IB Questionbank Mathematical Studies 3rd edition1

1.A geometric sequence has 1024 as its first term and 128 as its fourth term.

(a)Show that the common ratio is

2

1

.

(2)

(b)Find the value of the eleventh term.

(2)

(c)Find the sum of the first eight terms.

(3)

(d)Find the number of terms in the sequence for which the sum first exceeds 2047.968.

(3)

(Total 10 marks)

2.A field is 91.4 m long and 68.5 m wide.

(a)Calculate the area of the field in m2.

(b)Calculate the area of the field in cm2.

(c)Express your answer to (b) in the form a 10k where 1 a < 10 and k .

(Total 6 marks)

3.(a)Calculate

2

3

2

60

.

3

3

2

.

77

.

(1)

(b)Express your answer to part (a) in the form a 10k, where1 a < 10 and k .

(2)

(c)Juan estimates the length of a carpet to be 12 metres and the width to be 8 metres. He then estimates the area of the carpet.

(i)Write down his estimated area of the carpet.

(1)

When the carpet is accurately measured it is found to have an area of 90 square metres.

(ii)Calculate the percentage error made by Juan.

(2)

(Total 6 marks)

4.Jacques can buy six CDs and three video cassettes for $163.17

or he can buy nine CDs and two video cassettes for $200.53.

(a)Express the above information using two equations relating the price of CDs and the price of video cassettes.

(b)Find the price of one video cassette.

(c)If Jacques has $180 to spend, find the exact amount of change he will receive if he buys nine CDs.

(Total 6 marks)

5.Given that h =

4

2

2

d

l

-

,

(a)Calculate the exact value of h when l = 0.03625 and d = 0.05.

(2)

(b)Write down the answer to part (a) correct to three decimal places.

(1)

(c)Write down the answer to part (a) correct to three significant figures.

(1)

(d)Write down the answer to part (a) in the form a 10k, where 1 a < 10, k

.

(2)

(Total 6 marks)

6.The Venn diagram shows the numbers of pupils in a school according to whether they study the sciences Physics (P), Chemistry (C), Biology (B).

(a)Write down the number of pupils that study Chemistry only.

(1)

(b)Write down the number of pupils that study exactly two sciences.

(1)

(c)Write down the number of pupils that do not study Physics.

(2)

(d)Find n[(P

B)

C].

(2)

(Total 6 marks)