Free Printable Algebra 1 Semester 2 Review

1.

a)

axis of symmetry

b)

vertex

c)

minimum point

d)

maximum point

2.

Choose all that apply.

What are the the other names for quadratic roots?

a)

zeros on a graph

b)

solutions

c)

y-intercepts

d)

x-intercepts

3.

This is from a four term. What is the final answer after factoring completely.

2x(x – 8) + 5(x – 8)

a)

(x+5)(x-8)

b)

(2x-5)(x-8)

c)

5(x-8)

d)

2x(x-8)

4.

2 x² + 11x + 5

Factor completely. Find each factor in the answer bank below. Write both LETTERS for the factors.

A (2x + 5) B (2x + 1) C (x + 1) D (x – 2) E (x + 3)

F (x + 4) G (x + 5) H (x – 8) J (x + 9) K (x – 9)

a)

GK

b)

BG

c)

AC

d)

EF

5.

x² + x – 6

Factor completely. Find each factor in the answer bank below. Write both LETTERS for the factors.

A (2x + 5) B (2x + 1) C (x + 1) D (x – 2) E (x + 3)

F (x + 4) G (x + 5) H (x – 8) J (x + 9) K (x – 9)

a)

GH

b)

FG

c)

DE

d)

JK

6.

x² + 10x + 9

Factor completely. Find each factor in the answer bank below. Write both LETTERS for the factors.

A (2x + 5) B (2x + 1) C (x + 1) D (x – 2) E (x + 3)

F (x + 4) G (x + 5) H (x – 8) J (x + 9) K (x – 9)

a)

DJ

b)

BK

c)

CJ

d)

EJ

7.

What are the quadratic roots to (x - 3)(x + 5) = 0?

a)

x = {3, 5}

b)

x = (-5, 3)

c)

x = {-5, 3}

d)

x = {-3. 5}

8.

What are the solutions to (x - 5)(x + 3) = 0?

a)

(-5, 3)

b)

(-3, 5)

c)

x = {-3, 5}

d)

x = {-5, 3}

9.

Given the graph, what is A?

a)

vertex

b)

y-intercepts

c)

solutions to the graph

d)

axis of symmetry

10.

Given the graph, what is B?

a)

quadratic roots

b)

axis of symmetry

c)

y-intercept

d)

vertex

11.

Given the graph, what is D?

a)

axis of symmetry

b)

x-intercepts

c)

y-intercept

d)

vertex

12.

Given the graph, what is C?

a)

x-intercepts

b)

y-intercept

c)

vertex

d)

axis of symmetry

13.

What is the formula for the axis of symmetry?

a)

b)

c)

d)

maximum point

14.

What is the vertex form of a quadratic?

a)

b)

c)

d)

maximum point

15.

What is the quadratic formula?

a)

b)

c)

d)

maximum point

16.

What is the standard form of a quadratic equation?

a)

b)

c)

d)

maximum point

17.

What is the highest point on a quadratic graph?

a)

maximum

b)

minimum

18.

What is the lowest point on a quadratic graph?

a)

maximum

b)

minimum

19.

What is the answer to this problem?

a)

0

b)

x

c)

undefined

20.

What is the answer to this problem?

a)

0

b)

x

c)

undefined

21.

What does this graph represent?

a)

linear line

b)

quadratic equation

c)

exponential growth

d)

exponential decay

22.

What does this graph represent?

a)

exponential decay

b)

linear graph

c)

quadratic graph

d)

exponential growth

23.

What does this graph represent?

a)

linear line

b)

quadratic equation

c)

exponential growth

d)

exponential decay

24.

What is the standard form of a exponential line?

a)

b)

c)

d)

25.

In the exponential equation, what does b > 1 mean?

a)

exponential growth

b)

exponential decay

c)

nothing

26.

In the exponential equation, what does b < 1 mean?

a)

exponential growth

b)

exponential decay

c)

nothing

27.

What is the answer to the picture to the right?

a)

-16

b)

+/- 4

c)

0

d)

no solution

28.

√ab

a)

√a * √b

b)

√a / √b

c)

a(b)

d)

1 / ab

29.

Put √18 * √24 in simplest radical form.

a)

+/- 3√6

b)

+/- 6√3

c)

+/- 12√3

d)

+/- 4√6

30.

Put √48 in simplest radical form.

a)

+/- 2√3

b)

+/- 4√3

c)

+/- 6√8

d)

+/- 2√8

31.

Using y = x^2 + 7x + 12, identify the line of symmetry (a) .

32.

If something is not factorable, it is....

a)

not real

b)

prime

c)

composite

d)

0

33.

