ALGEBRA2 PRACTICE FINAL EXAM 3
PART I
Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits.
Write your answers on the scantron sheet provided. FOR EACH OF THE 5
QUESTIONS YOU OMIT ON PART I, FILL IN CHOICE (5) ON THE SCANTRON
SHEET.
3
radians in degree measure.
5
(1) 2 
(2) 54 
1. Express
2. Solve the equation for x: 3 x 
(1) -2
(3) 108 
(4) 216 
(5) omit
(3) -3
(4) 3
(5) omit
1
9
(2) 2
3. Given the function f ( x)  2 x 2  7 . Find the numerical value of f ( 2) .
(1) -23
(2) -15
(3) 1
(4) 9
(5) omit
4. Find the area of a triangle with two adjacent sides of lengths 51 and 35, and the
included angle measuring 1260. Express your answer to the nearest tenth.
(1) 524.6
(2) 722.0
(3) 1049.2 (4) 1444.1 (5) omit
5. Find the product: (5  i )(9  3i ) .
(1) 42
(2) 45 + 3i
(3) 42 – 24i (4) 45 – 21i (5) omit
6. Solve the equation 4cosx + 5 = 3 for all x in the interval 0  x  2 .

5
2
5

2
2
4
and
and
(1) and
(2)
(3) and
(4)
(5) omit
3
3
3
3
3
3
3
3
2
bg
7. If f ( x)  x 3 find f 216 .
(1) -12
(2) -36
(3)
1
36
(4)
1
12
8. The roots of the equation 3x 2  7 x  k  0 will be real when k = ?
50
(1) 0
(2)
(3) 4
(4) 5
12
9. The value of sin
I
F
 is:
G
H6 J
K 2 cosbg
3
2
(2) 1
(1)
(3) 2
(4)
5
2
(5) omit
(5) omit
(5) omit
10. The amplitude of the function y  2 cos(4 x) is:
(1) -2
(2) 2
(3) 4
(4) 90 
(5) omit
11. When simplified the function f ( x )  sec x  cot x  sin x is equivalent to:
(1) 1
(2) cosx
(3) tanx
(4) cotx
(5) omit
12. Find the value of x, to the nearest ten minutes, given sin x  0.4326 .
(1) 2530'
(2) 2540'
(3) 6430' (4) 6420'
(5) omit
13. If x  log 7 235 , find the value of x to the nearest hundredth.
(1) .36
(2) .47
(3) 2.44
(4) 2.81
(5) omit
14. In which quadrant does the difference of 2  3i , and ,4  7i lie?
(1) I
(2) II
(3) III
(4) IV
(5) omit
b
g
15. The expression 5x  2 y in expanded form equals:
(1) 25x2 – 4y2
(2) 25x2 + 4y2 (3) 25x2-20xy+4y2 (4)25x2-20xy–4y2 (5)omit
2
8a 2  16a
.
a 2  4a  4
8a
4a
(3)
(4)
a2
a2
16. Reduce the algebraic fraction to lowest terms:
(1) 4
(2)
8a
a2
(5) omit
17. The graph of the equation 2 x 2  2 y 2  98 is the conic section:
(1) parabola
(2) circle
(3) ellipse (4) hyperbola (5) omit
1
18. Express 3 log x  log y as a single logarithm.
4
x3
3x
(1) log x 3 4 y
(2) log
(3) log
4 y
1
y
4
3
(4) log xy (5) omit
4
19. If y varies inversely with x, and y = 15 when x = 6, find the value of y when x = 9.
(1) 10
(2) 3.6
(3) 22.5
(4) 90
(5) omit
20. If f ( x)  3x 2  x and g( x)  8x  5 find g ( f (2)) .
(1) 75
(2) 267
(3) 352
(4) 1078
(5) omit
21. Find the solution set for the inequality x 2  4 x  32  0 .
(1) 8  x  4
(2) 4  x  8 (3) x  8orx  4 (4) x  4orx  8 (5)omit
22. Find the value of angle X to the nearest degree if
arc A = 1650 and arc B = 750.
(1) 45 
(2) 90 
A
(3) 120 
(4) 240 
B
X
(5) omit
23. What is the solution set for the equation
1
3
(1)
(2)
2
2
2x  5  4  6 .
15
(3)
2
(4)
27
2
(5) omit
24. If cos A  0 and tan A  0 , in what quadrant does the terminal side of angle A lie?
(1) I
(2) II
(3) III
(4) IV
(5) omit
25. Simplify and express in a + bi form:
(1) 2 – 2i
4  5i
.
2  3i
23 2
 i
13 13
(2)
(3)
8
i
13
(4)
23
 2i
13
(5) omit
(3)
y( x  y)
x
(4)
y( x  y)
2
(5) omit
x y
26. Simplify the complex fraction: x
1 1

x y
(1) y
27. If log x 64 
(1) 512
(2) x
3
, find the value of x.
2
(2) .96
x2
.
2x  3
3
(2) x: x 
2
(3) 16
(4) 12
(5) omit
28. Find the domain of f ( x ) 
(1)
3U
R
x: x   V
S
T 2W
R
S
T
U
V
W
3U
R
Rx  3 U
(4) S
S
V
T 2W T 2V
W(5)
(3) x 
omit
29. Solve for all values of x given the equation: 3x  5  30 .
(1)
25 U
R
S
T3 V
W
(2)
25 35 U
R
S
T3 , 3 V
W
(3)
895 U
R
R35 25U(5)
(4) S , V
S
V
T3 W T3 3 W
3 5
.
5
3 5 1
(4)
(5) omit
5
30. Rationalize the denominator and express the answer in simplest terms:
(1) 3 5  1
(2) 3  5
(3)
3 5 5
5
omit
PART II
Answer all 5 questions from this part. Show all work for credit in the white examination
booklet provided. Four credits each.
31. Solve the following absolute value inequality and graph the solution set on the real
number line: x  5  7
32. For the equation 3x 2  8x  3  0 , find a) the sum of the roots and b) the product of
the roots.
33. Write in simplest form: 2 50  3 18 .
34. Solve the equation for x, show all work: tan(10 x  20) 0  cot( x  30) 0
35. Factor the following expression completely: 2 x 3  8x 2  90x .
PART III
Answer 3 out of the 4 questions in this section. All work necessary to the solution of the
question must be written in the white examination booklet or on graph paper, where
applicable.
36. Solve the following equation and express the roots in simplest a + bi form.
2 x 2  4  5x
37. a) One force of 50 pounds and one force of 85 pounds act on a body at the same point
so that the resultant force is 66 pounds. Find, to the nearest degree, the angle between
the original two forces.
b) In acute triangle RST, m <R = 420 , m <T = 1060 , and ST = 55. Find RT to the
nearest whole number.
1
38. a) On the same set of axes, sketch and label the graph of y  sin x and
2
y  2 cos 2 x in the interval 0  x  2 .
b) Based on the graphs drawn in part a find all values of x in the interval graphed
where the two functions are equal.
39. The table below represents data gathered by a research company.
a) Graph the scatter plot of the given information.
b) Find the exponential equation of best fit for the given data. Round decimals to
two places.
c) Find the correlation coefficient “r” correct to four decimal places.
d) Use the equation found in part b, with the rounded values, to estimate the value of
y when x = 8.
x
1
2
3
4
5
6
y
2
6
10
25
60
120