Free Printable Spring Semester Review Algebra 2

1.

Simplify $\left(3x\right)^2\cdot2x^4$ .

a)

$5x^6$

b)

$18x^6$

c)

$6x^8$

d)

$18x^8$

2.

Simplify $\frac{3y^2z}{15y^5}$ . Assume that no variable equals 0.

a)

$\frac{z}{5y^3}$

b)

$\frac{y^2z}{5}$

c)

$5y^3z$

d)

$\frac{y^7z}{5}$

3.

Todd is simplifying the expression $\left(3x^4+4x^2\right)\left(x^3-2x^2-1\right)$ . Which of the following shows the correct product?

a)

$3x^7+6x^6-4x^5+11x^4+4x^2$

b)

$3x^7-6x^6+4x^5-11x^4-4x^2$

c)

$3x^{12}-6x^8-11x^4+4x^6-4x^2$

d)

$3x^{12}-6x^8+4x^6-3x^4-4x^2$

4.

Simplify $3x\left(2x^2-y\right)$ .

a)

$5x^3-3xy$

b)

$12x-y$

c)

$6x^2-3y$

d)

$6x^3-3xy$

5.

Simplify $\left(x^2-2x-35\right)\div\left(x+5\right)$ .

a)

$x-30$

b)

$x+5$

c)

$x-7$

d)

$x^3+3x^2-45x-175$

6.

Which represents the correct synthetic division of $\left(x^2-4x+7\right)\div\left(x-2\right)$ ?

a)

-2 | 1 -4 7

b)

2 | 1 -4 7

c)

-2 | 1 -4 -7

d)

2 | 1 -4 -7

7.

Factor $m^2+9m+14$ completely.

(a)

8.

Identify the factors for $t^2+t-6$ .

a)

t - 5

b)

t - 2

c)

t - 3

d)

t + 3

e)

t + 2

9.

Find $f(3)$ for $f(x)=x^2-9x+5$ .

a)

-23

b)

-16

c)

-13

d)

41

10.

A factor of $x^3+4x^2-11x-30$ is ( x + 2 ). Find the remaining factors.

a)

6

b)

-x

c)

3x

d)

x - 3

e)

x + 5

11.

Which is not a root of the equation $x^3-x^2-10x-8=0$ ?

a)

1

b)

4

c)

-2

d)

-1

12.

Find all the rational zeros of $p(x)=x^3-12x-16$ .

a)

-2

b)

4

c)

2

d)

4

13.

Find $f(g(x))$ if $f(x)=x^2+5$ and $g(x)=2x$ .

a)

$4x^2+5$

b)

$2x^2+5$

c)

$2x+5$

d)

$4x+5$

14.

Find $f(g(x))$ if $f(x)=2x+5$ and $g(x)=3x+1$ .

a)

$2x^2+6$

b)

$3x^2+7$

c)

$6x+7$

d)

$2x+10$

15.

If $f(x)=3x+7$ and $g(x)=2x-5$ , find $g(f(-3))$ .

a)

-26

b)

-9

c)

-1

d)

10

16.

If $f(x)=x^2$ and $g(x)=3x-1$ , find $g(f(x))$ .

a)

$x^2-1$

b)

$9x^2-1$

c)

$3x^2-1$

d)

$9x^2-6x+1$

17.

Find the inverse of $g(x)=-3x+2$ .

(a)

Choose from the below words

g^-1(x) = -(x-2)/3

g^-1(x) = (-x/3) + 2

g^-1(x) = (-x/3) - 2

18.

Simplify $\sqrt[]{121}$ .

(a)

19.

Simplify $\sqrt[]{224}$ .

a)

15.0

b)

$2\ \sqrt[\ ]{14}$

c)

$4\ \sqrt[]{14}$

d)

14

20.

Simplify $(2+\sqrt{5})(3−\sqrt{5})$ .

a)

1 + √5

b)

1 - √5

c)

-1 + √5

d)

-1 - √5

21.

Simplify $\sqrt{75}+\sqrt{12}$ .

a)

21

b)

87

c)

10√3

d)

7√3

22.

Simplify the expression $\frac{2}{5}m^3\cdot\frac{1}{5}m^5$ .

a)

$\frac{2m^8}{25}$

b)

$\frac{3m^8}{5}$

c)

$\frac{2}{25m^8}$

d)

$\frac{2}{5m^2}$

23.

