Download Algebra 2 Final

Algebra 2 Review
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
Graph the exponential function.
1.
a.
c.
y
y
20
16
16
12
12
8
8
4
4
–6
–6
–4
–2
2
4
6
–4
–2
x
2
4
6
x
2
4
6
x
–4
–4
b.
d.
y
y
4
16
–6
12
–4
–2
–4
8
–8
4
–12
–6
–4
–2
2
4
6
x
–16
–4
–20
2.
a.
c.
y
–6
–4
y
20
20
16
16
12
12
8
8
4
4
–2
2
4
6
–6
x
–4
–2
–4
b.
d.
y
–4
4
6
x
2
4
6
x
–4
y
4
–6
2
20
16
–2
2
4
6
x
–4
12
–8
8
–12
4
–16
–6
–4
–20
–2
–4
Solve the equation by graphing.
3.
a. x = 35
b. x = 29
c. no solution
d. x = 36
Rationalize the denominator of the expression. Assume that all variables are positive.
4.
a.
c.
b.
d. none of these
Use Pascal’s Triangle to expand the binomial.
5.
a.
b.
c.
d.
6.
a.
b.
c.
d.
Evaluate the expression.
7.
a. 1
b. 120
c. 4
d. 5
8. 4!
a. 120
b. 6
c. 10
d. 24
9.
a. 181,440
b. 362,880
c. 36
d. 9
10. Use synthetic division to find P(–4) for
.
a. –371
b. 883
c. 63
d. –4
11. Solve
.
a. 4, –4
c. 4, –2
b. no solution
d. 4, –4, 2, –2
12. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
. Do not find the actual roots.
a. no roots
c. 1, 2
b. –2, 2
d. –2, –1, 1, 2
13. There are 7 students participating in a spelling bee. In how many ways can the students who go first¸ second¸ and
third in the bee be chosen?
a. 5,040 ways
c. 1 way
b. 35 ways
d. 210 ways
14. Find the inverse of
.
a.
c.
b.
d.
Divide and simplify.
15.
a.
b.
Solve. Check for extraneous solutions.
16.
c.
d.
a.

3
b.
3
5
5
and 1
c.
3
d. 1
5
Multiply and simplify if possible.
17.
a. –5
b. 5
c.
d. not possible
a.
b.
c.
d. not possible
18.
Use natural logarithms to solve the equation. Round to the nearest thousandth.
19.
a. 0.584
b. 0.434
c. 0.236
d. –1.230
Factor the expression.
20.
a.
b.
c.
d.
a.
b.
c.
d. no solution
21.
Expand the logarithmic expression.
22.
a.
c.
b.
d.
a.
c.
b.
d.
23.
24. Find all the real square roots of 0.0049.
a. 0.02214 and –0.02214
c. 0.07 and –0.07
b. 0.00245 and –0.00245
d. 0.22136 and –0.22136
25. Let
and
. Find
.
a. 26
b. –111
c. –58
d. 21
26. Let
and
. Find
and its domain.
a.
; all real numbers
b.
; all real numbers
c.
7
; all real numbers except x 
6
d.
; all real numbers except x 
4
3
Subtract if possible.
27.
a.
b.
c.
d. not possible to simplify
28. Simplify
a.
b.
. Assume that all variables are positive.
c.
d. none of these
Divide using synthetic division.
29.
a.
b.
30. Solve
a. 7
5
c.
d.
. Find all complex roots.
c. no solution
,
b.
d.
7 7
7
 ,
 ,
5 5
5
31. Write a polynomial function in standard form with zeros at –5, –2, and –3.
a.
c.
b.
d.
32. Graph
and its inverse.
y
y
a.
c.
–4
4
4
2
2
–2
2
4
x
–4
–2
2
–2
–2
–4
–4
4
x
b.
d.
y
–4
y
4
4
2
2
–2
2
4
–4
x
–2
2
–2
–2
–4
–4
Evaluate the logarithm.
33.
a. 7
b. –2
c. –1
d. 2
b. –6
by x + 2.
, R –34
c. 6
d. 5
34.
a. 4
35. Divide
a.
b.
c.
d.
Add or subtract. Simplify if possible.
36.
a.
c.
b.
d.
a.
c.
b.
d.
37.
38.
, R 42
4
x
a.
c.
b.
d.
Multiply.
39.
a.
b.
c.
d.
a.
b.
c.
d.
40.
41. Write –5x2(–3x2 + 2x3) in standard form. Then classify it by degree and number of terms.
a. –10x5 – 6x4; quartic binomial
c. –10x5 + 15x4; quintic binomial
4
b. –8x – 3x ; quintic binomial
d. –8x5 + 15x4; quintic trinomial
Multiply or divide. State any restrictions on the variables.
42.
a.
c.
b.
d.
a.
c.
b.
d.
43.
44. Use the Change of Base Formula to evaluate
a. -2.161
b. 2.485;
.
c. 1.544;
d. 1.079;
Simplify.
45.
a.
b.
c.
d. none of these
46.
a. 512
b. 4
c. 64
d.
a. 10
b. 100
c.
d.
47.
Solve the equation.
48.
a. 9
49. Let
a. 3x + 2
50. Solve
a. 13.2870
b. 16
c. 21
and
. Find f(x) + g(x).
b. 11x – 8
c. 11x + 2
. Round to the nearest ten-thousandth.
b. 0.2076
c. 0.7987
d. 11
d. 3x – 8
d. 13.1378
Solve the equation. Check the solution.
51.
a.
11
b.
6

