Foundation June 2023 Paper 2 Q12
12 Kai says that \(\;\) 3 : 2 \(\;\) is an equivalent ratio to \(\;\) 9 : 6
Jo says that \(\;\) 1.5 : 1 \(\;\) is an equivalent ratio to \(\;\) 9 : 6
Who is correct?
Tick one box.
- Both of them
- Kai only
- Jo only
- Neither of them
Give reasons for your answer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Ticks Both of them and gives valid reason for Kai eg references both values being divided (or multiplied) by 3 and gives valid reason for Jo eg references both values being divided (or multiplied) by 6 | B2 | oe valid reason eg1 \(9 \div 3 \times 2 = 6\) and \(9 \div 1.5 \times 1 = 6\) or eg2 \(9 \div 6 = 1.5\) and \(3 \div 2 = 1.5\) and \(1.5 \div 1 = 1.5\) B1 ticks Kai only and gives valid reason for Kai or ticks Jo only and gives valid reason for Jo or ticks Both of them and gives valid reason for Jo or Kai |
Additional guidance
| Ticks Both of them and gives correct reason for Kai or Jo and refs both values being divided (or multiplied) by 2 (to link Jo and Kai) | B2 |
| Accept a build-up method to imply multiplying by 3 or by 6 eg all three of 3 : 2 and 6 : 4 and 9 : 6 or all six of 1.5 : 1 and 3 : 2 and 4.5 : 3 and 6 : 4 and 7.5 : 5 and 9 : 6 | |
| Condone eg 3 : 2 \(\times\) 3 = 9 : 6 to imply both values are multiplied by 3 | |
| If evaluating \(6 \div 9 = 0.66\) and \(2 \div 3 = 0.66\) and \(1 \div 1.5 = 0.66\), accept 0.66(…) or 0.67 | |
| 3 is a factor of 9 and 2 is a factor of 6 (with no reference to \(\times\) 3) | B0 |
| 9 : 6 = 3 : 2 or \(\dfrac{9}{6} = \dfrac{3}{2}\) (not evaluated to 1.5 or shown \(\div\) 3) | B0 |
| 9 : 6 simplifies to 3 : 2 and 1.5 : 1 (with no reference to \(\div\) 3 or \(\div\) 6) | B0 |
| 3 : 2 and 1.5 : 1 are both equivalent to 9 : 6 (with no reference to \(\times\) 3 or \(\times\) 6) | B0 |