MAT170 – FINAL EXAM – REVIEW
MAT 170 Final Review Answers
There is a reasonable assumption that most of these answers are correct. If you find any incorrect answers, please contact your instructor as soon as possible.
PART I – ALGEBRA
A. Difference quotient - Section 1.3
1. [pic] 2. [pic] 3. [pic]
B. Function composition - Section 1.7
4. [pic] 5. [pic]
C. Inverse functions - Section 1.8
6. [pic] 7. [pic] 8. [pic]
9. [pic]
D. Zeros of polynomials - Section 2.3-2.5
10. zeros are 2, 0, –1 11. zeros are 1, 3i, –3i
E. Domains of function s- Sections 1.2-1.3
12. [pic] 13. [pic] 14. [pic]
15. [pic]
F. Exponential equations – Section 3.4
16. [pic] 17. [pic] 18. [pic]
G. Logarithmic equations – Section 3.4
19. [pic] 20. [pic] 21. [pic]
H. Application of rational functions – Section 2.6
22. The insect population approaches the size of 50 million.
23. In the long run the average cost approaches 20 dollars.
I. Application of quadratic functions – Section 2.2
24. Maximum time is [pic] seconds. Maximum height is [pic]feet.
25. The minimum percentage increase in tuition was approximately 3.47% when x = 6.57.
J. Application of exponential functions – Section 3.4
26. a) 8.71 years b) 8.67 years c) 8.65 years 27. 17.3%
K. Transformations – Section 1.6
28. [pic]
PART II – TRIGONOMETRY
L. Domain, ranges, and graph of trig functions – Sections 4.5-4.6
29. domain [pic]; range [ –1, 1]
30. domain [pic]; range [pic]
31. domain [pic]; range [pic]
32. Amplitude = 3, Period =[pic], Phase shift is left by [pic]
M. Pythagorean identity, summation, difference, double angle, half-angle formula problems – Sections 5.1-5.3
33. [pic] 34. [pic] 35. [pic] 36. [pic] 37. [pic]
38. [pic] 39. [pic] 40. [pic] 41. [pic] 42. [pic]
43. [pic] 44. [pic]
N. Inverse trigonometric functions – Section 4.7
45. [pic] 46. [pic]
O. Trig identities – Section 5.1
47. – 49. see instructor
P. Trig equations – Section 5.5
50. [pic] 51. [pic]
Q. Arc length – Section 4.1
52. 318 miles
R. Law of Sines and Law of Cosines – Sections 6.1 and 6.2
53. two possible answers: B1 ≈ 33.68°, C1 ≈ 131.32°, c1 ≈ 20.31 or B2 ≈ 146.32°, C2 ≈ 18.68°, c2 ≈ 8.66
54. 2969.05 meters
55. approximately 153.968 miles
56. 102.7°
S. Vectors and Dot Product – Sections 6.6-6.7
57. a. 16i – 11j b. –5i + j
58. a. 9 b. [pic] c. [pic] d. [pic]
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