Free Printable Algebra Essentials Review

1.

Find the value of y when x = 2

(a)

2.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

3.

Find the slope of the line.

a)

Undefined

b)

0

c)

1

d)

-1

4.

Are the following points a function?

(-2,-5), (-2,-1), (-2,1), (-2,3)

HINT

It's a function if EACH x-value is paired with only ONE y-value.

It's NOT a function if the SAME x-value REPEATS and is paired with TWO DIFFERENT y-values.

a)

Yes

b)

No

5.

Are the following points a function?

(0,2), (1,1), (2,2), (4,3)

HINT

It's a function if EACH x-value is paired with only ONE y-value.

It's NOT a function if the SAME x-value REPEATS and is paired with TWO DIFFERENT y-values.

a)

Yes

b)

No

6.

What is the y-intercept?

(a)

7.

Is this graph a function or not a function?

HINT: Remember the VERTICAL LINE TEST!

a)

Function

b)

Not a Function

8.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

9.

Find the slope:
y = 2x - 10

(a)

10.

^{What is the x- intercept of the line?}

a)

(1, 0)

b)

(2, 0)

c)

( -1, 0)

d)

(-2, 0)

11.

The term "solutions" is the same as

a)

y-intercept

b)

roots

c)

x-intercepts

d)

vertex

e)

zeros

12.

Where is the axis of symmetry for this parabola?

HINT: Remember that the axis of symmetry always passes through the VERTEX

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

13.

How many solutions does this graph have?

a)

one solution

b)

two solutions

c)

no real solutions

d)

cannot be determined with the given information

14.

The axis of symmetry is a line that goes through the...

a)

y-intercept

b)

x-intercept

c)

Vertex

d)

Solutions

e)

Zeros

15.

How many real solutions does the quadratic have?

a)

No real solutions

b)

One real solution

c)

Two real solutions

16.

What could the factored form of this function be?

a)

y = x(x + 4)

b)

y = x(x - 4)

c)

y = x(4x)

17.

Determine the interval of this functions DOMAIN.

a)

(-∞, 2)

b)

No Solution

c)

(-∞, ∞)

d)

(-∞, 1)

18.

Where is the axis of symmetry for this parabola?

HINT: Remember that the axis of symmetry always passes through the VERTEX

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

19.

Name the x-intercept(s)?

a)

(0, 0)

b)

(0, 4)

c)

(0, 0) and (0, 4)

d)

(0, 0) and (4, 0)

20.

What are the factors of the quadratic?

HINT: Think OPPOSITE

a)

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

b)

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

c)

$\left(x-6\right)\left(x+2\right)$

d)

$\left(x+6\right)\left(x-2\right)$

21.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

22.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

23.

a)

9^-4

b)

9^-45

c)

3^-4

d)

3^-45

24.

a)

0

b)

3

c)

1

d)

-1

25.

Simplify the following expression:

a)

14x⁶

b)

14x³

c)

9x³

d)

9x⁶

26.

Evaluate

$3^5\div3^8$

a)

$3^3$

b)

$3^{13}$

c)

$3^{40}$

d)

$3^{-3}$

27.

Evaluate

$\frac{2^4}{2^6}$

a)

$2^2$

b)

$2^{-2}$

c)

$2^{10}$

d)

$2^{24}$

28.

Simplify the following expression. $\frac{7^6}{7^1}$

a)

$7^6$

b)

$7^5$

c)

$7^7$

d)

$7^{-5}$

29.

When we raise a power to another power, we _____________ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

30.

n⁴ ⋅ n⁵

a)

$n^9$

b)

$n^{20}$

c)

n¹

d)

$n^{45}$

31.

Write $\sqrt[]{m^5}$ in exponential form:

a)

$m^{\frac{5}{2}}$

b)

$m^5$

c)

$m^{\frac{2}{5}}$

d)

$m^{\frac{1}{5}}$

32.

Given the radical expression $\sqrt[4]{x^3}$ ,

what will the expression be in exponential form?

a)

$4x^3$

b)

$x^{\frac{4}{3}}$

c)

$x^{\frac{3}{4}}$

d)

$\frac{3}{4}x$

33.

For the expression, select the equivalent expression(s) using radicals.

a)

b)

c)

d)

34.

What number fills the spot where the question mark (?) is located?

$6^{\frac{3}{4}}=\sqrt[\%]{6^?}$

(a)

35.

Given the radical expression $\sqrt[4]{x^3}$ ,

what does the x³ represent?

a)

Index

b)

Radicand

c)

Power

d)

Base

36.

Write the following expression in exponential form:

$\sqrt[]{a^5}$

a)

$a^{\frac{5}{2}}$

b)

$a^5$

c)

$5a^2$

d)

$a^{\frac{2}{5}}$

37.

What number fills in the place where the percent sign (%) is placed?

$\sqrt[10]{g^2}=g^{\frac{?}{\%}}$

(a)

38.

Given the radical expression $\sqrt[4]{x^3}$ ,

what does the 3 represent?

a)

Index

b)

Radicand

c)

Power

d)

Base

39.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

40.

Write the following as a Rational Exponent

a)

$x^{\frac{2}{5}}$

b)

$x^{\frac{5}{2}}$

c)

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

d)

$x^5$

41.

A collectible car has been going up in value by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

NOTE: Write your answer WITHOUT a comma or $ sign. It will be a decimal value.

(a)

42.

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?

Round to the nearest whole number.

(a)

43.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

Round your answer to the nearest whole number.

(a)

44.

Which of these functions is a growth function?

SELECT ALL THAT APPLY

a)

$f\left(x\right)=7\left(1.2\right)^x$

b)

$f\left(x\right)=5\left(0.8\right)^x$

c)

$f\left(x\right)=0.5\left(3\right)^x$

d)

$f\left(x\right)=3\left(\frac{4}{3}\right)^x$

45.

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. Suppose f(20) = 49. Which of the following is true?

a)

After 20 days, there are 49 ants in the colony.

b)

After 49 days there are 20 ants in the colony.

c)

The amount of ants times 20 is 49.

d)

After 20 days the amount of ants remaining decreases by 49.

46.

What is the value of 'b' in the function below?

$y=45\left(1.09\right)^x$

(a)

47.

A computer sells for $900 and loses 30% of its value per year. Which of the following equations can be represented to show the computer's value, V(t), t years after it is sold?

SELECT ALL THAT APPLY

(there are 2 correct solutions)

a)

$V\left(t\right)\ =\ 900\left(1\ -\ .30\right)^t$

b)

$V\left(t\right)\ =\ 900\left(0.70\right)^t$

c)

$V\left(t\right)\ =\ 900\left(1.70\right)^t$

d)

$V\left(t\right)\ =\ 900\left(30\right)^t$

e)

$V\left(t\right)\ =\ 900\left(1\ +\ .30\right)^t$

48.

What does the y-intercept of the graph represent?

a)

The amount of grams the material is gaining.

b)

The amount of grams the material is losing.

c)

The initial amount of years

d)

The initial amount of grams.

49.

Does the table show exponential growth or decay?

a)

Growth

b)

Decay

50.

What is the growth percent in the following function?

$f\left(x\right)=803\left(1.02\right)^x$

NOTE: You do not need to type the % sign with your answer.

(a)

51.

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)

52.

What is the parent function for a Quadratic equation?

a)

b)

c)

d)

y = x

e)

$y=a\cdot b^x$

53.

What transformations have happened to f(x) = 2^x if the new equation is

g(x) = -2^(x+3) - 6

SELECT ALL THAT APPLY

(three answers)

a)

reflect x-axis

b)

reflect y-axis

c)

left 3

d)

right 3

e)

down 6

54.

$f\left(x\right)=3^x\ \ \ \ and\ \ \ g\left(x\right)=0.2\left(3\right)^x$ What transformation has taken place from the parent function to g(x)

a)

Vertical Stretch (thinner)

b)

Vertical Compression (wider)

c)

Translation up 5 units

d)

Reflection across the x-axis

55.

For $y=a\left(x-h\right)^x+k$ , how does adding/subtracting a constant "h" transform the parent function?

a)

Horizontal shift

b)

Vertical Translation

c)

Reflection over the x-axis

d)

Reflection over the y-axis

56.

Which equation represents this graph?

HINT: The coordinates of the vertex of the parabola will help

a)

f(x) = (x - 4)² - 3

b)

f(x) = -(x - 4)² + 3

c)

f(x) = (x - 4)² + 3

d)

f(x) = -(x + 4)² + 3

57.

If the blue function is f(x)=√x, the red function must be...

a)

g(x)=√(-x)

b)

g(x)=√(x-1)

c)

g(x)=√x-1

d)

g(x)=-√x

58.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

HINT: Focus on the blue functions y-intercept and how far it moved to the right to make the red function.

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

59.

What transformation best describes the function?

a)

stretch

b)

shrink

c)

reflection

d)

shift down

60.

$f\left(x\right)=0.5^x\ \ \ \ and\ \ \ g\left(x\right)=-3\left(0.5\right)^x$ What transformations have taken place from the parent function to g(x)

HINT: There are two answers

a)

Vertical Stretch

b)

Vertical Compression

c)

Translation down 3 units

d)

Reflection across the x-axis

61.

a)

(x + 6)(x + 2)

b)

(x + 3)(x + 4)

c)

(x - 4)(x - 3)

d)

(x - 2)(x - 6)

62.

a)

(x - 3)(x + 4)

b)

(x - 2)(x + 6)

c)

(x +3)(x - 4)

d)

(x - 6 )(x + 2)

63.

