Free Printable Algebra 2H Semester 1 Exam Practice

1.

What are the dimensions of this matrix?

a)

4x3

b)

3x4

c)

3

d)

4

2.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

3.

Find A+B

(no calculator)

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

4.

In Matrix R (pictured) what element is in the second row, third column?

a)

8

b)

9.01

c)

6

d)

1

5.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

The column of the 1st must equal the row of the 2nd.

6.

How many rows are in a 7 x 3 matrix?

a)

7

b)

3

c)

21

d)

10

7.

You can multiply a 2X3 matrix by which matrix?

a)

2X2

b)

2X12

c)

3X12

d)

2X3

8.

Find the product of the two matrices.

(Calculator permitted)

a)

undefined

b)

-3 16
17 12
8 -10

c)

3 12
-15 -8
-1 -3

9.

If the matrices can be multiplied, what dimension is the product? If not, write undefined.

a)

undefined

b)

( 3 x 1 )

c)

( 1 x 2 )

d)

( 3 x 2 )

10.

Subtract.

(no calculator)

a)

A

b)

B

c)

C

d)

D

11.

Perform the indicated operation. If it’s not possible, select Not Possible.

Calculator permitted.

a)

7
-7
-6
20

b)

7
-9
-6
20

c)

Not Possible

d)

7
-9
2
20

12.

Multiply.

(no calculator)

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

13.

Find B-A.

(no calculator)

a)

-3 1

7 -1

b)

1 0

1 -4

c)

4 0

-6 1

d)

not possible because rows do not match columns

14.

find: B*A

Calculator permitted.

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

15.

Evaluate.

No caclulator.

a)

b)

c)

d)

16.

Find A+B

No calculator.

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

17.

Subtract.

no calculator

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

18.

What do w, x, y and z equal in this matrix subtraction?

no calculator

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

19.

√-4

a)

-2

b)

-2i

c)

2

d)

2i

20.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

21.

Evaluate (9 + 3i) (9 - 3i).

a)

81 -9i

b)

90

c)

81 + 27i -9i²

d)

81i - 9

22.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5+12i

c)

13

d)

13 + 12i

23.

The product of (3 -2i) and (7+6i) is

a)

21-12i

b)

9 + 4i

c)

33 + 4i

d)

21 + 16i

24.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

25.

Factor:
10x²+ 11x - 8

a)

(5x + 8)(2x - 1)

b)

(5x - 8)(2x + 1)

c)

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

d)

(2x + 8)(5x - 1)

26.

What is the axis of symmetry of the given function?

a)

y = 1

b)

y = -1

c)

x = 1

d)

x = -1

27.

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

28.

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

29.

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)

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

30.

Given this graph is the function of

y=x^2-2x-8

, what is the solution to

x^2=2x+8

?

a)

(1, 9)

b)

x = {-2, 4}

c)

(0, 8)

d)

x = {5, 2}

31.

$x^2-7x=0$

Solve by the method of your choice.

a)

x = 7 only

b)

x = 0 only

c)

x = 0 and 7

d)

There is no real answer for this equation.

32.

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

Solve by the method of your choice.

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)

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

33.

$2x^2=8x+3$

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

34.

What is/are the solution(s) to

3x^2-1=74

?

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

35.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

36.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

37.

Solve for x: -5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

38.

Solve by ANY method you have learned: x²−2x+11=0

a)

1±i√10

b)

1±√10

c)

-1±i√10

d)

-1±√10

39.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

40.

Simplify 3i + 2i

a)

5i

b)

5i²

c)

6i

d)

-5

41.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

42.

$\frac{-5+9i}{10i}=?$

a)

$\frac{-5+9i}{10}$

b)

$\frac{5+9i}{10}$

c)

$\frac{50-90i}{100}$

d)

$\frac{9+5i}{10}$

43.

4x+8y=20

-4x+2y=-30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

44.

