Foundation November 2019 Paper 1 Q15
15.
(a)
There are 45 swimmers in Top Swim club.
All swimmers are learning butterfly and backstroke and are asked which they prefer.
- \(\dfrac{3}{5}\) of all swimmers prefer backstroke.
- The number of juniors is double the number of seniors in the club.
- \(\dfrac{1}{6}\) of the juniors prefer butterfly.
Work out the proportion of swimmers who are seniors and prefer backstroke.
You may use the table to help you. [5]
| Prefer to swim | Total | ||
|---|---|---|---|
| Butterfly | Backstroke | ||
| Seniors | |||
| Juniors | |||
| Total | 45 | ||
(b)
The Sharks club has two types of membership: swimmers or divers.
The ratio of swimmers to divers is 8 : 3.
18 members of the club are divers.
How many members does The Sharks club have? [2]
| Scheme | Marks | Comments | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\left(\dfrac{3}{5} \text{ of } 45 = \right)\) 27 (prefer backstroke) | B1 | |||||||||||||||||
| \(\left(\dfrac{2}{3} \text{ of } 45 = \right)\) 30 (juniors) | B1 | |||||||||||||||||
| \(\left(\dfrac{1}{6} \text{ of } 30 = \right)\) 5 (junior and prefer butterfly) | B1 | STRICT FT ‘their 30’ if an integer | ||||||||||||||||
| 2 (senior and prefer backstroke) | B1 | STRICT FT ‘their 27’ – (‘their 30’ – ‘their 5’)
| ||||||||||||||||
| \(\dfrac{2}{45}\) oe; ISW | B1 | FT ‘their 2’ from their table |
| Scheme | Marks | Comments |
|---|---|---|
| (18 ÷ 3) × 11 or equivalent | M1 | May be in steps |
| 66 | A1 | If no marks, award SC1 for correctly finding the number of swimmers as 48; may be embedded in the ratio 48 : 18. |
| (7) |