E1-20110331 mathematics

1.Given that ε=｛1,2,3,4,5,6,7,8,9,10｝,list the elements of the

following sets.

﹙a﹚A=﹛x: 5x﹥37﹜﹙b﹚B=﹛x: x+5﹤12﹜

﹙c﹚C=﹛x: 6﹤2x﹤17﹜﹙d﹚D=﹛x: x2﹤37﹜

2.ε=｛2,3,4,5,6,7,8,9,10｝, A=﹛x: x is an even number﹜and B=﹛x: 7

﹤3x﹤25﹜

﹙a﹚list the elements of A, B, A∩B, A∪B and A∪B’.

﹙b﹚Find n(A∩B) and n(A’∩B’)

3.A and B two sets and the number of elements

in each set is shown in the Venn diagram .

Given that n(A)=n(B), calculate

﹙a﹚the value of x,

﹙b﹚n(A∪B) and n(A∩B’).

3x 3 2x+7

4.Given that A=﹛x: 2﹤x≤5, x∈R﹜and B=﹛x: 1≤x﹤3, x∈R﹜,express in

similar set notation each of the following sets: A∩B, A∪B and A’∩B’and A’∪B.

5.Of the 24 students in a class ,18 like to play basketball and 12 like

to play volleyball .It is given that

ε=｛students in the class｝,

B=﹛students who like to play basketball﹜and

V=﹛students who like to play volleyball﹜.

Let n(B∩V)=x and draw a Venn diagram to illustrate this information.

﹙a﹚Describe the set B∪V and express n(B∪V) in terms of x,

﹙b﹚Find the smallest possible value of x.

﹙c﹚Find the largest possible value of x.

Solve the simultaneous equations in questions 6-8

6.x+2y=5, 2x+y=2xy

7.4x2-9(y+1)2=36, 2x+3y=-5

8.3x-2y=1, (x-2)2+(2y+3)2=26

9.Find the coordinates of the points of intersection of the line x+2y=10

and the curve 2y2-7y+x=0

10.If (2,1) is a solution of the simultaneous equations

x2+xy+ay=b,

2ax+3y=b,

find the value of a and of b .Find also the other solution.

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