Foundation November 2021 Paper 3 Q9
9 \(\mathscr{E}\) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
Set A = {odd numbers}
Set B = {multiples of 5}
(a) The elements 1 and 2 have been entered on this Venn diagram.
Complete the Venn diagram to show all of the elements.
Complete the Venn diagram to show all of the elements.
[3]
(b) \(\mathscr{E}\) = {all positive integers}
Set L = {odd numbers}
Set M = {multiples of 2}
Three Venn diagrams, numbered 1 to 3, are shown below.
Which diagram best shows the relationship between Set L and Set M?
Give a reason for your choice. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| A only: [1] 3 7 9 11 13 A and B: 5 15 B only: 10 Outside: [2] 4 6 8 12 14 16 | 3 | B2 for one element misplaced or repeated or missing or B1 for one correct region | Condone 1 and/or 2 repeated |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [Venn diagram] 2 and [because] odd numbers cannot be multiples of 2 oe and no contradictions | 2 | B1 for choice of diagram 2 | Must justify using properties of elements. Accept “Odd numbers cannot be even” and “All multiples of 2 are even” |
Appendix
Exemplar responses for Q9b
| Response | Mark | |
|---|---|---|
| 2 because odds and multiples of 2 are different | 2 | |
| 2 L and M have nothing in common | Both marks earned | 2 |
| 2 There won’t be any numbers to fit both | 1 mark for 2 and BOD the reason implying nothing in common | 2 |
| 2 No numbers in each set share the same values therefore they are split and separate in set 2 | 1 mark for 2 and BOD the “values” for “properties”. Set 2 means “Diagram 2” | 2 |
| 2 None of the numbers are in the same group | 1 mark for 2 | 1 |
| 2 because odds are different | 1 mark for “2” reason insufficient as doesn’t say different to what | 1 |
| 2 both of them are equal as it has no middle | 1 mark for “2” reason incorrect | 1 |
| 1 anything | 0 |