$f\left(x\right)=5x-12$ What is $f\left(-4\right)$

a)

-32

b)

-3

c)

-12

d)

3

45.

Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

46.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

47.

Factor the expression: w² - 15w - 54

a)

(w + 6)(w - 9)

b)

(w + 3)(w - 18)

c)

(w + 2)(w - 27)

d)

(w - 6)(w + 9)

48.

$\left(6+8i\right)-\left(6+3i\right)$

a)

$-12+5i$

b)

$8$

c)

$-4+8i$

d)

$5i$

49.

$\left(-1-2i\right)\left(-6-6i\right)$

a)

$-7+16i$

b)

$24+24i$

c)

$12+12i$

d)

$-6+18i$

50.

4 Determine the value of the discriminant and name the nature of the solution for the following:

x² + 2x - 63

Remember: b² - 4ac

a)

256 - 2 reals - Rational

b)

√(-256 - 2 imaginary solutions

c)

√(137) - 2 reals - Irrational

d)

123 - 2 reals - Rational

51.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

52.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

53.

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

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

54.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

55.

What is the vertex of this Absolute Value Function?

y = lx + 2l - 1

a)

(-2, -1)

b)

(-2, 1)

c)

(-1, 2)

d)

(-1, 2)

56.

Solve for x and y
2x − 3y = −1
y = x − 1

a)

(-2,-3)

b)

(0,-1)

c)

(3,4)

d)

(4,3)

57.

a)

A

b)

B

c)

C

d)

D

58.

Solve the quadratic equation by factoring

a)

-6, -2

b)

-2, 6

c)

2, 6

d)

-6, 2

59.

Solve:
x² - 49 = 0

a)

x = -7, x = 7

b)

x = -7

c)

x = 7

d)

x = -7, x = 1

60.

√-36

a)

6

b)

-6

c)

-6i

d)

6i

61.

Find the vertex. y = x²+ 16x + 71

a)

V(-8, 7)

b)

V(-8, 3)

c)

V(8, 10)

d)

V(16, -2)

62.

Given
f(x)= 2x² + 5x - 17, find f(-1).

a)

f(-1) = -20

b)

f(-1) = -24

63.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

64.

Find the Difference.

(4x³-3x² + 6x - 4) - (-2x³ + x² -2)

a)

4x² - 6x³- 2x + 6

b)

3x + 5x²+ 1

c)

6X³ -4X² + 6X -2

d)

3x + 2

65.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

66.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

67.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

68.

What is the missing number in the formula for the quadratic equation, $5x^2-x\ +7\ =\ 0$ ?
$x\ =\frac{?\pm\sqrt{\left(\ -1\right)^2-4\left(5\right)\left(7\right)}}{2\left(5\right)}$

a)

7

b)

5

c)

-1

d)

1

69.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

70.

Write the absolute value equation given the following transformations:
Reflection over the x-axis
Horizontal shift right 2 units
Vertical shift down 7 units

a)

$y=-\left|x+2\right|-7$

b)

$y=\left|x-2\right|-7$

c)

$y=-\left|x-2\right|-7$

d)

$y=\left|x+2\right|-7$

71.

Solve
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

72.

What are the translations of this function?

y=(x-2)²+4 (Choose ALL that apply.)

a)

Horz shift right 2

b)

Horz shift left 2

c)

Vert shift up 4

d)

Vert shift down 4

73.

Which of these expressions is equivalent to 5n³-10n²+3n-6?

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

74.

$Simplify:\ \ \left(-2\ +\ 7i\right)\left(4\ -\ 2i\right)$

a)

$6+\ 32i$

b)

$-6\ +\ 32i$

c)

$22+32i$

d)

$6\ +\ 24i$

75.

Simplify

√-72

a)

7i √9

b)

4i √6

c)

6i √2

d)

3i √4

76.