11
c.
30

2
d.
15

7
30
52.
a. 1
b.
11
c.
11
d.
8
3
7
7
53. Suppose that x and y vary inversely, and x = 5 when y = 9. Write the function that models the inverse variation.
a.
c.
b. y = 1.8x
d.
54. Classify –2x4 + 2x3 + x2 by degree and by number of terms.
a. cubic binomial
c. quintic trinomial
b. quartic trinomial
d. quadratic binomial
55. Graph
.
a.
c.
y
–12
–8
12
8
8
4
4
–4
4
8
–8
–4
–4
–8
–8
–12
–12
d.
y
–8
–12
12 x
–4
b.
–12
y
12
12
8
8
4
4
4
8
–12
12 x
8
12 x
4
8
12 x
y
12
–4
4
–8
–4
–4
–4
–8
–8
–12
–12
Suppose Q and R are independent events. Find P(Q and R).
56. P(Q) = 0.66, P(R) = 0.59
a. 0.3894
b. 1.25
c. 0.0462
d. 0.07
Simplify the radical expression. Use absolute value symbols if needed.
57.
a.
b.
c.
d.
58. If all possible results are equally likely, what is the probability that a spin of the spinner will land on an upper case
letter or a vowel?
a. 0.5
b. 0.2
c. 0.3
d. 0.6
a.
b.
c.
d.
59.
Write the expression as a single logarithm.
60.
a.
c.
b.
d.
61. A polynomial equation with rational coefficients has the roots
a.
c.
b.
d.
. Find two additional roots.
62. Suppose you invest $100 at an annual interest rate of 2.3% compounded continuously. How much will you have in
the account after 10 years?
a. $1,258.60
b. $125.86
c. $1,023.27
d. $62.52
Graph the function. Identify the horizontal asymptote.
63.
a.
c.
y
14
12
12
10
10
8
8
6
6
4
4
2
2
–4 –3 –2 –1
–2
asymptote: x = 0
y
14
1
2
3
4
x
–4 –3 –2 –1
–2
asymptote: x = 3
1
2
3
4
x
b.
d.
y
y
14
1
12
10
–8 –6 –4 –2
–1
8
–2
6
–3
4
–4
2
–5
–4 –3 –2 –1
–2
2
4
6
8
–6
1
2
3
4
x
–7
asymptote: x = 0
asymptote: x = –4
64. Solve
. Round to the nearest thousandth.
a. 4.817
b. 3.217
c. 24.086
d. 19.286
Find any points of discontinuity for the rational function.
65.
a. x = 9, x = –4
b. x = –9, x = 4
c. x = –1, x = 6, x = 9
d. x = 1, x = –6, x = –9
Write the equation in logarithmic form.
66.
a.
b.
67. Write an equation for the translation of
c.
d.
that has the asymptotes x = 8 and y = –3.
a.
c.
b.
d.
Sketch the asymptotes and graph the function.
68.
x
a.
c.
y
10
y
10
5
–10
5
–5
b.
5
–10
10 x
–5
–5
–5
–10
–10
d.
y
10
10 x
5
10 x
y
10
5
–10
5
5
–5
5
–10
10 x
–5
–5
–5
–10
–10
69.
a.
c.
y
10
y
10
5
–10
–5
5
10 x
–10
10 x
–5
–10
–10
b.
