Higher June 2022 Paper 2 Q20
20 A company makes and sells boxes of washing powder.
The company wants to increase the amount of money it receives per kg of powder.
To get the required increase it can
increase the price to £5.88
or
reduce the mass of powder in the box by \(x\)%
Work out the value of \(x\) to 2 decimal places. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(5.88 \div 1.68\) or 3.5 or \(1.68 \div 5.88\) or [0.285, 0.29] or \(5.88 \div 5.60\) or 1.05 | M1 | oe eg \(\dfrac{7}{2}\) or \(\dfrac{2}{7}\) or \(\dfrac{21}{20}\) or \(5.6 \times 1.05 = 5.88\) |
| \(5.6(0) \div (5.88 \div 1.68)\) or \(5.6(0) \times (1.68 \div 5.88)\) or \(1.68 \div (5.88 \div 5.60)\) or 1.6 | M1dep | oe eg \(5.6(0) \div 3.5\) or \(5.6(0) \times\) [0.285, 0.29] or \(1.68 \div 1.05\) |
| their \(1.6 \div 1.68\) or [0.952, 0.9524] or \(1 -\) their \(1.6 \div 1.68\) or \(1 -\) [0.952, 0.9524] or [0.0476, 0.048] | M1dep | oe eg \(\dfrac{20}{21}\) or \(1 - \dfrac{20}{21}\) or \(\dfrac{1}{21}\) \(5.6(0) \div 5.88\) oe scores M3 \(1 - 5.6(0) \div 5.88\) oe scores M3 |
| 4.76 | A1 | |
| Alternative method 2 | ||
| \(5.88 \div 5.6(0)\) or 1.05 | M1 | oe eg \(\dfrac{21}{20}\) |
| \(1 \div\) their 1.05 | M1dep | oe eg \(1 \div \dfrac{21}{20}\) |
| [0.952, 0.9524] or \(1 -\) [0.952, 0.9524] or [0.0476, 0.048] | M1dep | oe eg \(\dfrac{20}{21}\) or \(1 - \dfrac{20}{21}\) or \(\dfrac{1}{21}\) \(5.6(0) \div 5.88\) oe scores M3 \(1 - 5.6(0) \div 5.88\) oe scores M3 |
| 4.76 | A1 | |
Additional guidance
| Up to M3 may be awarded for correct work with no, or incorrect answer, even if this is seen amongst multiple attempts | |
| \(\dfrac{0.28}{5.60} = 0.05\) is M0 unless 1.05 subsequently used | |
| \(5.60 \div 1.68\) with no further correct working | M0 |
| Note that 1.6 seen may be from an incorrect method eg \(1.68 \times 0.95 = 1.6\) does not score because \(1.68 \times 0.95\) is an incorrect method and the actual value of \(1.68 \times 0.95\) is 1.596 | |
| Any single calculation or set of calculations that lead to \(\dfrac{20}{21}\) or \(\dfrac{1}{21}\) | M3 |
| Some common oes for \(1 - 5.6(0) \div 5.88\) are \(\dfrac{5.88 - 5.6(0)}{5.88}\) or \(\dfrac{0.28}{5.88}\) and \(\dfrac{1.68 - 1.6}{1.68}\) or \(\dfrac{0.08}{1.68}\) | M3 |
| 3rd M1 oes include [0.952, 0.9524] \(\times\) 100 or [95.2, 95.24]% 100% \(-\) [0.952, 0.9524] \(\times\) 100 [0.0476, 0.048] \(\times\) 100 or (4.76, 4.8]% | |
| Values that score marks may be seen in ratios eg 5.88 : 1.68 (does not score at this stage) | |
| 3.50 : 1 | M1 |
| Allow working in pence eg \(588 \div 1.68\) or 350 | M1 |
| Allow working in grams eg \(5.88 \div 1680\) or 0.0035 | M1 |