Free Printable Regents Review 2024-2025

1.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

2.

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation 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

3.

a)

-2 and 10

b)

-2 and -10

c)

2 and 10

d)

2 and -10

4.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

5.

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

6.

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

-3

7.

a)

-6, -2

b)

-2, 6

c)

2, 6

d)

-6, 2

8.

Convert x²+6x+9 to factored form and identify the solution.

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

9.

Convert x²-9x+20 to factored form and solve.

a)

(x-10)(x+2); x=-2, 10

b)

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

c)

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

d)

Not factorable

10.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

11.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

12.

Factor:
x² - 10x - 24

a)

(x + 12)(x - 2)

b)

(x - 6)(x - 4)

c)

(x - 12)(x + 2)

d)

(x +6)(x - 4)

13.

What is the green dot on the parabola called?

a)

vertex

b)

root

c)

dot

d)

minimum value

14.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

15.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

16.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

17.

Identify the solutions of the graph?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

18.

Is this table a function or not a function?

a)

Function

b)

Not a Function

19.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

20.

What is the x-intercept?

a)

12

b)

-3

c)

8

d)

0

21.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

22.

Find the roots/zeros of x² + x - 2

a)

-1, 2

b)

-2, 1

23.

Find the roots/zeros of x² + 4x - 21

a)

-7, 3

b)

-3, 7

24.

Find the roots/zeros of x² - 3x - 10

a)

-2, 5

b)

-5, 2

25.

The x-intercepts of a quadratic equation are known as the _____.

a)

vertices

b)

squares

c)

zeros

d)

formulas

26.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

27.

Select the equation that has zeros at the points $\left(2,\ 0\right)\ and\ \left(-4,0\right)$ .

a)

$y=\left(x-2\right)\left(x-4\right)$

b)

$y=\left(x+2\right)\left(x-4\right)$

c)

$y=\left(x-2\right)\left(x+4\right)$

d)

$y=\left(x+2\right)\left(x+4\right)$

28.

Select the equation that has zeros at the points $\left(1,\ 0\right)\ and\ \left(5,0\right)$ .

a)

$y=\left(x-1\right)\left(x-5\right)$

b)

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

c)

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

d)

$y=\left(x+1\right)\left(x+5\right)$

29.

$f\left(x\right)$

is the same thing as ______.

a)

y

b)

x

c)

input

d)

an equation

30.

How do you read

f\left(x\right)

?

a)

f x

b)

f of x

c)

f parenthesis x

d)

f with an x inside parenthesis

31.

How would you write

y=2x-3

in function notation?

a)

$y=2x-3$

b)

$f=2x-3$

c)

$f\left(x\right)=2x-3$

32.

If f(x) = 2x + 1, what would be your first step to find f(1)?

a)

Plug a 1 in for all the x's

b)

Set the function equal to 1

c)

Only plug a 1 into the left side

d)

Only plug a 1 into the right side

33.

Given
$g\left(x\right)=4x-2$

Evaluate:

g\left(-7\right)

a)

$g\left(-7\right)=-30$

b)

$g\left(-7\right)=-26$

c)

$g\left(-7\right)=-36$

d)

$g\left(-7\right)=26$

34.

Given the graph,

find:

f\left(2\right)

a)

$f\left(2\right)=5$

b)

$f\left(2\right)=4$

c)

$f\left(2\right)=3$

d)

$f\left(2\right)=0$

35.

Given the graph,

find:

f\left(6\right)

a)

$f\left(6\right)=3$

b)

$f\left(6\right)=1$

c)

$f\left(6\right)=2$

d)

$f\left(6\right)=0$

36.

How do you know this is a function?

a)

Each input has one output

b)

It's a line

c)

It's not points

37.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

38.

What is the domain of a relation?

a)

the set of all x-values

b)

the set of all y-values

39.

Which is the set of all y-values or the outputs?

a)

Domain

b)

Range

c)

Relation

d)

Function

40.

What is the range of the mapping?

a)

{1, 2, 4}

b)

{0, 1, 2, 3}

c)

{0, 3}

d)

{1, 4}

41.

Is the relation shown a function?

a)

No, because the x-value 11 is paired with 5 and 8.

b)

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

42.

Is the relation shown in the mapping a function?

a)

No, because -1 and 4 are pared with 4.

b)

Yes, because every input is paired with exactly one output.

43.

