math studies ib syllabus
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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. Opening Problem. Section 13A - Foreign Exchange . - PowerPoint PPT PresentationTRANSCRIPT
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Material Taken From:
Mathematicsfor the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
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Math StudiesIB 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
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Opening Problem
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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.
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A bank exchanges 1 British pound (GBP) for 1.9 Australian dollars (AUD). Convert:
a) 40 GBP to AUDb) 500 AUD to GBP
Example 1
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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 USDb) USD to CHF• Convert:c) 3000 USD to GBPd) 10 000 francs to pounds
Example 2
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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
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You live in the U.S. - this table shows the value of the USD in other currencies:
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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 3
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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 4
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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.
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?
The service buys yen at 135.69The service sells yen at 132.08
Example 5
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BrainPop.comInterest
Section 13B – Simple Interest
Vocabulary:• Borrower• Lender• Principal/Capital – amount borrowed.• Interest
-Simple Interest-Compound Interest
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Simple Interest
C = capitalr = simple interest rate / per year / decimal n = number of time periods (in years)I = interest
100CrnI
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Calculate the simple interest on a loan of $8000 at a rate of 7% p.a. over 18 months.
Example 6
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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 7
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What flat rate of interest does a bank need to charge so that €5000 will earn €900 simple interest in 18 months?
Example 8
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How long will it take $2000 invested at a flat rate of 12.5% p.a. to amount to $3000?
Example 9
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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.
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1. Calculate the interest2. Calculate the total amount to be repaid
(capital + interest)3. Calculate the total number of payments4. Determine the amount of a regular payment
total to be repaidregular payment =number of repayments
Calculating Repayment
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Calculate the monthly repayments on a loan of $23 000 at 8% p.a. flat rate over 6 years.
Example 10
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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