Accelerated Precalculus Practice Final Exam
Calculator allowed.
1. Expand: log 3
a2b
c
2log a  log b
log c
(a)
3
(c)
1
2log a  log b  log c 
3
(b)
1  2log a  log b 

3 
log c

(d)
3
2log a  log b  log c
(e) none
2. Approximate loga 24 , given that loga 2  0.4307 and log a 3  0.6826 .
(a) 0.8820
(b) 1.9747
(c) 0.2940
(d) 1.1133
(e) none
(c) –2.7381
(d) 15.2755 (e) none
3. Solve for x: 32 x  5x 1
(a) –0.5563
(b) –1
4. What is the simplest form of
1
1
 x  3  x  1
3
x
4 3

x x2
2
(a)
(c)
x
3
x 1
x
(b)
x 3
x 7
(d)
x
x 1
5. Identify the vertical asymptote(s) in the function, f  x  
(a) x  2, x  0
(b) x  2, x  2
(c) x  2, x  0
(d) x  0
(e) none
x2  4
.
x 3  2x 2
(e) none
Accelerated Precalculus Practice Final Exam
6. Solve:
2x  5 4 x  1
3x  8


x
x 2
x  x  2
(a) 1
(b) 
2 1
(c)  ,
3 2
(d)
7. Given:
2
9
1  433
12
(e) none
 1 2
  x  9, x  0
f x   3
, find f  3 .
  x  3 2 , x  0

(a) 10
(b) 8
(c) 36
(d) 6
(e) none
8. Simplify: ln 3 e2 x
(a)
2e 1
 ln x
3 3
(b)
2
x
 ln
3
3
(c)
2 1
 ln x
3 3
(d)
2e
x
 ln
3
3
9. Find the slant asymptote: f  x  
(e) none
x 2  2x  1
x 1
(a) y = 1
(b) y = x – 1
(c) y = x + 1
(d) y = x + 3
(e) none
For questions 10 – 12, identify the equations as a:
(a) line
10.
(b) line segment
x  2t , t  0
y  3t  4
(c) point
11.
(d) ray
x  cos
y  5cos  2
(e) none
12.  

6
Accelerated Precalculus Practice Final Exam
For questions 13 – 15, identify the equations as a:
(a) cardioid
(b) limacon
(c) lemniscate
(d) rose
15. r  4cos3
14. r  3  3cos
13. r 2  9cos2
(e) none
For questions 16 and 17, identify the equations as a(n):
(a) parabola
(b) ellipse
(c) hyperbola
(d) none
16. 16x 2  24 xy  9 y 2  30x  40 y  0
17. x 2  6xy  5 y 2  4 x  22  0
18. A vector v has magnitude 6 and direction   210 . Find the component form of v .
(a) 3, 3
(b) 3 3,12
3
2
(d) 3 3, 3
(c) 3, 
(e) none
19. Find a unit vector in the direction of v  4i  3 j .
(a)
4 5 3 5
i
j
5
5
(b)
(c)
4 3
i j
5 5
(d)
4 27 3 27
i
j
27
27
2
2
i
j
2
2
(e) none
20. Find the area of a triangle with a = 121, b = 82, and c = 90.
(a) 9922
(b) 4691
(c) 523.2
(d) 3689.7
(e) none
Accelerated Precalculus Practice Final Exam
21. Find the area of a triangle given a = 72, b = 51, and A = 27 .
(a) 833.5
(b) 1315.3
(c) 1635.9
(d) 2630.6
(e) none
 5
22. In polar coordinates, which of the following is not a correct representation of  2,
 6


(a)  2,  
6

11 

(b)  2,
6 

11 

(c)  2, 
6 

7 

(d)  2,  
6 

(e) none
23. Find any zeros of r: r  2  4sin2
(a)
(c)
 5

3
(b) 0, , ,
2
2
,
6 6
 3 5 7
,
4 4
,
4
,
(d)
4
 5 13 17
, ,
,
12 12 12 12
(e) none
24. Find the distance between 5, 3, 2 and  3,2, 3 .
(a) 3 10
(b)
6
(c) 66
(d) 14
(e) none
25. Let u  i  2 j  k and v  3i  j  4k . Calculate cos where  is the angle between
u and v .
(a)
9
2 26
(b)
9
2 39
(c) 
3
2 26
(d) 
3
2 39
(e) none

?

