CH7 IB Practice 2014

Transcription

1 CH7 IB Practice 2014 Name 1. A woman deposits $100 into her son s savings account on his first birthday. On his second birthday she deposits $125, $150 on his third birthday, and so on. How much money would she deposit into her son s account on his 17th birthday? How much in total would she have deposited after her son s 17th birthday? 2. Mr Jones decides to increase the amount of money he spends on food by d GBP every year. In the first year he spends a GBP. In the 8th year he spends twice as much as in the 4th year. In the 20th year he spends 4000 GBP. Find the value of d. 3. The first four terms of an arithmetic sequence are shown below. 1, 5, 9, 13,... Write down the n th term of the sequence. Calculate the 100 th term of the sequence. Find the sum of the first 100 terms of the sequence. 4. On Vera s 18 th birthday she was given an allowance from her parents. She was given the following choices. Choice A Choice B Choice C Choice D $100 every month of the year. A fixed amount of $1100 at the beginning of the year, to be invested at an interest rate of 12% per annum, compounded monthly. $75 the first month and an increase of $5 every month thereafter. $80 the first month and an increase of 5% every month. Assuming that Vera does not spend any of her allowance during the year, calculate, for each of the choices, how much money she would have at the end of the year. IB Questionbank Mathematical Studies 3rd edition 1

2 (8) Which of the choices do you think that Vera should choose? Give a reason for your answer. On her 19 th birthday Vera invests $1200 in a bank that pays interest at r% per annum compounded annually. Vera would like to buy a scooter costing $1452 on her 21 st birthday. What rate will the bank have to offer her to enable her to buy the scooter? (Total 14 marks) 5. The population of Bangor is growing each year. At the end of 1996, the population was At the end of 1998, the population was Assuming that these annual figures follow a geometric progression, calculate the population of Bangor at the end of 1997; the population of Bangor at the end of The tuition fees for the first three years of high school are given in the table below. Year These tuition fees form a geometric sequence. Tuition fees (in dollars) Find the common ratio, r, for this sequence. If fees continue to rise at the same rate, calculate (to the nearest dollar) the total cost of tuition fees for the first six years of high school. IB Questionbank Mathematical Studies 3rd edition 2

3 7. A basketball is dropped vertically. It reaches a height of 2 m on the first bounce. The height of each subsequent bounce is 90% of the previous bounce. What height does it reach on the 8th bounce? What is the total vertical distance travelled by the ball between the first and sixth time the ball hits the ground? 8. The following is a currency conversion table: FFR USD JPY GBP French Francs (FFR) 1 p q US Dollars (USD) Japanese Yen (JPY) British Pounds (GBP) For example, from the table 1 USD = GBP. Use the table to answer the following questions. Find the values of p and q. Mireille wants to change money at a bank in London. (i) (ii) How many French Francs (FFR) will she have to change to receive 140 British Pounds (GBP)? The bank charges a 2.4% commission on all transactions. If she makes this transaction, how many British Pounds will Mireille actually receive from the bank? IB Questionbank Mathematical Studies 3rd edition 3

4 Jean invested 5000 FFR in Paris at 8% simple interest per annum. Paul invested 800 GBP in London at 6% simple interest per annum. (i) (ii) (iii) (iv) How much interest in FFR did Jean earn after 4 years? How much interest in US Dollars did Paul earn after 4 years? Who had earned more interest after 4 years? Explain your reasoning in part (iii). (7) (Total 13 marks) 9. Jane plans to travel from Amsterdam to Chicago. She changes 1500 Euros (EUR) to US Dollars (USD) at an exchange rate of 1 EUR to 1.33 USD. Give all answers in this question correct to two decimal places. Calculate the number of USD Jane receives. (1) Jane spends 1350 USD and then decides to convert the remainder back to EUR at a rate of 1 EUR to 1.38 USD. Calculate the amount of EUR Jane receives. (3) If Jane had waited until she returned to Amsterdam she could have changed her USD at a rate of 1 EUR to 1.36 USD but the bank would have charged 0.8% commission. Calculate the amount of EUR Jane gained or lost by changing her money in Chicago. 10. John invests X USD in a bank. The bank s stated rate of interest is 6% per annum, compounded monthly. Write down, in terms of X, an expression for the value of John s investment after one year. IB Questionbank Mathematical Studies 3rd edition 4

5 What rate of interest, when compounded annually (instead of monthly) will give the same value of John s investment as in part? Give your answer correct to three significant figures. Calculate the amount of EUR Jane gained or lost by changing her money in Chicago. 11. Miranti deposits $1000 into an investment account that pays 5% interest per annum. What will be the value of the investment after 5 years if the interest is reinvested? How many years would it take Miranti s investment of $1000 to double in value? At the beginning of each year Brenda deposits $1000 into an investment account that pays 5% interest per annum. Interest is calculated annually and reinvested. How much would be in Brenda s account after 5 years? (Total 10 marks) IB Questionbank Mathematical Studies 3rd edition 5