The path of a golf ball shot at an elevated driving range can be modeled by the function below. What is the maximum height of the golf ball?

f\left(x\right)=-5x^2+10x+15

a)

10 meters

b)

15 meters

c)

20 meters

d)

25 meters

77.

Determine the vertex of the function

y=x^2+18

a)

(18, 0)

b)

(0, 18)

c)

(-18, 0)

d)

(0, -18)

78.

Solve.

x^2-4=-3x+24

a)

x = 4 & x = -7

b)

x = -4 & x = 7

c)

x = 14 & x = -2

d)

x = 2 & x = -14

79.

Determine the number of and type of solution(s) to the equation

0=x^2-6x+9

a)

one real solution

b)

no real solutions & two imaginary solutions

c)

two real solutions

d)

three real solutions

80.

Find the solution to the system below. If there is a solution, then identify the y-coordinate.

x + 7y = 0

2x - 8y = 22

a)

1

b)

7

c)

-1

d)

-7

81.

a)

A

b)

B

c)

C

d)

D

82.

Solve for x and y
2x − 3y = −1
y = x − 1

a)

(-2,-3)

b)

(0,-1)

c)

(3,4)

d)

(4,3)

83.

Simplify:
(2 - 3i)(5 + 4i)

a)

22 - 7i

b)

22 + 7i

c)

22 - 7i²

d)

22 + 7i²

84.

What is $\sqrt{-1}$ equal to?

a)

$1$

b)

$i$

c)

$-1$

d)

$-i$

85.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

86.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

87.

Label the parts of a parabola. Drag and drop the word accordingly.

a)

Axis of Symmetry

b)

Root/Zero/x-intercept

c)

Vertex

d)

Y-intercept

1

2

3

4

1)

2)

3)

4)

88.

Label the parts of a parabola. Drag and drop the word accordingly.

a)

Axis of Symmetry

b)

Root/Zero/x-intercept

c)

Vertex

d)

Y-intercept

1

2

3

4

1)

2)

3)

4)

89.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

90.

Find the remainder

(2x³ - 5x - 7) / (x + 2)

a)

-9

b)

11

c)

-13

d)

-1

91.

Solve the depicted system algebraically

a)

(0,-7) and (1, 6)

b)

(0,-7) and (1, -6)

c)

(0, 7) and (1, -6)

d)

(-7,0) and (1, -6)

92.

Solve using the Quadratic Formula:

$2x^2-x-3=0$

a)

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

b)

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

c)

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

d)

$x=1,\ \frac{3}{2}$

93.

Which value(s) of x are solutions to the equation below?

\left(x-4\right)^2=25

a)

9

b)

$\sqrt{29}$

c)

9 and -1

d)

5 and -5

94.

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

x² + 4x - 1 = 0

a)

x = -2 ± √5

b)

x = -5 ± √2

c)

x = 2 ± √5

d)

x = -5 ± √5

95.

3x + 2y = 8
-x + y = -11

a)

(-5,6)

b)

(6,-11)

c)

(-6,-5)

d)

(6,-5)

96.

Solve by the Quadratic Formula:

$9u^2-11u+7=0$

a)

$\frac{-11\pm\sqrt{131}}{18}$

b)

$\frac{11\pm i\sqrt{131}}{18}$

c)

$\frac{11\pm\sqrt{131}}{-18}$

d)

$\frac{11\pm i\sqrt{373}}{18}$

97.

What is the maximum or minimum of the quadratic function:

y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

98.

For g(x) = (x + 10)²- 4, describe the transformation from the parent function.

a)

Slide left 10 and down 4 units

b)

Slide right 10 and down 4 units

c)

Slide left 10 and up 4 units

d)

Slide right 10 and up 4 units

99.

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

100.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

101.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

102.

Which equation is an absolute value graph shifted right 5 units?

a)

y = |x - 5|

b)

y = |x + 5|

c)

y = |x| + 5

d)

y = -5|x|

103.

Use your calculator to find the vertex of the function.

a)

(4, -2)

b)

(-4, 14)

c)

(2, 0)

d)

(8, 6)

104.

