IB MATH STUDIES SL 1: IB-Style Review Questions for Test
Two-Variable Statistics and Financial Mathematics (1.5, 1.9, 4.2 – 4.4)
1.
The following table of observed results gives the number of candidates taking a Mathematics
examination classified by gender and grade obtained.
Grade
Gender
5, 6 or 7
3 or 4
1 or 2
Total
Males
5000
3400
600
9000
Females
6000
4000
1000
11000
Total
11000
7400
1600
20000
The question posed is whether gender and grade obtained are independent.
(a)
Show clearly that the expected number of males achieving a grade of 5, 6 or 7 is 4950.
(2)
(b)
A  2 test is set up.
(i)
State the Null hypothesis.
(1)
(ii)
State the number of degrees of freedom.
(1)
(iii)
Calculate the value of  2 .
(1)
The critical value of  2 at the 5% level of significance is 5.991.
(iv) What can you say about gender and grade obtained?
(1)
(Total 6 marks)
2.
Ten students were given two tests, one on Mathematics and one on English.
The table shows the results of the tests for each of the ten students.
Student
A
Mathematics (x)
8.6
English (y)
33
(a)
B
C
13.4 12.8
51
30
D
E
F
G
H
I
J
9.3
1.3
9.4
13.1
4.9
13.5
9.6
48
12
23
46
18
36
50
Calculate, correct to two decimal places, the correlation coefficient r.
(6)
(b)
Use your result from part (a) to comment on the statement:
‘Those who do well in Mathematics also do well in English.’
(2)
(Total 8 marks)
3.
Sven is travelling to Europe. He withdraws $800 from his savings and converts it to euros. The
local bank is buying euros at $1: €0.785 and selling euros at $1: €0.766.
(a)
Use the appropriate rate above to calculate the amount of euros Sven will receive.
(b)
Suppose the trip is cancelled. How much will he receive if the euros in part (a) are
changed back to dollars?
(c)
How much has Sven lost after the two transactions? Express your answer as a percentage
of Sven’s original $800.
(Total 6 marks)
4.
Bob invests 600 EUR in a bank that offers a rate of 2.75% compounded annually. The interest is
added on at the end of each year.
(a)
Calculate how much money Bob has in the bank after 4 years.
(b)
Calculate the number of years it will take for the investment to double.
Ann invests 600 EUR in another bank that offers interest compounded annually. Her investment
doubles in 20 years.
(c)
Find the rate that the bank is offering.
(Total 6 marks)
5.
Give all answers in this question to the nearest whole currency unit.
In January 2008 Larry had 90 000 USD to invest for his retirement in January 2011.
He invested 40 000 USD in US government bonds which paid 4 % per annum simple interest.
(a)
Calculate the value of Larry’s investment in government bonds in January 2011.
(3)
Larry changed this investment into South African rand (ZAR) at an exchange rate of
1 USD = 18.624 ZAR.
(b)
Calculate the amount that Larry received in ZAR from the exchange.
(2)
He changed the remaining 50 000 USD to South African rand (ZAR) in January 2008.
The exchange rate between USD and ZAR was 1 USD = 10.608 ZAR. There was 2.5 %
commission charged on the exchange.
(c)
Calculate the value, in USD, of the commission Larry paid.
(2)
(d)
Show that the amount that Larry had to invest is 517 000 ZAR, correct to the nearest
thousand ZAR.
(3)
In January 2008, Larry deposited this money into a bank account that paid interest at a nominal
annual rate of 12 %, compounded monthly.
(e)
Find the value of the money in Larry’s bank account in January 2011.
(3)
(Total 13 marks)
6.
Members of a certain club are required to register for one of three games, billiards, snooker or darts.
The number of club members of each gender choosing each game in a particular year is shown in the
table below.
(a)
Billiards
Snooker
Darts
Male
39
16
8
Female
21
14
17
Use a  2 (Chi-squared) test at the 5% significance level to test whether choice of games
is independent of gender. State clearly the null and alternative hypotheses tested, the
expected values, and the number of degrees of freedom used.
