End-of-Course (EOC) Math 3

Required

1

What is the remainder when x^{3} - 1 is divided by (x + 2)?

Required

1

The function below, f(x), has (x - 7) and (x + 4i) as factors.

f(x) = 2x^{5} - 13x^{4} + 22x^{3} - 187x^{2} - 160x + 336

What is the total number of real zeros of f(x)?

Required

1

The graph of the function m(x) = x^{3} + 3x^{2} - 2x - 4 has a zero at -1. What are the other zeros of the function?

Required

1

Which expression is equivalent to (x^{2}-2x-37)÷{(x^2 - 3x - 40)}?

Required

1

Place (click and drag) into the appropriate boxes the values of A, B, and C that will make the equation shown below true.

Which expression is equivalent to \frac{(x² - 5x + 6)^{-1}}{(x - 2)^{-2}}÷\frac{(x - 3)^{-1}}{(x - 2)^{-2}} ?

Required

1

A company makes and boxes spaghetti.
One machine fills each box with approximately 32 ounces of spaghetti.
After the boxes are filled, another machine weighs each box.
A box is discarded if the weight of the box differs by more than 0.25 ounce from the target weight of 32 ounces.
Which inequality can be used to find the range of acceptable weights, x, of the spaghetti?

Required

1

The graph of an equation is shown below.

Which equation represents the graph?

Required

1

Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?

Required

1

Two functions are shown below.

f(x) = 2x^{3} + 2x - 3
g(x) = -0.5|x - 4|

What is the y-value when f(x) = g(x)?

Required

1

Which choice is equivalent to the expression shown below?

48x^{3}-243xy^{2}

Required

1

A polynomial, p(x), has a lead coefficient of 1 and exactly three distinct zeros.
x = -1 is a zero of multiplicity two
x = 2 is a zero of multiplicity one
x = 4 is a zero of multiplicity one
What choice shows p(x)?

Required

1

If f(x) = k(x - 2)^4, where k is positive, what is the effect on the graph of f(x) as k increases?

Required

1

Two piecewise functions are shown below.

h(x) = \begin{cases} -3x & \text{for } x < 2 \\ 4x + 1 & \text{for } x \ge 2 \end{cases}
g(x) = \begin{cases} x^2 + 2 & \text{for } x < 3 \\ x^3 & \text{for } x \ge 3 \end{cases}

What is the value of 3h(2) + 4g(1)?

Required

1

A function is shown below.

h(x) = \begin{cases} -\frac{1}{2}x - 15 & \text{for } x \leq -4 \\ 20 - 3x^2 & \text{for } x > -4 \end{cases}

What is the value of h(-4) + 3h(-2)?

Required

1

The graph of a function is shown below.

Place (click and drag) each interval into the column that describes the function on that interval.

A function is shown below:

H(x) = 4x^{3} - 5x^{2} - 23x + 6

What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

Required

1

Which function does not have the set of all real numbers as its domain?

Required

1

An equation is shown below.

9^{-3x + 2} = 48

What is the value of x to the nearest ten-thousandth?

Required

1

The diagram below shows an angle, θ, graphed in the xy-coordinate plane. Segment RT is the initial side of the angle, and segment RM is the terminal side. Segments RT and RM are radii of the unit circle centered at the origin R(0, 0).

The x-coordinate of point M is -\frac{1}{2}. What is the measure of \theta to the nearest thousandth of a radian?

Required

1

A function, f(x) = Asin(Bx) + H, has the following properties:
a period of 6,
a minimum value of 2,
f(2.5) = 5, and
A, B, and H are all positive constants.
Place (click and drag) values into the appropriate cells below that will create this function.

The vertices of a triangle are at (0, 0), (6, 6), and (9, 3). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x?

Required

1

In parallelogram MNPT, m∠M = (6x + 10)° and m∠N = (5x + 10.5)°. How many degrees is ∠T?

Required

1

In rectangle FGHI, diagonals \overline{FH} and \overline{GI} intersect at E.

IE = 3x + 4
EG = 5x - 6
What is the length of \overline{FH}?

Required

1

Triangle PMT is shown below.

What is the measure of segment PG?

Required

1

What is the length of a radius of the circle represented by the equation x^{2} + y^{2} - 4x - 4y + 4 = 0?

Required

1

David plans to cover the floor of his room with new material.
The floor is an isosceles trapezoid whose bases are 16 feet and 26 feet and sides are 13 feet in length.
Each piece of new material has an area of 2.5 square feet.
Assuming the pieces of new material can be cut as needed, how many pieces does David need?

Required

1

Which method is most likely to produce a random sample of 5 students from a school club?

Required

1

A high school randomly selected 75 of the 200 seniors at the school to take a sample college entrance exam. The mean grade point average (GPA) of the seniors selected was 2.85, and the standard deviation was 0.4. Select all of the statements that are true.

(Note: Margin of error ≈ 2 \frac{s}{\sqrt{n}}, where s is the standard deviation and n is the sample size.)

