Free Printable Algebra Concepts/Algebra II Concepts Review

1.

Calculate the length for each side of the triangle.

a)

AB = 3.6, BC = 4.5, AC = 4.1

b)

AB = 4.1, BC = 5.6, AC = 7.5

c)

AB = 4.5, BC = 3.6, AC = 4.1

d)

AB = 4.1, BC = 3.6, AC = 4.5

2.

What is the approximate perimeter of right triangle ABC? (round to the nearest whole number)

a)

17 units

b)

15 units

c)

14 units

d)

16 units

3.

What is the perimeter of the parallelogram? Round to the nearest hundredth if necessary.

a)

20.95 units

b)

20.94 units

c)

18.33 units

d)

18.32 units

4.

Kia walks to Jamie's house each morning. Kia and Jamie then walk together from Jamie's house to school. Each unit on the grid is 1 block.

How many blocks does Kia walk from her house to school each morning?

a)

4 blocks

b)

7 blocks

c)

9 blocks

d)

11 blocks

5.

Choose ALL the lines PARALLEL to the following line: y = 2/9x - 7

a)

y = 2/9x + 8

b)

y = 9/2x -12

c)

-2y = 9x + 8

d)

9y = 2x -18

6.

Select ALL of the lines that are PERPENDICULAR to y = 3/4x + 9

a)

y = 3/4x - 3

b)

y = -3/4x + 9

c)

y = -4/3x + 8

d)

3y = -4x + 5

e)

4y = -3x + 7

7.

What is the equation in Point-Slope form

of the line that goes through

the point (6,1) and has a slope of -3?

a)

y - 6 = -3(x - 1)

b)

y + 6 = -3(x + 1)

c)

y - 1 = -3(x - 6)

d)

y + 1 = -3(x + 3)

8.

Write the equation of a line perpendicular to the one pictured through the point (3,1) in point slope form.
(HINT: PERPENDICULAR LINES - FLIP AND SWITCH)

a)

y - 1 = 1/2 (x - 3)

b)

y + 1 = 2 (x + 3)

c)

y - 1 = - 1/2 (x - 1)

d)

y - 1 = - 2 (x - 3)

9.

Write the equation of a line parallel to y = -1/2x + 3 and that goes through the point (4, -1)

a)

y + 1 = -1/2(x - 4)

b)

y - 1 = -1/2(x + 4)

c)

y + 1 = 2(x - 4)

d)

y - 1 = 2(x + 4)

10.

Write the equation of a line perpendicular to y = 3x - 8 and that passes through the point (-3, -9)

a)

y + 9 = -1/3(x + 3)

b)

y - 9 = -1/3(x - 3)

c)

y + 9 = -3(x + 3)

d)

y - 9 = 3(x - 3)

11.

Find the Total Surface area of the cylinder.

a)

62.8m

b)

477.28 cm²

c)

235.5 cm³

d)

942 cm²

12.

What is the total surface area of the pyramid? Round to the nearest hundredth.

a)

1,024.01 square units

b)

809.54 square units

c)

1,065.54 square units

d)

1,179.02 square units

13.

Find the total surface area of the figure.

a)

353.43 $mm^2$

b)

833.67 $mm^2$

c)

176.7 $mm^2$

d)

566.76 $mm^2$

14.

Calculate the surface area.

a)

904.78 mm²

b)

452.39 mm²

c)

3,216.99 mm²

d)

3,392.92 mm²

15.

Find the volume of the Sphere

a)

78.5 m³

b)

392.5 m³

c)

523.6 m³

d)

62.8 cm³

16.

What is the volume?

a)

112 in³

b)

336 in³

c)

11.2 in³

d)

33.6 in³

17.

Find the volume of the following shape.

a)

4155.27 m³

b)

1038.82 m³

c)

804.24 m³

d)

1005.31 m³

18.

Identify the sets to which the following real number belongs. Check all that apply.

0.\overline{54}

a)

Natural Numbers

b)

Whole Numbers

c)

Integers

d)

Rational Numbers

e)

Irrational Numbers

19.

Identify the sets to which the following real number belongs. Check all that apply.

\pi

a)

Natural Numbers

b)

Whole Numbers

c)

Integers

d)

Rational Numbers

e)

Irrational Numbers

20.

Identify the sets to which the following real number belongs. Check all that apply.

