Higher November 2019 Paper 1 Q10
10 Saj makes Rose Pink paint and Cherry Pink paint.
He mixes red paint with white paint as shown.
| Rose Pink red : white = 1 : 2 | Cherry Pink red : white = 4 : 3 |
He makes 60 litres of Rose Pink paint.
To this Rose Pink paint he adds
80 litres of red paint and 28 litres of white paint.
Has he now made Cherry Pink paint?
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: total amount of each colour (judgement accepted that ratio is not 4 : 3) | ||
| \(60 \div (2 + 1)\) or 20 or 40 | M1 | |
| \(80 +\) their 20 or 100 | M1dep | |
| \(28 + 2 \times\) their 20 or 68 | M1dep | dep on first M1 only |
| 100 and 68 and No | A1 | |
| Alternative method 2: total of red and how much white should have been added or how much there should have been originally or how much there should be now | ||
| \(60 \div (2 + 1)\) or 20 or 40 | M1 | |
| \(80 +\) their 20 or 100 | M1dep | |
| their \(100 \div 4 \times 3\) or 75 | M1dep | dep on M2 |
| \((75 - 2 \times 20 =)\ 35\) and No or 40 and \((75 - 28 =)\ 47\) and No or 75 and 68 and No | A1 | comparing 35 to 28 |
| Alternative method 3: total of white and how much red should have been added or how much there should have been originally or how much there should be now | ||
| \(60 \div (2 + 1)\) or 20 or 40 | M1 | |
| \(28 + 2 \times\) their 20 or 68 | M1dep | |
| their \(68 \div 3 \times 4\) or \(90\dfrac{2}{3}\) or \(\dfrac{272}{3}\) | M1dep | dep on M2 |
| \(\left(90\dfrac{2}{3} - 20 =\right) 70\dfrac{2}{3}\) and No or 20 and \(\left(90\dfrac{2}{3} - 80 =\right) 10\dfrac{2}{3}\) and No or \(90\dfrac{2}{3}\) and 100 and No | A1 | comparing \(70\dfrac{2}{3}\) to 80 |
| Alternative method 4: total of red and what it should be for total amount of paint | ||
| \(60 \div (2 + 1)\) or 20 or 40 | M1 | |
| \(80 +\) their 20 or 100 | M1dep | |
| \((60 + 80 + 28) \div (4 + 3) \times 4\) or 96 | M1 | |
| 100 and 96 and No | A1 | |
| Alternative method 5: total of white and what it should be for total amount of paint | ||
| \(60 \div (2 + 1)\) or 20 or 40 | M1 | |
| \(28 + 2 \times\) their 20 or 68 | M1dep | |
| \((60 + 80 + 28) \div (4 + 3) \times 3\) or 72 | M1 | |
| 68 and 72 and No | A1 | |
Additional guidance
| 20 from \(80 \div 4\) is incorrect | |
| With no incorrect working, ‘He should have added 76 red and 32 white’ implies full marks | M1M1M1A1 |
| ‘No’ can be implied, eg on alt 1 accept 100 and 68 and ‘He needs 7 more white’ | M1M1M1A1 |
| Condone dubious notation eg 20 : 40 + 80 : 28 = 100 : 68, so No | M1M1M1A1 |
| Ignore further work if 100 and 68 and No are seen | M1M1M1A1 |
| Only works out the amounts of red and white there should be for the total amount of paint, eg, \(168 \div 7 \times 4 = 96\) and \(168 \div 7 \times 3 = 72\) | M0M0M1A0 |