Is this is a function or not a function?

a)

Function

b)

Not a Function

44.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

45.

a)

Function

b)

Not a Function

46.

a)

Function

b)

Not a Function

47.

a)

Function

b)

Not a Function

48.

Is this relation linear?

a)

Yes

b)

No

49.

Is this relation a function?

a)

Yes

b)

No

50.

Is this function linear or nonlinear?

a)

Linear

b)

Nonlinear

51.

Is this function linear or nonlinear?

a)

Linear

b)

Nonlinear

52.

Which of the following equations match the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

53.

How can I tell if an inequality will have a solid line?

a)

It has an equal sign.

b)

The symbol is greater than.

c)

The symbol has "or equal to."

d)

You just guess.

54.

Which graph best represents the following inequality?

a)

b)

c)

d)

55.

Determine whether point A is a solution to the linear inequality that is shown.

a)

Yes

b)

No

c)

Sometimes

56.

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

a)

Yes because it is located in the shaded region.

b)

No because it is located on the line and the line is dotted.

c)

Yes because it is located on the line.

d)

No because it is in the shaded region.

57.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

58.

This is a graph of which inequality?

a)

y > 4x - 2

b)

y > -2x + 4

c)

y < -2x

d)

y < 4X - 2

59.

According to the graph, which point is a solution? Choose all that apply.

a)

(0, 0)

b)

(4, 2)

c)

(-1, -5)

d)

(-3, 0)

60.

When graphing $y<\frac{3}{5}x-4$ , you will draw which of the following.

a)

A dotted line

b)

A solid line

c)

Shade up

d)

Shade down

61.

When graphing $y\ge-\frac{2}{7}x+1$ , you will draw which of the following.

a)

A dotted line

b)

A solid line

c)

Shade up

d)

Shade down

62.

How can I tell if an inequality will have a solid boundary line?

a)

It has an equal sign.

b)

The symbol is greater than.

c)

The symbol has "or equal to."

d)

You just guess.

63.

How can I tell if an inequality will have a dashed boundary line?

a)

It does not have an equal sign.

b)

The symbol is less than than.

c)

The symbol does not have "or equal to."

d)

You just guess.

64.

When graphing $y\ge-\frac{1}{2}x+7$ , you will draw which of the following? Select a type of line and the shading.

a)

A dotted line

b)

A solid line

c)

Shade above

d)

Shade below

65.

Is the number rational or irrational?

a)

Rational

b)

Irrational

66.

Is the number rational or irrational?

a)

Rational -

b)

Irrational

67.

Is the number rational or irrational?

a)

Rational

b)

Irrational

68.

Is the number rational or irrational?

a)

Rational

b)

Irrational

69.

Is the number rational or irrational?

a)

Rational

b)

Irrational

70.

Is the number 10 rational or irrational?

a)

Rational

b)

Irrational

71.

Is the number -12 rational or irrational?

a)

Rational -

b)

Irrational

72.

What is a rational number?

a)

A number that cannot be written as a fraction.

b)

A number that cannot be written as a repeating decimal.

c)

A number that can be written as a fraction.

73.

Is the number rational or irrational? $\sqrt{15}$

a)

Rational -

b)

Irrational

74.

Irrational numbers...

a)

cannot be written as a fraction.

b)

can be a repeating decimal.

c)

can be written as a fraction.

75.

$\sqrt[]{49}$

a)

Rational

b)

Irrational

76.

$\sqrt{3}$

a)

Rational Number

b)

Irrational Number

77.

Between which two integers is $\sqrt{32}$ ?

a)

2 and 3

b)

3 and 4

c)

4 and 5

d)

5 and 6

78.

$\sqrt{25}$

a)

Rational

b)

Irrational

79.

Level 1: Between what two integers is the square root of 44?

a)

3 and 4

b)

4 and 5

c)

5 and 6

d)

6 and 7

80.

Level 3: Estimate the square root.

a)

Between 4 and 5 and closer to 5

b)

Between 5 and 6 and closer to 6

c)

Between -4 and -5 and closer to -5

d)

Between -5 and -6 and closer to -6

81.

Between which two consecutive integers would you find $\sqrt[]{18}$

a)

4 and 5

b)

5 and 6

c)

6 and 7

82.

Consider the dimensional analysis conversion shown.

What will be the resulting units? $\frac{840\ months}{1}\cdot\frac{1\ year}{12\ months}$

a)

days

b)

months

c)

years

83.

