{1}{2}\) or 4.5. Could be implied by \(q = 4.5\)
Allow SC B1 if 0 scored but \(x\sqrt{x}\) is seen as \(x^{\frac{3}{2}}\) oe
| Scheme | Marks | AO |
|---|---|---|
| \(4\ldots\) | B1 | 1.1 |
| \(\ldots x^4\) | B1 | 1.1 |
| [2] |
Notes
B1: Obtain 4. Could be implied by \(p = 4\)
B1: Obtain \(x^4\). Could be implied by \(q = 4\)
Allow SC B1 if 0 scored but \(\sqrt{16x^8}\) seen
| Scheme | Marks | AO |
|---|---|---|
| \(\left(27x^6\right)^{\frac{1}{3}} = 3x^2\) | M1* | 1.1 |
| \(x^5 \times 3x^2 = 3x^7\) | M1dep* | 1.1 |
| A1 | 1.1 | |
| [3] |
Notes
M1*: Obtain either \(ax^2\) or \(3x^b\)
M1dep*: Correctly combine \(x^5\) and their \(3x^2\). Obtain either \(ax^7\) following their \(a\), or \(3x^{(5+b)}\) following their \(b\)
A1: Obtain correct answer. Could be implied by \(p = 3\), \(q = 7\)