Minbin has 1250 Japanese Yen which she wishes to exchange for Chinese Yuan.

Transcription

1 IBMS Unit 1 Review Sheet Name: This is a good review of the type of questions and material that will be on the TEST on Thursday, September 12 th. Topics include: number classification, rounding rules, sigfigs, scientific notation, metric system, arithmetic and geometric sequences, currency conversions, compound interest. Questions on this review may not review all topics tested for additional practice, see textbook. Paper 1 type questions 1. The table below shows some exchange rates for the Japanese Yen (JPY). Currency 1 JPY Canadian Dollar Chinese Yuan Euro Norwegian Kroner Minbin has 1250 Japanese Yen which she wishes to exchange for Chinese Yuan. Calculate how many Yuan she will receive. Give your answer to the nearest Yuan. Rupert has 855 Canadian Dollars which he wishes to exchange for Japanese Yen. Calculate how many Yen he will receive. Give your answer to the nearest Yen. Find how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places (Total 6 marks) 1

2 2. A Swiss bank shows currency conversion rates in a table. Part of the table is shown below, which gives the exchange rate between British pounds (GBP), US dollars (USD) and Swiss francs (CHF). Buy Sell GBP USD This means that the bank will sell its British pounds to a client at an exchange rate of 1 GBP = CHF. What will be the selling price for 1 USD? Andrew is going to travel from Europe to the USA. He plans to exchange 1000 CHF into dollars. The bank sells him the dollars and charges 2% commission. How many dollars will he receive? Give your answer to the nearest dollar (Total 8 marks) 3. The exchange rate from US dollars (USD) to French francs (FFR) is given by 1 USD = 7.5 FFR. Give the answers to the following correct to two decimal places. Convert 115 US dollars to French francs. Roger receives 600 Australian dollars (AUD) for 2430 FFR. Calculate the value of the US dollar in Australian dollars (Total 8 marks) 2

3 4. A rectangular field is 91.4 m long and 68.5 m wide. Calculate the area of the field in m 2. Calculate the area of the field in cm 2. Write your answer to part into three significant figures. (d) Express your answer to in the form a 10 k where 1 a < 10 and k. (e) Use your answer to part in the following: If you estimated that the area was about 7000 m 2, what would the percentage error be of your estimation? (d) (e) 5. 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. (Total 6 marks) Answer:... (Total 4 marks) 3

4 6. The first term of an arithmetic sequence is 16 and the eleventh term is 39. Calculate the value of the common difference. 16 The third term of a geometric sequence is 12 and the fifth term is. 3 All the terms in the sequence are positive. Calculate the value of the common ratio. 7. The speed of sound in air is given as 300 ms l (Total 8 marks) How many metres does sound travel in air in one hour? Express your answer to part (i) correct to two significant figures; (ii) in the form a 10 k, where 1 a < 10 and k.... (i)... (ii)... (Total 4 marks) 4

5 Paper 2 type questions 8. The first three terms of an arithmetic sequence are 2k + 3, 5k 2 and 10k 15. Show that k = 4. (3) (d) (e) Find the values of the first three terms of the sequence. Write down the value of the common difference. Calculate the 20 th term of the sequence. Find the sum of the first 15 terms of the sequence. (1) (1) (Total 9 marks) 9. A National Lottery is offering prizes in a new competition. The winner may choose one of the following. Option one: Option two: Option three: $1000 each week for 10 weeks. $250 in the first week, $450 in the second week, $650 in the third week, increasing by $200 each week for a total of 10 weeks. $10 in the first week, $20 in the second week, $40 in the third week continuing to double for a total of 10 weeks. Calculate the amount you receive in the tenth week, if you select (i) (ii) option two; option three. (6) What is the total amount you receive if you select option two? Which option has the greatest total value? Justify your answer by showing all appropriate calculations. (4) (Total 12 marks) 5

6 10. 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? (4) (Total 6 marks) 11. The table below shows the deposits, in Australian dollars (AUD), made by Vicki in an investment account on the first day of each month for the first four months in The interest rate is 0.75% per month compounded monthly. The interest is added to the account at the end of each month. Month Deposit (AUD) January 600 February 1300 March 230 April 710 Show that the amount of money in Vicki s account at the end of February is AUD. (3) Calculate the amount of Australian dollars in Vicki s account at the end of April. Vicki makes no withdrawals or deposits after 1st April How much money is in Vicki s account at the end of December 1999? From 1st January 2000 the bank applies a new interest rate of 3.5% per annum compounded annually. (d) In how many full years after December 1999 will Vicki s investment first exceed 3300 AUD? (Total 9 marks) 6