K&U = / 68. Appl = / 34. Comm = a 2 = b 2 + c 2 2ab cosa. MAP4C Final Exam Name:

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1 MAP4C Final Exam Name: K&U = / 68 Appl = / 34 Comm = Instructions: - you have 2.5 hours to complete this exam - conversion charts page will be provided - a full page help sheet is allowed - be sure to read questions very carefully - answer questions in the spaces provided - be sure to show your work where appropriate - be sure to save your Fathom files to your space and copy them to the Handin s folder - make answers clear and legible hard to read answers will be marked as incorrect a 2 = b 2 + c 2 2ab cosa sina sinb = a b = sinc c

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3 I. True/False: [K&U 20 marks] 1. T or F cos 25 = sin T or F For any angle θ, sin θ 1 3. T or F The cos -1 key on a scientific calculator can be used to find an angle in a right triangle if the hypotenuse and adjacent side are known 4. T or F The sine & cosine laws are generally used to find sides or angles in a non-right angled triangle 5. T or F sin 43 = sin T or F tan 43 = tan T or F 520 mm = 52 m 8. T or F 0.6 m 2 = 60 cm 2 9. T or F 2 lb = 8 oz 10. T or F 100 mph is approximately 60 km/h 11. T or F 145 lb is approximately 66 kg 12. T or F The dependent variable is the cause in a cause & effect relationship. 13. T or F A survey that you conduct yourself would be a primary source of data. 14. T or F A strong regression is indicated if r = T or F An outlier will always result in a misleading line of best fit. 16. T or F To use interpolation, a graph must be extended in order to make a prediction. 17. T or F 18. T or F 19. T or F 20. T or F The line of best fit is also called the least squared line. II. Matching: Write the corresponding letter in the blank provided [K/U 13 marks] 1. tangent ratio A. 72 F 2. cosine law B. 0.9 mm 3. reasonable room temperature C. opposite adjacent 4. temperature for a hot summer day D. r 2 = 1 5. x = 0 E. 6. F. c 2 = a 2 + b 2 2ab cos C 7. histogram G. 42 C 8. H. y intercept 9. I. 10. J. use of small sample size 11. strong negative linear relationship K. constant first differences 12. misleading graphs L. 52 F 13. bias data M. 32 C N. r = O. P. x intercept Q. R. distorted scales S. use of class intervals T. sina = sinb a b

4 III. Fill-in-the-Blanks: {use correct # of decimal places} [K/U 19 marks] 1. sin 54 = (4 decimal places) ; tan -1 (0.54) = (1 decimal place) 2. In a right triangle with sides of length 5, 12 and 13 one of the acute angles is L = gal (2 decimal places) ; 15 yd 3 = m 3 (2 decimal places) C = F (2 decimal places) ; 35 F = C (2 decimal places) In the formula P = 2(l + w) ; solve for l = The scatter plot seen on the right is of the world record 5000m times for women over the last 40 years. For this data, identify the following: i) Circle the line of best fit equation ii) coefficient of determination: iii) correlation coefficient : iv) type of correlation: v) describe the trend in non mathematical terms: Women 16.4 TimeMin Scatter Plot Year TimeMin = Year ; r^2 = 0.83 IV Full solutions. For each of the following questions show your work. You will be graded on communication as well. Knowledge 1. [6 marks] a) 2. Solve the following triangle (i.e. find all the missing sides and angles show work) [5 marks]

5 A 5cm B b 8cm C

6 3. [5marks] Application 4. Moore s Law was a prediction by Gordon Moore in 1965 that stated that the number of transistors that would fit on a computer chip would double every 2 years. The actual number of transistors on a chip is modeled by the formula t T = 135.,where T is the number of transistors on a 2 chip and t is the number of years since a) Graph the relation. Be sure to fill the graph and label the axes. (4 marks) b) How many transistors were on a chip in 1965? (1 mark) c) How long did it take for the number of transistors to actually double? (1 mark) d) How many transistors could we expect to see on a chip in 2010?

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8 5. Find the volume of the structure below in cubic metres. [4marks] 3.5 ft 8 ft 12 ft 10 ft V. Applications: [24 marks] {these questions will also be assessed for Comm} You are to do any 4 of the next 5 questions [each question is worth 6 marks] [FULL MARKS will only be given for well-organized and well-presented solutions] 1. A pilot is experiencing mechanical difficulties and must land at the A irpl an e nearest airport, either Flyville or F ly vill e Driveton. Which airport is closer, and by how much? k m D ri vet on

9 2. a) A cold remedy is packaged as packets of a powder that is to be mixed with 8 ounces of water. How many millilitres of water are required for one of these packets? b) The dosage of this remedy may be repeated after 3 to 4 h, but a person is not to exceed three doses in a 24-hour period. If each dose contains 50 mg of vitamin C, how much vitamin C will a person receive per day if taking the maximum recommended dosage of the cold medication? In Fathom, open the file Broadway.ftm. This is data on the Attendance and Receipts (in $) (among other data) of 22 Broadway shows. a) Make a scatterplot using the Attendance and Receipts attributes. (k2marks) b) Which is the cause and which is the effect? (k2marks) Cause Effect c) Which is the independent variable? (k1mark) d) What is the equation of the line of best fit? (k1mark) e) How much would you expect to bring in for an attendance of people? Explain your answer (A3marks) f) Why would using this data to predict the receipts if people attended not be realistic? (A2marks)

10 5. Open the file Rates.ftm. This is the US/Canadian exchange rate over a 10 year period. a) Describe the relationship between the variables. b) What would you expect the rate to be in 2000? Explain how you got your answer c) Predict the rate in the year How reliable would this answer be?

11 MAP4C Final Exam Name: K&U = /79 Appl = / 35 Comm = Instructions: - you have 2.5 hours to complete this exam - conversion charts page will be provided - a full page help sheet is allowed - be sure to read questions very carefully - answer questions in the spaces provided - be sure to show your work where appropriate - be sure to save your Fathom files to your space and copy them to the Handin s folder - make answers clear and legible hard to read answers will be marked as incorrect a 2 = b 2 + c 2 2ab cosa sina sinb = a b = sinc c

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13 I. True/False: [K&U 20 marks] 1. T or F cos 25 = sin T or F For any angle θ, sin θ 1 3. T or F The cos -1 key on a scientific calculator can be used to find an angle in a right triangle if the hypotenuse and adjacent side are known 4. T or F The sine & cosine laws are generally used to find sides or angles in a non-right angled triangle 5. T or F sin 43 = sin T or F tan 43 = tan T or F 520 mm = 52 m 8. T or F 0.6 m 2 = 60 cm 2 9. T or F 2 lb = 8 oz 10. T or F 100 mph is approximately 60 km/h 11. T or F 145 lb is approximately 66 kg 12. T or F The dependent variable is the cause in a cause & effect relationship. 13. T or F A survey that you conduct yourself would be a primary source of data. 14. T or F A strong regression is indicated if r = T or F An outlier will always result in a misleading line of best fit. 16. T or F To use interpolation, a graph must be extended in order to make a prediction. 17. T or F The graph of y = b x will always go through the point (0, 1) when b> T or F 10 = T or F The interest rate is the cost of borrowing money. 20. T or F The line of best fit is also called the least squared line. II. Matching: Write the corresponding letter in the blank provided [K/U 12 marks] 1. tangent ratio A. 72 F 2. cosine law B. 0.9 mm 3. reasonable room temperature C. opposite adjacent 4. temperature for a hot summer day D. r 2 = 1 5. x = 0 E. ( x m ) n 6. exponential equation F. c 2 = a 2 + b 2 2ab cos C 7. histogram G. A R i n [( 1+ ) 1] = i 8. multiply exponents H. y intercept 9. compound interest I. use of small sample size 10. strong negative linear relationship J. constant first differences 11. misleading graphs K. 52 F 12. bias data L. 32 C M. r = N A = P(1+ i) n O. x intercept P. y = a b x Q. x m x n R. use of class intervals S. sin A = sin B a b T. distorted scales

