Cambridge Additional Mathematics

Sets and Venn diagrams (Chapter 1) 31

6 36 students participated in the mid-year adventure trip.

19 students went paragliding, 21 went abseiling, and 16

went white water rafting. 7 went abseiling and rafting,

8 went paragliding and rafting, and 11 went paragliding

and abseiling. 5 students did all three activities.

Find the number of students who:

a went paragliding or abseiling

b only went white water rafting

c did not participate in any of the activities mentioned

d did exactly two of the activities mentioned.

7 There are 32 students in the woodwind section of the

school orchestra. 11 students can play the flute, 15 can

play the clarinet, and 12 can play the saxophone. 2

can play the flute and the saxophone, 2 can play the

flute and the clarinet, and 6 can play the clarinet and

the saxophone. 1 student can play all three instruments.

Find the number of students who can play:

a none of the instruments mentioned

b only the saxophone

c the saxophone and the clarinet, but not the flute

d only one of the clarinet, saxophone, or flute.

8 In a particular region, most farms have livestock and crops. A survey of 21 farms showed that 15 grow

crops, 9 have cattle, and 11 have sheep. 4 have sheep and cattle, 7 have cattle and crops, and 8 have

sheep and crops. 3 have cattle, sheep, and crops. Find the number of farms with:

a only crops b only animals c exactly one type of animal, and crops.

Review set 1A

1 Suppose S=fx 2 Z:2<x 67 g.

a List the elements ofS. b Find n(S).

c How many proper subsets doesShave?

2 Determine whether AμB for the following sets:

a A=f 2 , 4 , 6 , 8 g and B=fx 2 Z:0<x< 10 g

b A=? and B=fx 2 (2,3)g

c A=fx 2 Q :2<x 64 g and B=fx 2 R :0 6 x< 4 g

d A=fx 2 (¡1,3)g and B=fx 2 (¡1,4]g

3 Find the complement ofXgiven that:

a U=fthe 7 colours of the rainbowg and X=fred, indigo, violetg

b U=fx 2 Z:¡ 56 x 65 g and X=f¡ 4 ,¡ 1 , 3 , 4 g

c U=fx 2 Qg and X=fx 2 Q :x<¡ 8 g

d U=fx 2 Rg and X=fx 2 [¡ 3 ,1)[(4, 1 )g

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\031CamAdd_01.cdr Tuesday, 8 April 2014 10:22:55 AM BRIAN