Foundation June 2017 Paper 2 Q19
19 Ben and Katy throw darts at a target.
Ben’s ratio of hits to misses is 5 : 1
Katy’s ratio of hits to misses is 3 : 1
Ben says,
“5 is bigger than 3, so I must have more hits than Katy.”
Give an example to show that this might not be true. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 (hits and misses) | ||
| A counter example using both ratios or using numbers of hits and misses for both players | B2 | eg Katy could be 6 : 2 and Ben hit 5 eg Ben 10 hits and 2 misses and Katy 12 hits and 4 misses B1 for a correct number of hits and misses (not 3 and 1) or a correct equivalent ratio for Katy |
| Alternative method 2 (hits and total throws or proportion of hits) | ||
| A counter example using total throws and number of hits for both players or using proportion of hits for both players | B2 | eg Katy could have hit 6 out of 8, Ben hit 5 eg Katy could have \(\dfrac{18}{24}\) and Ben \(\dfrac{10}{12}\) B1 for a correct number of total throws and hits (not 3 out of 4) or a correct proportion of hits (not \(\dfrac{3}{4}\)) for Katy |
Additional guidance
| Must use the given ratios | |
| (Ben) 5 : 1 (Katy) 6 : 2 | B2 |
| 15 : 3 and 15 : 5 (so the same hits) | B2 |
| (Katy) 6 : 2 or (Katy) 6 hits and 2 misses | B1 |
| List of equivalent ratios for (Ben and) Katy with no counter example chosen | B1 |
| 15 : 3 and 9 : 3 | B1 |
| Fractions of hits out of total throws oe percentages or decimals or words eg \(\dfrac{5}{6}\) and \(\dfrac{3}{4}\) eg \(\dfrac{20}{24}\) and \(\dfrac{18}{24}\) eg \(\dfrac{5}{6}\) and \(\dfrac{6}{8}\) | B0 B1 B2 |
| Ben had (two) more throws – he had 6 and she had 4 | B0 |