Free Printable Q2 Algebra Final Study Guide

1.

|6 - 3i| =

a)

3

b)

3√3

c)

3√5

d)

9

e)

45

2.

The axis of symmetry for f(x) = $x^2-2x+3$

a)

-2

b)

-1

c)

1

d)

2

e)

1/2

3.

If f(x) = 4x + 1 and g(x) = $x^2$ - 3x + 1 , then (f+g)(-2) =

a)

-8

b)

-7

c)

8

d)

3

e)

4

4.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

5.

Convert the equation to slope-intercept form:
2x - 4y = 16

a)

y = 1/2 x + 4

b)

y = 1/2 x - 4

c)

y = -1/2 x - 4

d)

y = -1/2 x + 4

6.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

7.

Select the graph for y ≥ -3.

a)

A

b)

B

c)

C

d)

D

8.

Select the graph for 5x+ y ≤ -1 .

a)

A

b)

B

c)

C

d)

D

9.

What is the slope intercept form of the equation
12x-4y=-20

a)

y=12x-20

b)

y=3x+5

c)

y=-3x-5

d)

y=20y-12x

10.

Which of the following graphs represents the equation $y=-\frac{3}{4}x-2$ ?

a)

b)

c)

d)

11.

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)

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

12.

15 + 7x ≥ 29

a)

x ≥ 2

b)

x ≥ -2

c)

x ≤ 2

d)

x > 2

13.

Solve.
|y - 4| ≥ 8

a)

y ≤ -4 or y ≥ 12

b)

-4 ≤ y ≤ -12

c)

y ≤ 4 or y ≥ -12

d)

-12 ≤ x ≤ 4

14.

Solve. Select BOTH solutions.
$5\left|7+x\right|+2=17$

a)

$-10$

b)

$3$

c)

$4$

d)

$-4$

15.

|−2n| + 10 = −50

a)

{30, -30}

b)

{20,-20}

c)

{-5,5}

d)

No Solution

16.

Which graph matches the function:
y = -2|x - 3| + 5

a)

A

b)

B

c)

C

d)

D

17.

y=|x+1|−4

a)

A

b)

B

c)

C

d)

y=D

18.

Solve the system of equations.
x + 5y = -27
-2x - 5y = 24

a)

(3, 6)

b)

(-3, -6)

c)

(-3, -4)

d)

(3, -6)

19.

A line passes through points (-3, 1) and (2, -3). What is the slope of the line perpendicular to that line?

a)

$m=\frac{5}{4}$

b)

$m=-\frac{4}{5}$

c)

$m=5$

d)

$m=-4$

20.

Which statement best describes the relationship between the equations of the lines?

$y=\frac{1}{3}x-2$

$3x+y=9$

a)

The equations represent parallel lines.

b)

The equations represent perpendicular lines.

c)

The equations represent the same line.

d)

The relationship between the lines cannot be determined.

21.

(2 + 1) + 9 = (1 + 2) + 9

a)

Transitive Property

b)

Commutative Property

c)

Associative Property

d)

Distributive Property

22.

When f(x) = 2x and g(x) = x²+3

Find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

23.

When f(x) = 4x+8 and g(x) = x+3
Find $f\left(x\right)\cdot g\left(x\right)$

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

24.

When f(x) = 3x² + 7x and g(x) = 2x² - x - 1

Find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

25.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

26.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

27.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

28.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

29.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

30.

Perform the indicated operation

a)

b)

c)

d)

e)

not possible

31.

a)

b)

c)

d)

32.

What is the value of element a₂₃?

a)

2

b)

-1

c)

6

d)

1

33.

These matrices are being multiplied. Determine the dimension/size of the new matrix.

a)

Can't multiply them

b)

4 x 2

c)

3 x 3

d)

4 x 3

34.

Given the matrix $A = \begin{bmatrix} 1 & 3 \ -1 & 4 \end{bmatrix}$ , find $A^{-1}$ .

a)

$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

b)

$\begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}$

c)

$\begin{bmatrix} 1 & 3 \ -1 & 4 \end{bmatrix}$

d)

$\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$

e)

none of these

35.

