Higher June 2023 Paper 1 Q17
17 The functions g and h are such that
\[\mathrm{g}(x) = \frac{11}{2x - 5}\] \[\mathrm{h}(x) = x^2 + 4 \qquad x \geqslant 0\](a) What value of \(x\) must be excluded from any domain of g? (1)
(b) Solve \(\;\mathrm{gh}(x) = 1\) (3)
| Scheme | Marks |
|---|---|
| 2.5 | B1 |
| (1) |
Notes
B1: oe e.g. \(2\frac{1}{2}\), \(\dfrac{5}{2}\)
Accept \(x = 2.5\) oe and \(x \neq 2.5\) oe
Any response that contains 2.5 oe is also acceptable, APART FROM \(x \gt 2.5\) oe or \(x \lt 2.5\) oe or \(x \geqslant 2.5\) oe or \(x \leqslant 2.5\) oe
| Scheme | Marks |
|---|---|
| (gh(\(x\)) =) \(\dfrac{11}{2(x^2 + 4) - 5}\;(= 1)\) | M1 |
| \(11 - 3 = 2x^2\) oe eg \(x^2 = 4\) or \(2x^2 - 8 = 0\) or \(x^2 - 4 = 0\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 2 | A1 |
| (3) | |
| (4 marks) |
Notes
M1: correct expansion and rearrangement with \(x\) term on one side and number terms the other side or all terms on one side in an equation
A1: cao, an answer of ±2 gains M2 only
If no other marks awarded, award SCB1 for answer of 2.2 oe