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1. The Venn diagram shows the number sets , , and . Place each of the following numbers in the appropriate region of the Venn diagram. , –3, π, cos 120°, 2.7 × 10

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IB Questionbank Mathematical Studies 3rd edition 1

1. The Venn diagram shows the number sets , , and . Place each of the following numbers in the appropriate region of the Venn diagram.

4

1 , –3, π, cos 120°, 2.7 × 10

3

, 3.4 × 10

–2

(Total 6 marks)

2. (a) Write down the following numbers in increasing order.

3.5, 1.6 ×10

−19

, 60730, 6.073×10

5

, 0.006073×10

6

, , 9.8×10

−18

. (b) Write down the median of the numbers in part (a).

(c) State which of the numbers in part (a) is irrational.

(Total 6 marks)

(2)

IB Questionbank Mathematical Studies 3rd edition 2

3. The Venn diagram below shows the universal set of real numbers and some of its important subsets:

: the rational numbers, : the integers,

: the natural numbers.

Write the following numbers in the correct position in the diagram.

–1, 1, , , 3 . 333 3 , 16

7  3 .

(Total 6 marks)

4. Given the set of integers, the set of rational numbers, the set of real numbers.

(a) Write down an element that belongs to  . (b) Write down an element that belongs to  .

(c) Write down an element that belongs to .

(d) Use a Venn diagram to represent the sets , and .

(Total 6 marks)

(3)

IB Questionbank Mathematical Studies 3rd edition 3

5. (a) Given x = 2.6 × 10

4

and y = 5.0 × 10

–8

, calculate the value of w = x × y. Give your answer in the form a × 10

k

where 1 ≤ a < 10 and k  .

(b) Which two of the following statements about the nature of x, y and w above are incorrect?

(i) x  (ii) y  (iii) y  (iv) w < y (v) x + y 

(vi) w 1 < x

(Total 8 marks)

6. Let U = {–4, 3

– 2 , 1, , 13, 26.7, 69, 10

33

}.

A is the set of all the integers in U.

B is the set of all the rational numbers in U.

(a) List all the prime numbers contained in U.

(b) List all the members of A.

(c) List all the members of B.

(d) List all the members of the set A  B.

(Total 8 marks)

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