If a and b are roots of the equation in the picture, and a > b, what is the value of a + b?

a)

5

b)

-5

c)

11

d)

-11

34.

The point (-5, 2), what is the value of k?

a)

-5

b)

-2

c)

2

d)

5

35.

If a and b are roots (a < b) of the equation in the picture. What is the value of b^2 - a ^2?

a)

-21

b)

25

c)

4

d)

21

36.

What is the asymptote of this graph?

a)

y = 1

b)

y = -1

c)

y = 0

d)

x = 0

37.

What is the equation of this line?

a)

y = 4/5x + 3

b)

y = - 4/5x + 3

c)

y = 4/5x + 3

d)

y = - 4/5x - 3

38.

The way an infectious disease spreads through a new population can be modeled by __________.

a)

an exponential growth function

b)

a quadratic function

c)

exponential decay

d)

a linear growth function

39.

Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

40.

Find the product. Write in standard form.

(x - 1)(x - 8).

a)

x² + 9x + 8

b)

x²+ 9x - 8

c)

x² - 9x - 8

d)

x² - 9x + 8

41.

Which of the following is the vertex form of the equation of a parabola that has a vertex of (-4, 6) and passes through the point (-7, 24)?

a)

f(x) = 2(x + 4)² + 6

b)

f(x) = 2(x - 4)² + 6

c)

f(x) = (x + 4)² + 6

d)

f(x) = (x - 4)² - 6

42.

Find the product. Write in standard form.

-2(x - 1)(x - 8).

a)

2x² + 18x - 16

b)

-2x²+ 18x - 16

c)

2x² - 18x + 16

d)

-2x² - 18x + 16

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

A

b)

B

c)

C

d)

D

50.

a)

A

b)

B

c)

C

d)

D

51.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

52.

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

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

53.

What is the vertex form of a quadratic function?

a)

f(x) = 2a(x-h)² + k

b)

f(x) = a(x-h)² + k

c)

f(x) = (x+h)² + k

d)

f(x) = a(x-h) - k

54.

Identify the vertex of f(x) = -2(x+1)² + 3

a)

(h,k)

b)

(3, 1)

c)

(-1,-3)

d)

(-1,3)

55.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

56.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

57.

Add the following polynomials:
(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

a)

11x⁴ + 2x² + 14x

b)

16x⁴ + x² + 14x

c)

11x⁴ + x² + 14x

d)

11x⁴ + 2x² + 10x

58.

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

59.

Find the product:
-3x²(5x² + 3x)

a)

-15x⁴ - 9x²

b)

-15x⁴ - 9x³

c)

15x⁴ - 6x³

d)

-15x⁴ + 9x³

60.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

61.

$\frac{x^2+10x+24}{x^2-x-20}$ Simplify.

a)

$\frac{x+6}{x+4}$

b)

$\left(x+6\right)\left(x+4\right)$

c)

$x+6$

d)

$\frac{x+6}{x-5}$

62.

Simplify $\frac{x+9}{x^2-81}$

a)

$\frac{x-9}{x+9}$

b)

$\frac{1}{x-9}$

c)

$x+9$

d)

$\frac{1}{x+9}$

63.

Complete Step 1: FACTOR
$\frac{x^2\ -5x\ +\ 6}{x^2-4}\cdot\frac{\left(x\ +6\right)\left(x\ +\ 5\right)}{x^2+2x\ -15}$

a)

$\frac{\left(x\ -\ 3\right)\left(x\ -\ 2\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ +\ 5\right)\left(x\ -\ 3\right)}$

b)

$\frac{\left(x\ +\ 6\right)\left(x\ -\ 1\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ -5\right)\left(x\ -3\right)}$

64.

Complete Step 3: CANCEL
$\frac{\left(x-3\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\cdot\frac{\left(x+6\right)\left(x+5\right)}{\left(x+5\right)\left(x-3\right)}$

a)

$\frac{x+6}{x+2}$

b)

$\frac{x+2}{x+6}$

c)

$\frac{\left(x-3\right)}{\left(x+2\right)}\cdot\frac{\left(x+6\right)}{\left(x-3\right)}$

65.

Divide the Rational Expression
$\frac{x^2-4x-5}{x^2-3x+2}\div\frac{x^2-3x-10}{x^2-4}$

a)

$\frac{x-5}{x-1}$

b)

$\frac{x+1}{x-1}$

c)

$\frac{1}{x-1}$

d)

$x+1$

66.

$\frac{10m-20}{10m+70}\times\frac{m^2+8m+7}{m+1}$

a)

$\frac{m+2}{3}$

b)

$\frac{3}{20}$

c)

$m-2$

d)

$\frac{m+4}{m+7}$

67.

