Free Printable fa 24 adv alg 2 REVIEW final

1.

Name ALL the number set to which the following number belongs.

-√4

a)

natural, whole, integer, rational, real

b)

whole, integer, rational, real

c)

integer, rational, real

d)

rational, real

e)

irrational, real

2.

What value is equivalent to this expression?

$20-7\times2+\left(12\div3\right)$

a)

$78$

b)

$30$

c)

$10$

d)

$3$

3.

Simplify the expression according to the order of operations.
2×3−(14÷7+2)²+5=

a)

-5

b)

-75

c)

49

d)

-1

4.

10. Simplify.

\frac{9+3•6}{9÷3+6}

a)

3

b)

8

c)

72

d)

27

5.

Evaluate if x=2 and y=3
$\left(x+y\right)^3\div5\left(2\right)-30\ \div x$

a)

5

b)

4

c)

-5

d)

-4

6.

$5\left(2x\ +\ 6\right)\ =\ -4\left(-5\ -2x\right)+\ 3x$

a)

$x\ =-20$

b)

$x\ =\ 20$

c)

$x\ =-10$

d)

$x\ =\ 10$

7.

Solve for x :

\frac{2\left(x+4\right)}{-3}=-14

a)

x = 19

b)

x = 17

c)

x = -17

d)

x = -19

8.

Solve the equation:
4 - 6x - 2= -2(3x-1)

a)

no solution

b)

infinitely many solutions

c)

x = ⅓

d)

x = 4

9.

The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches, find the dimensions of the rectangle.

a)

9 in by 12 in

b)

3 in by 14 in

c)

10 in by 11 in

d)

8 in by 13 in

10.

The larger of 2 numbers is 5 less than triple the smaller number

If the sum of the two numbers is 71, find the two numbers.

(a)

11.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-5,1}

c)

{-3}

d)

No Solution

12.

Which is a solution of...

5(v + 3) > 10v - 10

a)

(-∞, 5)

b)

(5, ∞)

c)

(-5, ∞)

d)

(-∞, -5)

13.

What inequality is graphed?

a)

2 < x ≤ -3

b)

2 < x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

14.

Solve the absolute Value inequality and graph.

a)

A

b)

B

c)

C

d)

D

15.

Solve the inequality.

a)

$\left(-\infty,0\right)U\left(1,\infty\right)$

b)

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

c)

$\left(-6,\infty\right)U\left(-\infty,-7\right)$

d)

$\left(-3,\ \infty\right)U\left(-\infty,-8\right]$

16.

What is the correct interval notation for the graph?

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

17.

Simplify

\sqrt{24}

a)

$4\sqrt{6}$

b)

$2\sqrt{6}$

c)

$6\sqrt{2}$

d)

$6\sqrt{4}$

18.

Simplify:

3\sqrt{125}

a)

$75\sqrt{3}$

b)

$8\sqrt{5}$

c)

$15\sqrt{5}$

d)

$15\sqrt{25}$

19.

Which of the following is a perfect square?

a)

12

b)

90

c)

40

d)

64

20.

The sum of 4 consecutive even numbers is 364. What is the sum of the middle two numbers?

a)

91

b)

92

c)

183

d)

182

21.

What is the domain?

a)

all real numbers

b)

1<x<6

c)

{1,3,4,6}

d)

{-2,2,5}

22.

What is the range?

a)

{-2,2,5}

b)

{1,3,5,6}

c)

all real numbers

d)

-2<y<5

23.

Does the given table represent a function?

a)

Function

b)

Not a Function

24.

Is this set of ordered pairs a function or not a function?

{(-4,-1), (-3,-1), (-2,-3), (-1,0), (-3,2)}

a)

Function

b)

Not a function

25.

Which graph shows a relation that is not a function?

a)

b)

c)

d)

26.

What is the domain?

a)

[-2, 3]

b)

[-2, 3)

c)

(-2, 3]

d)

[-3, 4]

e)

(-3, 4]

27.

What is the range of the graph?

a)

[-7, 5)

b)

(-3, 1]

c)

[-3, 1)

d)

(-7, 5]

28.

Given the quadratic function $f(x)=x^2-5x+2$ , evaluate $f(-1)$ .

29.

Let w(x) = 3x - 7. If w(x) = 14, find x.

30.

What is the equation below, in standard form?

y = (4/5)x +2

a)

4x - 5y = -10

b)

4x - 5y = 2

c)

4x + 5y = -10

d)

4x + 5y = 2

31.

a)

y=-4x-12

b)

y=4x+12

c)

y=-4x+12

d)

y=-4x+3

32.

Match the equation to the graph:

$y\ =\ -\frac{1}{3}x\ +\ 3$

a)

b)

c)

d)

33.

