Free Printable EOC Fall Review 2022

Worksheets

EOC Fall Review 2022

Total questions: 50

Worksheet time: 3hrs 18mins

Name

Class

Date

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

1 complex zero

2 complex zeros

3 complex zeros

4 complex zeros

Consider the figure, where two chords, KM and KL, intersect the circle and create inscribed angle MKL. What is the measure of angle MKL?

130°

65°

30°

15°

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

(13x - 6)²

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

(13x + 6)²

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

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

Step 2

Step 3

Step 4

Step 5

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

(A) negative and decreasing

(B) negative and increasing

(D) positive and increasing

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?

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

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

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

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

The table shows the number of invasive plants in a forest, over time, t, in years. Which function, f(t), best models the number of invasive plants over time, t, where 0 ≤ t ≤ 3?

f(t) = 4t + 8

f(t) = 4(8)^t

f(t) = 8t + 4

f(t) = 8(4)^t

What is the inverse of the function g(x) = -10x + 5?

g⁻¹(x) = $\frac{x+5}{-10}$

g⁻¹(x) = $\frac{x-5}{-10}$

g⁻¹(x) = $\frac{x-10}{5}$

g⁻¹(x) = $\frac{x+10}{5}$

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

x = -5, -4

x = -5, 4

x = -4, 5

x = 4, 5

10.

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

-6

-3

11.

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.

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

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

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

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

12.

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?

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

Randomly select 8 students who are in the school play

Select the first 8 students who walk in the building

Select 8 students who wear the darkest jeans to school

13.

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?

0 centimeters

5 centimeters

30 centimeters

34 centimeters

14.

The table shows the values of the functions f(x) and g(x) for various values of x. For x = 5, complete the comparison. f(5) g(5). (a)

Choose from the below words

f(5) = g(5)

f(5) < g(5)

f(5) > g(5)

15.

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?

16.

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?

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

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

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

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

17.

A teacher asks five students each to write a description for a transformation of the function f(x)= 4(3)^x.

Click two students for which the description correctly represents the transformation given in the table.

g(x) = f(x) - 5

18.

Consider the function g(x), which represents the total cost of catering a meal, in dollars, where x is the number of people the meal will feed.

g(x) = { 152 + 22x, 0 < x ≤ 14

{ 30x, x > 14

Which statement is true?

A) The value g(16) is 480, and it represents the total cost of catering a meal for $16 a person.

B) The value g(16) is 480, and it represents the total cost of catering a meal that will feed 16 people.

C) The value g(16) is 504, and it represents the total cost of catering a meal for $16 a person.

D) The value g(16) is 504, and it represents the total cost of catering a meal that will feed 16 people.

19.

Consider the function f(x) = 4 · sin(2x) + 3. What is the amplitude of the function?

20.

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?

1,570.80 cubic inches

7,853.98 cubic inches

9,817.48 cubic inches

19,634.95 cubic inches

21.

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?

x² - 12x + 6

x² - 4x + 2

3x² - 12x + 6

3x² - 4x + 2

22.

Which graph has an appropriate scale?

both Graph I and Graph II

neither Graph I nor Graph II

only Graph I

only Graph II

23.

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 $\log_5(20) = x$ .

20^x = 5

5^x = 20

x²⁰ = 5

x⁵ = 20

24.

Which statement is true?

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

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

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

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

25.

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

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

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

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

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

26.

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

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

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

n² - 4n + 4

n² + 4n + 4

27.

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

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

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

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

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

28.

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?

As x increases, f(x) decreases.

As x increases, f(x) increases.

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

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

29.

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

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

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

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

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

30.

Consider the two exponential functions. Which statement is true?

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

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

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

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

31.

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?

census

experiment

sample survey

simulation

32.

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?

0.785 cm

1.571 cm

2.356 cm

6.283 cm

33.

Consider parallelogram QRST, where $\overline{SY}$ bisects $\angle RST$ , and $\overline{RZ}$ bisects $\angle QRS$ . What is the measure of $\angle SZR$ ?

39°

51°

78°

102°

34.

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?

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

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

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

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

35.

A security camera monitors a circular area with a diameter of 24 feet. If the camera is set to monitor only an arc measuring 135 degrees, what is the approximate area the camera will monitor, to the nearest square foot?

576 ft²

500 ft²

339 ft²

170 ft²

36.

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?

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

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

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

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

37.

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

As x increases, f(x) decreases.

As x increases, f(x) increases.

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

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

38.

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

2,035.75 cubic inches

678.58 cubic inches

169.65 cubic inches

113.10 cubic inches

39.

The diagram shows an angle, θ, graphed in the xy-coordinate plane. Segment MN is the initial side of the angle, and segment NP is the terminal side. Segments NP and NM are radii of the unit circle, which is centered at the origin N(0, 0). If the x-coordinate of point P, representing cos(θ), is equal to - $\frac{1}{2}$ , what is the measure of θ to the nearest hundredth of a radian?

1.57

2.09

2.36

2.62

40.

Commercial airplanes cruise at an average of 560 miles per hour. One commercial airplane is cruising at an average of x miles per hour. If the average cruising speed is allowed to vary by up to y miles per hour, and y is at most 15, which system of inequalities represents the scenario?

y ≥ |x - 560|, y ≤ 15

y ≥ |x + 15|, y ≤ 560

y ≥ |x - 15|, y ≤ 560

y ≥ |x + 560|, y ≤ 15

41.

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?

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.

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.

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.

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.

42.

Which choice would decrease the margin of error?

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

changing the time that the healthcare worker is collecting the data

decreasing the sample size

increasing the sample size

43.

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?

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

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

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

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

44.

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

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

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

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

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

45.

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?

56.5 cubic units

113.1 cubic units

169.6 cubic units

339.3 cubic units

46.

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)?

47.

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

x = 4

x = 8

x = 0

x = 12

48.

What is the length of the radius of the circle represented by the equation $x^2 + y^2 - 8x + 10y - 8 = 0$ , in units?

(a)

49.

Consider parallelogram KLMN. The perimeter of parallelogram KLMN is 60 cm. What is the value of x?

(a)

50.

What value of $t$ , to the nearest hundredth, makes the equation $7(10)^{2t} = 14$ true?

(a)

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EOC Fall Review 2022

Total questions: 50

Worksheet time: 3hrs 18mins

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