ALGEBRA2 PRACTICE FINAL EXAM 1
PART I
Answer all part I questions. Place answers on the answer sheet. Show all work on loose leaf and
attach to the answer sheet.
3
1. Express
radians in degree measure.
4
(1) 67.5 
(2) 135 
(3) 202.5˚
(4) 270 
2. Solve the equation for x: 6 x  216
(1) -3
(2) 3
(3) -4
(4) 4
3. Given the function f ( x)  (5  x) 2 . Find the numerical value of f ( 3) .
(1) -4
(2) 4
(3) 14
(4) 64
4. Find the product: (2  5i )(6  3i ) .
(1) 27
(2) 12 – 15i
3
5. If f ( x)  x 2 find f
(1)
50
3
(3) 12 – 39i
(4) 27 – 24i
1I
F
G
H25J
K.
(2)
3
50
(3)
1
25
(4) 125
6. The roots of the equation 2 x 2  5x  k  0 will be imaginary when k =?
(1) -3
(2) -2
(3) 3
(4) 4
7. Find the value of x, to the nearest degree, given cos x  0.4872 .
(1) 1 
(2) 29 
(3) 60˚
(4) 61 
8. If x  log 6 53 , find the value of x to the nearest hundredth.
(1) .45
(2) .54
(3) 2.22
(4) 1.83
9. In which quadrant does the sum of 2  3i , and ,4  7i lie?
(1) I
(2) II
(3) III
(4) IV
b g
10. The expression 3x  5 in expanded form equals:
(1)9x2+30x+25
(2)9x2+30x+5
(3)9x2+25
2
t 2  25
.
2t 2  9t  5
t 5
(3)
2t  1
(4)6x+10
11. Reduce the algebraic fraction to lowest terms:
(1) -t – 4
(2)
5
3
(4)
t 5
2t  1
12. The graph of the equation 3x 2  5 y 2  35 is the conic section:
(1) parabola
(2) circle
(3) ellipse
(4) hyperbola
13. Express 2 log x  3 log y as a single logarithm.
(1) log(2x – 3y)
(2) log
x2
y3
(3) log x 2 y 3
(4) log
2x
3y
14. If y varies inversely with x, and y = 7 when x = 2, find the value of y when x = 4.
(1) 1.14
(2) 3.5
(3) 14
(4) 56
15. If f ( x)  x 2  3x and g( x)  3x find f ( g (3)) .
(1) -54
(2) -9
(3) 18
(4) 54
16. Find the solution set for the inequality x 2  2 x  15  0 .
(1) x  5orx  3
(2) x  3orx  5
(3) 5  x  3
(4) 3  x  5
17. Find the value of angle X to the nearest degree if
arc A = 2100 and arc B = 1500.
(1) 30 
(2) 60 
(3) 180 
(4) 360˚
A
B
X
18. What is the solution set for the equation
(1) -1
(2) 11
x 8  4  7.
(3) 17
(4) 41
19. If tan A  0 and sec A  0 , in what quadrant does the terminal side of angle A lie?
(1) I
(2) II
(3) III
(4) IV
20. Simplify and express in a + bi form:
(1)
7 22
 i
41 41
(2)
7 22
 i
41 41
2  3i
.
4  5i
1 x

2
x
2
21. Simplify the complex fraction:
5
x
1 x
1  x2
(1)
(2)
5
10
22. If log x 8  3 , find the value of x.
(1) 2
(2) 24
(3)
1 2
 i
3 9
(4)
23 2
 i
41 41
(3)
5 x
2x
(4)
1  x2
5
(3) 512
(4) 6561
23. Find the domain of f ( x )  x  9 .
(1) x  -9
(2) x<-9
(3) x  -9
24. Solve for all values of x given the equation: 2 x  7  15 .
(1) {11}
(2) {4,11}
(3) {-4,11}
(4) x>-9
(4) {-11,4}
3
.
7
3 7
(4)
7
25. Rationalize the denominator and express the answer in simplest terms:
(1) 3
(2)
3
7
(3)
3 7
49
PART II
Show all work in the space provided on the answer sheet.
26. Solve the following absolute value inequality and graph the solution set on the real number
line: x  2  7
27. For the equation 2 x 2  6x  7  0 , find a) the sum of the roots and b) the product of the
roots
28. Write in simplest form: 2 72  3 32 .
29. Solve the equation for x, show all work: sin(4 x  8) 0  cos(2 x  30) 0
30. Factor the following expression completely: x 3  6x 2  40x .
PART III
Show all work in the space provided on the answer sheet.
31. Solve the following equation and express the roots in simplest a + bi form. x 2  4 x  12  0
32. The table below represents data gathered by a research company.
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 four decimal places.
d) Use the equation found in part b, with the rounded values, to estimate the value of y when
x = 15.
x
3
5
7
9
11
y
4
6
32
55
83
EASTER ASSIGNMENT ANSWER SHEET
This assignment is due Monday April 20th by 8:30 am. (NO excuses) Bring your completed
assignment to the Math office, Room E114, and place it in the box labeled “Mrs. Binaso.” The box
will be on the floor outside of the math office. It will be placed in hallway early so that H period
students can hand it in before going to H period. NO LATE assignments will be accepted. This will
be graded and counted as a quiz.
PART I:
Place the choice of the correct answer on the line provided. Show all work on loose leaf and attach
to this answer sheet.
1. ______
10. ______
18. ______
2. ______
11. ______
19. ______
3. ______
12. ______
20. ______
4. ______
13. ______
21. ______
5. ______
14. ______
22. ______
6. ______
15. ______
23. ______
7. ______
16. ______
24. ______
8. ______
17. ______
25. ______
9. ______
PART II:
Show all work in the space provided.
26.
27.
28
29.
30.
PART III:
Show all work in the space provided.
31.
32.