Solve $\sqrt{3x}+4=5$ for x.

a)

$x=-7$

b)

$x=\frac{1}{3}$

c)

$x=21$

d)

$x=\frac{25}{3}$

24.

If $g(x)=2x^3-54$ , find g(g(-1)).

25.

Which function represents exponential growth?

a)

y = (1/3)^x

b)

y = 4x^4

c)

y = 12(1/5)^x

d)

y = 10(3)^x

26.

The graph of which exponential function passes through the points (0, 4) and (1, 24)?

a)

y = 4(6)^x

b)

y = 3(8)^x

c)

y = 2(2)^x

d)

y = 10(3)^x

27.

Solve $8\left(x+2\right)^2=2x+4$ for x.

a)

$x=-2$

b)

$x=-\frac{7}{4}$

c)

$x=2$

d)

$x=-\frac{4}{7}$

28.

Write the equation $4^3=64$ in logarithmic form.

a)

$\log_43=64$

b)

$\log_34=64$

c)

$\log_{64}4=3$

d)

$\log_464=3$

29.

Write the equation $\log_{12}\ 144=2$ in exponential form.

(a)

30.

Evaluate $\log_82$ .

a)

3

b)

$\frac{1}{3}$

c)

16

d)

64

31.

Solve $\log_3\ n$ = 2 for n.

a)

6

b)

5

c)

8

d)

9

32.

Solve $\log_610+\log_6x=\log_640$ .

a)

4

b)

5

c)

30

d)

15

33.

Express $\log_922$ in terms of common logarithms.

(a)

34.

Evaluate e^ln 4.

(a)

35.

Evaluate $3\log64+\log\ 5+\log_9\ \frac{1}{3}$ . Round to the nearest hundredth.

36.

Simplify the expression: $\frac{\text{24pn}}{\text{18p}^2}$ .

a)

$\frac{4n}{3p}$

b)

$\frac{4pn}{3}$

c)

$\frac{4p}{3n}$

d)

$\frac{4}{3}$

37.

Simplify the expression: $\frac{6a+12}{5a+10}$ .

a)

$\frac{6}{5}$

b)

24

c)

12a + 12

d)

24a

38.

Simplify the expression: $\frac{x}{x^2\ -y^2\ }-\frac{y}{x\ -\ y\ }$ .

a)

$\frac{x-xy-y^2}{\left(x+y\right)\left(x-y\right)\ }$

b)

$y^3/(x^3-x^2y-xy^2+y^3)$

c)

(x + y / y)

d)

$1/(y(x-y))$

39.

Comparing lions in the zoo to lions in the wild is an example of what type of study?

a)

An observational study

b)

A survey

c)

An experiment

d)

A null hypothesis

40.

A survey given to 30 random freshmen from the 560 students at McAllen High School concludes that 65% of the freshmen attend home sporting events. What is the population of this survey?

a)

All 560 high school students

b)

The 30 freshmen surveyed

c)

People attending sporting events

d)

All freshmen at the school

41.

A theoretical probability distribution is constructed for the number of tails when tossing a coin 5 times. What probability is paired with the outcome of 5 tails?

a)

1/5

b)

1/10

c)

1/16

d)

1/32

42.

The probability that a certain team will win a baseball game is 1/3. In a 5-game series, what is the probability that the team will win all five games?

a)

1/81

b)

2/243

c)

1/3

d)

1/243

43.

Factor completely: 5x²-15x+10.

Choose All of the factors.

a)

(5x - 2)

b)

5

c)

(x - 2)

d)

(x - 1)

e)

15

44.

Factor the polynomial:
5x² - 13x + 6

a)

(x + 3)(5x - 2)

b)

(x - 2)(5x - 3)

c)

(x + 2)(5x + 3)

d)

(x - 3)(5x + 2)

45.

Which is one of the factors:

6x² + 5x - 6

a)

(x - 6)

b)

(x - 1)

c)

(3x + 2)

d)

(2x + 3)

46.

Simplify the expression $\sqrt{49x^2}$ .

a)

7x

b)

7x^2

c)

49x

d)

49

47.

