Free Printable Adv Alg 2 Final Exam Review Spring 2022

1.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

2.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

3.

Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8

a)

(5, 8)

b)

(5, -8)

c)

(-5, -18)

d)

(-5, 8)

4.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

5.

If a system of equations has infinitely many solutions, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

the same line (coinciding lines)

6.

Solve the system of equations to find the value of y.

a)

-2

b)

3

c)

-3

d)

2

7.

Inconsistent system is a system of equations that has

a)

one solution

b)

two solutions

c)

infinitely many solutions.

d)

has no solution

8.

A consistent system that has exactly one solution

a)

inconsistent

b)

consistent

c)

dependent

d)

independent

9.

Which system of linear inequalities is represented by the graph?

a)

y≤2x-1
y>-2x+3

b)

y>2x-1
y≤-2x+3

c)

y<2x-1
y≥-2x+3

d)

y≤2x-1
y>2x+3

10.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

11.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

12.

Given f(x) = x² - 3 and g(x) = x - 3, find f(g(f(3))).

a)

0

b)

3

c)

6

d)

9

13.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

14.

Factor 4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

15.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

16.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

17.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

2x(2x+3)(2x-3)

d)

PRIME

18.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

19.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

20.

Simplify (-5a^-3)(3a⁶b)

a)

-15a³b

b)

-15a⁹b

c)

45ab²

d)

-45a⁹b²

21.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

22.

Multiply: (6p² −8p−1)(−p² +6p−1)

a)

44p³ + 2p + 1

b)

−1p⁴+ 4p³ − 5p² + 2p + 1

c)

−6p⁴+ 44p³ − 53p² + 2p + 1

23.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x^2-3x+8-\frac{9}{x+1}

c)

$3x^2+3x+8+\frac{7}{x+1}$

d)

3x³ + 3x² + 8x + 7

24.

Simplify

(3 - 2x + 4x²) - (3x² - 10) + (14x - 5)

a)

x² + 16x + 8

b)

x² + 12x - 12

c)

x² + 12x + 8

d)

x² - 16x - 12

25.

f(x)=x²-4
h(x)=3x+3
f(h(x))

a)

3x²-9

b)

12x²+8x+5

c)

16x²-36x+20

d)

9x²+18x+5

26.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

27.

Multiply:
(3a + 4)²

a)

6a²+12a+16

b)

9a²+24a+16

c)

9a²+12a+16

d)

9a²+16

28.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

(2h - 2)(2h + 2)

d)

(h - 4)(4h - 1)

29.

What is the complex conjugate of 4 - 3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

30.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

31.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

32.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

33.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

34.

Which one of these are not a zero of $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$ ?

a)

0

b)

1

c)

-5

d)

-1

35.

What is the multiplicity of the zero x=1 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

2

b)

1

c)

4

d)

3

36.

How does a multiplicity of 2 affect the graph?

a)

cross

b)

bounce

c)

wiggle (change direction)

37.

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

a)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

b)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

c)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

d)

$f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

38.

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

a)

$f\left(x\right)=x^4\left(x-5\right)^2\left(x-3\right)$

b)

$f\left(x\right)=x^4\left(x+5\right)^2\left(x+3\right)$

c)

$f\left(x\right)=x\left(x-5\right)^4\left(x-3\right)^2$

d)

$f\left(x\right)=x\left(x+5\right)^2\left(x+3\right)^4$

39.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

40.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

41.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

42.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

43.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

44.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

45.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

46.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

47.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

48.

$5\sqrt{2}\cdot4\sqrt{10}$

a)

$20\sqrt{20}$

b)

$10\sqrt{40}$

c)

$40\sqrt{5}$

d)

$9\sqrt{13}$

49.

$3\sqrt{6}\left(\sqrt{6}-2\sqrt{10}\right)$

a)

$18-12\sqrt{15}$

b)

$6\sqrt{15}$

c)

$-3\sqrt{24}$

d)

$3\sqrt{36}-6\sqrt{60}$

50.

$\left(4\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}-\sqrt{3}\right)$

a)

$20\sqrt{2}-14\sqrt{6}+2\sqrt{3}$

b)

$46-14\sqrt{6}$

c)

$32\sqrt{6}$

d)

$40-14\sqrt{6}+6\sqrt{3}$

51.

$\left(10-3\sqrt{2}\right)\left(10+3\sqrt{2}\right)$

a)

$82-\sqrt{2}$

b)

$20-6\sqrt{2}$

c)

$100-60\sqrt{2}$

d)

82

52.

a)

x = 2

b)

x = 4

c)

x = 7

d)

x = 9

53.

a)

x = -6

b)

x = 3

c)

x = -3

d)

x = 5±

54.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

55.

Which function represents the given graph?

a)

b)

c)

d)

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

a)

A

b)

B

c)

C

d)

D

59.

a)

A

b)

B

c)

C

d)

D

60.

a)

A

b)

B

c)

C

d)

D

61.

(2∛4)+(7∛4)

a)

9∛8

b)

52

c)

9∛16

d)

9∛4

62.

(6√2)-(4√18)

a)

(6√2)-(4√18)

b)

1-6√18

c)

2√2

d)

-6√2

63.

5√48x²

a)

10x√3

b)

15x√3

c)

20x√3

d)

25x√3

64.

What are the transformations of this functions compared to the parent function?

a)

Shifted down 2

b)

Shifted up 2

c)

Shifted left 2

d)

Shifted right 2

65.

What are the transformations of this functions compared to the parent function?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

66.

Which is the graph of the square root parent function?

a)

A

b)

B

c)

C

d)

D

67.

a)

y ≥ 0

b)

x ≥ -2

c)

x ≤ -2

d)

y ≥ 2

68.

a)

A

b)

B

c)

C

d)

D

69.

Find the product

a)

A

b)

B

c)

C

d)

D

70.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

71.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

72.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

73.

Add

$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ 1$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

d)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-\frac{1}{4},\ 2$

74.

Add

$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$

a)

$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

b)

$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$

c)

$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

d)

$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

75.

log₃81 =

a)

2

b)

3

c)

4

d)

5

76.

a)

100

b)

2

c)

10

d)

1

77.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

78.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

79.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

80.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

81.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

82.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

83.

Rewrite as a single logarithm:

\log3\ +\ \log7

a)

log 10

b)

log 21

c)

log 3/7

d)

log 3/log 7

84.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

$\frac{\log_260}{\log_210}$

d)

$\log_270$

85.

BONUS: Expand log₆(5x³/y).

a)

log₆5x³-log₆y

b)

log₆5+log₆x³-log₆y

c)

log₆5+3log₆x-log₆y

Adv Alg 2 Final Exam Review Spring 2022

Total questions: 85

Worksheet time: 4hrs 11mins

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