Quiz about EOC Fall Review 2022

Question 1

How many complex zeros does the polynomial $$y = 4x^3 + 3x^2 + 5x - 2$$ have?

Accepted Answer

3 complex zeros

Answer

1 complex zero

Answer

2 complex zeros

Answer

4 complex zeros

Question 2

Which expression is equivalent to $$169x^2 - 36$$ ?

Accepted Answer

(13x - 6)(13x + 6)

Answer

(13x - 6)²

Answer

(13x + 6)²

Answer

(13x + 6)(13x + 6)

Question 3

Consider parallelogram HJKL and a student's work to prove HJ cong KL. Which step has an incorrect justification?

Accepted Answer

Step 2

Answer

Step 3

Answer

Step 4

Answer

Step 5

Question 4

Consider the function graphed on the coordinate plane. Which best describes the values of the function when x > 5?

Accepted Answer

(D) positive and increasing

Answer

(A) negative and decreasing

Answer

(B) negative and increasing

Answer

(C) positive and decreasing

Question 5

A parent has 32 feet of plastic dividers to create a rectangular fenced-in play area for a toddler. If the parent wants the play area to be as large as possible, what is the width, in feet, of the fenced-in area the parent should set up?

Accepted Answer

The width of the fenced-in area the parent should set up is 8 feet.

Answer

The width of the fenced-in area the parent should set up is 6 feet.

Answer

The width of the fenced-in area the parent should set up is 10 feet.

Answer

The width of the fenced-in area the parent should set up is 12 feet.

Question 6

What are the zeros of the equation y = (x + 4)(x - 5)?

Accepted Answer

x = -4, 5

Answer

x = -5, -4

Answer

x = -5, 4

Answer

x = 4, 5

Question 7

Consider the graph of two equations, f(x) and g(x). For what value of x is f(x) = g(x)?

Accepted Answer

-3

Answer

-6

Answer

0

Answer

8

Question 8

The expression $$\frac{4}{3}\pi r^3$$ represents the volume of a ball with a radius of r inches.

Complete the inequality to represent the possible radii of the ball, in inches, when the volume is greater than 280 cubic inches.

Accepted Answer

$$\frac{4}{3}\pi r^3>280$$

Answer

$$\frac{4}{3}\pi r^3<280$$

Answer

$$\frac{4}{3}\pi r^3\le280$$

Answer

$$\frac{4}{3}\pi r^3\ge280$$

Question 9

A teacher wants to determine which of three desserts to buy for a class party. Which is the most appropriate sampling method to produce an unbiased, representative sample of the population?

Accepted Answer

Randomly select 8 students' names from a hat containing all students' names

Answer

Randomly select 8 students who are in the school play

Answer

Select the first 8 students who walk in the building

Answer

Select 8 students who wear the darkest jeans to school

Question 10

The expression -2x³+ x² +5x +30 represents the height above the ground, in centimeters, of a model car on a toy racetrack, where x is the number of seconds since the model car starts moving on the racetrack, and $$0\ \le x\le3$$ . What is the initial height above the ground of the model car on the toy racetrack?

Accepted Answer

30 centimeters

Answer

0 centimeters

Answer

5 centimeters

Answer

34 centimeters

Question 11

The number of lines in a pattern increases in each consecutive layer of the pattern. The expression 10(3)²ⁿ represents the number of lines in the nth layer of the pattern. If a student rewrites the expression as 10(r)ⁿ, what is the value of r?

Accepted Answer

9

Answer

6

Answer

8

Answer

18

Question 12

An artist designs a mural for a convention center. The artist graphs a portion of the outline of the mural on a coordinate plane. Which equation best represents the graph?

Accepted Answer

y = (x - 1)(x + 5)(x + 9)

Answer

y = (1 - x)(5 - x)(9 - x)

Answer

y = (1 - x)(x + 5)(x + 9)

Answer

y = (x - 1)(5 - x)(9 - x)

Question 13

A washing machine has a cylindrical drum. The height of the drum is 25 inches, and the radius of the drum is 10 inches.

Approximately how much empty space is inside the drum?

Accepted Answer

7,853.98 cubic inches

Answer

1,570.80 cubic inches

Answer

9,817.48 cubic inches

Answer

19,634.95 cubic inches

Question 14

The area, in square units, of a rectangle is represented by the expression 9x³ - 12x² + 6x. If the width, in units, is 3x, what is the length, in units?

Accepted Answer

3x² - 4x + 2

Answer

x² - 12x + 6

Answer

x² - 4x + 2

Answer

3x² - 12x + 6

Question 15

Which graph has an appropriate scale?