$\left(x-6\right)\left(x-3\right)=0$ Solve the equation

a)

x = 1; x = -6

b)

x = ⅓, x = -6

c)

x = 6; x = 3

d)

x = 6; x = - ⅓

105.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

106.

Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)

a)

2x²+x+1

b)

2x²-5x+3

c)

2x²-x+1

d)

4x²-5x+3

107.

Multiply

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

108.

Which equation would you use to find

f\left(29\right)

a)

Top

b)

Middle

c)

Bottom

109.

Which equation would you use to find

f\left(-5\right)

a)

Top

b)

Middle

c)

Bottom

110.

Which equation would you use to find

f\left(0\right)

a)

Top

b)

Middle

c)

Bottom

111.

Please find

f\left(8\right)

a)

5

b)

-6

c)

10

d)

undefined

112.

Please find

f\left(0\right)

a)

5

b)

-6

c)

10

d)

undefined

113.

Please find

f\left(-6\right)

a)

5

b)

22

c)

-9

d)

undefined

114.

Please find

f\left(2\right)

a)

0

b)

4

c)

-1

d)

-8

115.

Please find

f\left(0\right)

a)

0

b)

-4

c)

-9

d)

-8

116.

Please find

f\left(-1\right)

a)

-2

b)

-3

c)

11

d)

undefined

117.

Please find

f\left(10\right)

a)

9

b)

19

c)

-22

d)

undefined

118.

Please find

f\left(-6\right)

a)

-7

b)

-13

c)

26

d)

undefined

119.

Please find

f\left(0\right)

a)

4

b)

5

c)

-4

d)

-5

120.

Please find

f\left(7\right)

a)

4

b)

5

c)

-4

d)

-5

121.

Please find

f\left(-5\right)

a)

0

b)

10

c)

-4

122.

Write the given equation in vertex form:

y=x²+6x-2

a)

y=(x+3)²+7

b)

y=(x+3)²-11

c)

y=(x+6)²-2

d)

y=(x-3)²-38

123.

Write the given equation in vertex form:

y=x²+10x-5

a)

y=(x+10)²-105

b)

y=(x+5)²+25

c)

y=(x+5)²+20

d)

y=(x+5)²-30

124.

Write the given equation in vertex form:

y=x²+12x-5

a)

y=(x+6)²-31

b)

y=(x+6)²-41

c)

y=(x+12)^2-5

d)

y=(x-6)²-31

125.

Write the given equation in vertex form:

y=x²-14x+2

a)

y=(x+7)²-47

b)

y=(x-7)²-51

c)

y=(x-14)²+2

d)

y=(x-7)²-47

126.

The graph of a quadratic function is shown. The vertex and two points are labeled. Drag and drop the numbers and operations to write the equation for the parabola in vertex form. y = (a) (x (b) (c) )² - (d)

Choose from the below words

$\frac{1}{2}$

-

1

6

$\frac{3}{2}$

12

4

$\frac{11}{36}$

8

+

127.

Identify the vertex and whether the graph opens up or down. (a)

Choose from the below words

(5, 2); opens up

(5, 2); opens down

(-5, 2); opens up

(-5, 2); opens down

128.

The graph of a quadratic function is shown. The vertex and two points are labeled. Drag and drop the numbers and operations to write the equation for the parabola in vertex form. y = (a) (x (b) (c) )² - (d)

Choose from the below words

$\frac{1}{2}$

-

1

6

$\frac{3}{2}$

12

4

$\frac{11}{36}$

8

+

129.

Which of the following is the correct equation for the given graph? (a)

Choose from the below words

f(x) = -(x + 2)2 - 4

f(x) = -(x - 2)2 - 4

f(x) = -3(x - 2)2 - 4

f(x) = -3(x + 2)2 - 4

130.

Write the given equation in vertex form:

y=x²+16x+100

a)

y=(x+8)²+36

b)

y=(x+8)²-36

c)

y=(x-8)²+164

d)

y=(x+8)²

131.

Write the given equation in vertex form:

y=x²-10x+10

a)

y=(x-10)²+10

b)

y=(x+5)²+35

c)

y=(x-5)²+15

d)

y=(x-5)²-15

132.

Find the Vertex: y= -5x²-20x - 26

a)

(-2, -6)

b)

(2, 6)

c)

(6,2)

d)

(3, 6)

133.

Which formula allows you to find the x-value of the vertex from a standard form equation?

a)

$x=-\frac{b}{2a}$

b)

$x=\frac{\left(p+q\right)}{2}$

c)

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

d)

$x=h$

134.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

135.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

136.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

f(x) = (x - 4)² + 65

137.

Convert f(x) = 4x² - 32x + 2 to vertex form.

a)

f(x) = 4(x + 4)² - 62

b)

f(x) = 4(x - 4)² - 62

c)

f(x) = 4(x - 8)² - 62

d)

f(x) = 4(x + 8)² - 62

138.

Identify the vertex.

a)

(5, 2)

b)

(5, -2)

c)

(-5, 2)

d)

(-5, -2)

139.

Which of the following equations matches vertex form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

140.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

141.

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

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

142.

Solve the quadratic inequality:

$x^2-4x-5\le0$

a)

$-1\le x\le5$

b)

$-5\le x\le1$

c)

$x\ge5\ ,\ \ x\le-1$

d)

$x\le-5\ ,\ \ \ x\ge1$

143.

Solve the quadratic inequality:

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

a)

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

b)

$-6<x<-3$

c)

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

d)

$3<x<6$

144.

Solve the quadratic inequality:

$x^2+11x+10\ge0$

a)

$x\le-10\ ,\ \ x\ge-1$

b)

$x\ge-10\ ,\ \ x\le-1$

c)

$-10\le x\le-1$

d)

$x\le1,\ x\ge10$

145.

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)

$-7\le x\le4$

146.

Is (2, 3) part of the solution set?
y < 2x²-3x+1

a)

Yes

b)

No

147.

Which inequality is shown?

a)

y< -x²

b)

y≤ -x²

c)

y> -x²

d)

y≥ -x²

148.

Which inequality is shown?

a)

y < -5(x-2)(x-4)

b)

y < -5(x+2)(x+4)

c)

y > -5(x-2)(x-4)

d)

y > -5(x+2)(x+4)

149.

(2,2) is a solution to the inequality 2x-6y>x²+4x-8

a)

True

b)

False

150.

Which is a solution to the following system?
y < 6x²+ 2x - 1
y ≥ -2x² - x + 3

a)

(0, 0)

b)

(0, -3)

c)

(1, 5)

d)

(1, -8)

151.

What is the vertex?
y = -2x² + 4x + 3

a)

(0, 3)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

152.

Find the y-intercept of f(x) = 2x²-2x + 1

a)

2

b)

-2

c)

1

d)

-1

153.

If the discriminant is positive, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

154.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solutions

155.

Is (2, 3) part of the solution set?
y < 2x²-3x+1

a)

Yes

b)

No

156.

Which graph is shown?

a)

y<-2x²-8x-12

b)

y>-2x²-8x-12

c)

y≤-2x²-8x-12

d)

y≥-2x²-8x-12

157.

Which graph is shown?

a)

y≥x²-6x+12

b)

y>x²-6x+12

c)

y≤x²-6x+12

d)

y<x²-6x+12

158.

Find the solution(s).

a)

(-1,7) and (0,5)

b)

(-4,2) and (-5,8)

c)

(-2,6) and (10,15)

d)

(-2,4) and (6,12)

159.

$y\ge\frac{1}{2}x^2-2x-2;\ y<-x^2+5$

Graph the system of inequalities.

a)

b)

c)

d)

160.

A solution to the system of inequalities: y < -1/2x + 3 and y < (x+1)²is :

a)

(0, 6)

b)

(-1, 4)

c)

(2, 1)

d)

(3, 4)

161.

Find the solution:
y = x² - 4x + 6
y = x + 2

a)

(3, 1) and (6, 4)

b)

(-1, 1) and (4, 2)

c)

(1, 3) and (4, 6)

d)

(1, 4) and (3, 6)

162.

Find the solution.

a)

(2,3) and (3,4)

b)

(-3,-15) and (4,-8)

c)

(-3,10) and (8,4)

d)

(-8,3) and (-4,10)

163.

a)

10

b)

-10

c)

10i

d)

-10i

164.

Simplify -4√-63

a)

3i√7

b)

-12i√7

c)

-12√7

d)

36√7

165.

Simplify:
3√-81

a)

-27

b)

3i√3

c)

27i

d)

9i

166.

Multiply
(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

167.

Multiply
(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

168.

Simplify.

a)

b)

c)

d)

169.

What are the factors of
$x^2+5x+4$

a)

$\left(x+2\right)\left(x+3\right)$

b)

$\left(x-1\right)\left(x-4\right)$

c)

$\left(x-1\right)\left(x+5\right)$

d)

$\left(x+1\right)\left(x+4\right)$

170.

What are the factors of
$2x^2+5x-12$

a)

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

b)

$\left(x-3\right)\left(x+8\right)$

c)

$\left(2x+1\right)\left(x-12\right)$

d)

$\left(2x+3\right)\left(x-8\right)$

171.

What are the factors of
$4m^2-25$

a)

$\left(4m-5\right)\left(4m+5\right)$

b)

$\left(2m-5\right)\left(2m+5\right)$

c)

$\left(2m-10\right)\left(2m-15\right)$

d)

$\left(4m-1\right)\left(m-24\right)$

172.

What are the factors of
$3p^2-7p-6$

a)

$\left(p+3\right)\left(3p-2\right)$

b)

$\left(p+2\right)\left(p-9\right)$

c)

$\left(3p+2\right)\left(p-3\right)$

d)

$\left(3p-9\right)\left(3p+2\right)$

173.

What are the factors of
$5b^2-11b+2$

a)

$\left(5b-1\right)\left(b-2\right)$

b)

$\left(b-1\right)\left(b-10\right)$

c)

$\left(b-2\right)\left(b-5\right)$

d)

$\left(5b-2\right)\left(b-5\right)$

174.

What are the factors of
$8g^2-18g-5$

a)

$\left(g+2\right)\left(g-20\right)$

b)

$\left(8g-1\right)\left(g+5\right)$

c)

$\left(2g+1\right)\left(4g-5\right)$

d)

$\left(4g+1\right)\left(2g-5\right)$

175.

What are the factors of
$2n^2+12n+16$

a)

$2\left(n+1\right)\left(n+8\right)$

b)

$\left(2n+2\right)\left(n+8\right)$

c)

$2\left(n+2\right)\left(n+4\right)$

d)

$\left(n+16\right)\left(2n+1\right)$

176.

What are the factors of
$49x^2-100$

a)

$\left(7x-10\right)\left(7x+10\right)$

b)

$\left(x-4\right)\left(x-25\right)$

c)

$\left(x+10\right)\left(x-10\right)$

d)

$\left(49x-10\right)\left(x+10\right)$

177.

The area of a rectangular painting is $2x^2+13x-7$ units. Which of the following could be the dimensions of the painting?
*Hint: Factor the trinomial*

a)

$\left(2x+1\right)$ units by $\left(2x+7\right)$ units

b)

$\left(x-1\right)$ units by $\left(x+14\right)$ units

c)

$\left(x+1\right)$ units by $\left(2x+7\right)$ units

d)

$\left(2x-1\right)$ units by $\left(x+7\right)$ units

178.

Which binomial is a factor of
$9x^2-25$

a)

$\left(x+5\right)$

b)

$\left(3x-25\right)$

c)

$\left(9x-5\right)$

d)

$\left(3x+5\right)$

179.

Which binomial is a factor of
$3k^2+16k-12$ ?

a)

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

b)

$\left(k+18\right)$

c)

$\left(k-6\right)$

d)

$\left(3k-6\right)$

180.

Which expression is a factor of
$x^2-3x-28$

a)

$\left(x+7\right)$

b)

$\left(x-4\right)$

c)

$\left(x-7\right)$

d)

$\left(x-3\right)$

181.

Factor 4y³+ y + 12y²+ 3 by grouping. Remember to look for Standard Form, then for common factors.

a)

4y²(y + 3) + 3

b)

4y³+ 12y²+ y + 3

c)

(4y² + 1)(y + 3)

182.

Factor x³ – 2x – 4x² + 8 by grouping. Remember to look for Standard Form, then for common factors.

a)

x³ - 4x² - 2x + 8

b)

(x – 4)(x² – 2)

c)

(x – 2)(x² – 4)

183.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

184.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

185.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

186.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

187.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

188.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

189.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

190.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

191.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

192.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

193.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

194.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

195.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

196.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

197.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

198.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

199.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

200.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

201.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

202.

Factor the polynomial completely.

a)

A

b)

B

c)

C

d)

D

203.

4w⁴ + 16w² + 15

a)

(w² + 10)(w² + 6)

b)

(2w²+ 5)(2w² + 3)

c)

(w² + 15)(4w² + 1)

d)

(2w + 5)(2w + 3)

204.

Factor completely:

x⁴-10x²+9

a)

(x-9)(x-1)

b)

(x²-9)(x²+1)

c)

(x-3)(x+3)(x²-1)

d)

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

205.

Factor Completely: x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

206.

16x⁴ - 49

a)

(4x² - 7)(4x² + 7)

b)

(4x - 7)(4x + 7)

c)

(2x - 7)(2x + 7)(4x² + 7)

d)

cannot be factored

207.

Factor Completely (GCF and difference of squares):

5x⁴-5

a)

5(x²-1)(X²+1)

b)

25(x²-1)(x²+1)

c)

5(x+1)(x-1)(x²+1)

d)

5(x⁴-1)

208.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

209.

Factor this sum of cubes:
2x³ + 128

a)

2(x³ + 64)

b)

(x + 4)(x² - 4x + 16)

c)

2(x - 4)(x² + 4x + 16)

d)

2(x + 4)(x² - 4x + 16)

210.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

(x - 2)(x + 2)(2x + 5)

211.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

212.

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

a)

6, 3, -3

b)

-6, 3, -3

c)

-6, 3i, -3i

d)

6, 3i, -3i

213.

Solve the following equation:
x⁴ + x² - 90 = 0

a)

3, -3, ±√10

b)

3, -3

c)

±√10

d)

3

214.

a)

b)

c)

d)

215.

Factor: 27x³ + 8. Then describe how to find the three solutions.

a)

(3x + 2)(9x² - 6x + 4). Next, set (3x + 2) equal to 0 and solve. Finally, use the Quadratic Formula for (9x² - 6x + 4).

b)

(9x + 2)(3x² + 18x + 4). Next, set (9x + 2) equal to 0 and solve. Finally, use the Quadratic Formula for (3x² + 18x + 4).

c)

(3x²+4)(9x + 2). Next, set (3x² + 4) equal to 0 and solve. Finally, set (9x + 2) equal to 0 and solve.

d)

(27x + 8)(x² - 216x + 64). Next, set (27x + 8) equal to 0 and solve. Finally, use the Quadratic Formula for (x² - 216x + 64).

216.

a)

b)

c)

d)

Algebra 2H Semester 1 Exam Practice

Total questions: 216

Worksheet time: 20hrs 44mins

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