Convert to Slope-Intercept Form then match the equation to the correct graph.

$x+3y=-9$

a)

b)

c)

d)

34.

From the equation y = 3x + 18, what is the value of the x-intercept?

a)

-6

b)

6

c)

18

d)

3

35.

Find the graph of this linear equation.

6x - 4y = 24

a)

b)

c)

d)

36.

Are the equations parallel, perpendicular, or neither?

a)

Parallel

b)

Perpendicular

c)

Neither

37.

Write the equation of the line through (-4, 2) and (0, -5)

a)

y = -(7/4)x - 5

b)

y = -7x + 26

c)

y = (2/3) x - 9

d)

y = 2x - 5

38.

Write an equation in point-slope form for the line with the given slope m = 3 that contains the point (-1, -2). Then convert to slope-intercept form.

(a)

39.

A holiday meal costs $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs, including delivery, for x people?

a)

y = 12.5x + 30

b)

y = 12.5 + 30

c)

y = 12.5 + 30x

40.

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

a)

y = 1.5x + 12

b)

y = 12x + 1.5

c)

y = 0.67x - 8

d)

y = -8x + 0.67

41.

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Use the trend line to predict how many chapters would be in a book with 180 pages.

a)

12 chapters

b)

15 chapters

c)

18 chapters

d)

21 chapters

42.

Solve by graphing.
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

43.

Graph the Following:

y = 4x+3

y = -x-2

44.

Solve the system by substitution.

5x + 4y= −14
y = −7x − 15

a)

(-2, -1)

b)

(1, -2)

c)

(-2, 1)

d)

(-1, -2)

45.

Find the solution to the system below.
3x + y = 19
2x - y = 6

a)

No solution

b)

(4, 5)

c)

(5, 4)

d)

(14, 5)

46.

Which System of Equations represents one with no solution?

a)

b)

c)

d)

e)

I have no idea

47.

What is the solution to the system?

a)

(5,-3,2)

b)

(-3,5,2)

c)

no solution

d)

infinite solutions

48.

1. The cost of 5 squashes and 2 zucchinis is $1.32. Three squashes and 1 zucchini cost $0.75. Write a system of equations.

a)

5q + 2z = 1.32
1z = 0.75

b)

5q + 2z = 1.32
3q + 1z = 0.75

c)

q + z = 1.32
q + z = 0.75

d)

5q + 2z = 0.75
3q + 1z = 1.32

49.

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets in total. How many of each type of ticket were sold?

a)

10 adults, 11 children

b)

12 adults, 9 children

c)

11 adults, 10 children

d)

9 adults, 12 children

50.

Which of the following inequalities matches the given graph?

a)

y ≥ 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y≤ 2/5x + 1

d)

y ≥ -2/5x - 1

51.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, 20)

c)

(3, 5)

d)

(0, -2)

52.

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13.

a)

7x + 13y < 81

b)

7x + 13y ≥ 81

c)

7x + 13y ≤ 81

d)

7x + 13y > 81

53.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

54.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

55.

Which of the following is NOT a solution to the systems of inequalities?

a)

(0, 0)

b)

(-4, 0)

c)

(2, 2)

d)

(3, 1)

56.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

a)

x+y≤300
7.5x+5.5y≥2000

b)

x+y<300
7.5x+5.5y≥2000

c)

x+y≤300
7.5x+5.5y≤2000

d)

x+y>2000
7.5x+5.5y≤300

57.

Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming.

a)

x + y ≥ 25
x + y ≤ 8

b)

100x + 25 y ≤ 100
2x + 8y ≤ 14

c)

x + y ≥ 100
8x + 25y ≤ 14

d)

8x + 25y ≥ 100
x + y ≤ 14

58.

Pick ALL correct answers.

Which are solutions to the system?

a)

(-5,4)

b)

(-5,-2)

c)

(0,10)

d)

(5,10)

e)

(0,-5)

59.

Which system is graphed?

a)

y>-\frac{1}{4}x-3

y>2x+6

b)

$y>\frac{1}{4}x-3$
$y\le-2x+6$

c)

$y\le-2x+6$
$y<-\frac{1}{4}x-3$

d)

$y\le-2x+6$
$y>-\frac{1}{4}x-3$

60.

Are the equations parallel, perpendicular, or neither?

a)

Parallel

b)

Perpendicular

c)

Neither

61.

Simplify $\sqrt[]{-100}-2\sqrt[]{-16}$

4 lines

62.

$3\sqrt{-90}$

a)

$3i\sqrt{10}$

b)

$9i\sqrt{10}$

c)

$27i\sqrt{10}$

63.

Simplify:
(10+ 15i)-(48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

64.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

65.

i¹²⁹

a)

-i

b)

i

c)

1

d)

-1

66.