Accelerated Precalculus Practice Final Exam
1 1
1
26. Which of the following statements is true about the vectors u   i  j  k and
2 3
4
4
v  2i  j  k ?
3
(a) u and v are orthogonal
(b) u and v are parallel
(c) u is a unit vector of v
(d) The angle between u and v is

4
.
(e) None
27. Find the area of the parallelogram having v  i  2 j  2k and w  3i  2 j  k as adjacent
sides.
(a) 3
(b) 10
(c)
103
(d)
69
(e) none
28. Eliminate the parameter and find a corresponding rectangular equation:
x  t3

 y  1t
(a) y3  3 y 2  3 y  x  1  0
(b) y3  3 y 2  3 y  x  1  0
(c) y 3  x  1  0
(d) y 3  x  1  0
(e) none
29. Express in trig form: 3 - 8i. (cis is an abbreviation for cos + i sin)
(a) 73cis69
(b) 55cis249
(c) 73cis111
(d) 55cis291
(e) none
30. Convert from rectangular to polar form: 3x  2 y  1  0
(a) r 
1
3sin  2cos
(c) r  3cos  2sin  1
(b) r 
1
3cos  2sin
(d) r  3sin  2cos  1
(e) none
Accelerated Precalculus Practice Final Exam
31. Eliminate the parameter and find the rectangular equation.
x  3  2cos
y  1  3sin
(a)
 x  32   y  12  1
(b)
 x  32   y  12  1
(c)
 x  22   x  32  1
(d)
 x  12   y  32  1
9
4
9
1
4
9
9
4
(e) none
32. Given u  1,2,1 and v  3,1,2 , find u  v .
(a) 3,1, 5
(b) 3, 1, 5
(c) 3,1, 5
(d) 3,1, 5
(e) none
33. Given a triangle with sides a = 4, b = 5, and A  40 , how many triangles are possible?
(a) one
(b) two
(c) zero
(d) not enough information
(c) 1
(d) 0
1 0 2
34. 0 1 0 
2 0 1
(a) 5
35.
(b) 3
(e) –3
x x ln x

1 1  ln x
(a) 1  2xlnx
(b) 3  lnx  xlnx
(c) 3  2xlnx
(d) x
(e) 1
Accelerated Precalculus Practice Final Exam

 2 
36. Evaluate cos arctan     .
 3 

(a) 3 13
(c) 
2 13
13
37. Given sin  
3 13
13
(d)
2 13
13
(e) none
1
and tan  0 , find cos .
5
26
5
(b)
26
5
2 6
5
(d)
2 6
5
(a) 
(c)
(b)
(e) none
38. What is a possible equation of the following sinusoid:

(a) y  2sin x  1
(b) y  2cos x  1
4


(c) y  2sin  x  1 
4

(d) y  2sin x  1
4

(e) none
39. Give an equivalent expression for sin5xcos3x  cos5xsin3x .
(a) cos8x
(b) sin8x
(c) cos2x
(d) sin2x
(e) none
40. Given triangle with C = 80.3, c = 52.7, and b = 41.6, find B.
(a) 77.7
(b) 82.4
(c) 51.1
(d) 0.8
(e) none
Accelerated Precalculus Practice Final Exam
1
41. Given sin x   and tan x  0, find sin 2x.
8
(a) 
3 7
32
(b) 
65
32
(c)
3 7
32
(d) 
1
4
(e) none
42. Which is the equation of the cosecant function beginning exactly two periods to the


right of y  3csc  2x    2 ?
3

13

(a) y  3csc2  x 
6


 2

11

(b) y  3csc2  x 
6


 2

13

(c) y  3csc  2x 
6


 2

11

(d) y  3csc  2x 
6


 2

(e) none
43. Find all the solutions in the interval 0,2  : 6cos2 x  5sinx  2  0 .
(a) 1.3333,  4.4749,
 5
,
(b)
6 6
(c) 2, 5.1416
(d)
 5
6
,
6
7 11
,
6
6
(e) none
1 1

44. Determine the period of the function: y  sin  x   
2 3

2
1
(a)
(b)
(c) 6
(d) 3
(e) none
2
3
45. Solve the equation log a 3  log a b  c for b.
c
(a)
3a
3
(b) c
a
a
(c)
3c
3c
(d) a
ac
(e)
3
Accelerated Precalculus Practice Final Exam
Answer Key:
1. C
2. B
3. C
4. D
5. D
6. C
7. D
8. C
9. D
10. D
11. B
12. A
13. C
14. A
15. D
16. A
17. C
18. D
19. C
20. D
21. B
22. C
23. D
24. A
25. D
26. B
27. E
28. A
29. E
30. B
31. B
32. A
33. B
34. E
35. D
36. B
37. D
38. D
39. D
40. C
41. A
42. A
43. B
44. C
45. B