14 III. Fill-in-the-Blanks: {use correct # of decimal places} [K/U 15 marks] 1. sin 54 = (4 decimal places) ; tan -1 (0.54) = (1 decimal place) 2. In a right triangle with sides of length 5, 12 and 13 one of the acute angles is L = gal (2 decimal places) ; 15 yd 3 = m 3 (2 decimal places) C = F (2 decimal places) ; 35 F = C (2 decimal places) % annual interest compounded monthly for 5 years. i =, n = 6. In the formula P = 2(l + w) ; solve for l = 7. The initial value for equation V=0.5(2 t ) is 8. The scatter plot seen on the right is of the world record 5000m times for women over the last 40 years. For this data, identify the following: i) Circle the line of best fit equation ii) coefficient of determination: iii) correlation coefficient : iv) type of correlation: v) describe the trend in non mathematical terms: Women 16.4 TimeMin Scatter Plot Year TimeMin = Year ; r^2 = 0.83 IV Full solutions. For each of the following questions show your work. You will be graded on communication as well. Knowledge 1. Solve for x: [3 marks each] a) numerically. b) algebraically. 1.2 x = x = Solve the following triangle (i.e. find all the missing sides and angles show work) [5 marks] A 5cm B b 8cm C

15 3. Determine the weekly payment for a 20 year mortgage of $150,000 at an interest rate of 6.5%. (5marks) N I% PV PMT FV P/Y C/Y PMT = Total Paid Cost of Borrowing? 4. a) Simplify. (3 marks each) i) ( 5a 4 b 8 ) 2 ( 5a 2 b 6 ) ii) 8a 4 b 4ab 3 2 b) Write each in root notation, then evaluate. (2 marks each) 5 4 i) 81 ii) Application 5. Moore s Law was a prediction by Gordon Moore in 1965 that stated that the number of transistors that would fit on a computer chip would double every 2 years. The actual number of transistors on a chip is modeled by the formula t T = 135.,where T is the number of transistors on a 2 chip and t is the number of years since a) Graph the relation. Be sure to fill the graph and label the axes. (4 marks) b) How many transistors were on a chip in 1965? (1 mark) c) How long did it take for the number of transistors to actually double? (1 mark) d) How many transistors could we expect to see on a chip in 2010? (1 mark)

16 6. Find the volume of the structure below in cubic metres. [6 marks] 3.5 ft 8 ft 12 ft 10 ft 7. A pilot is experiencing mechanical difficulties and must land at the nearest airport, either Flyville or Driveton. Which airport is closer, and by how much? (6 marks) A irpl an e 83.2 F ly vill e k m D ri vet on

17 8. a) A cold remedy is packaged as packets of a powder that is to be mixed with 8 ounces of water. How many millilitres of water are required for one of these packets? (3 marks) b) The dosage of this remedy may be repeated after 3 to 4 h, but a person is not to exceed three doses in a 24-hour period. If each dose contains 50 mg of vitamin C, how much vitamin C will a person receive per day if taking the maximum recommended dosage of the cold medication? (3 marks) 9. Deanna is saving to purchase a used car. She needs $4500 in three years. She finds an investment that allows her to make regular deposits every six months and offers an interest rate of 5% compounded semi-annually. a) What must her regular deposits be to reach her goal of $4500? (3 marks) b) How much interest will she earn? (2 marks) 10. In Fathom, open the file Broadway.ftm. This is data on the Attendance and Receipts (in $) (among other data) of 22 Broadway shows. a) Make a scatterplot using the Attendance and Receipts attributes. (k2marks) b) Which is the cause and which is the effect? (k2marks) Cause Effect c) Which is the independent variable? (k1mark) d) What is the equation of the line of best fit? (k1mark) e) How much would you expect to bring in for an attendance of people? Explain your answer (A3marks) f) Why would using this data to predict the receipts if people attended not be realistic? (A2marks)