Rationalize the denominator and simplify completely.

a)

$\frac{-3-i}{4}$

b)

$\frac{3+i}{4}$

c)

$\frac{-3+i}{4}$

d)

$\frac{3-i}{4}$

67.

Find the zeros/solutions of this quadratic function from its graph. Select all that apply.

a)

-4

b)

4

c)

0

d)

2

e)

-5

68.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

69.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

70.

$3p^2-17p=30-8p$

a)

$\left\{3,5,-2\right\}$

b)

$\left\{2,-5\right\}$

c)

$\left\{-2,5\right\}$

d)

$\left\{-6,15\right\}$

71.

$3x^2-3x\ +13\ =0$

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

a)

$\frac{-3\pm7i\sqrt{3}}{6}$

b)

$\frac{3\pm7i\sqrt{3}}{6}$

c)

$\frac{-3\pm i\sqrt{163}}{6}$

d)

$\frac{3\pm i\sqrt{163}}{6}$

72.

Solve the following quadratics equation by completing the square...

x² + 6x - 3 = 0

a)

$-3\pm2\sqrt{3}$

b)

$3\pm2\sqrt{3}$

c)

$12\pm\sqrt{3}$

d)

$-12\pm\sqrt{3}$

73.

Solve using square roots.
5b² + 4 = -41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 9i, b = -9i

d)

3i, -3i

74.

Billy is 10 years older than his little brother and the product of their ages is 56. How old is Billy?

a)

28

b)

4

c)

14

d)

8

75.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

76.

Based on the table, which function can best be used to model this situation?

a)

h(t) = 99t² + 858

b)

h(t) = -4.9t² + 295t + 0.6

c)

h(t) = -4.9t² + 295t + 2

d)

h(t) = 99t² + 1,470.3

77.

Match the following imaginary variables to their equivalent form.

a)

$\sqrt[]{-1}$

1.

$i$

b)

-1

2.

$i^2$

c)

$-i$

3.

$i^3$

d)

$1$

4.

$i^4$

78.

SELECT ALL THE ANSWERS that would be expressions of an imaginary number.

a)

$-\ \sqrt[]{4}$

b)

$\sqrt[]{-4}$

c)

$\sqrt[]{-12}$

d)

$\sqrt[]{16}$

79.

Which of the following are equivalent to i⁴⁴? Select all that apply.

a)

i⁴

b)

-1

c)

i²

d)

1

80.

Which of the following is equivalent to $i^7+i^8+i^9+i^{10}$

a)

$1$

b)

$2+i$

c)

$1-i$

d)

$0$

81.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

82.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

83.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

84.

What is the discriminant and how many solutions would this quadratic have?

-3x² - 5x + 15 = 7

a)

205, 2 Solutions

b)

-71, No Solutions

c)

121, 2 Solutions

d)

121, 1 Solution

85.

Solve using the quadratic formula & simplify completely.

$2x^{2\ }-4x+7=0$

a)

$\frac{2\pm2i\sqrt{10}}{2}$

b)

$\frac{2\pm i\sqrt{10}}{2}$

c)

$\frac{4\pm\sqrt{40}}{4}$

d)

$\frac{2\pm2i\sqrt{40}}{4}$

86.

How do I find…

When an object hits the ground?

a)

Find the x-value using the axis of symmetry

b)

Find the axis of symmetry and substitute it into the equation

c)

Find the y-intercept

d)

Find the x-intercepts and choose positive value

87.

How do I find…

The time it takes to get to the highest point?

a)

Find the x-value using the axis of symmetry

b)

Find the axis of symmetry and substitute it into the equation

c)

Find the y-intercept

d)

Find the x-intercepts and choose positive value

88.

How do I find…

The highest point?

a)

Find the x-value using the axis of symmetry

b)

Find the axis of symmetry and substitute it into the equation

c)

Find the y-intercept

d)

Find the x-intercepts and choose positive value

89.

Find the quadratic equation for the relationship of the horizontal distance and the height of the ball.

a)

-18x² + 2.11x + 4.21

b)

-.06x²+1.06x + 7.9

c)

-6x²+1.06x + 79

d)

-.12x² + 2.11x + 4.22

90.

Find the height of the ball when it traveled a distance of 10 feet.

a)

12.8 ft

b)

13.3 ft

c)

11.1 ft

d)

17 ft

91.

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

a)

length = 26 yd, width = 21 yd

b)

length = 21 yd, width = 26 yd

c)

length = 21 yd, width = 16 yd

d)

length = 16 yd, width = 21 yd

92.