What will the resulting units be?

a)

inches

b)

meters/ft

c)

feet

d)

inches/ft

84.

What will the resulting units be?

a)

cubic feet per day

b)

gallons per hour

c)

gallons per day

d)

cubic feet per hour

85.

Consider the dimensional analysis conversion shown.

What will be the resulting units? $\frac{630\ days}{1}\cdot\frac{1\ week}{7\ days}\cdot\frac{1\ year}{52\ weeks}$

a)

days

b)

weeks

c)

months

d)

years

86.

Consider the dimensional analysis conversion shown.

What will be the resulting units? $\frac{7200\ days}{1}\cdot\frac{1\ year}{360\ days}\cdot\frac{1\ decade}{10\ years}$

a)

days

b)

months

c)

years

d)

decades

87.

Consider the dimensional analysis conversion shown.

What will be the resulting units? $\frac{21,120\ ft}{1\ \min}\cdot\frac{1\ mile}{5280\ ft}\cdot\frac{60\ \min}{1\ hour}$

a)

feet/hour

b)

feet/min

c)

miles/hour

d)

miles/min

88.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

89.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

90.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor? Hint: decay factor is (1-r) where r is the rate as a decimal

a)

^.08

b)

^1.08

c)

.92

d)

8

91.

What is the initial value for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

92.

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

93.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

94.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

95.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

96.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

97.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

98.

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

99.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ What is the growth rate?

a)

The ants are growing by 3 times

b)

The ants are growing by 2 times

c)

The equation doesn't tell us

100.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ How many ants did you begin with?

a)

There was 2 ants

b)

There was 3 ants

c)

The equation doesn't tell us

101.

Is the table linear or exponential?

a)

Linear Table

b)

Exponential Table

102.

Is the situation linear or exponential?

a)

Linear Situation

b)

Exponential Situation

103.

Is the table linear or exponential?

a)

Linear Table

b)

Exponential Table

104.

Is the table linear or exponential?

a)

Linear Table

b)

Exponential Table

105.

Is the table linear or exponential?

a)

Linear Table

b)

Exponential Table

106.

Linear or Exponential?

A student writes a paragraph every ten minutes.

a)

Linear

b)

Exponential

107.

Linear or Exponential?

A virus infected double the population every day.

a)

Linear

b)

Exponential

108.

Linear or Exponential?

1, 4, 16, 64, ...

a)

Linear

b)

Exponential

109.

Linear or Exponential?

4, 8, 12, 16, ...

a)

Linear

b)

Exponential

110.

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

a)

14327

b)

4309

c)

839

d)

7680

111.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

112.

Factor

k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

113.

Factor

k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

114.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

115.

Factor
x² - 9x + 20

a)

(x - 10)(x - 2)

b)

(x - 20)(x - 1)

c)

(x - 10)(x + 2)

d)

(x - 5)(x - 4)

116.

Factor
x²+ 3x + 2

a)

(x + 2)(x + 1)

b)

(x + 3)(x - 1)

c)

(x + 3)(x + 1)

d)

(x - 3)(x + 1)

117.

Factor Completely
$x^2-4x+3$

a)

$\left(x-3\right)\left(x+1\right)$

b)

$\left(x-7\right)\left(x+4\right)$

c)

$\left(x-3\right)\left(x-1\right)$

d)

$\left(x+3\right)\left(x-1\right)$

118.

4x² - 25

a)

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

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

119.

The expression $w^4-36$ is equivalent to

a)

$\left(w^2-18\right)\left(w^2-18\right)$

b)

$\left(w^2+18\right)\left(w^2-18\right)$

c)

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

d)

$\left(w^2+6\right)\left(w^2-6\right)$

120.

If f(x) = 4x + 5, what is the value of f(-3)?

a)

-2

b)

-7

c)

17

d)

4

121.

Given:

$f\left(x\right)=\left(x-2\right)^2+4$

$g\left(x\right)=\left(x-5\right)^2+4$

When compared to the graph of f(x), the graph of g(x) is

a)

shifted 3 units to the left

b)

shifted 3 units to the right

c)

shifted 5 units to the left

d)

shifted 5 units to the right

122.

a)

Anne

b)

Bob

c)

Carrie

d)

Dylan

123.

When solving $p^2+5=8p-7$ , Kate wrote

$p^2+12=8p$ . The property she used us

a)

the associative property

b)

the commutative property

c)

the distributive property

d)

the addition property of equality

124.

