Download Math Studies Review on Financial Math and Logic

IB Math Studies Semester Review Samples – Fall 2015
1) Given the arithmetic sequence: u1 = 124, u2 = 117, u3 = 110, u4 = 103, …
a) Write down the common difference of the sequence.
b) Calculate the sum of the first 50 terms of the sequence.
c) uk is the first term in the sequence that is negative. Find the value of k.
77.2 × 33
2) a) Calculate 3.60 × 22
b) Express your answer to part (a) in the form 𝑎 × 10𝑘 , where 1 ≤ 𝑎 < 10 𝑎𝑛𝑑 𝑘 𝜖 𝑍.
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)
ii)
Write down his estimated area of the carpet.
When the carpet is accurately measured, it is found to have an area of 90
square metres. Calculate the percentage error made by Juan.
3) Tyler wants to invest $1000 in a savings account for a car. The current interest rate is
4.75%. Calculate the value of Tyler’s investment after 3 years if it is compounded
a) yearly
b) twice a year
c) monthly
d) daily
4) Sam invests 6000 USD in a bank that offers interest compounded annually. His
investment doubles in 15 years. Find the rate that the bank is offering.
5) The following table shows the age distribution of a sample of teachers who like diet
coke at SCHS.
Ages
20 ≤ x < 30
30 ≤ x < 40
40 ≤ x < 50
50 ≤ x < 60
60 ≤ x < 70
Number who like diet coke
5
4
3
2
3
a) Calculate an estimate of the mean age of those who like diet coke.
b) Which class is the modal class?
c) In which class is the median?
d) Draw a histogram to represent the data. Let 1 cm represent 10 years on the horizontal
axis and 1 cm represent a frequency of 1 on the vertical axis.
6) Solve 3x 2  11x  4  0 .
7) The following table gives the exchange rate from USD to EUR and from USD to JPN.
Give all answers to this question correct to two decimal places.
1 USD
1 USD
0.6337 EUR
99.7469 JPN
a) Enrico has 475 USD. How many euros is this worth?
b) Enrico goes to a bank to exchange his dollars. The bank charges a 3% commission.
How many euros does Enrico receive?
c) Find the exchange rate from EUR to JPN.
8) The following data represents test scores on the last math test.
98
75
78
87
76
92
94
86
73
83
89
91
a) Draw a box and whisker plot to represent the data.
b) Calculate the interquartile range.
9) A fair six-sided die had the numbers 1,2,3,4,5,6 written on its faces. A fair four-sided
die has the numbers 1,2,3,4 written on its faces. The two dice are rolled at the same time.
a) Make a diagram showing the possible outcomes.
b) Find the probability that the two dice show the same number.
c) Find the probability that the difference of the two numbers shown on the dice is 1.
d) Find the probability that the number shown on the 4-sided die is greater than the
number shown on the 6-sided die, given that the difference between the two numbers is 1.