Accepted Answer

only Graph I

Answer

both Graph I and Graph II

Answer

neither Graph I nor Graph II

Answer

only Graph II

Question 16

For this item, click on the equation to select the correct answer.

Consider the logarithmic equation. $$\log_5(20) = x$$ Select the equation which represents an exponential equation equivalent to $$\log_5(20) = x$$ .

Accepted Answer

5x = 20

Answer

20x = 5

Answer

x20 = 5

Answer

x5 = 20

Question 17

Which statement is true?

Accepted Answer

The remainder of x³ + 3x² - 2x - 6 divided by (x + 3) is 0.

Answer

The remainder of x³ + 3x² - 2x - 6 divided by (x - 3) is -42.

Answer

The remainder of x³ + 3x² - 2x - 6 divided by (x - 3) is 0.

Answer

The remainder of x³ + 3x² - 2x - 6 divided by (x + 3) is 42.

Question 18

Consider the absolute value function graphed on the coordinate plane. Which function is best represented by the graph?

Accepted Answer

f(x) = |x - 5| - 3

Answer

f(x) = |x - 3| - 5

Answer

f(x) = |x + 3| - 5

Answer

f(x) = |x + 5| - 3

Question 19

Which expression is equivalent to $$\frac{(n+6)(n-2)}{n-4} imes \frac{(n-2)(n-4)}{n+6}$$ , where $$n eq -6, 4$$ ?

Accepted Answer

n² - 4n + 4

Answer

$$\frac{n^2-4n\ +4}{n^2\ +2n\ -\ 24}$$

Answer

$$\frac{n^2+4n\ +4}{n^2\ +2n\ -\ 24}$$

Answer

n² + 4n + 4

Question 20

The graph represents the associated trigonometric ratio given by $$y = \cos(x)$$ for different angles, $$x$$ . Which statement is true about $$y = \cos(x)$$ ?

Accepted Answer

The graph represents a function because for each angle input, there is exactly one ratio output.

Answer

The graph does not represent a function because for each angle input, there is exactly one ratio output.

Answer

The graph does not represent a function because for some angle inputs, there is more than one ratio output.

Answer

The graph represents a function because for some angle inputs, there is more than one ratio output.

Question 21

The graph represents the population, f(x), of mosquitoes in an area x days after a new repellent is introduced. Which statement is true about the graph of the function?

Accepted Answer

As x increases, f(x) decreases.

Answer

As x increases, f(x) increases.

Answer

The function has a y-intercept at (60,0).

Answer

The function has an x-intercept at (0,60).

Question 22

A student is solving the equation $$7 (3^x) = 63$$ . Which describes a first step the student could use to solve the equation correctly?

Accepted Answer

The student can divide both sides of the equation by 7, resulting in $$3^x = 9$$ .

Answer

The student can divide both sides of the equation by 7, resulting in $$3^x = 441$$ .

Answer

The student can multiply both sides of the equation by 7, resulting in $$3^x = 9$$ .

Answer

The student can multiply both sides of the equation by 7, resulting in $$3^x = 441$$ .

Question 23

Consider the two exponential functions. Which statement is true?

Accepted Answer

The y-intercept of Function 1 is smaller than the y-intercept of Function 2.

Answer

The y-intercept of Function 1 is equal to the y-intercept of Function 2.

Answer

The y-intercept of Function 1 is greater than the y-intercept of Function 2.

Answer

The y-intercepts of the two functions cannot be compared.

Question 24

A teacher is researching how much time students at school spend on homework each night. The teacher asks 50 students in the school cafeteria how much time each student spends on homework the night before and records the answers. Which type of study is the teacher conducting?

Accepted Answer

sample survey

Answer

census

Answer

experiment

Answer

simulation

Question 25

Consider the circle, where point N is on the circumference of circle M, which has a radius equal to 1 cm. Ray MN forms an angle of $$\frac{3\pi}{4}$$ radians with the positive x-axis. What is the approximate length of the arc between the initial and terminal sides of the angle?

Accepted Answer

2.356 cm

Answer

0.785 cm

Answer

1.571 cm

Answer

6.283 cm

Question 26

A designer plans to cover a rectangular floor with tile by creating a large rectangle with green tile surrounded by a large border created with white tile. - The green rectangle has a width of w feet and a length that is 3 feet longer than its width. - The floor has a width of 3w feet and a length that is 5 feet longer than its width. Which function, f(w), represents the area, in square feet, that will be covered with white tile?