630

a)

Natural Numbers

b)

Whole Numbers

c)

Integers

d)

Rational Numbers

e)

Irrational Numbers

21.

Classify the Number: -23

a)

Rational

b)

Real, rational, integer

c)

integer

d)

Real, irrational, whole

22.

Classify √35.

a)

Rational, Integer

b)

Whole, Integer, Rational

c)

Irrational, Integer

d)

Irrational

23.

Jason runs at a pace of 7 miles per hour and his friend runs at a pace represented by the equation y = 6x where y is distance in miles and x is time in hours. Who runs faster?

a)

Jason because he runs at a pace of 6 miles per hour.

b)

His friend because he runs at a pace of 6 miles per hour.

c)

Jason because he runs at a pace of 7 miles per hour.

d)

His friend because he runs at a pace of 7 miles per hour.

24.

The weight of Brandi's luggage is represented by the equation y = 40x, where y represents the weight in lbs and x represents the number of bags. The weight of Javier's luggage is represented in the graph. Compare their rates.

a)

Brandi's luggage weighs more because it weighs 40 lbs per bag.

b)

Javier's luggage weighs more because it weighs 40lbs per bag.

c)

Brandi's luggage weighs more because it weighs 30 lbs per bag.

d)

Javier's luggage weighs more because it weighs 30 lbs per bag.

25.

Who has the greater rate of change?

a)

CJ has a greater rate of change with 13/2

b)

Holland has a greater rate of change with 6

c)

CJ has a greater rate of change with 2/13

d)

They have the same rate of change.

26.

Tom is deciding between two cars based upon the gas consumption. He wants to get the car that gets more miles per gallon.
Car A traveled 90 miles using 5 gallons of gas. Car B traveled 168 miles using 8 gallons of gas. How many mpg does car A get? How many mpg does Car B get? Which car should Tom buy?

a)

Car A 21 mpg, Car B 18 mpg, Car B

b)

Car A 16 mpg, Car B 21 mpg. Car A

c)

Car A 18 mpg, Car B 21 mpg, Car A

d)

Car A 18 mpg, Car B 21 mpg Car B

27.

Lacey bought a new purse that originally cost $25 and is on sale for $15. Find the percent of change in the price in the purse.

a)

Decrease of 40%

b)

Decrease of 10%

c)

Decrease of 30%

d)

Decrease of 20%

28.

60 miles per hour into meters per second

a)

28.6 meters per second

b)

28.6 meters per minute

c)

26.8 meters per second

d)

26.8 meters per minute

29.

How many pounds are in 3 kilograms? (1 kg = 2.20lbs)

a)

6.60 lbs

b)

5.50 lbs

c)

4.40 lbs

d)

3.30 lbs

e)

2.20 lbs

30.

How many grams are in 2.5 pounds? (1 lb = 454 g)

a)

1100 g

b)

1115 g

c)

1135 g

d)

1150 g

e)

1175 g

31.

Solve:

a)

-9

b)

-28

c)

9

d)

4

32.

Solve for k

a)

165

b)

17

c)

1/17

d)

1/165

33.

Solve:

a)

18

b)

3

c)

4

d)

6

34.

Solve for b

a)

8

b)

17/12

c)

4/3

d)

1/8

35.

A person ate 2400 calories in a day. Of these, 36% came from fat. How many calories came from fat?

a)

984

b)

830

c)

1142

d)

864

36.

Ms. Hensley's family owns a green bean farm. If Ms. Hensley can grow 225 bushels in 3 acres, how many bushels can she grow in 9.6 acres?

a)

720 bushels

b)

675 bushels

c)

75 bushels

37.

6 of the 16 students in Mrs. Crew's class were serving detention. What is the percent of students serving detention?

a)

16%

b)

60%

c)

37.5%

d)

62.5%

38.

Thomas is trying to determine the average height of high school male students. Because he is on the basketball team, he uses the heights of the 14 players on the team, which are given below in inches.

69, 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77, 82 Calculate the mean

a)

74.6

b)

1044

c)

6.5

d)

74.1

39.

Thomas is trying to determine the average height of high school male students. Because he is on the basketball team, he uses the heights of the 14 players on the team, which are given below in inches.

69, 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77, 82

Calculate the median

a)

74.5

b)

6.5

c)

74.6

d)

74, 76

40.

Thomas is trying to determine the average height of high school male students. Because he is on the basketball team, he uses the heights of the 14 players on the team, which are given below in inches.

