Decimals and Sets

IGCSE Edexcel Mathematics
1.1 Decimals
1.3 Sets & Venn Diagrams
Remember:
∪ means union (all elements in either set)
∩ means intersection (elements in both sets)
n(A) means the number of elements in set A

Given:
ξ = {all decimal numbers from 0 to 10}
A = {1.5, 2.3, 3.7, 4.2, 5.8, 6.1}
B = {3.7, 4.2, 6.1, 7.4, 8.5}
C = {2.3, 4.2, 6.1, 8.9}

Questions

1. List the elements in A ∩ B [2]
A ∩ B =
2. List the elements in A ∪ B [2]
A ∪ B =
3. Find n(B ∩ C) [2]
n(B ∩ C) =
4. List the elements in A ∩ B ∩ C [2]
A ∩ B ∩ C =
5. Find n(A ∪ C) [2]
n(A ∪ C) =
6. Draw a Venn diagram to represent sets A and B. Show all elements in the correct regions. [4]
7. Which element appears in all three sets A, B, and C? [1]
8. List the elements that are in set A but not in set B. [2]
9. Put all the elements from A ∪ B ∪ C in order from smallest to largest. [2]
10. How many elements are in (B ∪ C) but not in A? [2]

Total: [21 marks]

Mark Scheme

1. A ∩ B = {3.7, 4.2, 6.1} [2]

Award 2 marks for all three correct. Award 1 mark for two correct.

2. A ∪ B = {1.5, 2.3, 3.7, 4.2, 5.8, 6.1, 7.4, 8.5} [2]

Award 2 marks for all eight correct with no repeats. Award 1 mark for 6-7 correct.

3. n(B ∩ C) = 2 [2]

B ∩ C = {4.2, 6.1}. Award 2 marks for correct answer. Award 1 mark for correct intersection shown but incorrect count.

4. A ∩ B ∩ C = {4.2, 6.1} [2]

Award 2 marks for both correct. Award 1 mark for one correct.

5. n(A ∪ C) = 7 [2]

A ∪ C = {1.5, 2.3, 3.7, 4.2, 5.8, 6.1, 8.9}. Award 2 marks for correct answer. Award 1 mark for correct union shown but incorrect count.

6. Venn diagram [4]

Award marks as follows:
• 1 mark for two overlapping circles labelled A and B
• 1 mark for {3.7, 4.2, 6.1} in the intersection
• 1 mark for {1.5, 2.3, 5.8} in A only
• 1 mark for {7.4, 8.5} in B only

7. 4.2 and 6.1 (accept either or both) [1]

Award 1 mark for either 4.2 or 6.1 (or both).

8. {1.5, 2.3, 5.8} [2]

Award 2 marks for all three correct. Award 1 mark for two correct.

9. 1.5, 2.3, 3.7, 4.2, 5.8, 6.1, 7.4, 8.5, 8.9 [2]

Award 2 marks for all nine in correct order. Award 1 mark for all nine listed but with 1-2 ordering errors.

10. 2 elements [2]

(B ∪ C) = {3.7, 4.2, 6.1, 7.4, 8.5, 8.9}. Elements not in A are {7.4, 8.9}. Award 2 marks for correct answer of 2. Award 1 mark for identifying the correct elements {7.4, 8.9} but incorrect count.

Total: [21 marks]