$\frac{u-v}{8v}+\frac{6u-3v}{8v}$

a)

$\frac{7u-4v}{16v}$

b)

$\frac{7u-4v}{8v}$

c)

$\frac{7u+2v}{8v}$

d)

$\frac{7u+2v}{16v}$

68.

Subtract $\frac{5}{x}-\frac{4}{x}$

a)

$\frac{9}{x}$

b)

$\frac{1}{x}$

c)

$\frac{1}{x^2}$

d)

$\frac{9}{x^2}$

69.

Simplify the expression

a)

6x / 20xy

b)

3 / 10y

c)

(6x+1) / (20xy)

d)

3 / 20xy

70.

a)

A

b)

B

c)

C

71.

a)

A

b)

B

c)

C

72.

At what times is the height 99 feet?

a)

2 and 3

b)

1.25 and 3

c)

2 and 1.75

d)

1.5 and 3.5

73.

Which time has the same height as 2.25 seconds?

a)

2.5

b)

3.5

c)

2.75

d)

3

74.

A ball is kicked in the air. The flight of the ball is modeled by the following table. Let x represent the time in the air and the right column represent the height of the ball. What are the x-intercepts?

a)

(0,0) and (15,75)

b)

(15,75) and (20,0)

c)

(-1,-21) and (10,100)

d)

(0,0) and (20,0)

75.

LT18

$\left(\frac{15a^4b^8c^{19}d^{-10}e^{-41}}{95a^{-6}b^{-10}c^{15}d^{-100}e^{15}}\right)^0=$

a)

$0$

b)

$1$

c)

$\frac{3a^{10}b^{18}c^4d^{90}}{19e^{56}}$

d)

$\frac{c^4}{80a^2b^2d^{90}e^{26}}$

76.

LT23:

$y=-2x^2+3$

What is the domain of the quadratic function?

a)

all real numbers

b)

$x\ge3$

c)

$x\le3$

d)

$x\ge-2$

e)

$x\le-2$

77.

LT23:

$y=-2x^2+3$

What is the range of the quadratic function?

a)

all real numbers

b)

$y\ge3$

c)

$y\le3$

d)

$y\ge-2$

e)

$y\le-2$

78.

LT29:

Simplify √63

a)

9√7

b)

3√7

c)

3√9

d)

7√9

79.

LT27:

This table represents what kind of function?

a)

Linear

b)

Exponential Growth

c)

Exponential Decay

d)

Quadratic

80.

LT27:

Is the table linear, exponential, or quadratic?

a)

Linear

b)

Exponential

c)

Quadratic

d)

none of these

81.

LT26:

How many solutions does this system of equations have?

a)

one solution

b)

two solutions

c)

three solutions

d)

no solutions

82.

LT26:

How many solutions does this system of equations have?

a)

one solution

b)

two solutions

c)

no solutions

d)

All of the above

83.

LT23:

Which of the following are true about the quadratic function shown? (You can choose more than one answer)

a)

There are two roots

b)

the axis of symmetry is at x = -2

c)

the vertex is a maximum

d)

the vertex is (-2, 0)

84.

LT23:

How can you tell whether a parabola is facing up or facing down by looking at the equation?

a)

The vertex tells you the direction of the opening

b)

The value of "a" tells you the direction of the opening.

c)

All parabolas open upward

d)

All parabolas open downward

85.

LT21:

Factor out the GFF: 2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

86.

LT20
Find the product. Write your answer in standard form.

$\left(6y-2\right)^2$

a)

$36y^2-4$

b)

$6y^2-4$

c)

$36y^2-24y+4$

d)

$36y^2+4$

87.

Is the following function and example of decay or growth?

f(x) = 2(0.85)^x

a)

Exponential Decay

b)

Exponential Growth

88.

A polynomial that contains 3 terms is called a ________________________.

a)

binomial

b)

monomial

c)

trinomial

d)

triomial

89.

A polynomial that contains 2 terms is called a ___________________.

a)

binomial

b)

monomial

c)

trinomial

d)

duonomial

90.

A polynomial that contains only 1 term is called a _________________.

a)

binomial

b)

monomial

c)

trinomial

d)

uninomial

91.

Write an equation in point slope form of equation of line

point (7,10) and has a slope of -2?

a)

y-10 = -2(x+7)

b)

y-10 = -2(x-7)

c)

y+10 = -2(x+10)

d)

y -10 = -2x+2

92.

a)

A

b)

B

c)

C

d)

D

93.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

94.

Simplify

a)

b)

c)

d)

e)

95.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

96.

Identify the 'b' value: y = 16x²-24

a)

16

b)

-8

c)

0

d)

-24

97.

Find the slope of the line containing these two points:
(-5, 1) and (-6, -3)

a)

m = 4/11

b)

m = 1/4

c)

m = -2

d)

m = 4

98.

Which of the following equations is represented by the graph?

a)

b)

c)

d)

99.

Describe the solutions for the given graph.

a)

One real solution.

b)

Two real solutions.

c)

No real solutions.

d)

Infinite solutions.

100.

How long did it take for the ball to reach its maximum height?

a)

4 seconds

b)

1 second

c)

2 seconds

d)

.5 seeconds

101.

a)

b)

c)

d)

102.

Identify the type of function of the attached table.

a)

Linear

b)

Exponential

c)

Quadratic

103.

Identify the type of function of the attached table.

a)

Linear

b)

Exponential

c)

Quadratic

104.

Identify the type of function for the following situation: Bacteria growth

a)

Linear

b)

Exponential

c)

Quadratic

105.

Quadratic equations have...

a)

a common difference/constant rate of change

b)

a common multiplier/common ratio

c)

common second difference

106.

What represents the y-intercept in the equation $y=ax^2+bx+c$ ?

a)

a

b)

b

c)

c

d)

x

107.

Is the pattern linear, exponential of quadratic?

a)

linear

b)

exponential

c)

quadratic

108.

Is the pattern linear, exponential of quadratic?

a)

linear

b)

exponential

c)

quadratic

109.

What type of function does this situation represent?

Throwing a baseball in the air

a)

Quadratic Function

b)

Exponential Function

c)

Linear Function

d)

Not a function

110.

Which student represents a Quadratic Function?

a)

Beth

b)

Maria

c)

Tracy

d)

None of the above

111.

Which student represents an Exponential Function?

a)

Beth

b)

Maria

c)

Tracy

d)

None of the above

112.

What is the factored form of x³+7x²-2x-14?

a)

(x²-2)(x-7)

b)

(x²+2)(x+7)

c)

(x²+2)(x-7)

d)

(x²-2)(x+7)

113.

$\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}$

State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

114.

Which value of x makes the expression undefined?

a)

-2

b)

2

c)

-6

d)

-3

115.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

116.

Simplify

a)

$\frac{x+9}{x-9}$

b)

$\frac{1}{(x-9)}$

c)

$x-9$

d)

$\frac{1}{(x+9)}$

e)

$x+9$

117.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

118.

Simplify.

a)

$\frac{m+6}{m-3}$

b)

$\frac{7}{m-3}$

c)

$\frac{7}{m+6}$

d)

$\frac{1}{m+6}$

119.

Complete Step 1: FACTOR
$\frac{x^2\ -5x\ +\ 6}{x^2-4}\cdot\frac{\left(x\ +6\right)\left(x\ +\ 5\right)}{x^2+2x\ -15}$

a)

$\frac{\left(x\ -\ 3\right)\left(x\ -\ 2\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ +\ 5\right)\left(x\ -\ 3\right)}$

b)

$\frac{\left(x\ +\ 6\right)\left(x\ -\ 1\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ -5\right)\left(x\ -3\right)}$

120.

Divide the Rational Expression
$\frac{x^2-4x-5}{x^2-3x+2}\div\frac{x^2-3x-10}{x^2-4}$

a)

$\frac{x-5}{x-1}$

b)

$\frac{x+1}{x-1}$

c)

$\frac{1}{x-1}$

d)

$x+1$

121.

Given the sum

$\frac{3x}{x+2}+\frac{6x+1}{\left(x+2\right)\left(x-5\right)}$

What is the LCD (lowest common denominator)?

a)

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

b)

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

c)

$x-5$

d)

$x+2$

122.

$\frac{2x+3}{x+7}-\frac{x-4}{x+7}=$

a)

$1$

b)

$\frac{x-1}{x+7}$

c)

$\frac{1}{x+7}$

d)

$\frac{2x^2-5x-12}{x+7}$

123.

$\frac{2m-n}{8n}+\frac{6m-3n}{8n}=$

a)

$m-1$

b)

$\frac{8m-4n}{16m^2}$

c)

$\frac{2m-n}{2n}$

d)

$\frac{8m+2n}{8n}$

124.

Simplify $\frac{7n}{3n-18}+\frac{n+3}{3}$

a)

$\frac{8n+3}{3n-15}$

b)

$\frac{n^2+4n-18}{3\left(n-6\right)}$

c)

$\frac{7\left(n+3\right)}{3\left(3n-18\right)}$

d)

$\frac{7n+n+3}{3n-18+3}$

Algebra 1 Semester 2 Review

Total questions: 124

Worksheet time: 6hrs 45mins

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