69, 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77, 82

Calculate the mode

a)

74, 76

b)

74.5

c)

74.6

d)

6.5

41.

Thomas is trying to determine the average height of high school male students. Because he is on the basketball team, he uses the heights of the 14 players on the team, which are given below in inches.

69, 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77, 82 Calculate the range

a)

13

b)

6.5

c)

74.6

d)

74, 76

42.

The histogram shown summarizes the responses of 100 people when asked, “What was the price of the last meal you purchased?” Based on the histogram, which of the following could be the interquartile range of the prices?

a)

40

b)

21

c)

10

d)

5

e)

3

43.

How many data points fall between 110 and 160 if there are 280 data points total?

a)

280

b)

140

c)

40

d)

200

44.

What is the median of the data?

a)

200

b)

100

c)

90

d)

140

45.

The box and whisker plots below, illustrate the scores earned by 2 biology classes on a recent test.

Select all statements that are supported by the plots above.

a)

The range of the 3^rd period scores is less than the range of the 5^th period scores.

b)

The median of the 5^th period scores is greater than the median of the 3^rd period scores.

c)

The number of students who took the test is larger in the 5^th period class than in the 3^rd period class.

d)

The interquartile range is the same for both classes.

e)

The 3^rd period class has a higher median but has a lower range than the 5^th period class.

46.

The data below shows the scores of two groups of ten students on a math quiz and a science quiz.

Math: 72, 92, 88, 67, 54, 58, 64, 76, 65, 72

Science: 84, 78, 56, 89, 54, 68, 75, 78, 84, 60

Based on the data, which statements are true?

a)

The median score was greater for math, but the variability was greater for science.

b)

The median score was greater for science, but the variability was greater for math.

c)

Both the median score and variability for the math scores are less than that of the science scores.

d)

Both the median score and variability of the math scores are greater than that of the science scores.

e)

The range for science is less than the range for math.

47.

The ages of the starting players of two soccer teams are shown below.

Tarrasques: 16, 18, 15, 14, 17, 17, 18, 16, 17, 14, 17

Dragons: 18, 14, 17, 15, 15, 14, 16, 18, 16, 18, 16

Based on this data, select all the true statements below.

a)

The median of ages on the Tarrasques team is greater than the median of ages on the Dragons team.

b)

The mean of the ages on the Tarrasques team is greater than the median of the ages on the Dragons team.

c)

The median of ages on the Tarrasques team is one greater than the range of ages on the Dragons team.

d)

The mean of the ages on the Tarrasques team is less than the mean of the ages on the Dragons team.

e)

The mean of the ages on the Tarrasques team is greater than the mean of the ages on the Dragons team.

48.

Find the median, first quartile, third quartile, and interquartile range of the data.

32, 53, 72, 66, 47, 54, 49, 67, 71

a)

Median: 54

First Quartile: 49

Third Quartile: 67

IQR: 18

b)

Median: 54

First Quartile: 48

Third Quartile: 69

IQR: 21

c)

Median: 54

First Quartile: 48

Third Quartile: 69

IQR: 22

d)

Median: 54

First Quartile: 49

Third Quartile: 69

IQR: 20

49.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

50.

Solve for d. Simplify your answer.

$\frac{7}{6}d+\frac{3}{4}=-\frac{1}{3}$

a)

$\frac{5}{14}$

b)

$\frac{-13}{14}$

c)

$-1\ \frac{1}{14}$

d)

$1\ \frac{9}{14}$

51.

Solve for x.

a)

2

b)

18/5

c)

26/5

d)

6

52.

Solve!

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

53.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

54.

Solve the equation for x: $\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

55.

What is the probability of the spinner landing on an odd number?

a)

4/8

b)

4/4

c)

1/4

d)

1/3

56.

The two spinners above are spun. What is the probability of getting a perfect square (1,4,9,16), then the letter Z?

a)

3/20

b)

9/20

c)

1/8

d)

11/40

57.

A basket contains four apples and six peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. What is the probability that both pieces of fruit are apples.

a)

2/15

b)

3/17

c)

1/19

d)

6/21

58.

How many ways ways can you arrange 13 people who are waiting in line?

a)

6,227,020,800

b)

13

c)

91

59.

There are 6 meats and 10 veggies available to make a sandwich. How many sandwiches have 3 meats and 5 veggies?

a)

5,020

b)

5,030

c)

5,040

d)

5,050

60.

