Higher June 2023 Paper 4 Q13
13 Here are two pieces of work.
Each shows a question and the first line of an incorrect solution.
For each part, describe the error made in the first line of the solution.
You do not need to complete the solution.
Question:
Simplify. \(\frac{2}{x - 1} + \frac{3}{x + 4}\)
Solution:
\(\frac{2}{x - 1} + \frac{3}{x + 4} = \frac{2(x - 1) + 3(x + 4)}{(x - 1)(x + 4)}\)
Question:
Solve. \(x^2 + 7x + 5 = 0\)
Solution:
\(x = -\frac{7 \pm \sqrt{7^2 - 4 \times 1 \times 5}}{2 \times 1}\)
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| An error in the numerators identified | 1 | See appendix | |
Appendix: exemplar responses for Q13(a)
| Response | Mark |
|---|---|
| Swop brackets in the numerator | 1 |
| They multiplied the 2 by \((x - 1)\) it should have been \((x + 4)\) | 1 |
| The brackets have been multiplied by the wrong number it should be \(2(x + 4)\) | 1 |
| The \((x - 1)\) and \((x + 4)\) should be the other way round | 1 |
| The numerators have been multiplied by the wrong/own denominators | 1 |
| (Correct answer is given) | 1 |
| They have multiplied the wrong numerator by the wrong denominator | 1 |
| It should be this \(\frac{2(x + 4) + 3(x - 1)}{(x - 1)(x + 4)}\) (single fraction only) | 1 |
| They multiply the numerator and the denominator rather than the opposite denominator | 1(BOD) |
| They did not cross multiply | 0 |
| They have multiplied their denominators by their numerators instead of adding them | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| This question was discounted and all candidates were awarded 1 mark. | 1 | ||
Notes
Editor’s note: the solution line shown is not actually wrong: \(x = -\frac{7 \pm \sqrt{7^2 - 4 \times 1 \times 5}}{2 \times 1}\) gives the same two values as \(x = \frac{-7 \pm \sqrt{7^2 - 4 \times 1 \times 5}}{2 \times 1}\), because \(\pm\) covers both signs, which is presumably why the part was discounted.