Multiply

a)

b)

c)

d)

36.

Find the inverse of the matrix.

a)

b)

c)

d)

No Inverse Exists

37.

Find the determinant of the matrix

a)

A

b)

B

c)

C

d)

D

38.

Evaluate the determinant of the matrix.

a)

68

b)

-49

c)

-83

d)

-75

39.

Solve the system.

a)

(3, -5, -2)

b)

(-4, 1, 3)

c)

(3, 5, 8)

d)

(4, 5, 2)

40.

Rob bought 15 concert tickets worth $322.50. Floor tickets cost $25.00 each while balcony tickets cost $17.50 each. How many tickets of each type did Rob buy?

a)

7 floor tickets, 8 balcony tickets

b)

8 floor tickets, 7 balcony tickets

c)

9 floor tickets, 6 balcony tickets

d)

10 floor tickets, 5 balcony tickets

41.

4x + 8y = 20
−4x + 2y = −30

a)

(-1, 7)

b)

(-7, 1)

c)

(7, -1)

d)

(1, -7)

42.

Solve the system of equations by substitution.

a)

(-6, 10)

b)

(-2, 10)

c)

(-2, 7)

d)

(-6, 8)

43.

Solve the system using matrices
x + 2y = 2
5x - 6y = - 54

a)

(-6, 4)

b)

(-8, 4)

c)

(8, 4)

d)

(6, 4)

44.

Does this graph in the back have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

45.

If 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)

46.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

47.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

48.

The minimum of a quadratic function is

a)

The lowest point (vertex) on a graph when a parabola opens up; the point where the graph changes from decreasing to increasing

b)

The highest point (vertex) on a graph when a parabola opens down; the point where the graph changes from increasing to decreasing

49.

The maximum of a quadratic function is

a)

The highest point (vertex) on a graph when a parabola opens down; the point where the graph changes from increasing to decreasing

b)

The lowest point (vertex) on a graph when a parabola opens up; the point where the graph changes from decreasing to increasing

50.

What is the orange line called?

a)

Line of Solutions

b)

Roots

c)

Vertex

d)

Axis of Symmetry

51.

The graph of a quadratic function is called a

a)

line

b)

parabola

c)

half oval

d)

vertex form

52.

If the vertex of this graph is (2, -1), what is the axis of symmetry?

a)

x= -1

b)

x = 2

c)

y = -1

d)

x = -2

53.

Does the quadratic have a max/min vertex, and does the parabola open up/down?

a)

max/ opens down

b)

min/ opens up

c)

max/ opens up

d)

min/ opens down

54.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

55.

What is the name of this form:
y = a(x - h)² + k

a)

vertex form

b)

standard form

c)

factored form

d)

zero form

56.

What is the name of this form:
y = ax² + bx + c

a)

vertex form

b)

standard form

c)

factored form

d)

zero form

57.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

58.

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

59.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

60.

What is the domain of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ 0

d)

x ≥ 0

61.

What is the range of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ -1

d)

x ≥ 0

62.

What is the domain and the range for the graph?

a)

Domain : -2 ≤ x ≤ 2
Range : 0 ≤ y ≤ 4

b)

Domain : 0 ≤ x ≤ 4
Range : -2 ≤ y ≤ 2

c)

Domain : All real #s
Range : y ≤ 4

d)

Domain : -2 ≤ x ≤ 2
Range : y ≤ 4

63.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

64.

What is the domain and the range for the graph?

a)

Domain : -2 ≤ x ≤ 2
Range : 0 ≤ y ≤ 4

b)

Domain : 0 ≤ x ≤ 4
Range : -2 ≤ y ≤ 2

c)

Domain : All real #s
Range : y ≤ 4

d)

Domain : -2 ≤ x ≤ 2
Range : y ≤ 4

65.

If 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)

66.

