| 1 |
(CIE $0606 / 2018 / \mathrm{m} / 22 / \mathrm{q} \mathrm{l})$  (a) Using set notation, write down the set represented by the shaded region.[1] (b) $\varepsilon={1,2,3,4,5,6,7,8,9,10} $ A={x:x is a prime number} B={x:x is an even number} C={1,2,3,4,8} (i) Complete the Venn diagram to show the elements of each set.  |
| 2 | (CIE $0606 / 2018 / \mathrm{s} / 21 / \mathrm{q} \mathrm{l})$ A,B and C are subsets of the same universal set. (i) Write each of the following statements in words. (a) $A \not\subset B$[1] (b) $A \cap C \neq \phi$[1] (ii) Write each of the following statements in set notation (a) There are three elements in set A or B or both.[1] (b) x is an element of A but it is not an element of C.[1] |
| 3 | (CIE $0606 / 2018 / \mathrm{s} / 22 / \mathrm{q} \mathrm{2})$ (a) On the Venn diagram below, shade the region that represent $A \cup B'$  $(P \cup Q \cup R)'=\phi$ ; $P' \cap (Q \cap R)=\phi $ $n(Q \cap R)=8$ ; $n(P \ cap R)=8$ ; $n(P\cap Q)=10$ $n(P)=21$ ; $n(Q)=15$ ; $n(\varepsilon)=30$ Complete the Venn diagram to show this information and state the value of $n(R)$  |
| 4 | (CIE $0606 / 2018 / \mathrm{w} / 21 / \mathrm{q} 1 \mathrm{l})$  There are 70 girls in a year group at a school. The Vemn diagram gives some information about the numbers of these girls who play rounders $(R)$, hockey $(H)$ and netball $(N)$ $$\mathrm{n}(R)=28 \quad \mathrm{n}(H)=38 \quad \mathrm{n}(N)=35$$ Find the value of $x$ and hence the number of girls who play netball only. |
| 5 |
(CIE $0606 / 2018 / \mathrm{w} / 22 / \mathrm{q}2$ ) There are 105 boys in a year group at a school. Some boys play football $(F)$ and some play cricket ( $C)$. $x$ boys play both football and cricket. The number of boys that play neither game is The same as The number of boys that play both. 40 boys play cricket. The number of boys that only play football is twice The number of boys that only play cricket. Complete the Venn diagram and find the value of $x$. [5] |
| 6 |
(CIE 0606/2018/w/23/q2) On each of the Venn diagrams below, shade the region indicated. |
| 7 |
(CIE 0606/2019/m/12/q1) (a)Given that $\varepsilon = {x:1<x<20}$, $A=${multiples of 3} $B=${multiples of 4}, Find (i) n(A), (ii) $n(A \cap B)$ (b) On the Venn diagram below, draw the sets P,Q, and R such that $P \subset Q$ and $Q \cap R = \phi$   |
| 8 |
(CIE 0606/2019/s/11/q1) (a)On the Venn diagrams below, shade the region indicated.  $$P \subset R, Q \subset R \text { and } P \cap Q=\emptyset$$ [2]  |
| 9 |
(CIE 0606/2019/s/12/q1) (a) On the Venn diagrams below, shade the region that indicated  $P=$ {$x:cos2x=0.5$} $Q=$ {$x:sinx=0.5$} Find $P \cap Q$ |
| 10 |
(CIE 0606/2019/s/13/q1) Describe, using set notation, the relationship between the sets shown in each of the Venn diagrams below.  |
| 11 |
(CIE 0606/2019/w/11/q1) Using set notation, describe the regions shaded on the Venn diagrams below.  |
| 12 | (CIE 0606/2019/w/13/q1) In a group of 145 students, the numbers studying mathematics, physics and chemistry are given below. All students study at least one of the three subjects. $x$ students study all 3 subjects 24 students study both mathematics and chemistry 23 students study both physics and chemistry 28 students study both mathematies and physics 50 students study chemistry 75 students study physics 80 students study mathematics(i)Using the Venn diagram, find the value of $x$.  |
| 13 | (CIE 0606/2019/w/22/q1) On each of the Venn diagrams below, shade the region indicated.  |
Short Answer
- $(P\cup Q)\cap R'$
- (i)(a) A is not a [proper] subset of B (i)(b) A and C are mutually exclusive or A intersection C is the empty set (ii)(a) $n( A\cup C) = 3 $ (ii)(b) $x\in (A\cap C')$
-
- { $x=8$}
- { $x=15$}
-
- (a)(i) 6 (ii) 1 (b) Show (c) $S' \cap T' $ or $(S \cup T)' $ , $(X \cap Y) \cup(X \cap Z)$
- (a)
(b) $P \cap Q=\left\{30^{\circ}, 150^{\circ}\right\}$ - $\quad A \cap B=\phi, Z \subset(X \cap y)$
- $\quad \operatorname{A}^{\prime} \cap B,\left(x\cap y\right) \cup(x \cap Z)$
- (i) $x=15$ (ii) 43
0 Comments