Solve the quadratic inequality:

$x^2-14x+48>0$

a)

$x<6\ ,\ \ x>8$

b)

$6<x<8$

c)

$-8<x<-6$

d)

$x<-8\ ,\ \ x>-6$

48.

Solve the quadratic inequality:

$x^2-4x-32<0$

a)

$x<-4\ ,\ \ x>8$

b)

$-8<x<4$

c)

$-4<x<8$

d)

$x<-8\ ,\ \ x>4$

49.

Solve the quadratic inequality:

$x^2-13x+22\le0$

a)

$x\le-11\ ,\ \ x\ge-2$

b)

$-11\le x\le-2$

c)

$2\le x\le11$

d)

$x\ge11\ ,\ \ x\le2$

50.

Solve the quadratic inequality:

$x^2+9x+18<0$

a)

$x<-6\ ,\ \ x>-3$

b)

$-6<x<-3$

c)

$x<3\ ,\ \ x>6$

d)

$3<x<6$

51.

Solve the quadratic inequality:

$x^2+3x-28\ge0$

a)

$x\ge4\ ,\ \ x\le-7$

b)

$x\ge7\ ,\ \ x\le-4$

c)

$-4\le x\le7$

d)

$-7\le x\le4$

52.

Solve the quadratic inequality:

$x^2+10x+16<0$

a)

$2<x<8$

b)

$-8<x<-2$

c)

$-8<x<2$

d)

$-2<x<8$

53.

Solve the quadratic inequality:

$x^2-49\ge0$

a)

$x\le-7\ ,\ \ x\ge7$

b)

$x\le0\ ,\ \ x\ge7$

c)

$-7\le x\le7$

d)

$-7\le x\le0$

54.

Which of the following is not a solution to -x² + 3x + 10 < 0 ?

a)

-2

b)

-1

c)

5

d)

8

55.

Which of the following graph is the same as the interval $\left[-5,4\right]$ ?

a)

b)

c)

d)

56.

Which of the following shows the graph of the solution set of $x^2-5x-14>0$ ?

a)

b)

c)

d)

57.

Which of the following is the same as the given graph?

a)

$\left(-2,\ 3\right)$

b)

$\left[-2,\ 3\right]$

c)

undefined

d)

$\left(-\infty,\ -2\right)\cup\left(3,\ \infty\right)$

58.

Which is the solution set of $\left(x+3\right)\left(x-2\right)>0$ ?

a)

$\left(-2,\ 3\right)$

b)

$\left(-3,2\right)$

c)

$\left(-\infty,-3\right)\cup\left(2,\infty\right)$

d)

$\left(-\infty,-3\right)\cup\left(2,\infty\right)$

59.

Which of the following is the same as the given graph? (check all that apply)

a)

$\left\{x|\ x\ge-5<\cup\ \ x\le4\right\}$

b)

$\left[-5,\ 4\right]$

c)

$\left(-\infty,\ 5\right]\ \cup\ \left[4,\ \infty\right)$

d)

$\left\{x|-5\le\ x\le4\right\}$

60.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make the equation equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

61.

Which of the following is an example of quadratic inequality? Select all that apply.

a)

2x² + 3x + 4 > 0

b)

15x ≤ 10

c)

x² - x +15 < -30

d)

x² + 4x - 5 = 0

62.

Give the correct factor of x² -12x + 27.

a)

(x + 3) (x + 9)

b)

(x - 3) (x - 9)

c)

(x - 3) (x + 9)

d)

(x + 3) (x - 9)

63.

Solutions are in the ___________ area of a quadratic inequality.

a)

non-shaded

b)

shaded

c)

vertex

d)

axis of symmetry

64.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

65.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

66.

Give the correct name for
2x³+5x

a)

Linear Binomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Linear Trinomial

67.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

68.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

69.

The unit circle...

a)

Has center at (1,1)

b)

Has a circumference of 1

c)

Has a diameter of 1

d)

Has a radius of 1

70.

Which of the following angles are co-terminal to 330^o?

a)

-330^o, 330^o

b)

510^o, -210^o

c)

690^o, -30^o

d)

420^o, -330^o

71.

Which of the following angles are co-terminal to -75^o?

a)

-365^o, 75^o

b)

285^o, -435^o

c)

105^o, -255^o

d)

425^o, -335^o

72.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

73.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

74.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

75.