(13)
The following year the choice of games was widened and the figures for that year are as follows:
(b)
Billiards
Snooker
Darts
Fencing
Male
4
15
8
10
Female
10
21
17
37
If the  2 test were applied to this new set of data,
(i)
why would it be necessary to combine billiards with another game?
(ii)
which other game would you combine with billiards and why?
(2)
(Total 15 marks)
7.
Ten students were asked for their average grade at the end of their last year of high school and their
average grade at the end of their last year at university. The results were put into a table as follows:
(a)
Student
High School grade, x
University grade, y
1
2
3
4
5
6
7
8
9
10
90
75
80
70
95
85
90
70
95
85
3.2
2.6
3.0
1.6
3.8
3.1
3.8
2.8
3.0
3.5
Total
835
30.4
Find the correlation coefficient r, giving your answer to two decimal places.
(2)
(b)
Describe the correlation between the high school grades and the university grades.
(2)
(c)
Find the equation of the regression line for y on x in the form y = ax + b.
(2)
(Total 6 marks)
8.
The scatter diagram below shows the relationship between the number of vehicles per thousand of
population and the number of people killed in road accidents over an eight year period in Calmville.
Number of people killed
in road accidents
Relationship between number of vehicles and people
killed in road accidents in Calmville
900
800
700
600
500
400
300
200
100
0
0
50
100
150
200
250
300
350
Number of vehicles per 1000 of population
Let x be the number of vehicles per thousand and y be the number of people killed.
(a)
(i)
Calculate the correlation coefficient r.
(ii)
Explain clearly the statistical relationship between the variables x and y
(4)
(b)
Write the equation of the regression line of y on x, expressing it in the form y = mx + c
(where m and c are given correct to 3 significant figures).
(2)
(c)
Use your equation in part (b) to answer the following questions.
(i)
There were 250 vehicles per 1000 of population. Find the number of people killed.
(ii)
Explain why it is not a good idea to use the regression line to estimate the number
of people killed when the number of vehicles is 150 per thousand.
(3)
(Total 9 marks)
9.
The following table gives the exchange rate from US dollars to euros and from US dollars to
Japanese yen. Give all answers in this question correct to two decimal places.
(a)
1 USD
0.6337 EUROS
1 USD
99.7469 YEN
Enrico has 475 USD.
(i)
How many euros is this worth?
Enrico goes to a bank to exchange his dollars. The bank charges 3 % commission.
(ii)
How many euros does Enrico receive?
(4)
(b)
Find the exchange rate from euros to yen.
(2)
(Total 6 marks)
10.
Astrid invests 1200 euros for five years at a nominal annual interest rate of 7.2 %, compounded
monthly.
(a)
Find the interest Astrid has earned during the five years of her investment.
Give your answer correct to two decimal places.
(Total 3 marks)
11.
The value of a car decreases each year. This value can be calculated using the function
v = 32 000rt, t  0, 0  r  1,
where v is the value of the car in USD, t is the number of years after it was first bought and r is
a constant.
(a)
(b)
(i)
Write down the value of the car when it was first bought.
(ii)
One year later the value of the car was 27 200 USD. Find the value of r.
Find how many years it will take for the value of the car to be less than 8000 USD.
(Total 6 marks)
12.
Eight students in Mr. O’Neil’s Physical Education class did pushups and situps. Their results
are shown in the following table.
Student
Number of pushups (x)
Number of situps (y)
1
24
32
2
18
28
3
32
38
4
51
40
5
35
30
6
42
52
7
45
48
8
25
52
The graph below shows the results for the first seven students.
y
60
50
number
of 40
situps
(y) 30
20
10
O
10
20
30
40
50
number of pushups (x)
60
x
(a)
Plot the results for the eighth student on the graph.
(b)
If x = 34 and y = 40 , draw a line of best fit on the graph.
(c)
A student can do 60 pushups. How many situps can the student be expected to do?
(Total 8 marks)