Higher June 2024 Paper 2 Q6
6 Andy, Luke and Tina share some sweets in the ratio 1 : 6 : 14
Tina gives \(\dfrac{3}{7}\) of her sweets to Andy.
Tina then gives \(12\dfrac{1}{2}\)% of the rest of her sweets to Luke.
Tina says,
“Now all three of us have the same number of sweets.”
Is Tina correct?
You must show how you get your answer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Yes, supported by correct figures | P1 | for a process to find the number of sweets Tina gives to Andy, eg \(14 \div 7 \times 3\ (= 6)\) or for a process to work with fractions of the total to find fraction given to Andy, eg \(\dfrac{14}{21} \times \dfrac{3}{7}\ \left(= \dfrac{2}{7}\right)\) or for dividing a given number (eg 441) in the ratio 1 : 6 : 14 (= 21 : 126 : 294) |
| P1 | for a process to find number for Andy and Tina after first exchange, eg A = \(1 + \text{``}6\text{''}\ (= 7)\) and T = \(14 - \text{``}6\text{''}\ (= 8)\) or for a process to find the number of sweets Tina gives to Luke eg \((14 - \text{``}6\text{''}) \times \dfrac{12.5}{100}\ (= 1)\) or for a process to work with fractions of the total to find fraction given to Luke, eg for \(\dfrac{(14 - \text{``}6\text{''})}{21} \times \dfrac{12.5}{100}\) or process to work out the number of sweets given to Andy and Luke for their total, eg \(\text{``}294\text{''} \div 7 \times 3\ (= 126)\) and \((\text{``}294\text{''} - \text{``}126\text{''}) \times \dfrac{12.5}{100}\ (= 21)\) | |
| P1 | for a process to find the final amounts or final shares for at least two of Andy, Luke and Tina eg two of \(1 + \text{``}6\text{''}\ (= 7)\), \(6 + \text{``}1\text{''}\ (= 7)\), \(14 - \text{``}6\text{''} - \text{``}1\text{''}\ (= 7)\) or \(\dfrac{1}{21} + \dfrac{\text{``}2\text{''}}{7}\ \left(= \dfrac{7}{21}\right)\), \(\dfrac{6}{21} + \text{``}\dfrac{1}{21}\text{''}\ \left(= \dfrac{7}{21}\right)\), \(\dfrac{14}{21} - \text{``}\dfrac{2}{7}\text{''} - \text{``}\dfrac{1}{21}\text{''}\ \left(= \dfrac{7}{21}\right)\) or \(\text{``}21\text{''} + \text{``}126\text{''}\ (= 147)\), \(\text{``}126\text{''} + \text{``}21\text{''}\ (= 147)\), \(\text{``}294\text{''} - \text{``}126\text{''} - \text{``}21\text{''}\ (= 147)\) | |
| C1 | Yes, supported by full working and accurate figures for Andy, Luke and Tina |
Additional guidance
May work with an equivalent ratio, eg 21 : 126 : 294 and do \(294 \div 7 \times 3\ (= 126)\) as a first step
May work in multiples of \(x\) for all marks
Accurate figures with no supportive working scores 0