What is the reference angle for 275°?

a)

85°

b)

95°

c)

-85°

d)

-95°

76.

What is the reference angle?

a)

112

b)

68

c)

158

d)

248

77.

What is the reference angle?

a)

43

b)

-43

c)

47

d)

-47

78.

Match the following basic trigonometry vocabulary with their definitions:

a)

a circle with a center at (0,0)

1.

unit circle

b)

description of positive and negative angles in standard position sharing the same terminal side

2.

coterminal angles

c)

the side of an angle at which rotation ends

3.

terminal side

d)

the position of an angle havin the vertex at the origin& the initial side along the positive x-axis

4.

standard position

e)

the side of a right triangle opposite the right angle

5.

hypotenuse

79.

Now, for Quadrant I of the Unit Circle, please complete the coordinates before we move onto finish Degrees to Radians. Recall the importance of Desmos.

Recall the importance of thinking in terms of two number lines intersecting at, "(0, 0)."

a)

\left(\frac{\sqrt[]{2}}{2}\ ,\ \frac{\sqrt[]{2}}{2}\right)

b)

\left(\frac{\sqrt[]{3}}{2}\ ,\ \frac{\sqrt[]{1}}{2}\right)

c)

\left(\frac{\sqrt[]{1}}{2}\ ,\ \frac{\sqrt[]{3}}{2}\right)

1

2

3

1)

2)

3)

80.

Find the least common denominator of the expression

a)

18

b)

6x

c)

3xy

d)

6xy

81.

Which expressions are equivalent to $x^{\frac{3}{7}}$ ?

Choose ALL that apply!

a)

$\sqrt[7]{x^3}$

b)

$\left(x^7\right)^{\frac{1}{3}}$

c)

$\left(x^{\frac{1}{7}}\right)^3$

d)

$\left(\sqrt[7]{x}\right)^3$

e)

$\sqrt[3]{x^{\frac{1}{7}}}$

82.

Properties of Exponents

When multiplying exponential terms with the same base, the exponents (a) .

When dividing exponential terms with the same base, the exponents (b) .

When taking powers of exponential terms with the same base, the exponents (c) .

When exponential terms have a (d) exponent, it changes levels & (e) .

Choose from the below words

add

subtract

multiply

negative

signs

divide

positive

inverse

powers

83.

Use the properties of exponents to find an equivalent expression

$8^{\frac{5}{3}}$

*Choose all that apply

a)

$32$

b)

$\left(\sqrt[3]{8}\ \right)^5$

c)

$\sqrt[5]{8^3}$

d)

$\frac{1}{8^{\frac{3}{5}}}$

e)

$2^5$

84.

$\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}$ Simplify

a)

$\frac{m-5}{m-2}$

b)

$\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}$

c)

$\frac{m^2+2m-32}{m^2+14m+49}$

d)

$\frac{-5}{2m^2}$

85.

$\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}$

a)

$\frac{2}{m-64m^2}$

b)

$\frac{16m^2}{8m^2\left(m-8\right)}$

c)

$\frac{2}{64m^4\left(m-8\right)}$

d)

$\frac{2}{m-8}$

86.

$\frac{2x+3}{x+7}-\frac{x-4}{x+7}=$

a)

$1$

b)

$\frac{x-1}{x+7}$

c)

$\frac{1}{x+7}$

d)

$\frac{2x^2-5x-12}{x+7}$

87.

$\frac{x^2+10x+25}{x^2-9}\cdot\frac{x^2+3x}{x+5}=$

a)

$\frac{x\left(x+5\right)}{x+3}$

b)

$\frac{x\left(x-5\right)}{x-3}$

c)

$\frac{x\left(x+5\right)}{x-3}$

d)

$\frac{x\left(x-5\right)}{x+3}$

88.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

89.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function becomes the domain of its inverse.

d)

The domain of a function becomes the range of its inverse.

90.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

91.

Given $f\left(x\right)=-\frac{1}{2}\ \sqrt[]{x-4}+2$ .

Find an equation for $f^{-1}\left(x\right)$ , the inverse of f (x).

Solve for y.

y = ?

92.

Given $y=-\frac{2}{5}x^2+4$

What is the Domain?