Accepted Answer

f(w) = 3w(3w + 5) - w(w + 3)

Answer

f(w) = 3w(3w + 5) + w(w + 3)

Answer

f(w) = 2(3w + 3w + 5) + 2(w + w + 3)

Answer

f(w) = 2(3w + 3w + 5) - 2(w + w + 3)

Question 27

The expression 349(1 - 0.08)^t represents the value of a wireless speaker system t years since the system was purchased. What does (1 - 0.08) represent?

Accepted Answer

the factor by which the value of the system is multiplied for every 1 year that passes

Answer

the factor by which the value of the system is multiplied 8 times for every year that passes

Answer

the factor by which the value of the system is multiplied for every 8 years that pass

Answer

the factor by which the value of the system is multiplied for every 8 months that pass

Question 28

Consider the graph of the exponential function, f(x) = (16/27)(3/2)^x. Which statement is true?

Accepted Answer

As x increases, f(x) increases.

Answer

As x increases, f(x) decreases.

Answer

The x-intercept of the function is located at (1,0).

Answer

The y-intercept of the function is located at (1,0).

Question 29

A decoration is made of 6 spherical balls, each with a radius of 3 inches. Approximately what is the volume of the decoration?

Accepted Answer

678.58 cubic inches

Answer

2,035.75 cubic inches

Answer

169.65 cubic inches

Answer

113.10 cubic inches

Question 30

A triangle is drawn on a map and connects the homes of three friends. If the three friends plan to meet at a location that is equidistant from each of their homes, which statement is true?

Accepted Answer

The three friends plan to meet at the circumcenter of the triangle because the circumcenter is the intersection of the perpendicular bisectors of a triangle's sides and is equidistant from each vertex of the triangle.

Answer

The three friends plan to meet at the circumcenter of the triangle because the circumcenter is the intersection of a triangle's angle bisectors and is equidistant from each side of the triangle.

Answer

The three friends plan to meet at the incenter of the triangle because the incenter is the intersection of a triangle's angle bisectors and is equidistant from each side of the triangle.

Answer

The three friends plan to meet at the incenter of the triangle because the incenter is the intersection of the perpendicular bisectors of a triangle's sides and is equidistant from each vertex of the triangle.

Question 31

Which choice would decrease the margin of error?

Accepted Answer

increasing the sample size

Answer

changing the doctor's office where the healthcare worker is collecting the data

Answer

changing the time that the healthcare worker is collecting the data

Answer

decreasing the sample size

Question 32

A teacher conducts an experiment to determine if students are faster at correctly matching vocabulary words with their definitions, based on whether or not a student uses flash cards as a study method. The students are given a list of 20 words and are randomly assigned a study method. The table shows the results of five different students from each study method, which have a difference means of 1.94 minutes.

If a simulation shows that an observed difference of 1.94 minutes or more occurs exactly 140 of 200 times, which statement is true?

Accepted Answer

An observed difference of 1.94 minutes is not statistically significant because the outcome occurs frequently in the simulation.

Answer

An observed difference of 1.94 minutes is not statistically significant because the outcome occurs very infrequently in the simulation.

Answer

An observed difference of 1.94 minutes is statistically significant because the outcome occurs frequently in the simulation.

Answer

An observed difference of 1.94 minutes is statistically significant because the outcome occurs very infrequently in the simulation.

Question 33

Which expression is equivalent to $$\frac{x}{x-1} = \frac{x+4}{x-1}$$ , where $$x eq 1$$ ?

Accepted Answer

$$\frac{-4}{x-1}$$

Answer

$$\frac{x-4}{x-1}$$

Answer

$$\frac{x+4}{x-1}$$

Answer

$$\frac{4}{x-1}$$

Question 34

The vertices of a rectangle are located at (1,1), (1,7), (4,7), and (4,1). What is the approximate volume of the figure created by rotating the rectangle about x = 4?

Accepted Answer

169.6 cubic units

Answer

56.5 cubic units

Answer

113.1 cubic units

Answer

339.3 cubic units

Question 35

Consider the function f(x) which has factors (x - 6) and (x - 3i). f(x) = x⁵ - 6x⁴ + 7x³ - 42x² - 18x + 108. What is the total number of distinct real zeros of f(x)?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 36

What is the value of $$x$$ in the equation $$\frac{4}{x-4} = \frac{x-8}{x-4}$$ ?

Accepted Answer

x = 12

Answer

x = 4

Answer

x = 8

Answer

x = 0

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