Higher November 2018 Paper 2 Q9
9 The diagrams show the position of a tap when off and fully on.
The tap is fully on when the angle of turn is 180°
When fully on, water flows out of the tap at 14 litres per minute.
The rate at which water flows out is in direct proportion to the angle of turn.
The tap is turned 135°
The water flows into a tank with a capacity of 79.8 litres.
Will it take less than \(7\dfrac{1}{2}\) minutes to fill the tank?
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 comparing with 7.5 minutes | ||
| \(180 \div 135\) or \(180 \div 14\) or \(79.8 \div 14\) or \(79.8 \div 135\) | M1 | oe or reciprocals |
| \(\dfrac{14 \times 135}{180}\) or 10.5 or \(\dfrac{79.8 \times 180}{135}\) or 106.4 | M1dep | oe or reciprocals |
| \(\dfrac{79.8 \times 180}{14 \times 135}\) or 7.6 | M1dep | oe eg \(79.8 \div 10.5\) or \(106.4 \div 14\) |
| No and 7.6 (and 7.5) | A1 | oe eg No and 7 minutes 36 seconds (and 7 minutes 30 seconds) |
| Alternative method 2 comparing with 79.8 litres | ||
| \(135 \div 180\) or \(14 \div 180\) or \(7.5 \times 14\) or \(7.5 \div 180\) | M1 | oe or reciprocals |
| \(\dfrac{14 \times 135}{180}\) or 10.5 or \(\dfrac{7.5 \times 135}{180}\) or 5.625 | M1dep | oe or reciprocals |
| \(\dfrac{7.5 \times 135 \times 14}{180}\) or 78.75 | M1dep | oe eg \(10.5 \times 7.5\) or \(5.625 \times 14\) |
| No and 78.75 | A1 | |
| Alternative method 3 comparing with 14 litres per minute | ||
| \(180 \div 135\) or \(180 \div 7.5\) or \(79.8 \div 135\) or \(79.8 \div 7.5\) | M1 | oe or reciprocals |
| \(\dfrac{7.5 \times 135}{180}\) or 5.625 or \(\dfrac{79.8 \times 180}{135}\) or 106.4 | M1dep | oe or reciprocals |
| \(\dfrac{79.8 \times 180}{7.5 \times 135}\) or [14.18, 14.19] | M1dep | oe |
| No and [14.18, 14.19] | A1 | |
| Alternative method 4 comparing new rate of flow with rate required | ||
| \(135 \div 180\) or \(14 \div 180\) | M1 | oe or reciprocals |
| \(\dfrac{14 \times 135}{180}\) or 10.5 | M1dep | oe |
| \(79.8 \div 7.5\) or 10.64 | M1 | oe |
| No and 10.5 and 10.64 | A1 | |
| Alternative method 5 comparing with 135 degrees | ||
| \(180 \div 14\) or \(180 \div 7.5\) or \(79.8 \div 14\) or \(79.8 \div 7.5\) | M1 | oe or reciprocals |
| \(180 \div 14\) and \(79.8 \div 7.5\) or \(180 \div 7.5\) and \(79.8 \div 14\) | M1dep | oe or matching reciprocals |
| \(\dfrac{79.8 \times 180}{7.5 \times 14}\) or 136.8 | M1dep | dep on M2 |
| No and 136.8 | A1 | |
Additional guidance
| No may be implied eg It takes more | |
| 7.3(0) used for 7.5 may score up to M3 | |
| \(7\dfrac{1}{2}\) minutes converted to 7.3(0) or 7 minutes 50 seconds | A0 |
| Ignore incorrect conversion of 7.6 to minutes and seconds if 7.6 seen | |
| Use the scheme that awards the most marks and ignore choice |