June 2025 Paper 1 Q1
1
(a) Sketch the function \(y = |2x-3|\). [2]
(b) In this question you must show detailed reasoning.
Solve the equation \(|2x-3| = 4-x\). [3]
Solve the equation \(|2x-3| = 4-x\). [3]
| Scheme | Marks | AO |
|---|---|---|
 | B1 B1 | 1.1 1.1 |
| [2] |
Notes
B1: V shaped graph (approximately symmetric for vertical mirror line)
Must be for positive and negative values of \(x\)
B1: Single vertex at (1.5, 0), and (0, 3) seen
| Scheme | Marks | AO |
|---|---|---|
| DR \(2x-3 = 4-x\) and \(2x-3 = -(4-x)\) | B1 | 1.1a |
| Either \(3x = 4+3\) or \(x = -4+3\) | M1 | 1.1 |
| \(x = \frac{7}{3}\) or \(x = -1\) | A1 | 1.1 |
| [3] |
Notes
B1: Two correct linear equations equating \(2x-3\) to \(\pm(4-x)\) oe
M1: Attempts to solve at least one equation.
A1: Both values seen
Alternative method
| Scheme | Marks |
|---|---|
| \((2x-3)^2 = (4-x)^2\) | B1 |
| \(3x^2-4x-7=0\) | M1 |
| \(x = \frac{7}{3}\) or \(x=-1\) | A1 |
B1: Correct equation seen
M1: Collects terms to form 3 term quadratic and attempt to solve
A1: Both values seen