Required

1

The police chief of a town is trying to determine the average speed of drivers on a specific road.
The police chief took a random sample of the speeds of 100 drivers on the road.
The mean was 48.5 miles per hour, with a standard deviation of 2.5 miles per hour.
The police chief wanted to decrease the margin of error of his next sample.
Which choice would decrease the margin of error?

(Note: Margin of error ≈ 2\frac{s}{\sqrt{n}}, where s is the standard deviation and n is the sample size.)

End-of-Course (EOC) Math 3

What is the remainder when x^{3} - 1 is divided by (x + 2)?

The function below, f(x), has (x - 7) and (x + 4i) as factors.f(x) = 2x^{5} - 13x^{4} + 22x^{3} - 187x^{2} - 160x + 336What is the total number of real zeros of f(x)?

The graph of the function m(x) = x^{3} + 3x^{2} - 2x - 4 has a zero at -1. What are the other zeros of the function?

Which expression is equivalent to (x^{2}-2x-37)÷{(x^2 - 3x - 40)}?

Which expression is equivalent to \frac{(x² - 5x + 6)^{-1}}{(x - 2)^{-2}}÷\frac{(x - 3)^{-1}}{(x - 2)^{-2}} ?

The graph of an equation is shown below.Which equation represents the graph?

Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?

Two functions are shown below.f(x) = 2x^{3} + 2x - 3g(x) = -0.5|x - 4|What is the y-value when f(x) = g(x)?

Which choice is equivalent to the expression shown below?48x^{3}-243xy^{2}

A polynomial, p(x), has a lead coefficient of 1 and exactly three distinct zeros.x = -1 is a zero of multiplicity twox = 2 is a zero of multiplicity onex = 4 is a zero of multiplicity oneWhat choice shows p(x)?

If f(x) = k(x - 2)^4, where k is positive, what is the effect on the graph of f(x) as k increases?

Two piecewise functions are shown below.h(x) = \begin{cases} -3x & \text{for } x < 2 \\ 4x + 1 & \text{for } x \ge 2 \end{cases}g(x) = \begin{cases} x^2 + 2 & \text{for } x < 3 \\ x^3 & \text{for } x \ge 3 \end{cases}What is the value of 3h(2) + 4g(1)?

A function is shown below.h(x) = \begin{cases} -\frac{1}{2}x - 15 & \text{for } x \leq -4 \\ 20 - 3x^2 & \text{for } x > -4 \end{cases} What is the value of h(-4) + 3h(-2)?

A function is shown below:H(x) = 4x^{3} - 5x^{2} - 23x + 6What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

Which function does not have the set of all real numbers as its domain?

An equation is shown below.9^{-3x + 2} = 48 What is the value of x to the nearest ten-thousandth?

The vertices of a triangle are at (0, 0), (6, 6), and (9, 3). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x?

In parallelogram MNPT, m∠M = (6x + 10)° and m∠N = (5x + 10.5)°. How many degrees is ∠T?

In rectangle FGHI, diagonals \overline{FH} and \overline{GI} intersect at E.IE = 3x + 4EG = 5x - 6What is the length of \overline{FH}?

Triangle PMT is shown below.What is the measure of segment PG?

What is the length of a radius of the circle represented by the equation x^{2} + y^{2} - 4x - 4y + 4 = 0?

Which method is most likely to produce a random sample of 5 students from a school club?

What is the remainder when x^{3} - 1 is divided by (x + 2)?

The function below, f(x), has (x - 7) and (x + 4i) as factors.f(x) = 2x^{5} - 13x^{4} + 22x^{3} - 187x^{2} - 160x + 336What is the total number of real zeros of f(x)?

The graph of the function m(x) = x^{3} + 3x^{2} - 2x - 4 has a zero at -1. What are the other zeros of the function?

Which expression is equivalent to (x^{2}-2x-37)÷{(x^2 - 3x - 40)}?

Which expression is equivalent to \frac{(x² - 5x + 6)^{-1}}{(x - 2)^{-2}}÷\frac{(x - 3)^{-1}}{(x - 2)^{-2}} ?

The graph of an equation is shown below.Which equation represents the graph?

Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?

Two functions are shown below.f(x) = 2x^{3} + 2x - 3g(x) = -0.5|x - 4|What is the y-value when f(x) = g(x)?

Which choice is equivalent to the expression shown below?48x^{3}-243xy^{2}

A polynomial, p(x), has a lead coefficient of 1 and exactly three distinct zeros.x = -1 is a zero of multiplicity twox = 2 is a zero of multiplicity onex = 4 is a zero of multiplicity oneWhat choice shows p(x)?

If f(x) = k(x - 2)^4, where k is positive, what is the effect on the graph of f(x) as k increases?

Two piecewise functions are shown below.h(x) = \begin{cases} -3x & \text{for } x < 2 \\ 4x + 1 & \text{for } x \ge 2 \end{cases}g(x) = \begin{cases} x^2 + 2 & \text{for } x < 3 \\ x^3 & \text{for } x \ge 3 \end{cases}What is the value of 3h(2) + 4g(1)?

