PRECALCULUS SPRING EXAM REVIEW
Work these on NOTEBOOK PAPER, NOT on this packet. You may use your calculator.
1. Evaluate the following: given that .
a. – 106 b. 110 c. 83 d. – 118
2. Solve: .
a. b.
c. d.
3. All of the following are possible rational roots of except:
- – b. c. d.
4. Solve and check algebraically the following equation:
a. – 5 b. – 16 c. – 5 and – 16 d. 5 and 16
5. What is the value of ?
- b. 4 c. – 4 d.
6. Solve:
a. b. c. d.
7. Solve:
- b. c. d.
8. Solve:
a. b.
c. d.
9. Solve: for x.
a.x = 5 b. c. d.
10. Find the center and radius of the circle with equation:
a. (3, 4); 6 b. (3, 4); 11 c. (3, 4); 6 d. (3, 4); 11
11.Use logarithms to solve the following:
a. – 1.677 b. 1 c. 1.677 d. –1.404
12. Find the foci of the ellipse:.
a. (5,0), (5, 0) b. (0,4),(0, 4) c. (3,0), (3, 0) d. (0,3), (0,3)
13. Find the 12th term of the arithmetic sequence with
a. 144.5b. 20.5 c. 20.5d. 28
14. Find the sum of the first nine terms of the arithmetic series: 3 + 8 + 13 +…
a. 43 b. 207 c. no sum d. 1,464,843
15. has at most how many negative real roots?
a. 0 b. 1 c. 2 d. 3
16. Solve the equation: , given that one root is – 5.
a. – 5, 5, 3 b.c. d.
17. Solve: .
a. b.
c. d.
18. In , a = 15, b = 24, c = 18. Find .
a. 38.625b. 41.491c. 48.509d. 92.866
19. In a parallelogram, two adjacent sides meet at an angle of 50°. The sides are 20 and 28 feet
long. Determine the length of the longer diagonal.
a. 18.056. b. 21.542 c. 39.293 d. 43.634
20. Find the eighth term of the geometric sequence with .
a. 25 b. 60 c.8748d. 26,244
21. Find the equation of the circle withand as endpoints of the diameter.
a. b.
c. d.
22. In Find the length of side a.
a. 11.956b. 12.273 c. 24.355 d. 38.307
23. If is a root of , what is another root?
a. b. c. d.
24. Find the equation of the parabola with focus and directrix .
a. b.
c. d.
25. Find the equation of the parabola with vertex (-2, 5) and focus (2, 5).
a. b. c. d.
26. Tomball had a population of 7000 in 1980. The town grows by the function
where k = 0.034. Find the population of Tomball in the year 2000.
a. 144,841 b. 13,817 c. 7,238 d. 4760
27. Find the area of given
a. 397.173 b. 746.974 c. 794.346 d. 1493.947
28. Express point in polar coordinates.
a. b. c. d.
29. The rectangular form of is:
a. b. c. d.
30. Find the sum of the first nine terms of the geometric series: 300 – 150 + 75 - …
a. b. c. d.
31. In Find the length of side a.
a. 23.017 b. 26.891 c. 35.628d. 36.960
32. Rewrite as a single logarithm:
a. b. c. d.
33. Express point P in rectangular coordinates:
- b. c. d.
34. What is the polar form of
a. b. c. d.
35. Identify the conic.
a. circle b. parabola c. ellipse d. hyperbola
36. Evaluate:
a. 121 b. 2500 c. d. –60.5
37. Solve for x :
a. log 4.5 – log 5 b. log 5 – log 4.5 c. log d.
38. Graph the hyperbola:
39. Graph the ellipse:
40. Name the asymptotes and intercepts.
(a) (b) (c)
41. Use DeMoivre’s Theorem to simplify . Leave your answer in rectangular form.
42. Find the three cube roots of .
43. Find the sum of the series: if possible.
44. Given how many positive real roots could have?
How many negative real roots could have?
45. Matching:
i) (A) rose with odd number of petals
ii) (B) rose with even number of petals
iii) (C) limacon
iv) , b even(D) cardioid
v) , b odd(E) circle
46. Convert to rectangular form.
(a) r = 2(b) (c)
47. Find the horizontal and vertical components of a vector with a magnitude of 18 and an
angle of 43° with the x-axis.
48. Given the vectors , find:
(a) (b) (c) the angle between
49. Given the vectors , find:
(a) (b) (c) the angle between
50. Solve:
51. Solve:
52. Solve:
53. Solve:
54. Solve:
55. The population P of bears in a national park after t years is modeled by the function
.
(a) How many bears were there after six years?
(b) After how many years will there be 50 bears in the park?
______
On problems 56 and 57, write a function, graph it on your calculator, and use the calculator to
find the answers.
56. Find two positive numbers such that the sum of the first and four times the second is 48, and
the product is a maximum. What is the product?
57. A cylindrical metal container, open at the top, is to have a capacity of . The cost of
material used for the bottom of the container is $0.12 per sq. in., and the cost of the material
used for the curved part is $0.06 per sq. in. Find the dimensions that will minimize the cost
of the material, and find the minimum cost. (Volume of a cylinder = and
Surface Area of an open cylinder = )
______
58. Use the given graph to answer the questions below.
(a) f is increasing on ______
(b) f is decreasing on ______
(c)Relative max. at ______
(d) Relative min. at ______
(e)f is concave up on ______
(f)f is concave down on ______
(g)Inflection point(s) at ______
FORMULA CHART
You will have a sheet like this to use on the exam.
CIRCLE/ ELLIPSE
PARABOLA
/ HYPERBOLA
SEQUENCES AND SERIES
Arithmetic: Arithmetic:
Geometric: Geometric:
Geometric:
DeMoivre’s Theorem
/ Complex Roots Theorem
VECTORS
Dot product:
Angle between two vectors: