Free Printable Algebra 2 Finale Exam

1.

Which of the following numbers is irrational? (a)

Choose from the below words

√8

¾

2

-1.325

2.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

3.

Which represents a rational number?

a)

√110

b)

√324

c)

√65

d)

√80

4.

Which property of multiplication is shown below:
1 × 83 = 83

a)

Commutative Property

b)

Associative Property

c)

Identity Property

d)

Zero Property

5.

The commutative property of multiplication states that the order of the numbers in an equation:

a)

Should go from least to greatest

b)

Doesn't change the product

c)

Should go from greatest to least

d)

Is always important

6.

Rewrite (9 x 6) x 5 using the associative property.

a)

270

b)

9 x 30

c)

9 x (6 x 5)

d)

5 x 9 + 5 x 6

7.

States that the product of the number and 1 is that number.

a)

Identity Property of Zero

b)

Identity Property of Multiplication

c)

Identity Property of Addition

d)

Multiplicative Property of Zero

8.

Which of these illustrates the associative property of multiplication?

a)

3 x (2 x 7) = (3 x 2) x 7

b)

6(3 + 1) = (6 x 3) + (6 x 1)

c)

4 x 23 = 23 x 6

d)

5 x 0 = 0

9.

a)

A

b)

B

c)

C

d)

D

10.

Find and explain the error.
5 - 3 + 2
5 - 5
0

a)

There is no error.

b)

Addition was done first and you should have subtracted first

c)

There is a subtraction error

11.

Solve the following:
-2 x (3 + 8 ÷ 4)²

a)

-16

b)

1.375

c)

4

d)

-50

12.

What is the value of the expression
x² + y² + x - y
when x = -1 and y = 3

a)

6

b)

8

c)

12

d)

16

13.

evaluate bc + 5a
when a = 3, b = 4, and c = -6

a)

9

b)

38

c)

-38

d)

-9

14.

a²-b²Evaluate if a=4 and b =-2

a)

4

b)

20

c)

-4

d)

12

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

17.

a)

A

b)

B

c)

C

d)

D

18.

$8x\ -\ 3y\ =\ 12$ (solve for y)

Looking at the equation above, what step you need to do first?

If you don't know, click on the video to rewatch example.

Write the problem on a piece of paper/ notebook to solve!

4 lines

19.

Write the following equation in slope intercept form. $4x-8y=72$

a)

$y=\frac{1}{2}x-9$

b)

$y=-4x+72$

c)

$y=-4x-9$

d)

$y=4x+9$

20.

Write the following equation in slope intercept form.

$6x-7y=-35$

a)

$y=\frac{7}{6}x-5$

b)

$y=\frac{6}{7}x+5$

c)

$y=\frac{5}{7}x\ -6$

d)

$y=-\frac{6}{7}x\ -5$

21.

IR = V

(solve for R)

Watch video for help on example!

Solve the problem on a piece of paper / notebook.

a)

R = IV

b)

R = I/V

c)

R = V/I

d)

R = V - I

22.

ax + c = R

(solve for x)

Watch video for help on example!

Solve the problem on a piece of paper / notebook.

a)

ax = R + c

b)

ax = R - c

c)

x = a(R-c)

d)

x = (R-c) / a

23.

F = (GMm) / r²

(solve for G)

Solve the problem on a piece of paper / notebook.

a)

G = (Fr²) / (Mm)

b)

G = FMmr²

c)

Fr²= GMm

d)

Fr²M²= G

24.

$K\ =\ \frac{1}{2}mv^2$ Solve the following equation for m.

Solve the problem on a piece of paper / notebook.

a)

b)

c)

d)

25.

Solve for p
$A\ =\ \frac{1}{2}pa$

a)

$A-\frac{1}{2}a\ =\ p$

b)

$\frac{2A}{a}=p$

c)

$\frac{A}{2a}=p$

d)

$2A-a\ =\ p$

26.

Solve for d
$C\ =\ \pi d$

a)

$C\ -\ \pi=d$

b)

$C\ +\ \pi=d$

c)

$\pi C=d$

d)

$\frac{C}{\pi}=d$

27.

Solve for x
l 5x l = 40

a)

x = 8 and x =-8

b)

x = 35 and x = -35

c)

Only x = 8

d)

No Solution

28.

Solve for x
l 2x−1 l = 9

a)

x = 5 and x =-4

b)

x = 5 and x = -5

c)

Only x = 5

d)

No Solution

29.

Solve for x
3 l 4w−1 l −5 = 10

a)

x = 1.5 and x =-1

b)

x = -1.5 and x = 1

c)

x =1 and x = -1

d)

No Solution

30.

Solve for x
2 lx−4l+8=18

a)

x = 9 and x =-1

b)

x = 1 and x = -9

c)

x= 4 and x = -2

d)

No Solution

31.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

32.

Solve |2x –3| + 5 =10.

a)

-1, 1

b)

-1, 4

c)

-1, -4

d)

1, 4

33.

Solve.

8 - 9|10r - 9| = -73

a)

r = 9/5, r = 0

b)

r = 0, r = 5

c)

r = 9/5, r = 1

d)

r = -63/10, r= 0

34.

6(2x -1) ≥ 3(4x + 1)

a)

All Real Numbers

b)

No Solution

c)

x ≥ 3/8

d)

x ≤ -3/8

35.

-2(5 + 6n) < 6(8 − 2n)

a)

No Solution

b)

Infinite Solutions

c)

x < 0

d)

x > 0

36.

A relation where every input yields one and only one output is called what?

a)

Relation

b)

Linear

c)

Exponential

d)

Function

37.

Which relation is NOT a function?

a)

{(1,-5), (3,1), (-5,4), (4,-2)}

b)

{(2,7), (3,7), (4,7), (5,8)}

c)

{(1,-5), (-1,6), (1,5), (6,-3)}

d)

{(3,-2), (5,-6), (7,7), (8,8)}

38.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

39.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

40.

Is this a function?

a)

Yes

b)

No

41.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

42.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

43.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

44.

If

f\left(x\right)=3x-12

, what is f(12)?

a)

-6

b)

36

c)

24

d)

4

45.

If $f\left(x\right)=-\left(\frac{3}{2}\right)x+5$ , what is $f\left(2\right)$ ?

a)

2

b)

3

c)

4

d)

5

46.

If $f\left(x\right)=-\left(\frac{3}{2}\right)x+5\$ and $f\left(x\right)=-1$ what is the value of x?

a)

2

b)

3

c)

4

d)

5

47.

Slopes of parallel lines are...

a)

opposite reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

48.

Slopes of perpendicular lines are...

a)

opposite reciprocals.

b)

opposites.

c)

identical.

d)

always 7.

49.

What slope is parallel to:
m = 3/4

a)

4/3

b)

3/4

c)

-3/4

d)

-4/3

50.

Which two lines are parallel?

I. 3y=-2x-3

II. 3y=-4-2x

III. 4y-3x=-1

a)

I and III

b)

II and III

c)

I and II

d)

None

51.

What is the x-intercept shown on the graph?

a)

(2, 0)

b)

(-2, 0)

c)

(0, 3)

d)

(3, 0)

52.

What is the y-intercept shown on the graph?

a)

(0, -2)

b)

(3, 0)

c)

(0, 3)

d)

None of these.

53.

What is the x-intercept shown on the graph?

a)

(4, -2)

b)

(0, -2)

c)

(4, 0)

d)

(0, 4)

54.

Give the y-interecept
5x + y = 5

a)

(1,0)

b)

(0,5)

c)

(5,0)

d)

(0,1)

55.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

56.

What is the y-intercept of the equation?
y = 3x - 12

a)

y = 1 or (0, 1)

b)

y = 12 or (0, 12)

c)

y = -1 or (0, -1)

d)

y = -12 or (0, -12)

57.

Write an equation

m = - 1/2 through ( -2, 4 )

a)

y = - 3/2x + 3

b)

y = 3/2x + 3

c)

y = - 1/2x + 3

d)

y = 3x - 3/2

58.

Write the equation of the line that passes through the points ( 0, - 5 ) and ( 4, 3 )

a)

y = 2x - 5

b)

y = 1/2x - 5

c)

y = 2x + 5

d)

y = 1/2x + 5

59.

Which of the following is the equation of the line that has a slope of 3 and passes through the point ( - 1, 9 )?

a)

y = - 3x + 12

b)

y = 3x + 3

c)

y = 3x + 12

d)

y = 3x - 3

60.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (1, -2)

d)

One Solution: (-2, 1)

61.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (0, 4)

d)

One Solution: (0, 6)

62.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

63.

A system of equations with one solution will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

64.

Solve using elimination.

4x + 8y = 20

-4x + 2y = -30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

65.

For the following equations, which coefficients would be easier to make opposites?

2x + 3y = 12

4x - 7y = - 54

a)

2x and 4x

b)

3y and -7y

66.

Let's multiply the top equation by -2. What would be our new equation?

2x + 3y = 12

4x - 7y = - 54

a)

4x - 6y = -24

b)

-4x - 6y = 12

c)

-4x - 6y = 24

d)

-4x - 6y = -24

67.

Your Turn:

Solve by elimination

2x + 9y = -7

6x - 3y = 9

a)

(-1, -1)

b)

(2,-1)

c)

(1,1)

d)

(1,-1)

68.

1) -4x-2y=-12
4x+8y=-24

a)

(6,-6)

b)

(-6,6)

c)

(6,6)

d)

(-6,-6)

69.

Solve the system by substitution.

5x + 4y= −14
y = −7x − 15

a)

(-2, -1)

b)

(1, -2)

c)

(-2, 1)

d)

(-1, -2)

70.

y = -2x + 18
y = 8

a)

(5, 8)

b)

(-5, 8)

c)

(2, 8)

d)

(-2, 8)

71.

Solve the following system:

-7x-2y=-13

x=2y+11

a)

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

b)

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

c)

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

d)

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

72.

1) Solve the system of linear equations.

a)

(-1, 5, 2)

b)

(1, -5, -2)

c)

no solution

d)

infinitely many solutions

73.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

74.

On the graph, which portion of the piecewise function is represented in red?

a)

x

b)

0.5x + 2.5

c)

-1

d)

0.5x + 2

75.

a)

A

b)

B

c)

C

d)

D

76.

What is the domain of the graph?

a)

1≤ x ≤ 4

b)

1 < x < 4

c)

1≤ y ≤ 4

d)

1 < y < 4

77.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

78.

What is m(-3) if:

a)

-3

b)

0.5

c)

3

d)

-3.5

79.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

80.

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

a)

maximum

b)

minimum

c)

neither

d)

both

81.

Factor x²-16

a)

(x+4)²

b)

(x-4)²

c)

(x-16)(x+16)

d)

(x-4)(x+4)

82.

Factor Completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

83.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

84.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

85.

Factor 6x²-27x

a)

(6x+1)(x+3)

b)

3x(2x-9)

c)

6x(x-9)

d)

(3x-9)(2x+3)

86.

Factor x²+ 6x + 9 and solve for x.

a)

(x+3)(x+3); x = -3

b)

(x+4)(x+5); x=-4, -5

c)

(x-3)(x-3); x=3

d)

Not factorable

87.

Simplify: $\sqrt{225}$

a)

15, -15

b)

20, -20

c)

25,- 25

d)

30, -30

88.

Simplify: $\sqrt{9}$

a)

3, -3

b)

8, .8

c)

7, .7

d)

6, -6

89.

Simplify: $\sqrt{64}$

a)

3, -3

b)

8, -8

c)

7,-7

d)

6, -6

90.

What letter usually represent imaginary number?

a)

a

b)

i

c)

j

d)

x

91.

a)

i

b)

-1

c)

1

d)

-i

92.

Your Turn!

\sqrt{-9}

a)

$\pm3$

b)

$\pm3i$

c)

$\pm9i$

d)

$\pm9$

93.

Simplify

a)

± 6

b)

± 6i

c)

± √6i

d)

± √6

94.

$x^2+81=0$

a)

$\pm\sqrt{9i}$

b)

$\pm9$

c)

$\pm9i$

d)

$\pm3i$

95.

Your Turn!

i^{22}

a)

$\sqrt{-1}$

b)

$-1$

c)

$-i$

d)

1

96.

$i^{79}$

a)

i

b)

1

c)

-1

d)

-i

97.

(-4i)(3i)(4i)

a)

24

b)

-48i

c)

48i

d)

60

98.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

99.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

100.

Factor:
x² - 10x - 24

a)

(x + 12)(x - 2)

b)

(x - 6)(x - 4)

c)

(x - 12)(x + 2)

d)

(x +6)(x - 4)

101.

What are the factors of 3x²-17x+10

a)

(x-5)(3x-2)

b)

(x+5)(3x+2)

c)

(3x-5)(x-2)

d)

(x+5)(3x-2)

102.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

103.

What are the factors of x²-8x-48

a)

(x-12)(x+4)

b)

(x+12)(x-4)

c)

(x+12)(x+4)

d)

(x-12)(x-4)

104.

Find the factors of x²-81

a)

(x-9)(x+9)

b)

(x+9)(x+9)

c)

(x-9)(x-9)

d)

Can't be factored

105.

Find the factors of 5x²+20x+20

a)

5(x+2)(x+2)

b)

5(x-2)(x-2)

c)

5(x+2)(x-2)

d)

(5x+2)(x+2)

106.

Find the factors of 4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

107.

Factor:
3x²-17x+10

a)

(x-5)(3x-2)

b)

(x+5)(3x+2)

c)

(3x-5)(x-2)

d)

(x+5)(3x-2)

108.

Factor:
4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

109.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

110.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

111.

x²-14x-51=0

a)

x= 17, -3

b)

x= -17, 3

c)

x= -17, -3

112.

3x²+9x-30=0

a)

x= 2, -5

b)

x= 5, -2

c)

x= -5, -2

113.

6x²-x-2=0

a)

x= -2/3, 1/2

b)

x= 2/3, -1/2

c)

x= -2/3, -1/2

114.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

115.

Solve by factoring:3x² + 5x + 2 = 0

a)

x = -2/3 and x = -1

b)

x = -3/2 and x = -1

c)

x = 2/3 and x = 1

d)

x = 2/3 and x = -1

116.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

117.

Solve by factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

118.

Find the value of the discriminant: 4x²-7x+8

a)

√79

b)

√-79

c)

-79

d)

-7±i√79/8

119.

Solve: (x-4)²-18 = 0

a)

x = 4 + 3√2

b)

x = 8.24, -.24

c)

x = 4 ± 3√2

d)

x = 4 ± √18

120.

The quadratic whose roots are -3 and 4.

a)

x²+x-12

b)

x²-x + 12

c)

x²+x+12

d)

x²-x-12

121.

Simplify:
(2+3i)/(5+2i)

a)

(11 + 16i)/29

b)

(16 + 11i)/29

c)

16/29

d)

(4 + 11i)/29

122.

Which equation is perpendicular to y = 2x + 5?

a)

y = -1/2x + 7

b)

y = 1/2x + 7

c)

y = 2x + 7

d)

y = -2x + 7

123.

What is the equation of the line that passes through (0,4) and (5,0)?

a)

y = -4/5x + 0

b)

y = -4/5x + 5

c)

y = -4/5x + 9

d)

y = -4/5x + 4

124.

Evaluate:
∣-6∣⋅2³ - (5-7)²

a)

32

b)

52

c)

44

d)

48

125.

What would you add to
x²-16x+___ to complete the square?

a)

4

b)

64

c)

16

d)

8

126.

What is the solution set to x² = 2x – 5?

a)

{±i}

b)

{2 ± 2i}

c)

{1 ± 2i}

d)

{1, 2}

127.

How many solutions will this system have?

a)

No solution

b)

One Solution

c)

I Don't Know

d)

Infinitely Many Solutions

128.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

129.

Solve the equation by factoring:
x²-6x+8=0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

130.

Solve the equation by factoring:
5x² - 35x + 60 = 0

a)

3, -4

b)

-3, 4

c)

3, 4

d)

-3, -4

131.

What are the solutions to the system of equations graphed below?

a)

(2, 0)

b)

(0, 4)

c)

(-2,0)

d)

(0, -4)

e)

No Solution

132.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

133.

What is the range of the function?

a)

[-1, +∞)

b)

(-1,1)

c)

[1.5, +∞)

d)

(-2, 2)

134.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

135.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

136.

f(x) = $2x^2$ + 3

g(x) = 3x - 2

f(x) - g(x) = ?

a)

$5x^2$ + 1

b)

$2x^2-3x+5$

c)

$2x^2-3x\ +\ 1$

d)

$-x^2+5$

137.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

138.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

139.

Describe the transformation of the graph y = -2(x + 5)³

a)

Shrink by 2, Reflected over y-axis, Right 5

b)

Stretch by 2, Reflected over x-axis, Left 5

c)

Stretch by 2, Reflected over x-axis, Right 5

d)

Shrink by 2, reflected over y-axis, Left 5

140.

Find f(-3) in the function
f(x) = x³ - 3x² +5x -18

a)

-87

b)

-33

c)

150

d)

-121

141.

Solve for x:
8x² + 24 = 0

a)

x = ± i √ (3)

b)

x = ± 3i

c)

x = ± √(3)

d)

x = ± 2

142.

Multiply
(4 - 9i)(7 + i)

a)

37 - 59i

b)

19 - 59i

c)

19 - 67i

d)

28 - 72i

143.

Simplify: i¹²¹

a)

i

b)

-i

c)

1

d)

-1

144.

Solve 𝑥²= 5𝑥 − 10

a)

b)

c)

d)

145.

Where is the mistake in the process of completing the square to solve x² - 8x + 4 = 0?

Step 1: x² - 8x = -4

Step 2: x² - 8x + 16 = -4 + 16

Step 3: (x + 4)² = 12

Step 4: x + 4 = ±√12

Step 5: x = -4 ±2√3

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

146.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

147.

7x+4y =12
x + 2y = -4

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

148.

-4x-2y=-12
4x+8y=-24

a)

(5,6)

b)

(6,-6)

c)

(6,-2)

d)

(4,-3)

149.

4x+8y=20
-4x+2y=-30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

150.

x-y=11
2x+y=19

a)

(10,-1)

b)

(-1,10)

c)

(3,-4)

d)

(6,7)

151.

-6x+5y=1
6x+4y=-10

a)

(1,-1)

b)

(0,-1)

c)

(1,1)

d)

(-1,-1)

152.

Solve the system:
x + 6y = 17
x - 3y = 8

a)

(5, 2)

b)

(11, 1)

c)

(1, 11)

d)

no solution

153.

5x - 4y =-16
x+ 2y = -6

a)

(-4,-1)

b)

(5,-1)

c)

(-5,-1)

d)

(4,1)

154.

7x+4y =12
x + 2y = -4

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

155.

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

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

156.

What is the solution to this system?
x = 7 - 2y
2x + y = 5

a)

(-1,4)

b)

(4,-1)

c)

(1,3)

d)

(3,1)

157.

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.
Solve:
x + y = 55
x - y = 3

a)

(26, 23)

b)

(26, 29)

c)

(29, 26)

d)

(29, 32)

158.

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

a)

20 Multiple Choice

b)

10 Multiple Choice

c)

15 Multiple Choice

d)

5 multiple choice

159.

In a pasture, there are horses and chickens. If there are a total of 28 animals and 80 legs, how many chickens and horses are there?

a)

10 horses, 18 chickens

b)

16 horses, 12 chickens

c)

12 horses, 16 chickens

d)

18 horses, 10 chickens

160.

The perimeter of a rectangle is 44. The length is 4 more than the width.
Find the dimensions of the figure

a)

8,12

b)

14,18

c)

9,13

d)

2,6

161.

Sally and John are siblings. John is one less than 3 times Sally's age. The sum of their ages is 23. How old is John, How old is Sally?

a)

15,8

b)

20,3

c)

17,6

d)

18,5

162.

Daniel and Aliyah are siblings. Daniel is one more than 3 times Aliyah's age. The difference of of their ages is 25. How old is Daniel? How old is Aliyah?

a)

37,12

b)

35,10

c)

42,17

d)

68,43

163.

5) Solve the system of linear equations.

a)

(1, 0, -1)

b)

(-2, 1, 0)

c)

no solution

d)

infinitely many solutions

164.

Find f(-3) in the function
f(x) = x³ - 3x² +5x -18

a)

-87

b)

-33

c)

150

d)

-121

165.

What is the equation of the inequality:

a)

y > - ½x - 4

b)

y > -2x - 4

c)

y ≥ - ½x - 4

d)

y > ½x - 4

166.

How is the equation shifted from its parent graph: y = x²?
y = - (x + 8)² + 12

a)

Right 8, up 12, reflected in the x axis

b)

Left 8, up 12, reflected in the x axis

c)

Right 8, down 12, reflected in the x axis

d)

Left 8, up 12

167.

Solve for x:
8x² + 24 = 0

a)

x = ± i √ (3)

b)

x = ± 3i

c)

x = ± √(3)

d)

x = ± 2

168.

What is the Greatest Common Factor of the terms listed?

49b⁵, 21b³,7b

(a)

169.

Which is the solution to the system of equations:

a)

(-1,-6)

b)

(3,-13)

c)

(4,-11)

d)

(-3,-4)

170.

Which is a true statement about the system of equations graphed below?

a)

A.The system of equations does not have a solution because

the lines do not intersect.

b)

The system of equations has one solution, although it is not

visible on the graph.

c)

The system of equations has an infinite number of solutions.

d)

None of the statements above are true.

171.

Jacobi wants to solve the system of equations below by using elimination. So far he has lined up the equations as shown:

Which of the following describes the next step Jacobi should take?

a)

Multiply each term in the 1st equation by -1

b)

Multiply each term in the 2nd equation by -2

c)

Multiply each term in the 2nd equation by 2

d)

Add the two equations together

172.

Solve the system by substitution.

y = −6x + 3
−18x − 3y = 4

a)

(−3, 8)

b)

(−8, −3)

c)

(2, −3)

d)

No Solution

173.

The solution of a system of linear equations is...

a)

the y-intercept (b)

b)

the intersection of the two equations on a graph

c)

the second equations' answers

d)

the slope (m)

174.

When you graph the exact same equation twice,

a)

you will have no solution.

b)

you will have one solution.

c)

you will have infinite solutions.

d)

you will graph a giraffe.

175.

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

176.

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

177.

3) Solve the system of linear equations.

a)

(3, 1, -5)

b)

(-3, 1, -1)

c)

no solution

d)

infinitely many solutions

178.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

179.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

180.

$3x^2-10x+1=0$

Solve using the quadratic formula. Leave your answer in exact form.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

181.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

182.

Solve by taking the square root:

x² = 49

a)

-7

b)

7

c)

-7,7

d)

49

183.

If there are no real solutions, the discriminant is

a)

zero

b)

a postive number

c)

a negative number

d)

a perfect square

184.

$b^2-4ac$ is called the . . .

a)

Square root

b)

Quadratic formula

c)

X-intercepts

d)

Discriminant

185.

Solve using the quadratic formula. $f\left(x\right)=2x^2-4x+7$

a)

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

b)

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

c)

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

d)

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

186.

Solve using the Quadratic Formula: $-x^2+4x=13$

a)

$2\pm3i$

b)

$-2\pm3i$

c)

$2\pm i\sqrt{17}$

d)

$-2\pm i\sqrt{17}$

187.

Is $\sqrt{-4}$ a real or imaginary number?

a)

real

b)

imaginary

188.

7x+4y =12
x + 2y = -4

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

189.

x + 2y = -4
x - 2y = 8

a)

(2,5)

b)

(2,-3)

c)

(2,-2)

d)

(-3,2)

190.

7x - 2y = 6
x - 2y = -6

a)

(2,4)

b)

(3,-2)

c)

(1,2)

d)

(-2,-4)

191.

x-4y = 16
5x + 4y = 8

a)

(4,-3)

b)

(-3,4)

c)

(4,3)

d)

(3,-4)

192.

5x - 2y = 6
x - 2y = -2

a)

(2,2)

b)

(2,1)

c)

(1,2)

d)

(-2,-2)

193.

x + y = 3
3x - y = 1

a)

(2,1)

b)

(-1,2)

c)

(1,2)

d)

(-2,-1)

194.

x -2y = -2
3x - 2y = 6

a)

(4,3)

b)

(-3,4)

c)

(-2,-3)

d)

(-3,-4)

195.

3x - 2y = -8
5x + 2y = -8

a)

(1,-4)

b)

(-1,-4)

c)

(-4,1)

d)

(-2,1)

196.

x - 4y = -4
x + 2y = 8

a)

(2,2)

b)

(4,2)

c)

(2,-2)

d)

(4,-2)

197.

x - 2y = 4
3x +2y = 4

a)

(-2,-1)

b)

(4,-1)

c)

(2,-1)

d)

(4,1)

198.

x - 2y = 4
2x -y = -1

a)

(-2,-3)

b)

(-3,-2)

c)

(2,3)

d)

(3,2)

199.

5x + 3y = 6
x - 3y = 12

a)

(3,3)

b)

(-3,-3)

c)

(3,-3)

d)

(3,-2)

200.

x - y = -2
y = -2

a)

(1,-2)

b)

(-1,-2)

c)

(-4,-2)

d)

(4,-2)

201.

2x - 3y = 6
7x - 3y = -9

a)

(3,4)

b)

(4,-3)

c)

(-4,-3)

d)

(-3,-4)

202.

3x + y = 4
x + 2y = -2

a)

(2,2)

b)

(-2,-2)

c)

(2,-2)

d)

(-2,2)

203.

2x + y = -3
x - 2y = -4

a)

(-2,1)

b)

(1,-2)

c)

(2,1)

d)

(1,2)

204.

x = - 3
2x + 3y = 6

a)

(4,3)

b)

(-4,3)

c)

(-3,4)

d)

(3,-4)

205.

x + 4y = -8
5x - 4y = -16

a)

(4,1)

b)

(1,4)

c)

(-4,-1)

d)

(-1,-4)

206.

2x - 3y = 6
7x - 3y = -9

a)

(-3,-4)

b)

(3,4)

c)

(-4,-3)

d)

(4,3)

207.

5x - 4y = =-16
x+ 2y = -6

a)

(-4,-1)

b)

(5,-1)

c)

(-5,-1)

d)

(4,1)

208.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

209.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

210.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

211.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

212.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

213.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

214.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

215.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

216.

Find the missing value "c" to create a perfect square trinomial:
x² + 26x + ___

a)

13

b)

136

c)

169

d)

26

217.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

218.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

219.

Solve by completing the square. Round.
x² -4x = 5

a)

11 and -7

b)

1 and 3

c)

1.73 and -1.73

d)

5 and -1

220.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

221.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

222.

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

223.

Solve by completing the square. Round.
x² -4x = 5

a)

11 and -7

b)

1 and 3

c)

1.73 and -1.73

d)

5 and -1

224.

#1 Simplify $\sqrt[]{343}$

225.

#2 Simplify $\sqrt[]{112}$

226.

#3 Simplify $\sqrt[]{54}$

227.

#4 Simplify $\sqrt[]{216}$

228.

#5 Simplify $\sqrt[]{-147}$ = (a) (b) $\sqrt[]{}$ (c)

Choose from the below words

7

i

3

5

2

6

8

229.

#6 Simplify $\sqrt[]{-36}$ = (a)

Choose from the below words

6i

36

2

2i

3i

6

-6

230.

#7 Simplify $\sqrt[]{-72}$ = (a) (b) (c)

Choose from the below words

6

i

$\sqrt[]{2}$

-6

$\sqrt[]{36}$

$\sqrt[]{6}$

$\sqrt[]{-2}$

231.

#8 Simplify $\sqrt[]{-12}$ = (a) (b) (c)

Choose from the below words

2

i

$\sqrt[]{3}$

3

$\sqrt[]{2}$

$\sqrt[]{-3}$

-2

6

232.

#9 Simplify $\sqrt[]{8}$

233.

#10 Simplify $\sqrt[]{50}$

234.

#11 Simplify $\sqrt[]{-128}$ = (a) (b)

Choose from the below words

8i

$\sqrt[]{2}$

8

-8

$\sqrt[]{-2}$

4

$\sqrt[]{4}$

235.

#12 Simplify $\sqrt[]{-512}$ = (a) (b)

Choose from the below words

16i

$\sqrt[]{2}$

8i

$\sqrt[]{8}$

-16

$\sqrt[]{-2}$

4i

4

236.

#13 Simplify (-6 - 7i) + (2 + 6i)

a)

-5

b)

-4 + i

c)

-4 - i

d)

-8 + 13i

237.

Match the following

a)

- 7+ 15i

1.

6i + 6i - (7-3i)

b)

2 - 14i

2.

4 - 8i + -2-6i

c)

3 -11i

3.

-5 - 4i + 8 - 7i

d)

9 - 6i

4.

2 - (-4+6i)+3

e)

-6 + i

5.

2i - 8 - (-2 + i)

Algebra 2 Finale Exam

Total questions: 237

Worksheet time: 32hrs 13mins

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