Foundation June 2017 Paper 2 Q32
32. Rosa starts a 27 km cycle race at 14:20.
She finishes the cycle race at 16:00.
Rosa set herself a target of achieving an average speed of 20 km per hour for the race.
(a)
Did Rosa achieve her target?
You must show all your working. [3]
(b)
During the cycle race Rosa stopped for 25 minutes to mend a puncture.
Had she not needed to stop to mend her puncture, how would this have impacted on her
- average speed and
- achieving her target?
You must show all your working. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 27 ÷ \(1\tfrac{2}{3}\) or equivalent full method | B2 | Allow \(1\tfrac{2}{3}\) =1.66 or 1.67 for B2, but not \(1\tfrac{2}{3}\) = 1.6 Award B2 for sight of 4.5 m/s B1 for 27 ÷ 1 hour 40 minutes or 27 ÷ 100 Allow B1 for 27 ÷ 1.4(0) or 27 ÷ 1.6 |
| 16.2 (km per hour) AND states or implies target not achieved | B1 | CAO, must be exactly 16.2 (km per hour) from sight of 27 ÷ \(1\tfrac{2}{3}\) Unsupported 16.2 (km per hour) AND states or implies target not achieved is awarded B2 only (as answer may have been rounded to 16.2 km per hour from incorrect use of time) If no marks, allow SC1 for the appropriate interpretation of 27 ÷ ‘their time given in hours’ correctly evaluated, allowing \(\tfrac{1}{3}\) hour written as 0.3 |
Alternatives
| Scheme | Marks |
|---|---|
| (20 km/h means) 30 km in \(1\tfrac{1}{2}\) hours | M1 |
| Attempts 14(:)20 + \(1\tfrac{1}{2}\) | m1 |
| (Finish time would be) 15(:)50 AND (Didn’t finish until 16:00 so) states or implies target not met | A1 |
OR
| Scheme | Marks |
|---|---|
| (Time would be) 60 × 27/20 | M1 |
| 81(minutes) or 1 hour 21 minutes | A1 |
| (Rosa would needed to have finished by 14:20 + 1 hr 21 minutes ) 15(:)41 AND states or implies target not met (as she finished at 16:00) | B1 |
OR
| Scheme | Marks |
|---|---|
| (Distance would be) 20 × \(1\tfrac{2}{3}\) | M1 |
| \(33\tfrac{1}{3}\) (km) or 33.33(... km) (A0 for 33.3(km)) | A1 |
| (Rosa cycled) less than \(33\tfrac{1}{3}\) (km) (or 33.33...km) AND states or implies target not met | B1 |
(Use of 20 × \(1\tfrac{2}{3}\) as 20 × 1.6 is awarded M1 only)
| Scheme | Marks | Comments |
|---|---|---|
| Impact statement, e.g. ‘meets target’, ‘beats target’ AND sight of (27 ÷ 1.25) 21.6 (km per hour) | E2 | For E2 FT use of ‘their time in hours’ – 25 minutes used correctly with appropriate impact statement E1 for sight of 21.6 (km per hour) If no marks, SC1 for FT attempt 27 ÷ ‘their time – 25 minutes written incorrectly’ with appropriate impact statement, e.g. time used in (a) is 1.4, uses 1.4 – 25 minutes in calculating average speed ‘27 ÷ 1.15 = 23.47... so meets target’ |
| (5) |