Welcome to the thrilling game of Deal or No Deal! Isla is in the hot seat, and these are the dollar amounts still in play:

$1,000,000.00

$300,000.00

$50,000.00

$1000.00

$1

The banker has just made an offer of $195,000.00. Based on expected value alone, should Isla take the offer?

a)

No, the expected value is higher, $270,200.20

b)

Yes, the expected value is lower, $170,200.20

c)

No, the expected value is higher, $470,200.20

d)

Yes, the expected value is lower, $190,200.20

61.

Solve

a)

A.

b)

B.

c)

C.

d)

D.

62.

What is the solution of the given equations?

$y=\frac{3}{2}x-12\ \ \ and\ \ \ 2x-y=28$

(a)

Choose from the below words

(32, 36)

(-17, 34)

(36, 32)

63.

What is the y value of the given equations?

$2x+y=4\ \ \ and\ \ \ \ y=4x+1$

(a)

Choose from the below words

3

13

64.

What is the solution to the given equations?

$y=\frac{1}{4}x-8\ \ \ and\ \ \ \ y=-\frac{1}{2}x-5$

a)

$\left(4,\ 7\right)$

b)

$\left(\frac{1}{4},\ \frac{1}{2}\right)$

c)

$\left(-5,\ 16\right)$

d)

$\left(4,\ -7\right)$

65.

m - 7 + 5m = 11

a)

m = 6

b)

m = -2

c)

m = 4

d)

m = 3

66.

-10(2m + 1) = - 50

a)

m = -7

b)

m = 20

c)

m = 5

d)

m = 2

67.

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

68.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

69.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

70.

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)

71.

Find the domain and range of the INVERSE of the following function

a)

Domain: {-2, -1, 1, 8}

Range: {2, 3, 5}

b)

Domain: {2, 3, 5}

Range: {-2, -1, 1, 8}

c)

Domain: {-1, 8, 1, -2}

Range: {3, 2, 3, 5}

d)

Domain: {3, 2, 3, 5}

Range {-1, 8, 1, -2}

72.

If this is the table for f(x), what is the correct table for f^-1(x)?

a)

b)

c)

d)

73.

$h\left(x\right)=-\frac{2}{x-1}-3$
Find the inverse of the function.

a)

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

b)

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

c)

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

d)

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

74.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

75.

Solve for k.
2k - 9≤ -19

a)

k ≤ -5

b)

k ≤ 5

c)

k < -5

d)

k < 5

76.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, -10)

c)

(-1, 5)

d)

(5, 20)

77.

Which of the following equations match the given graph?

a)

$y\le-\frac{5}{4}x+3$

b)

$y\ge-\frac{5}{4}x+3$

c)

$y<-\frac{4}{5}x+3$

d)

$y>-\frac{5}{4}x+3$

78.

a)

y ≤ 2x - 4

b)

y ≥ 2x - 4

c)

y < 2x - 4

d)

y > 2x - 4

79.

What is the DOMAIN of this linear function?

a)

$\left[-6,\ 6\right]$

b)

$\left[0,\ 6\right]$

c)

$\left(-\infty,\ \infty\right)$

d)

No Solution

80.

What is the RANGE of this linear function?

a)

-6 ≤ y ≤ 6

b)

0 ≤ y ≤ 6

c)

2 ≤ y ≤ 8

d)

4 ≤ y ≤ 3

81.

What is the DOMAIN of the function graphed on the grid?

a)

-4 ≤ x < 5

b)

-4 ≤ x ≤ 5

c)

-3 ≤ x < 3

d)

-3 < x ≤ 3

82.

What is the RANGE?

a)

$\left(-\infty,\ 6\right]$

b)

$\left[-10,\ 6\right]$

c)

$\left[-10,\ \infty\right)$

d)

$\left(-\infty,\ \infty\right)$

83.

What is the x-intercept?

a)

12

b)

-3

c)

8

d)

0

84.

What is the y-intercept?

a)

12

b)

-3

c)

8

d)

0

85.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

86.

What is the maximum value?

a)

5

b)

0

c)

-5

d)

2

87.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

88.

