Higher June 2019 Paper 2 Q14
14 Ali and Mel are making 3-digit codes.
The digit 0 is not used.
Ali only uses odd digits.
Mel only uses even digits.
(a) Ali can make \(x\) more codes than Mel.
Assume that digits cannot be repeated.
Work out the value of \(x\). [3 marks]
(b) In fact, digits can be repeated.
What does this tell you about the actual value of \(x\)?
Tick one box. [1 mark]
- It is bigger than my answer to part (a)
- It is smaller than my answer to part (a)
- It is the same as my answer to part (a)
| Answer | Mark | Comments |
|---|---|---|
| (Ali) \(5 \times 4 \times 3\) or 60 or (Mel) \(4 \times 3 \times 2\) or 24 | M1 | oe eg (Ali) \(5 \times 12\) or (Mel) 4! |
| \(5 \times 4 \times 3 - 4 \times 3 \times 2\) or 60 – 24 | M1dep | oe implies M2 |
| 36 with no incorrect method seen | A1 | SC1 answer 61 |
Additional guidance
| Ignore any listing of possible codes | |
| 48 – 12 = 36 (incorrect method seen) | M0M0A0 |
| 1st M1 Further work eg1 60 followed by \(60 \times 3\) eg2 \(6 \times 4 = 24\) followed by \(24 \times 2 = 48\) | M0 |
| Answer | Mark | Comments |
|---|---|---|
| ✓ It is bigger than my answer to part (a) ☐ It is smaller than my answer to part (a) ☐ It is the same as my answer to part (a) | B1 |