d.
y
10
y
10
5
–10
–5
5
10 x
–10
10 x
–5
–10
–10
70. Write 4x3 – 12x2 – 40x in factored form.
a. 4x(x – 5)(x + 2)
c. 2x(x + 4)(x – 5)
b. –5x(x + 2)(x + 4)
d. 4x(x + 2)(x + 5)
71. Find the zeros of
. Then graph the equation.
a. 3, –4
c. 0, 3, –4
y
–6
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
b. 0, –3, 4
4
6
x
2
4
6
x
d. 3, –4, –3
y
–6
2
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
72. Zach wrote the formula w(w – 1)(2w + 4) for the volume of a rectangular prism he is designing, with width w,
which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree
and by number of terms.
a.
; quintic trinomial
b.
; cubic trinomial
c.
; quartic trinomial
d.
; quadratic monomial
Add if possible.
73.
a.
b.
c.
d. not possible to simplify
Graph the function.
74.
a.
c.
y
10
y
10
5
–10
5
–5
b.
5
–10
10 x
–5
–5
–5
–10
–10
d.
y
10
75.
–5
10 x
5
10 x
y
10
5
–10
5
5
5
10 x
–10
–5
–5
–5
–10
–10
a.
c.
y
–4
4
4
2
2
–2
2
4
–4
x
–2
–2
–2
–4
–4
b.
d.
y
–4
y
4
2
2
2
4
–4
x
4
x
2
4
x
y
4
–2
2
–2
–2
–2
–4
–4
Write the expression as a single natural logarithm.
76.
a.
b.
c.
d.
77. Find the least common multiple of
and
.
a.
c.
b.
d.
78. Graph the relation and its inverse. Use open circles to graph the points of the inverse.
x
–8
–6
–1
3
y
–1
10
3
–4
a.
c.
y
–8
8
8
4
4
–4
4
8
–8
x
–4
–4
–4
–8
–8
b.
d.
y
–8
y
8
4
4
4
8
x
8
x
4
8
x
y
8
–4
4
–8
–4
–4
–4
–8
–8
79. For the equation
, find the number of complex roots and the possible number of real roots.
a. 6 complex roots; 0, 2, 4 or 6 real roots
b. 3 complex roots; 1 or 3 real roots
c. 6 complex roots; 1 or 3 real roots
d. 3 complex roots; 0, 2, 4 or 6 real roots
80. Find the zeros of
and state the multiplicity.
a. 3, multiplicity –2; 3, multiplicity 5
b. –2, multiplicity 3; 5, multiplicity 3
c. –2, multiplicity 3; 3, multiplicity 5
d. 3, multiplicity –2; 5, multiplicity 3
81. Determine which binomial is a factor of
.
a. x + 15
b. x – 18
c. x + 5
d. x – 5
Algebra 2 Final
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
A
D
C
A
A
D
D
D
A
B
D
D
D
A
B
C
D
B
B
B
C
B
D
C
B
A
C
B
A
B
C
B
B
C
A
D
B
C
C
B
C
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
A
B
A
B
B
A
C
D
B
B
C
D
B
B
A
B
D
A
C
C
B
B
B
B
D
A
B
B
A
C
B
B
A
B
C
D
A
A
B
D