Higher November 2019 Paper 3 Q25
25 Here is a sketch of a speed-time graph for the first part of a journey.
The total distance for the journey is 130 kilometres.
How far is left to travel? [4 marks]
Answer in km
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Correct method to work out any viable distance, eg \(\dfrac{1}{2} \times \dfrac{5}{60} \times 102\) or 4.25 (first section) or \(102 \times \dfrac{40}{60}\) or 68 (second section) or \(\dfrac{1}{2}(102 + 96) \times \dfrac{15}{60}\) or \(96 \times \dfrac{15}{60}\) and \(\dfrac{1}{2} \times 6 \times \dfrac{15}{60}\) or 24 and 0.75 or 24.75 (third section) or \(\dfrac{1}{2}\left(\dfrac{40}{60} + \dfrac{45}{60}\right) \times 102\) or 72.25 (first and second sections) | M1 | |
| Correct method to work out all parts of distance, eg \(\dfrac{1}{2} \times \dfrac{5}{60} \times 102\) or 4.25 and \(102 \times \dfrac{40}{60}\) or 68 and \(\dfrac{1}{2}(102 + 96) \times \dfrac{15}{60}\) or 24.75 | M1dep | 97 scores M1M1 |
| \(130 -\) their whole distance or \(130 - 97\) | M1dep | eg \(130 -\) their \(4.25 -\) their \(68 -\) their 24.75 dep on M2 |
| 33 | A1 | |
| Alternative method 2 | ||
| Correct method to work out \(60 \times\) any viable distance, eg \(\dfrac{1}{2} \times 5 \times 102\) or 255 (first section) or \(102 \times 40\) or 4080 (second section) or \(\dfrac{1}{2}(102 + 96) \times 15\) or \(96 \times 15\) and \(\dfrac{1}{2} \times 6 \times 15\) or 1440 and 45 or 1485 (third section) or \(\dfrac{1}{2}(40 + 45) \times 102\) or 4335 (first and second sections) | M1 | |
| Correct method to work out \(60 \times\) all parts of distance, eg \(\dfrac{1}{2} \times 5 \times 102\) or 255 and \(102 \times 40\) or 4080 and \(\dfrac{1}{2}(102 + 96) \times 15\) or 1485 | M1dep | 5820 implies M1M1 |
| \(130 -\) their whole distance or \(130 - \dfrac{5820}{60}\) or \(130 - 97\) | M1dep | eg \(130 - \dfrac{\text{their } 255 + \text{their } 4080 + \text{their } 1485}{60}\) dep on M2 |
| 33 | A1 | |
Additional guidance
Accept fractions used as decimals correct to 2 dp or better