Math C30 Final Exam
Math C30 Practice Final Exam 2010-2011
1. Convert 245(14’56” to (2 marks)
a) a decimal (3 decimal places)
b) radians (do not leave pi in your answer) (3 decimal places)
3. Convert [pic] to (2 marks)
a) degrees (round to 5 decimal places)
b) degrees, minutes and seconds
4. Find the value of each of the following trigonometric ratios. Round to 5 decimal places if necessary (1 mark each)
a) [pic] b) [pic]
c) [pic] d) [pic][pic]
5. Give the exact value (do NOT give a decimal answer!!!!) of each of the following trig ratios. Be aware of sign notation. (2 marks each)
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
f) [pic]
6. Which point, on the unit circle, would the terminal arm of a 855( angle in standard position pass through? (3 mark)
7. Sketch one period of the following functions starting at the horizontal shift. If there is no shift, start at zero. Be sure to label all axis and include any relevant information.
[pic] (7 marks)
8. Superimpose the graph of the function reciprocal to the one shown overtop of the graph State the equation of the function you are sketching. (4 marks each).
[pic]
9. Solve of the following trigonometric equation. Be sure to find ALL SOLUTIONS and write your solutions as a solution set for the range [pic].
[pic] (4 marks)
10. For each triangle find the indicated side length or angle using whichever law necessary. Give all side lengths to one decimal place and all angles to the nearest degree.
a) In ΔUFC, u = 17, f = 11, c = 18. Solve for angle F. (4 marks)
b) In (ABC A = 57(, a = 17 mm and B = 64(. Solve for side c. (4 marks)
11. For the following triangle state:
(a) how many solutions there are, and
(b) solve for them.
If there are no solutions the question is worth 1 mark, if there is one solution the question is worth 3 marks and if there are 2 solutions it is worth 6 marks. (Be careful!)
[pic]
12. A forest ranger in a tower 128.0 m high sights two fires in the same line of sight with angles of depression of 42˚ and 61˚. How far apart are the fires? (5 marks)
13. If[pic], [pic] and [pic], [pic]. Find the exact value of [pic] (5 marks)
14. Complete any 5 of the following 8 proofs. Label all your steps in proper 2 column format (3 marks each = 15 marks for this section).
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
f) [pic]
g) [pic]
h) [pic]
14. For each of the following equations state whether it is a hyperbola, parabola, ellipse, circle, straight line or inverse relationship. (5 marks)
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
16. Determine the equation in both standard form [pic] and general form [pic] of the ellipse with foci at (-2, 2) and (6, 2) and one vertex at (2, -3). (7 marks)
17. Prove that the product of a multiple of 4 and a multiple of 7 will always be divisible by 14. (4 marks)
18. Prove, by mathematical induction, that [pic] for all natural numbers. (5 marks)
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