Where is this graph increasing or decreasing?

a)

Increasing: $\left(-7,\ -3\right)$

Decreasing: $\left(-7,\ 2\right)$

b)

Increasing: $\left(0,\ 2\right)$

Decreasing: $\left(-3,\ 0\right)$

c)

Increasing: $\left(-3,\ 0\right)$

Decreasing: $\left(0,\ 2\right)$

d)

Increasing: $\left(-7,\ 2\right)$

Decreasing: $\left(-7,\ -3\right)$

89.

Label the transformations that a, b, c, & d represent in a function.

a)Vertical Stretch/Shrink

b)Vertical Shift

c)Horizontal Stretch/Shrink

d)Horizontal Shift

1

2

3

4

1)

2)

3)

4)

90.

What are the following transformations?

g(x) = - (x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

91.

What are the following transformations:
g(x) = f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

92.

If the blue is y=x^2,the red must be

a)

y=(x+3)²

b)

y=(x-3)²

c)

y=x²+3

d)

y=x²-2

93.

Even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

94.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

95.

The red graph shows the graph of y=f(x)

Identify the blue graph...

a)

y = f(x - 3)

b)

y = f(x) - 3

c)

y = f(x + 3)

d)

y = f(x) + 3

96.

The red graph shows the graph of y=f(x)

Identify the blue graph...

a)

y = f(-x)

b)

y = -f(x)

c)

y = f(x - 1)

d)

y = f(x) - 1

97.

Solve the following quadratic...

x² - 16 = 0

a)

x = -2, 8

b)

x = 2, -8

c)

x = 4, -4

d)

x = -1, -16

98.

Solve the following quadratic...

x² + 12x + 20 = 0

a)

x = 5, 4

b)

x = 2, 10

c)

x = -5, -4

d)

x = -2, -10

99.

What are the solutions to
v² + 6v + 5 = 0

a)

(1,0) and (0,0)

b)

(5, 0) and (-7, 0)

c)

(-5, 0) and (-1, 0)

d)

(6,0) and (0,0)

100.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

101.

Find the zeros of the following quadratic function.

$f\left(x\right)\ =\ x^2\ -\ x\ -30$

a)

{x = -5, 6}

b)

{x = -6, 5}

c)

{x = -3, 10}

d)

{x = -10, 3}

102.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

103.

$x^2+5x\ +8\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-5\pm\sqrt{57}}{2}$

b)

$\frac{5\pm\sqrt{57}}{2}$

c)

$\frac{-5\pm i\sqrt{7}}{2}$

d)

$\frac{5\pm i\sqrt{7}}{2}$

104.

$x^2-6x\ +12\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$3\pm i\sqrt{3}$

b)

$3\pm\ \sqrt{3}$

c)

$\frac{6\pm\sqrt{-12}}{2}$

d)

$3\pm i$

105.

Convert to vertex form:

y = x² - 14x + 36

a)

y = (x + 7)² + 13

b)

y = (x - 7)² - 13

c)

y = (x - 7)² + 13

d)

y = (x + 7)² - 13

106.

What transformations have occurred in the function: $f\left(x\right)=-3\left(x-1\right)^2+6$

a)

Reflection across the x-axis; Vertical stretch of 3; Right 1; Up 6

b)

Horizontal compression of 3; Left 1; Down 6

c)

Horizontal stretch of 1; Reflection across the x-axis; Up 6

d)

Reflection across the x-axis; Vertical stretch of 3; Left 1; Up 6

107.

Which graph has factors of (x+1) and (x-3) ?

a)

b)

c)

d)

108.

Given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

109.

What is vertex of the quadratic function x²+4x-21?

a)

(4, -21)

b)

(-2,-25)

c)

(2, -21)

d)

(4, -25)

110.

What are the zeros of x²+9x+14

a)

2, 7

b)

-2, -7

c)

2, -7

d)

-2, 7

111.

Select the transformations of the following equation

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

(select all that apply)

a)

vertical compression

b)

Reflects across x-axis

c)

Shifts right 2 units

d)

Shifts left 2 units

112.

What are the increasing and decreasing intervals for the function: $g\left(x\right)=-2\left(x-3\right)^2+1$ ?

a)

Increasing: (−∞, 3)

Decreasing: (3, ∞)

b)

Increasing: (−∞, 1)

Decreasing: (1, ∞)

c)

Increasing: (2, ∞)

Decreasing: (-∞, 2)

d)

Increasing: (1, ∞)

Decreasing: (-∞, 1)

113.