A function is shown below.h(x) = \begin{cases} -\frac{1}{2}x - 15 & \text{for } x \leq -4 \\ 20 - 3x^2 & \text{for } x > -4 \end{cases} What is the value of h(-4) + 3h(-2)?

A function is shown below:H(x) = 4x^{3} - 5x^{2} - 23x + 6What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

Which function does not have the set of all real numbers as its domain?

An equation is shown below.9^{-3x + 2} = 48 What is the value of x to the nearest ten-thousandth?

The vertices of a triangle are at (0, 0), (6, 6), and (9, 3). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x?

In parallelogram MNPT, m∠M = (6x + 10)° and m∠N = (5x + 10.5)°. How many degrees is ∠T?

In rectangle FGHI, diagonals \overline{FH} and \overline{GI} intersect at E.IE = 3x + 4EG = 5x - 6What is the length of \overline{FH}?

Triangle PMT is shown below.What is the measure of segment PG?

What is the length of a radius of the circle represented by the equation x^{2} + y^{2} - 4x - 4y + 4 = 0?

Which method is most likely to produce a random sample of 5 students from a school club?

The function below, f(x), has (x - 7) and (x + 4i) as factors.

f(x) = 2x^{5} - 13x^{4} + 22x^{3} - 187x^{2} - 160x + 336

What is the total number of real zeros of f(x)?

The graph of an equation is shown below.

Which equation represents the graph?

Two functions are shown below.

f(x) = 2x^{3} + 2x - 3
g(x) = -0.5|x - 4|

What is the y-value when f(x) = g(x)?

Which choice is equivalent to the expression shown below?

48x^{3}-243xy^{2}

A polynomial, p(x), has a lead coefficient of 1 and exactly three distinct zeros.
x = -1 is a zero of multiplicity two
x = 2 is a zero of multiplicity one
x = 4 is a zero of multiplicity one
What choice shows p(x)?

Two piecewise functions are shown below.

h(x) = \begin{cases} -3x & \text{for } x < 2 \\ 4x + 1 & \text{for } x \ge 2 \end{cases}
g(x) = \begin{cases} x^2 + 2 & \text{for } x < 3 \\ x^3 & \text{for } x \ge 3 \end{cases}

What is the value of 3h(2) + 4g(1)?

A function is shown below.

h(x) = \begin{cases} -\frac{1}{2}x - 15 & \text{for } x \leq -4 \\ 20 - 3x^2 & \text{for } x > -4 \end{cases}

What is the value of h(-4) + 3h(-2)?

A function is shown below:

H(x) = 4x^{3} - 5x^{2} - 23x + 6

What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

An equation is shown below.

9^{-3x + 2} = 48

What is the value of x to the nearest ten-thousandth?

In rectangle FGHI, diagonals \overline{FH} and \overline{GI} intersect at E.

IE = 3x + 4
EG = 5x - 6
What is the length of \overline{FH}?

Triangle PMT is shown below.

What is the measure of segment PG?

The function below, f(x), has (x - 7) and (x + 4i) as factors.

f(x) = 2x^{5} - 13x^{4} + 22x^{3} - 187x^{2} - 160x + 336

What is the total number of real zeros of f(x)?

The graph of an equation is shown below.

Which equation represents the graph?

Two functions are shown below.

f(x) = 2x^{3} + 2x - 3
g(x) = -0.5|x - 4|

What is the y-value when f(x) = g(x)?

Which choice is equivalent to the expression shown below?

48x^{3}-243xy^{2}

A polynomial, p(x), has a lead coefficient of 1 and exactly three distinct zeros.
x = -1 is a zero of multiplicity two
x = 2 is a zero of multiplicity one
x = 4 is a zero of multiplicity one
What choice shows p(x)?

Two piecewise functions are shown below.

h(x) = \begin{cases} -3x & \text{for } x < 2 \\ 4x + 1 & \text{for } x \ge 2 \end{cases}
g(x) = \begin{cases} x^2 + 2 & \text{for } x < 3 \\ x^3 & \text{for } x \ge 3 \end{cases}

What is the value of 3h(2) + 4g(1)?

A function is shown below.

h(x) = \begin{cases} -\frac{1}{2}x - 15 & \text{for } x \leq -4 \\ 20 - 3x^2 & \text{for } x > -4 \end{cases}

What is the value of h(-4) + 3h(-2)?

A function is shown below:

H(x) = 4x^{3} - 5x^{2} - 23x + 6

What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

An equation is shown below.

9^{-3x + 2} = 48

What is the value of x to the nearest ten-thousandth?

In rectangle FGHI, diagonals \overline{FH} and \overline{GI} intersect at E.

IE = 3x + 4
EG = 5x - 6
What is the length of \overline{FH}?

Triangle PMT is shown below.

What is the measure of segment PG?