David wanted to go on an amusement park ride. A sign posted at the entrance read “You must be greater than 42 inches tall and no more than 57 inches tall for this ride.” Which inequality would model the height, x, required for this amusement park ride?

a)

$42<x\le57$

b)

$42>x\ge57$

c)

$42<x$ or $x\le57$

d)

$42>x$ or $x\ge57$

125.

When 3a + 7b > 2a - 8b is solved for a, the result is

a)

a > -b

b)

a < -b

c)

a < -15b

d)

a > -15b

126.

The area of a rectangle is represented by $3x^2-10x-8$ . Which expression can also be used to represent the area of the same rectangle?

a)

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

b)

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

c)

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

d)

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

127.

a)

I and III

b)

I and IV

c)

II and III

d)

II and IV

128.

a)

A, only

b)

B, only

c)

A and C, only

d)

A,B, and C

129.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

130.

Which equation is NOT a linear equation?

a)

y = 2x - 3

b)

y = 8

c)

y = x²

d)

y = x

131.

What is the solution to the system of equations provided?

a)

The system has no solution

b)

There are many solutions

c)

(2,2)

d)

(2,-2)

132.

What is one point that lies in the solution set of the system of inequalities graphed?

a)

(0, 4)

b)

(-4, 1)

c)

(2, 4)

d)

(4, -1)

133.

If A = 3x² - 6x and B = 12x- 6x², what is B - A?

a)

-9x² + 18x

b)

9x² - 18x

c)

-3x² + 6x

d)

-3x²

134.

Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and Large cups for $2.50. If Ashley sold a total of 155 cups for $265, which system could be used to determine the number of small (x) and large (y) cups she sold?

a)

x + y = 265
1.25x+2.5y=155

b)

x + y = 155
2.5x+1.25y=265

c)

x + y = 265
2.5x+1.25y=155

d)

x + y = 155
1.25x+2.5y=265

135.

What is the minimum value?

a)

64

b)

58

c)

66

d)

60

136.

What is the maximum value?

a)

58

b)

66

c)

64

d)

60

137.

A relation is graphed on the set of axes above. Based on the graph the relation is

a)

a function because it passes the horizontal line test

b)

a function because it passes the vertical line test

c)

not a function because it fails the horizontal line test

d)

not a function because it fails the vertical line test

138.

a)

A

b)

B

c)

C

d)

D

139.

If f(x)=3x-9, find f(5).

a)

f(5) = 6

b)

f(5) = 16

c)

f(5) = -4

d)

f(5) = 24

140.

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.

a)

a + c = 21
6a + 4c = 104

b)

a + c = 104
6a + 4c = 21

c)

a + c = 21
6c + 4a = 104

d)

a + c = 104
6c + 4a = 21

141.

Find the vertex of
f(x) = -x²- 4x + 12

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

142.

Factor 9x² - 100

a)

(3x + 10)(3x - 10)

b)

(3x - 10)(3x - 10)

c)

(3x + 10)(3x + 10)

d)

(3x + 10i)(3x - 10i)

143.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

144.

Kevin has 4 full boxes of new pencils and 3 used pencils. Altogether he has 23 pencils. How many pencils are in each box? Which equation represents the word problem?

a)

4x = 23

b)

3x = 23

c)

4 + x + 3 = 23

d)

4x + 3 = 23

145.

What test do we use to see if a graph is a function or not?

a)

Horizontal

b)

Vertical Line test

c)

Jump Test

d)

Random Line Test

146.

What should the graph of an absolute value function look like?

a)

a V shape

b)

a line

c)

a U shape

d)

a diamond

147.

Describe the correlation in the graph shown.

a)

Strong Negative

b)

Strong Positive

c)

Weak Negative

d)

Weak Positive

148.

Solve for the zeros

(x-11) (5x+1) = 0

a)

x = 11 or x = -1/5

b)

x = -11 or x = -1/5

c)

x = 11 or x = 1/5

d)

x = -11 or x = 1/5

149.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

150.

$ax^2+bx+c=0$

You can tell this is a quadratic equation because

a)

it has two variables

b)

it has a negative sign

c)

it has a fractional coefficient

d)

the leading coefficient has an exponent of 2

151.

Which parent function is this?

a)

Quadratic

b)

Cubic

c)

Linear

d)

Rational

Regents Review 2024-2025

Total questions: 151

Worksheet time: 7hrs 50mins

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