How many real and imaginary solutions does this graph have?

a)

one real solution

no imaginary solutions

b)

two real solutions

c)

two imaginary solutions

d)

one real solution

one imaginary solution

114.

How many real and imaginary solutions does the quadratic have?

a)

Two imaginary solutions

b)

One real solution

One imaginary solution

c)

Two real solutions

d)

One real solution

No imaginary solutions

115.

What is the domain and range in this graph?

a)

D: (-∞, ∞)

R: (-1, ∞)

b)

D: (-4, 2)

R: (-1, ∞)

c)

D: (-∞, ∞)

R: (-∞, ∞)

d)

D: (-4, 2)

R: (-2.5, 2.5)

116.

Even or Odd degree?

a)

even

b)

odd

117.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

118.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

119.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

120.

Determine the end behavior of the graph.

a)

As x→ -∞, y→ -∞
As x→ +∞, y→ +∞

b)

As x→ -∞, y→ -∞
As x→ +∞, y→ -∞

c)

As x→ -∞, y→ +∞
As x→ +∞, y→ +∞

d)

As x→ -∞, y→ +∞
As x→ +∞, y→ -∞

121.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

122.

Identify the zeros

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

123.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

124.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

125.

10n²+100n+250

a)

10(n+5)²

b)

10(n-5)²

c)

10(n+5)(n-5)

d)

(5n+10)²

126.

Write 4x³+2x²-6x in factored form.

a)

2x(2x-3)(x+1)

b)

4x(2x+3)(x-1)

c)

2x(2x+3)(x-1)

d)

4x(2x-3)(x+1)

127.

Divide 3x^2 + 7x + 2 by x + 2.

a)

3x + 3

b)

3x - 1

c)

3x + 1

d)

3x - 3

128.

Find all factors of the polynomial x⁴ - 12x³ + 49x² - 78x + 40 by long division.

a)

(x-1)(x-2)(x-4)(x-5)

b)

(x+1)(x-2)(x-4)(x-5)

c)

(x-1)(x-2)(x+4)(x-5)

d)

(x-1)(x-2)(x-4)(x+5)

129.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

130.

Identify the missing term to complete the solution.

a)

4

b)

-4

c)

5

d)

-5

131.

Use the remainder theorem to find the value of p(c):

p(x) = 4x³ + 3x + 38, c = -2.

a)

p(-2) = 0 so

4x³ + 3x + 38 =

(x + 2)(4x³ - 8x + 19)

b)

p(-2) = 0 so

4x³ + 3x + 38 =

(x - 2)(4x³ - 8x + 19)

c)

p(-2) = 48

d)

p(-2) = 60

132.

Find the following using the Remainder Theorem for:

$f(x)=2x^4+6x^3-5x^2-60$

$f\left(-1\right)$

133.

Find the y intercept for $\frac{x^2-5x+6}{x^2-4x+3}$

a)

(0, 1) and (0, 3)

b)

(0, 2)

c)

(0, 3)

d)

(0, 6)

134.

What is the equation for the horizontal asymptote?

a)

y=1

b)

y=2

c)

x=1

d)

x=2

135.

What is the vertical asymptote?

a)

y=6

b)

y=-6

c)

x=2

d)

x=-2

136.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

137.

What are the decreasing intervals of this function?

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,3\right)U\left(3,\infty\right)$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,3\right)\left(4,\infty\right)$

138.

Consider the function:

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

Does the function have any holes?

a)

yes, when $x=3$

b)

yes, when $x=0$

c)

yes, when $x=-2$

d)

The function does not have any holes.

139.

Consider the function

$y=\frac{3x-12}{x^2-2x-8}$

When $x=4,$ the function has a . . .

a)

Hole

b)

Vertical Asymptote

c)

Neither

140.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

141.

a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

142.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

143.

Solve for w:
$\frac{4}{w-2}=\frac{-1}{w+3}$

a)

2

b)

-2

c)

4

d)

-4

144.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

145.

Solve for x: $\frac{5}{x+2}=\frac{1}{x-4}$

a)

x = 5

b)

x = 4

c)

x = $\frac{11}{2}$

d)

x = -4

146.

Solve for x: $\frac{8}{x+3}=\frac{3}{x-5}$

a)

x = 49/5

b)

x = -5

c)

x = -49/5

d)

x = 5

Algebra Concepts/Algebra II Concepts Review

Total questions: 146

Worksheet time: 8hrs 47mins

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