Factor:
x²+ 81

a)

Prime (not factorable)

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

64.

Factor:
x²- 225

a)

( x + 15) ( x + 15)

b)

Prime

c)

( x - 15) ( x + 15)

d)

( x - 15) ( x - 15)

65.

Factor $x^2+7x+6$

a)

(x + 6)(x + 1)

b)

(x - 6)(x + 1)

c)

(x + 6)(x - 1)

d)

(x - 6)(x - 1)

66.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

67.

Factor completely: x²- 12x + 20

a)

(x - 2)(x - 10)

b)

(x + 2)(x - 10)

c)

(x - 2)(x + 10)

d)

(x + 2)(x + 10)

68.

Factor:
x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

69.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

70.

Factor
x² +17x - 60

a)

(x - 20)(x + 3)

b)

(x + 12)(x - 5)

c)

(x - 12)(x + 5)

d)

(x + 20)(x - 3)

71.

Factor out the GCF

3x³ + 9x

a)

3x (x²+ 3)

b)

3x ( x³ + 9)

c)

x (3x² + 9)

d)

3x (x³ + 3x)

72.

Factor using GCF or monomial factoring:

2n²- 8n³

a)

2n²(n - 4n²)

b)

2n²(1 - 4n)

c)

2n³(10 - 8n²)

d)

3n(1 - 4n)

73.

What is the GCF? 2x²-4x+8

a)

2x

b)

2

c)

x

d)

1

74.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

75.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

76.

Factor:

7x+49

a)

$7x\left(x+49\right)$

b)

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

c)

$49\left(x+7\right)$

d)

$x\left(7+49\right)$

77.

$12c^2-20a^2$

Factor:

a)

$2\left(6c^2-10a^2\right)$

b)

$4\left(3c^2-5a^2\right)$

c)

$2a^2c^2\left(6-10\right)$

d)

$4\left(ca\right)^2\left(3-5\right)$

78.

Factor out the GCF: $5x^2+15x^3$

a)

$5x^2\left(1+3x\right)$

b)

$5x\left(x+3x^2\right)$

c)

$5\left(x^2+3x^3\right)$

79.

Factor out the GCF: $4x^2+10x^3$

a)

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

b)

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

c)

$2\left(2x^2+5x^3\right)$

80.

Factor out the GCF: $9x+36$

a)

$9\left(x+4\right)$

b)

$3\left(3x+12\right)$

c)

$9\left(x+36\right)$

81.

Solve for x: (2x - 6)(x + 1)

a)

-6, 1

b)

3, -1

c)

-3, 1

d)

-3, -1

82.

How many solutions are there?

a)

0

b)

1

c)

2

d)

3

83.

What are the solutions to the given quadratic equation?

a)

(0, -1), (0, 3)

b)

(1, 4)

c)

x = 1

d)

(- 1, 0), (3, 0)

84.

$\left(h+8\right)\left(9h+7\right)=0$

a)

$h=-8.\ h=-\frac{7}{9}$

b)

$h=8,\ h=\frac{7}{9}$

c)

$h=-8,\ h=\frac{7}{9}$

d)

$h=8,\ h=-\frac{7}{9}$

85.

$\left(2q+1\right)\left(q-9\right)=0$

a)

$q=-\frac{1}{2},\ q=9$

b)

$q=\frac{1}{2},\ q=-9$

c)

$q=-\frac{1}{2},\ q=-9$

d)

$q=\frac{1}{2},\ q=9$

86.

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

87.

Solve for the values of x:
(2x - 1)(x + 4) = 0

a)

{ 1/2, -4 }

b)

{ 1/2, 4 }

c)

{ 2, -4 }

d)

{ -2, 4 }

88.

Solve and find your x-intercepts:
0=x(x - 6)

a)

x=0 and x=-6

b)

x=1 and x=-6

c)

x=0 and x=6

d)

x=6

89.

What is the vertex and axis of symmetry?

a)

Vertex (2, -2)

AOS: x = 2

b)

Vertex (-2, 2)

AOS: x = -2

c)

Vertex (2, -2)

AOS: x = -2

d)

Vertex (-2, 2)

AOS: x = 2

90.

What are the solutions?

SELECT ALL THAT APPLY

f(x) = (x - 5)(x + 9)(x - 2)

a)

2

b)

5

c)

-9

d)

9

e)

-5

Algebra Essentials Review

Total questions: 90

Worksheet time: 3hrs 10mins

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