Higher November 2021 Paper 1 Q24
24
(a) \(\text{f}(x) = cx + d\)
\(\text{f}(4) = 7\)
\(\text{f}(10) = 22\)
Work out the values of \(c\) and \(d\). [3 marks]
(b) \(\text{g}(x) = 2x \quad\) and \(\quad \text{h}(x) = \dfrac{x - 1}{2}\)
Circle the expression for \(\quad \text{hg}(x)\) [1 mark]
- \(\dfrac{2x^2 - x}{2}\)
- \(\dfrac{2x - 1}{2}\)
- \(x^2 - x\)
- \(x - 1\)
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: eliminates \(d\) | ||
| \(4c + d = 7\) and \(10c + d = 22\) | M1 | oe equations |
| \((10 - 4)c = 22 - 7\) or \(6c = 15\) or \(c = 2.5\) | M1dep | oe correct equation in \(c\) eg \(10c + 7 - 4c = 22\) |
| \(c = 2.5\) and \(d = -3\) | A1 | oe fraction or mixed number for \(c\) |
| Alternative method 2: eliminates \(c\) | ||
| \(4c + d = 7\) and \(10c + d = 22\) | M1 | |
| \((10 - 4)d = 70 - 88\) or \(6d = -18\) or \(d = -3\) | M1dep | oe correct equation in \(d\) eg \(4\left(\dfrac{22 - d}{10}\right) + d = 7\) |
| \(c = 2.5\) and \(d = -3\) | A1 | oe fraction or mixed number for \(c\) |
| Alternative method 3: works out the difference or the equation of the function through the points | ||
| (difference =) \(\dfrac{22 - 7}{10 - 4}\) or 2.5 | M1 | (gradient =) \(\dfrac{22 - 7}{10 - 4}\) or (\(m\) =) 2.5 |
| \(c = 2.5\) | M1dep | oe fraction or mixed number |
| \(c = 2.5\) and \(d = -3\) | A1 | oe fraction or mixed number for \(c\) |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{2x - 1}{2}\) | B1 |