Higher June 2024 Paper 5 Q2
2 Kai has these four number cards.
| 0 | 2 | 5 | 9 |
Kai takes two of the cards at random without replacement and finds the positive difference between the two numbers.
(a) Complete the table to show all of the possible differences. [2]
| First card | |||||
|---|---|---|---|---|---|
| Difference | 0 | 2 | 5 | 9 | |
| Second card | 0 | 2 | 5 | 9 | |
| 2 | 2 | 3 | |||
| 5 | 5 | ||||
| 9 | 9 | ||||
(b) Find the probability that Kai takes two cards with a difference that is an even number or a factor of 10. [2]
| Answer | Marks | Part marks and guidance | ||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | B1 for 3 or 4 correct entries | For 2 marks, ignore entries in shaded squares if they are 0’s For B1 ignore shaded squares | |||||||||||||||||||||||||||||||||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{6}{12}\) oe nfww | 2 | If shaded squares are blank or all have zeros FT their 12 entries for 2 marks | isw conversion/cancelling after their correct probability Do not accept ratio or words If table correct and shaded squares have zeros allow answer \(\frac{10}{16}\) oe for 2 marks |
| M1 for all their even numbers and all factors of 10 identified only | M1 may be seen on table by e.g. ringing values or listing | ||
| IF Shaded SQUARES are counted: FT their 16 entries B2FT their table Or M1 for all their even numbers and all factors of 10 identified only | We only accept the 16 squares in the Grid, not the card values Count zero as an even number If table correct apart from all zeros in shaded squares allow all even numbers and factors of 10 [0’s in shaded squares] identified | ||
| If 0 scored SC1 for answer \(\frac{6}{16}\) | For SC1 allow answer \(\frac{3}{8}\) if \(\frac{6}{16}\) seen first | ||