$x^2+4x+3=0$

a)

x = 1 and -3

b)

x = -1 and -3

c)

x = -1 and 3

d)

x = 1 and 3

93.

a)

A

b)

B

c)

C

d)

D

94.

a)

A

b)

B

c)

C

d)

D

95.

a)

A

b)

B

c)

C

d)

D

96.

a)

A

b)

B

c)

C

d)

D

97.

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

98.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

99.

y=2x²-6x+1 is in what form?

a)

Vertex Form

b)

Factored form

c)

Standard Form

d)

Cannot be determined

100.

What is the arrow pointing at? How can you use this value?

a)

The arrow is pointing at the y-intercept. The x-value is the axis of symmetry and the y-value of this point is equivalent to the maximum/minimum

b)

The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum and the y-value is the axis of symmetry

c)

The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

d)

The arrow is pointing at the vertex. The x-value is the axis of symmetry and the y-value is equivalent to the minimum/maximum

101.

Factor the quadratic trinomial: $x^2+6x$

102.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

103.

A parabola is upside-down when a is:

a)

negative

b)

positive

c)

0

d)

infinite

104.

Which point is an example of a y-intercept?

a)

(3,4)

b)

(-2,8)

c)

(0,4)

d)

(5,0)

105.

Solve by factoring
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

106.

Name the parent function.

a)

square root

b)

quadratic

c)

cubic

d)

exponential

107.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

108.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

109.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

110.

What is the name of this parent function?

a)

Quadratic Function

b)

Square Root Function

c)

Exponential Function

d)

Absolute Value Function

111.

What is the name of this parent function?

a)

Quadratic Function

b)

Linear Function

c)

Cubic Function

d)

Square Root Function

112.

Name the parent function.

a)

linear

b)

quadratic

c)

cubic

d)

logarithmic

113.

Name the parent function.

a)

cube root

b)

square root

c)

quadratic

d)

linear

114.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

115.

Describe the transformations of the following function: f(x) = |x+6| - 4

a)

Left 6, Down 4

b)

Right 6, Down 4

c)

Right 6, Up 4

d)

Left 6, Up 4

116.

Describe the transformations of the following function: f(x) = (x + 9)² - 4

a)

Right 3, Down 4

b)

Right 9, Down 4

c)

Down 4, Left 9

d)

Vertical Stretch of 3, Left 9

117.

Describe the transformation of f(x+5)

a)

Right "5" units -->

b)

Left "5" units <--

c)

Up "5" units

d)

Down "5" units

118.

Describe the transformation of f(x-5)

a)

Right "5" units -->

b)

Left "5" units <--

c)

Up "5" units

d)

Down "5" units

119.

Describe the transformation of f(x) + 5

a)

Right "5" units -->

b)

Left "5" units <--

c)

Up "5" units

d)

Down "5" units

120.

Describe the transformation of f(x) - k

a)

Right "k" units

b)

Left "k" units

c)

Up "k" units

d)

Down "k" units

121.

Name the parent function.

a)

constant

b)

quadratic

c)

linear

d)

exponential

122.

Which parent function is this?

a)

Quadratic

b)

Cubic

c)

Linear

d)

Rational

123.

Which parent function is this?

a)

Absolute Value

b)

Exponential

c)

Rational

d)

Linear

124.

Which parent function is this? f(x)=x³

a)

Linear

b)

Quadratic

c)

Cubic

d)

Rational

e)

Exponential

125.

Which parent function is this? f(x)= $\frac{1}{x}$

a)

Linear

b)

Quadratic

c)

Cubic

d)

Rational

e)

Exponential

126.

Which of the following parent functions does not have a domain

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

?

a)

b)

c)

d)

127.

Which of the following parent functions has a range of $\left(0,\infty\right)$

a)

b)

c)

d)

128.

Which of the following parent functions have a range of $\left[0,\infty\right)$ ? Select all that apply.

a)

b)

c)

d)

129.

a)

A

b)

B

c)

C

d)

D

e)

E

130.

a)

A

b)

B

c)

C

d)

D

e)

E

131.

a)

A

b)

B

c)

C

d)

D

e)

E

132.

a)

A

b)

B

c)

C

d)

D

e)

E

133.

Write an equation for the functions shown in the graph

a)

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

b)

$f\left(x\right)\ =\ \left(x\ -1\right)^3\ +\ 2$

c)

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

d)

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

134.

a)

$y=\sqrt[3]{x-2}-2$

b)

$y=3^{x-2}-2$

c)

y=3(x-2)²-2

d)

y=3|x-2|-2

135.

Where is the vertex of $y=3\left(x-26\right)^2+14$ ?

a)

(26, 14)

b)

(14, 26)

c)

(-26, 14)

d)

(3, 14)

e)

(3, 26)

fa 24 adv alg 2 REVIEW final

Total questions: 135

Worksheet time: 9hrs 5mins

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