Solve by factoring: x² =7x +18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

e)

none of these

67.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

68.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

69.

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

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

70.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

71.

Simplify: i³¹

a)

i

b)

-i

c)

1

d)

-1

72.

Simplify: i⁷²

a)

i

b)

-i

c)

1

d)

-1

73.

Simplify: (8 + 2i) + ( -2 - 3i)

a)

10 - i

b)

10 + 5i

c)

6 + 5i

d)

6 - i

74.

Write in standard form: (5 + 3i)(5 - 3i)

a)

34

b)

16

c)

25 - 30i + i²

d)

24 - 30i

75.

a)

A

b)

B

c)

C

d)

D

76.

a)

A

b)

B

c)

C

d)

D

77.

Where is point C located?

a)

2 + i

b)

-3

c)

2i

d)

-1 - i

78.

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg.
What are the constraints?

a)

x≤10, y≤3, x+y≤12

b)

0≤x≤10, 0≤y≤3, x+y≤12

c)

x≥0, y≥0, 10x+3y≤12

d)

x≤10, y≤3, 10x+3y≤12

79.

What do you call the area where all the shading overlaps?

a)

the answer

b)

the feasible region

c)

the void

d)

the objective function

80.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y . What combination of soybeans and corn will maximize profit?

a)

4 acres of soybeans and 2 acres of corn

b)

6 acres of soybeans and 0 acres of corn

c)

3 acres of soybeans and 3 acres of corn

d)

0 acres of soybeans and 5 acres of corn

81.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

82.

Let $a>b>0>c>d$ , which one of the following must be positive.

a)

$b^c$

b)

a+c

c)

$\frac{a}{d}$

d)

b.c

e)

none of these

83.

Given the graph f(x), f(f(5))=?

a)

0

b)

1

c)

2

d)

3

e)

4

84.

How many points of the intersection does the following system of equations have?

$y=1-x\ \$

$y=2-x^2$

a)

0

b)

1

c)

2

d)

3

e)

infinite

85.

if the lines $y_1=\left(n+1\right)x+12\ and\ y_2=\left(2n-3\right)x+2$ are parallel, then n could be equal to

a)

1

b)

2

c)

3

d)

4

e)

5

86.

Which of the following expressions is equivalent to $6x^3-5x^2y-24xy^2+20y^3$

a)

$x^2\left(6x-5y\right)-4y^2\left(6x-5y\right)$

b)

$x^2\left(6x-5y\right)+4y^2\left(6x-5y\right)$

c)

$x^2\left(6x-5y\right)-4y^2\left(6x+5y\right)$

d)

$x^2\left(6x+5y\right)-4y^2\left(6x-5y\right)$

e)

none of these

87.

Suppose the graph $f\left(x\right)=\left|x-5\right|+4\$ is translated as 3 units left and 2 units up. If the translated graph representing $g\left(x\right)$ , find $g\left(-3\right)=?$

a)

-11

b)

17

c)

1

d)

17

e)

11

88.

Which number is an irrational number?

a)

-15 / 7

b)

square root of 88

c)

square root of 25

d)

0.3333....

89.

4.56789789342984729... would classify as...

a)

whole

b)

irrational

c)

rational

d)

integer

90.

A one-airplane airline wants to determine the best mix of passengers to serve each day.

The airplane that seats 25 people has 8 flights per day. There are two types of passengers: first class (F) and coach (C). Each flight, the airline makes $15 per first class passenger and $10 per coach passenger.

The marketing objectives of the airplane owner are to carry at least 13 first class passengers and 67 coach passengers each day. In addition, in order to break even, they must at least carry a minimum of 110 total passengers each day.

a. Write a system of linear inequalities representing the constraints of the scenario. Be sure to define your variables.

b. Graph the feasible region in the -coordinate plane.

c. Determine the number of first class and coach passengers that will maximize profit.

4 lines

Q2 Algebra Final Study Guide

Total questions: 90

Worksheet time: 6hrs 46mins

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