Higher November 2021 Paper 4 Q10
10 Alex, Blake and Charlie play a computer game.
Alex goes first and scores \(n\) points.
- Blake scores 8 points less than 3 times the number of points scored by Alex.
- Charlie scores 25 more points than Blake.
- The three people score a total of 618 points.
Work out how many points they each score.
You must show your working. [7]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 87 253 278 with correct working | 7 | B1 for \(3n - 8\) B1 for \(3n - 8 + 25\) or better M1 for writing a correct equation equal to 618 using their expressions e.g. \(n + 3n - 8 + 3n - 8 + 25 = 618\) or better | “Correct working” requires evidence of at least B1 B1 Expressions could start from B or C. |
| M1 for simplifying their equation e.g. \(7n + 9 = 618\) A1FT for correctly solving their equation e.g. \(n = 87\) M1 for substituting their 87 into both expressions e.g. 3×87 – 8 and 3×87 – 8 + 25 oe | |||
| Trials: B1 for one complete trial with \(n \geqslant 3\) B1 for second complete trial \(n \geqslant 3\) If 0 or 1 scored SC3 for 87, 253, 278 with B1 only or SC2 for 87, 253, 278 with no working | See appendix for a more complete set of trials | ||
Appendix: Question 10 trials
| \(n\) | \(3n - 8\) | \(3n - 8 + 25\) | Total |
|---|---|---|---|
| 10 | 22 | 47 | 79 |
| 20 | 52 | 77 | 149 |
| 30 | 82 | 107 | 219 |
| 40 | 112 | 137 | 289 |
| 50 | 142 | 167 | 359 |
| 60 | 172 | 197 | 429 |
| 70 | 202 | 227 | 499 |
| 80 | 232 | 257 | 569 |
| 90 | 262 | 287 | 639 |
| 100 | 292 | 317 | 709 |
| increments | +1 | +3 | +3 | +7 |
|---|---|---|---|---|
| e.g. | add 4 | add 12 | add 12 | add 28 |
| 24 | 64 | 89 | 177 |