Material Taken From:
Mathematics
for the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese,
Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
Math Studies
IB Syllabus
Topic
Status
Hours
1
Introduction to the GDC

3
2
Number and algebra

14
3
Sets, logic and probability
most of it
20
4
Functions
half of it
24
5
Geometry and Trigonometry

20
6
Statistics

24
7
Introductory differential calculus
15
8
Financial mathematics
10
Opening Problem
Section 13A - Foreign Exchange
Vocabulary:
• Currency – money
• Exchange Rate – establishes a relationship between the
value of currencies. These are constantly changing.
• Conversion – exchanging/converting currencies.
• Commission – amount/percentage made by exchanging
agency.
Example 1
A bank exchanges 1 British pound (GBP) for
1.9 Australian dollars (AUD). Convert:
a) 40 GBP to AUD
b) 500 AUD to GBP
Example 2
The table alongside shows the transfer rates between US dollars
(USD) and Swiss francs (CHF), and British pounds (GBP).
• Write down the exchange rate from:
a) CHF to USD
b) USD to CHF
• Convert:
c) 3000 USD to GBP
d) 10 000 francs to pounds
Commission
• Banks and other currency traders earn a
commission for exchanging currency.
• commission rate between 0.5% to 3%
• a ‘flat fee’
• no commission, but worse exchange rates
You live in the U.S. this table shows the value of the USD in other currencies:
Example 3
Use the currency conversion table to perform the following:
a) Convert 4000 USD into Euros.
b) How much does it cost in US dollars to buy 5000 yen?
c) How many US dollars can you buy for 2000 Swedish
kronor?
Example 4
A bank changes US dollars to other currency at a fixed
commission of 1.5%. Max wishes to convert $200 US
to baht where $1 US buys 40.23 Thai baht.
a) What commission is charged?
b) What does the customer receive?
Example 5
A currency exchange service exchanges 1 euro for
Japanese yen with the buy rate 135.69, and sell rate
132.08. Cedric wishes to exchange 800 Euros for yen.
The service buys yen at 135.69
The service sells yen at 132.08
a) How many yen will he receive?
b) If the yen in a were exchanged immediately back to Euros,
how many Euros would they be worth?
c) What is the resultant commission on the double transaction?
Section 13B – Simple Interest
BrainPop.com
Interest
Vocabulary:
• Borrower
• Lender
• Principal/Capital – amount borrowed.
• Interest
-Simple Interest
-Compound Interest
Simple Interest
Crn
I
100
C = capital
r = simple interest rate / per year / decimal
n = number of time periods (in years)
I = interest
Example 6
Calculate the simple interest on a loan of $8000
at a rate of 7% p.a. over 18 months.
Example 7
How much money has been borrowed if the flat
rate of interest is 8% p.a. and the simple interest
owed after 4 years is $1600?
Example 8
What flat rate of interest does a bank need to
charge so that €5000 will earn €900 simple
interest in 18 months?
Example 9
How long will it take $2000 invested at a flat
rate of 12.5% p.a. to amount to $3000?
Calculating Repayment
• Repayments are often made in regular
payments over the length of the loan.
• These may be weekly, fortnightly, monthly or
another period of time.
Calculating Repayment
1. Calculate the interest
2. Calculate the total amount to be repaid
(capital + interest)
3. Calculate the total number of payments
4. Determine the amount of a regular payment
total to be repaid
regular payment =
number of repayments
Example 10
Calculate the monthly repayments on a loan of
$23 000 at 8% p.a. flat rate over 6 years.
Homework
• 13A.1, pg 422
– #1, 3, 5
• 13A.2, pg 424
– #1, 3, 5
• 13A.3, pg 425
– #1, 3
• 13B.1 ,pg 427
– #1, 3, 5, 7, 9
• 13B.2, pg 430
– #1, 3