INSTRUCTOR SAMPLE E. Check that your exam contains 25 questions numbered sequentially. Answer Questions 1-25 on your scantron.

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1 MATH 41 FINAL EXAM NAME SECTION NUMBER INSTRUCTOR SAMPLE E On your scantron, write and bubble your PSU ID, Section Number, and Test Version. Failure to correctly code these items may result in a loss of 5 points on the exam. On your scantron, bubble letters corresponding to your answers on indicated questions. It is a good idea for future review to circle your answers in the test booklet. Check that your exam contains 5 questions numbered sequentially. Answer Questions 1-5 on your scantron. Each multiple choice question is worth 6 points. THE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELECTRONIC DEVICE IS NOT PERMITTED IN THIS EXAMINATION. THE USE OF NOTES OF ANY KIND IS NOT PERMITTED DURING THIS EXAMINATION.

2 MATH 41 FINAL EXAM, SAMPLE E PAGE 1. Solve the equation x x 4 = 0 for x. a) x = 1 +, b) x = 1 +, c) x = 1 + i 1, 1 i d) x = 1 + i 1, 1 i Which of the following is the solution set of the inequality x ? a), 0] b) [ ], 0 c) [, 0] d), ] [0, )

3 MATH 41 FINAL EXAM, SAMPLE E PAGE. Solve the following inequality for x: x + 4x + 4x < 0. a), 0) b), ), 0) c), 0) d), ) x 1 4. Find the domain of fx) = x. a) [1, ) b), 1] c) [1, ), ) d), 1], )

4 MATH 41 FINAL EXAM, SAMPLE E PAGE 4 5. Which of the following functions is odd? a) fx) = x 4 + x b) fx) = 7 c) fx) = x d) fx) = x What is the inverse function of fx) = x 4 x 9? a) f 1 x) = x + x 9 b) f 1 x) = 9x 4 x c) f 1 x) = x 9 x 4 d) f 1 x) = x 9x 4

5 MATH 41 FINAL EXAM, SAMPLE E PAGE 5 7. Rewrite the quadratic function fx) = x 18x in standard form ax h) + k. a) fx) = x ) 1 b) fx) = x ) 0 c) fx) = x 6) 0 d) fx) = x 6) 1 8. Find the remaining zeros of fx) = x x 5x + 6 given that c = 1 is a zero. a), b), c), d),

6 MATH 41 FINAL EXAM, SAMPLE E PAGE 6 9. Which of the following describes the graph of fx) = x + x 1? x 9 a) The graph has two x-intercepts and two vertical asymptotes. b) The graph has one x-intercept, two vertical asymptotes, and one removable discontinuity. c) The graph has one x-intercept, one vertical asymptote, and one removable discontinuity. d) The graph has two x-intercepts, one vertical asymptote, and one removable discontinuity. 10. Solve for x: 11 4x = 8. a) x = b) x = c) x = 1 d) x =

7 MATH 41 FINAL EXAM, SAMPLE E PAGE Find the domain of log 7 6 x ). a) [ 6, 6] b), 6) 6, ) c) 6, 6) d) 6, 6) 1. Solve for x: log x + log x 8) =. a) x = 1, x = 9 b) x = 1 c) x = 9, x = 1 d) x = 9

8 MATH 41 FINAL EXAM, SAMPLE E PAGE 8 1. Convert the angle π 9 radians to degrees. a) 40 b) 5 c) 50 d) A gear with a radius of 8 centimeters is turning at π radians per second. What is 9 the linear velocity at a point on the outer edge of the gear? a) π 7 cm/sec b) 8π 9 cm/sec c) 9π 8 cm/sec d) 7π cm/sec

9 MATH 41 FINAL EXAM, SAMPLE E PAGE Find the length of the missing side of the right triangle. 4 a) 10 b) 14 c) d)

10 MATH 41 FINAL EXAM, SAMPLE E PAGE A telephone pole is 40 feet tall. How long should a cable be if it is to be attached to the top of the pole and the ground, and is to make an angle of 0 with the ground? a) 80 feet b) 40 feet c) 0 feet d) 40 feet

11 MATH 41 FINAL EXAM, SAMPLE E PAGE Evaluate csc 11π ). a) 1 b) c) d) 18. Which of the following is true of the graph of fx) = sin x? a) The range is, ) b) The graph obtains a relative maximum at x = π + n π, where n is any integer. c) The x-intercepts are of the form n π, where n is any integer. d) The graph obtains a relative minimum at x = π integer. + n π, where n is any

12 MATH 41 FINAL EXAM, SAMPLE E PAGE Determine which of the following equations corresponds to the graph below: 1 Π 5 Π Π Π Π Π Π 6 Π Π Π 5 Π 6 Π a) y = sin x + π ) 6 b) y = sin x π ) c) y = sin x + π ) d) y = sin x π ) 6

13 MATH 41 FINAL EXAM, SAMPLE E PAGE 1 0. Which of the following functions determines the graph pictured below? Π Π 4 Π Π 4 Π 4 Π Π 4 Π a) y = tan x π ) 4 b) y = tan x + π) c) y = tan x + π ) 4 d) y = cot x + π ) 4

14 MATH 41 FINAL EXAM, SAMPLE E PAGE Evaluate tan sin 1 1 )). a) 1 b) c) 1 d) 1. Which of the following is equal to the trigonometric expression a) sin θ b) cot θ c) csc θ d) tan θ 1 csc θ 1 1 csc θ + 1?

15 MATH 41 FINAL EXAM, SAMPLE E PAGE 15. Which of the following is equal to cos175 ) cos55 ) + sin175 ) sin55 )? a) b) c) 1 d) 4. Simplify cosx + y) cosx y). a) sin x sin y b) sin x sin y c) cos x cos y d) cos x

16 MATH 41 FINAL EXAM, SAMPLE E PAGE Find all solutions on the interval [0, π) to the equation sin θ = sin θ. a) θ = π 6, 5π 6 b) θ = 0, π, π 6, 5π 6 c) θ = π, π d) θ = π, π, π, π

17 MATH 41 FINAL EXAM, SAMPLE E PAGE 17 sin θ + cos θ = tan θ = sec θ 1 + cot θ = csc θ sinα + β) = sin α cos β + cos α sin β sinα β) = sin α cos β cos α sin β cosα + β) = cos α cos β sin α sin β cosα β) = cos α cos β + sin α sin β tan α + tan β tanα + β) = 1 tan α tan β tan α tan β tanα β) = 1 + tan α tan β sinα) = sin α cos α cosα) = cos α sin α = 1 sin α = cos α 1 sin α = ± 1 cos α cos α = ± 1 + cos α tan α = 1 cos α sin α = sin α 1 + cos α sin α cos β = 1 [sinα + β) + sinα β)] cos α sin β = 1 [sinα + β) sinα β)] cos α cos β = 1 [cosα β) + cosα + β)] sin α sin β = 1 [cosα β) cosα + β)] sin α + sin β = sin α + β sin α sin β = sin α β cos α + cos β = cos α + β cos α cos β = sin α + β cos α β cos α + β cos α β sin α β

18 MATH 41 FINAL EXAM, SAMPLE E PAGE 18 FINAL EXAM- SAMPLE E 1. A. B. B 4. A 5. C 6. B 7. B 8. B 9. C 10. B 11. C 1. D 1. A 14. B 15. B 16. A 17. D 18. D 19. C 0. A 1. C. D. C 4. A 5. B

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