Easy -1.8 This is a straightforward one-step linear inequality requiring only basic algebraic manipulation (multiply by 5, collect terms, divide). It's significantly easier than average A-level questions, which typically involve multiple steps or concepts.
Awarded for seeing either of the two inequalities; allow even with incorrect signs
\(x > 5\) only
A1
Final answer
Question 2a:
Answer
Marks
Guidance
\(x = \sqrt{1+2y}\) or \(x^2 = 1 + 2y\)
M1
Allow swapping x and y at any stage
\(\frac{x^2}{2} - \frac{1}{2}\)
A1
Correct answer or equivalent; no need to write \(f^{-1}(x)\)
Correct domain
B1
Do not allow \(y \geq 0\), \(f^{-1}(x) \geq 0\) or \(x > 0\)
Question 2b:
Answer
Marks
Guidance
'It is one-to-many'
B1 BOD
Allow if 'It' refers to \(g(x)\) or \(g^{-1}(x)\); B0 if candidate specifically says '\(g(x)\) is one-to-many'
## Question 1:
| Inequality question | M1 | Awarded for seeing either of the two inequalities; allow even with incorrect signs |
| $x > 5$ only | A1 | Final answer |
## Question 2a:
| $x = \sqrt{1+2y}$ or $x^2 = 1 + 2y$ | M1 | Allow swapping x and y at any stage |
| $\frac{x^2}{2} - \frac{1}{2}$ | A1 | Correct answer or equivalent; no need to write $f^{-1}(x)$ |
| Correct domain | B1 | Do not allow $y \geq 0$, $f^{-1}(x) \geq 0$ or $x > 0$ |
## Question 2b:
| 'It is one-to-many' | B1 BOD | Allow if 'It' refers to $g(x)$ or $g^{-1}(x)$; B0 if candidate specifically says '$g(x)$ is one-to-many' |