Higher June 2018 Paper 2 Q21
21 Liz and Tia are walking towards a shop along different straight paths.
The diagram shows their positions at 2 pm
Not drawn accurately
(a) Assume they walk at the same speed.
Who will arrive at the shop first?
You must show your working. [3 marks]
(b) In fact, Liz walks at a faster speed than Tia.
How does this affect the answer to part (a)? [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(80^2 + 60^2 - 2 \times 80 \times 60 \times \cos 75\) or \(6400 + 3600 - 9600 \cos 75\) or 7515.(…) | M1 | oe |
| \(\sqrt{\text{their } 7515.(\ldots)}\) or [86.6, 86.7] or 87 | M1dep | |
| [86.6, 86.7] and Liz or 87 and Liz | A1 | accept 86 and Liz or 90 and Liz with full method seen |
| Alternative method 2 | ||
| \(80^2 + 60^2 - 2 \times 80 \times 60 \times \cos 75\) or \(6400 + 3600 - 9600 \cos 75\) or 7515.(…) | M1 | oe |
| (\(80^2 =\)) 6400 and 7515.(…) and Liz | A2 | |
Additional guidance
| \(80^2 + 60^2 - 2 \times 80 \times 60 \times \cos 75\) seen followed by processing error can score up to M2 | |
| eg \(80^2 + 60^2 - 2 \times 80 \times 60 \times \cos 75\) \(= 6400 + 3600 - 9600 \cos 75\) \(= 400 \cos 75 = 103.5\) | M1 |
| \(\sqrt{103.5}\) | M1depA0 |
| You may need to check on your calculator whether to award M1dep after first M1 with a processing error seen | |
| eg \(80^2 + 60^2 - 2 \times 80 \times 60 \times \cos 75 = 3654\) (processing error) | M1 |
| 60.4 (square root of 3654 is implied) | M1depA0 |
| Ignore any reasons given | |
| Alt 2 not possible to score M1A1 | |
| Answer [86.6, 86.7] and Liz (possibly from scale drawing) | M1M1A1 |
| [86.6, 86.7] (possibly from scale drawing) | M1M1 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 (answer Liz in (a)) | ||
| No change | B1 | oe eg Liz will still arrive first or Liz will be there even earlier (than Tia) |
| Alternative method 2 (answer Tia in (a)) | ||
| Not possible to tell | B1ft | oe eg Liz might arrive before Tia or it depends on how much faster Liz walks or it could be either of them |
| Alternative method 3 (answer they arrive at same time in (a)) | ||
| Liz will arrive first | B1ft | oe eg Liz wins |
| Alternative method 4 (neither Liz or Tia in (a)) | ||
| If Liz had arrived first there would be no change and if Tia had arrived first it would not be possible to tell | B1ft | oe |
Additional guidance
| If correct decision is made, ignore non-contradictory further work | |
| Alt 1 Liz will arrive earlier | B1 |
| Alt 1 No | B0 |
| Alt 2 Yes | B0 |