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IB Mathematical Studies SL Fall Final Exam 2016 1. Emma places €8000 in a bank account that pays a nominal interest rate of 5% per annum, compounded quarterly. (a) Calculate the amount of money that Emma would have in her account after 15 years. Give your answer correct to the nearest Euro. (3) (b) After a period of time she decides to withdraw the money from this bank. There is €9058.17 in her account. Find the number of months that Emma had left her money in the account. (3) 2. At what interest rate, compounded annually, would you need to invest $100 in order to have $125 in 2 years? (4) 3. 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. (a) 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. (b) 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. (c) Calculate the amount of EUR Jane gained or lost by changing her money in Chicago. (2) 4. The table below shows some exchange rates for the Japanese Yen (JPY).
Minbin has 1250 Japanese Yen which she wishes to exchange for Chinese Yuan. (a) Calculate how many Yuan she will receive. Give your answer to the nearest Yuan. (2) Rupert has 855 Canadian Dollars which he wishes to exchange for Japanese Yen. (b) Calculate how many Yen he will receive. Give your answer to the nearest Yen. (2) (c) Find how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places. (2) 5. The table below shows the cost of travelling by train in Amsterdam between different areas (zones) of the city.
Janneke is travelling first class from one part of the city to another. She is travelling through 10 zones. (a) Write down the cost of her ticket. Joost has a student card that entitles him to a reduction of 40% on all fares. (b) Calculate how much Joost pays for a second class ticket for 23 zones. The student card costs 15 euros. (c) Calculate how many journeys of 23 zones in second class that Joost must make to cover the cost of his student card. 6. Mal is shopping for a school trip. He buys 50 tins of beans and 20 packets of cereal. The total cost is 260 Australian dollars (AUD). (a) Write down an equation showing this information, taking b to be the cost of one tin of beans and c to be the cost of one packet of cereal in AUD. (1) Stephen thinks that Mal has not bought enough so he buys 12 more tins of beans and 6 more packets of cereal. He pays 66 AUD. (b) Write down another equation to represent this information. (1) (c) Find the cost of one tin of beans. (2) (d) (i) Sketch the graphs of these two equations. (ii) Write down the coordinates of the point of intersection of the two graphs. (4) 7. (a) Write down the following numbers in increasing order. 3.5, 1.6 ×10^{−19}, 60730, 6.073×10^{5}, 0.006073×10^{6}, p, 9.8×10^{−18}. (b) Write down the median of the numbers in part (a). (c) State which of the numbers in part (a) is irrational. (Total 6 marks) 8. Consider the numbers p, –5, and the sets , , and . Complete the following table by placing a tick in the appropriate box if the number is an element of the set.
(Total 6 marks) 9. (a) Consider the numbers 2, and the sets , , ,_{ }and . Complete the table below by placing a tick in the appropriate box if the number is an element of the set, and a cross if it is not.
(3) (b) A function f is given by f : x ® 2x^{2} – 3x, x Î {–2, 2, 3}. (i) Draw a mapping diagram to illustrate this function. (ii) Write down the range of function f. (3) 10. (a) Calculate . (1) (b) Express your answer to part (a) in the form a ´ 10^{k}, where 1 £ a < 10 and kÎ . (2) (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) Write down his estimated area of the carpet. (1) When the carpet is accurately measured it is found to have an area of 90 square metres. (ii) Calculate the percentage error made by Juan. (2) 11. Let x = 7.94. (a) Calculate the value of . (b) (i) Give your answer correct to three decimal places. (ii) Write your answer to (b)(i) as a percentage. (c) Give your answer to part (b)(i) in the form a × 10^{k}, where 1£ a <10, k . 12. (a) Calculate exactly (1) (b) Write the answer to part (a) correct to 2 significant figures. (1) (c) Calculate the percentage error when the answer to part (a) is written correct to 2 significant figures. (2) (d) Write your answer to part (c) in the form a ´ 10^{k} where 1 £ a < 10 and k Î . (2) 13. Give all answers in this question correct to the nearest dollar Clara wants to buy some land. She can choose between two different payment options. Both options require her to pay for the land in 20 monthly installments. Option 1: The first installment is $2500. Each installment is $200 more than the one before. Option 2: The first installment is $2000. Each installment is 8% more than the one before. (a) If Clara chooses option 1, (i) write down the values of the second and third installments; (ii) calculate the value of the final installment; (iii) show that the total amount that Clara would pay for the land is $88 000. (7) (b) If Clara chooses option 2, (i) find the value of the second installment; (ii) show that the value of the fifth installment is $2721. (4) (c) The price of the land is $80 000. In option 1 her total repayments are $88 000 over the 20 months. Find the annual rate of simple interest which gives this total. (4) (d) Clara knows that the total amount she would pay for the land is not the same for both options. She wants to spend the least amount of money. Find how much she will save by choosing the cheaper option. (4) 14. The first three terms of an arithmetic sequence are 2k + 3, 5k − 2 and 10k −15. (a) Show that k = 4. (3) (b) Find the values of the first three terms of the sequence. (1) (c) Write down the value of the common difference. (1) (d) Calculate the 20^{th} term of the sequence. (2) (e) Find the sum of the first 15 terms of the sequence. (2) 15. The first term of an arithmetic sequence is 0 and the common difference is 12. (a) Find the value of the 96^{th} term of the sequence. (2) The first term of a geometric sequence is 6. The 6^{th} term of the geometric sequence is equal to the 17^{th} term of the arithmetic sequence given above. (b) Write down an equation using this information. (2) (c) Calculate the common ratio of the geometric sequence. (2) 16. The fifth term of an arithmetic sequence is 20 and the twelfth term is 41. (a) (i) Find the common difference. (2) (ii) Find the first term of the sequence. (1) (b) Calculate the eightyfourth term. (1) (c) Calculate the sum of the first 200 terms. (2) 17. Consider the geometric sequence 8, a, 2,… for which the common ratio is . (a) Find the value of a. (b) Find the value of the eighth term. (c) Find the sum of the first twelve terms. 18. A geometric progression G_{1} has 1 as its first term and 3 as its common ratio. (a) The sum of the first n terms of G_{1} is 29 524. Find n. (3) A second geometric progression G_{2} has the form 1, , , … (b) State the common ratio for G_{2}. (1) (c) Calculate the sum of the first 10 terms of G_{2}. (2) (d) Explain why the sum of the first 1000 terms of G_{2} will give the same answer as the sum of the first 10 terms, when corrected to three significant figures. (1) (e) Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10 terms of the sequence 2, 3 , 9 , 27 … Give your answer correct to one decimal place. 
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