Download ALGEBRA 2 PRACTICE FINAL EXAM June 4 PART I

ALGEBRA 2 PRACTICE FINAL EXAM June 4
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.
1. Given the function f ( x)  x 2  3 . Find the numerical value of f ( 4) .
(1) -13
(2) -1
(3) 19
(4) −5
(5) omit
2. If x  log4 828 , the value of x to the nearest hundredth is:
(1) 4.83
(2) 4.84
(3) 4.85
(4) 4.86
(5) omit
b
g
3. The expression 2 x  1 in expanded form equals:
(1) 4 x 2  1 (2) 4 x 2  1
2
(3) 4 x 2  2 x  1 (4) 4 x 2  4 x  1
(5) omit
4. The graph of the equation 2 x 2  5y 2  8 is a:
(1)circle
(2) hyperbola (3)ellipse
(4) parabola
(5) omit
5. If y varies inversely with x, and y = 6 when x = 2 , find the value of x when y = 3.
2
(1) 1
(2) 6
(3) 4
(4)
(5) omit
3
6. Express
(1) 480
8
radians in degree measure.
3
(2) 420
(3) 300
7. Solve the equation for x: 2 x  10  6
(1) −2
(2) 2
(3) 4
(4) 240
(5) omit
(4) 5
(5) omit
8. Find the solution set for the inequality x 2  4 x  12  0 .
(1) 2  x  6 (2) 6  x  2 (3) x  2 or x  6 (4) x  6 or x  2 (5) omit
9. Find the area of a triangle with two adjacent sides of lengths 6.3 and 10.2, and the
included angle measuring 80 . Express your answer to the nearest tenth.
(1) 63.3
(2) 31.6
(3) 15.8
(4) 32.1
(5) omit
Use the formula Area = (1/2)ab sin C
1
10. Solve the equation 2 sin x  2  0 for all x in the interval 0  x  2 .

5

3

4

7
(1) and
(2) and
(3) and
(4) and
(5) omit
3
3
4
4
5
5
6
6
11. Find the product: (2  3i )(5  2i ) .
(1) 10 − 6i
(2) 10 − 6i2 (3) 16 + 11i
12. If f ( x )  x
(1) 9
2
3
(4) 16 − 11i
(5) omit
b g
find f 27 .
(2) 3
(3)
1
9
(4)
13. What is the solution set for the equation
(1) {13}
(2) {7}
(3) {7,13}
1
3
x 9  4.
(4) {25}
(5) omit
(5) omit
14. The roots of the equation 3x 2  8x  k  0 will be imaginary when k =
(1) 3
(2) 4
(3) 5
(4) 6
(5) omit
15. The value of sin
(1) −1
FG 3 IJ  tanFG  IJ is:
H 2 K H 4K
(2) 0
(3) 1
16. The period of the function y  3 sin
(1) 3
(2)
1
3
(4) Undefined (5) omit
FG 1 xIJ is:
H3 K
(3) 120
17. Simplify and express in a + bi form:
(1)
1 5
 i
12 12
(2)
(4) 1080
(5) omit
2i
.
5i
1 5
1
5
1 5
 i (3)
 i (4)
 i
13 13
12 12
13 13
(5) omit
18. Find the value of x, to the nearest degree, given cos x .9731 .
(1) 13
(2) 14
(3) 76
(4) 77
(5) omit
19. If Z1 = 8 + 3i and Z2 = 6 − 9i, in which quadrant does Z1 + Z2 lie?
(1) I
(2) II
(3) III
(4) IV
(5) omit
2
20. Reduce the algebraic fraction to lowest terms:
(1)
x 5
x2
(2)
x  10
x2
(3)
x 5
x2
x 2  7 x  10
.
x2  4
(4)
7 x  10
4
(5) omit
sin 2   cos2 
21. When simplified the expression
is equivalent to:
sec 
(1) tan 
(2) sin 
(3) cos
(4) csc 
(5) omit
2
2
Use the identity sin   cos   1
x
22. The expression log 2 is equivalent to:
y
(1) log x  log y (2) 2(log x  log y) (3) log x  2 log y (4) log x  2 log y (5) omit
23. If f ( x)  2 x  1and g( x)  4 x  12 find f ( g(3)) .
(1) 3
(2) 1
(3) 0
(4) 16
(5) omit
24. Find the value of angle X to the nearest degree if
arc A = 146 and arc B = 60 .
Use the formula X=(1/2)(arcA-arcB)
A
(1) 43
(2) 60 (3) 86
B
(4) 103 (5) omit
X
25. If cos A  0 and sin A  0 , in what quadrant does the terminal side of angle A lie?
(1) I
(2) II
(3) III
(4) IV
(5) omit
1 1

26. Simplify the complex fraction: 5 x
4
3x
x 5
3x  15
3x  15
3x  3
(1)
(2)
(3)
(4)
(5) omit
20
20
4
4
27. If log x 64  3 , find the value of x.
(1) 3
(2) 4
(3) 2
28. Find the domain of f ( x ) 
(1) x  3
(2) x  5
x3
.
x 5
(3) x  3,5
3
(4) 8
(5) omit
(4) x  5
(5) omit
29. Solve for all values of x given the equation: 3x  2  11 .
RS
T
(1) 3,
13
3
UV
W
(2) {3}
(3)
RS 13UV
T3W
RS
T
(4) 3,
13
3
UV
W
(5) omit
30. Rationalize the denominator and express the answer in simplest terms:
(1) 4 2
(2)
8 2
2
(3)
16
2
(4) 4
8
.
2
(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  4  9 .
[4]
32. For the equation 2 x 2  7 x  4  0 , find a) the sum of the roots and b) the product
of the roots.
[4]
33. Write in simplest form: 7 8  3 50 .
34. Solve the equation for x, show all work: sin(2 x  20)  cos(6x  10)
[4]
[4]
35. Factor the following expression completely: 3x  27 .
2
[4]
4
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. [Each question selected is worth 10 points]
36. Solve the following equation and express the roots in simplest a + bi form.
x 2  6x  13  0
37. Answer both parts a and b.
a) Two men try to pull a pig out of a ditch. One man applies a force of 180 pounds
while the other man applies a force of 220pounds. The resultant force is 280
pounds. Find the angle between the two applied forces, rounded to the nearest
degree.
AND
b) In acute triangle ABC, side a = 12, side b = 14, and the m<A = 56 . Find m<C
to the nearest degree.
38. a) On the same set of axes, sketch and label the graphs of the
1
equations y  3 sin 2 x and y  cos x in the interval 0  x  2 .
2
b) Based on the graphs drawn in part a, determine the number of values of x in the
interval graphed where the two functions are equal.
39. The number of home runs hit in the major leagues has increased steadily over the
past six years while the number of stolen bases has decreased. The table below
contains the data for the past six years for one team.
Home
78
82
88
85
93
102
Runs
Stolen
91
78
60
55
51
52
Bases
a. Graph the scatter plot of the given information.
b. Find the linear equation of best fit for the given data. Round decimals to
two places.
c. Find the correlation coefficient “r” correct to 4 decimal places.
d. Use the equation found in part b to estimate the number of Stolen Bases
for this team if it hits 120 Home Runs.
5