( (a) , (b) )

Choose from the below words

$-\infty$

$\infty$

4

-4

3

-3

\frac{5}{2}

-\frac{5}{2}

93.

Given $y=-\frac{2}{5}x^2+4$

What is the Range?

$y\le$ (a)

Choose from the below words

4

-4

3

-3

\frac{5}{2}

-\frac{5}{2}

0

-\infty

\infty

94.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

95.

Find the inverse of the function.
$f\left(x\right)=\frac{3x-15}{2}$

a)

$f^{-1}\left(x\right)=-x-5$

b)

$f^{-1}\left(x\right)=3x+5$

c)

$f^{-1}\left(x\right)=\frac{15+2x}{3}$

d)

$f^{-1}\left(x\right)=\frac{2}{3}x-\frac{19}{3}$

96.

How many minutes are in a school year, 187 days?

a)

269,280 min.

b)

16, 200 min.

c)

16, 156 min.

d)

269,000 min.

97.

This past summer our rain gauge collected 0.80 yards of rain. Express this amount in centimeters.

a)

73 cm

b)

73.2 cm

c)

74 cm

d)

73.152 cm

98.

What is the conversion for g-->mg?

a)

1 g --> 1/1000 mg

b)

1 g --> 100 mg

c)

1000 g --> 1 mg

d)

1 g --> 1000 mg

99.

How many centimeters are in an inch?

a)

2.54 inches

b)

2.54 cm

c)

12 inches

d)

10 cm

100.

You never learned dimensional analysis so you have been working at a fast food restaurant for 35.0000 years wrapping burgers. Each hour you wrap 184 burgers. You work 8 hours per day, 5 days a week. How many burgers have you wrapped? (1 year --> 52 weeks)

a)

13,395,200 burgers

b)

18,753,300 burgers

c)

40,185,600 burgers

d)

56,259,800 burgers

101.

You roof has a leak. If it leaks at a rate of 14 drops per minute, how many hours will it take to fill a 5 gallon bucket? (20 drops = 1 mL; 30 mL = 1oz; 64 oz = 1 gal) [Round answer to 2 sig figs]

a)

230 hours

b)

950 hours

c)

190 hours

d)

1900 hours

102.

A backyard pool is 15.8 feet wide, 19.2 feet long and 5.5 feet deep. What is this pool's volume in cubic meters? [1 meter = 3.28 ft] Round your final answer to 3 sig figs.

a)

1610 m³

b)

47.3 m³

c)

16,600 m³

d)

55.9 m³

103.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

104.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

105.

Is the leading coefficient positive or negative

a)

positive

b)

negative

106.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

107.

What is the minimum of this graph?

a)

2

b)

4

c)

-3

d)

-1

108.

Which graph is NOT a polynomial function?

a)

b)

c)

d)

109.

Find the correct statement about the zeros.

a)

−5 is a zero with multiplicity 1

b)

−5 is a zero with multiplicity 2

c)

−2 is a zero with multiplicity 1

d)

2 is a zero with multiplicity 2

110.

How many zeroes are shown in the graph?

a)

1

b)

2

c)

3

d)

4

111.

Select all intervals for which $f\left(x\right)=\left(x-5\right)^2\left(x+2\right)^2$ is positive.

a)

from $x=-\infty$ to $x=-2$

b)

from $x=-2$ to $x=5$

c)

from $x=5\$ to $x=\infty$

d)

none

112.

In the following polynomial, which of the x-intercepts will "bounce". $f\left(x\right)=\left(x-1\right)^4\left(x-2\right)^5\left(x-3\right)$

a)

x = 1

b)

x = 1, 2

c)

x = 1, 3

d)

x = 2, 3

e)

x = 2

113.

For the following polynomial, will the left side of the graph have an arrow pointing up, or an arrow pointing down? $f\left(x\right)=-\left(x-1\right)^4$

a)

Up

b)

Down

114.

What is the range of the function?

a)

$\left[3,\ -\infty\right)$

b)

$\left[3,\ \infty\right)$

c)

All Real Numbers

d)

[-2, 2]

115.

What is the domain of this function?

a)

All real numbers

b)

[-17, 12]

c)

$\left[-17,\ \infty\right)$

d)

[-4, 2.5]

Spring Semester Review Algebra 2

Total questions: 115

Worksheet time: 29hrs 45mins

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