Unit 2 2024 — Unit Plan

A group of friends went to a movie theater and paid $$15.00$ for each movie ticket. The group of friends shared one container of popcorn that cost $$8.99$. Which equation can be used to determine the total cost, $c$, for $n$ tickets and the container of popcorn?

A. $c = 15n + 8.99$
B. $c = 8.99n + 15$
C. $c = 15(n + 8.99)$
D. $c = 8.99(n + 15)$

A scatter plot is shown below.

Image Description: A scatter plot on a coordinate plane with the $x$-axis from $0$ to $12$ and the $y$-axis from $0$ to $12$. Points are plotted at approximately: $(1, 1)$, $(2, 1)$, $(3, 2)$, $(3, 3)$, $(3, 5)$, $(4, 4)$, $(4, 4)$, $(4, 7)$, $(5, 2)$, $(5, 4)$, $(5, 4)$, $(6, 6)$, $(6, 6)$, $(6, 7)$, $(7, 6)$, $(7, 8)$, $(7, 8)$, $(8, 4)$, $(8, 6)$, $(8, 8)$, $(9, 7)$, $(10, 6)$, $(10, 9)$. The data shows a positive linear trend.

Which pair of points could be used to draw a line that best represents the relationship of the data?

A. $(4, 7)$ and $(8, 4)$
B. $(3, 3)$ and $(9, 7)$
C. $(2, 4)$ and $(6, 4)$
D. $(3, 2)$ and $(3, 4)$

Triangle ABC is rotated $90°$ about the origin and then reflected over the $y$ axis to form triangle $A'B'C'$. One of the angles in triangle ABC has a measure of $115°$. One of the angles in triangle $A'B'C'$ has a measure of $40°$. Which is the measure of an angle in triangle ABC?

A. $25°$
B. $75°$
C. $155°$
D. $180°$

What is the value of $x$ in the equation $\frac{2}{3}x - 7 = 5 - \frac{3}{5}x$?

A. $3\frac{18}{19}$
B. $9\frac{9}{19}$
C. $15\frac{1}{5}$
D. $19\frac{1}{5}$

Two electricians, Electrician A and Electrician B, offer pricing plans for their work. Each electrician charges an initial fee for a service call plus an hourly rate. The charges for each electrician are represented by the equation and the table shown below.

ELECTRICIAN A

$C = 25x + 50$

ELECTRICIAN B

Which statement comparing the charges for each electrician is true?

A. Electrician A has an initial fee and an hourly rate that are both less than those for Electrician B.
B. Electrician A has an initial fee and an hourly rate that are both greater than those for Electrician B.
C. Electrician A has an initial fee that is less than that for Electrician B. The hourly rate for Electrician A is greater than that for Electrician B.
D. Electrician A has an initial fee that is greater than that for Electrician B. The hourly rate for Electrician A is less than that for Electrician B.

What is the slope of the line on a coordinate plane that passes through the points $(2, 2)$ and $(-1, -2)$?

A. $-\frac{4}{3}$
B. $-\frac{3}{4}$
C. $\frac{3}{4}$
D. $\frac{4}{3}$

A sphere has a radius of $4$ inches. A cone has a radius of $3$ inches and a height of $8$ inches. Which expression represents the difference in volume, in cubic inches, between the sphere and the cone?

A. $\pi\left[\frac{4}{3}(4^3) - \frac{1}{3}(3^2)(8)\right]$
B. $\pi\left[\frac{4}{3}(4^2) - \frac{1}{3}(3^2)(8)\right]$
C. $\pi\left[\frac{4}{3}(4^3) - \frac{1}{3}(8^2)(3)\right]$
D. $\pi\left[\frac{4}{3}(4^2) - \frac{1}{3}(8^2)(3)\right]$

Which value of $x$ makes the equation $x^3 = 64$ true?

A. $4$
B. $8$
C. $16$
D. $32$

The scatter plot below shows the weight, in pounds, of an alligator as it grows at a zoo. The line $y = 0.3x + 5.8$ has been drawn to best represent the relationship between the alligator's weight and growth time.

Image Description: A scatter plot titled "ALLIGATOR'S WEIGHT." The $x$-axis is labeled "Time (weeks)" and ranges from $0$ to $50$. The $y$-axis is labeled "Weight (pounds)" and ranges from $0$ to $30$. Data points are scattered showing a positive linear trend.

Which statement best describes what the number $0.3$ in the equation represents in this situation?

A. The starting weight, in pounds, of the alligator.
B. The approximate number of pounds the alligator gains each week.
C. The maximum number of pounds the alligator gains each week.
D. The average number of pounds of food the alligator is fed each week.

Trapezoid ABCD and its image A'B'C'D' are shown on the coordinate plane below.

Image Description: A coordinate plane with the $x$-axis and $y$-axis ranging from $-10$ to $10$. Trapezoid ABCD is in the left half of the plane with vertices at $A(-10, -4)$, $B(-8, -8)$, $C(-4, -8)$, and $D(-4, -4)$. Trapezoid A'B'C'D' is in the right half of the plane with vertices at $A'(10, -4)$, $B'(8, -8)$, $C'(4, -8)$, and $D'(4, -4)$.

Which series of transformations could be applied to map trapezoid ABCD onto trapezoid A'B'C'D'?

A. reflection over the $x$ axis and then a rotation of $180°$ about the origin
B. reflection over the $x$ axis and then a rotation of $90°$ about the origin
C. reflection over the $y$ axis and then a rotation of $180°$ about the origin
D. reflection over the $y$ axis and then a rotation of $90°$ about the origin

Which equation represents a linear function?

A. $y = \frac{1}{2}x - 3$
B. $y = x^2 + 5$
C. $y = x^2 + 2x$
D. $y = \frac{1}{5}x^3$

On a coordinate plane, triangle ABC is rotated $90$ degrees clockwise about the origin and then dilated with a scale factor of $2$ centered at the origin to form triangle A'B'C'. Which statement describes the relationship between triangle ABC and triangle A'B'C'?

A. They are similar and congruent.
B. They are similar but not congruent.
C. They are congruent but not similar.
D. They are neither congruent nor similar.

One of the angles in a triangle measures $x$ degrees. Another angle in the triangle measures $y$ degrees. Which expression represents the measurement, in degrees, of the third angle of the triangle?

A. $180 - (x + y)$
B. $180 - x + y$
C. $x + y - 180$
D. $x + y + 180$

Which expression is equivalent to $3^5$?

A. $\frac{3^{10}}{3^5}$
B. $\frac{3^{15}}{3^3}$
C. $\frac{9^{10}}{3^5}$
D. $\frac{9^3}{9^5}$

Which list of numbers could represent the side lengths of a right triangle?

A. $5, 10, 13$
B. $5, 12, 17$
C. $10, 24, 26$
D. $10, 24, 68$

The table below represents a function.

Which statement describes the function?

A. The function is nonlinear because the $y$ intercept is $0$.
B. The function is linear because the rate of change is constant.
C. The function is linear because the $y$ intercept is a constant value.
D. The function is nonlinear because the rate of change is not constant.

Quadrilateral FGHJ is rotated about the origin to form quadrilateral F'G'H'J'.

Image Description: A coordinate plane with the $x$-axis ranging from $-7$ to $7$ and the $y$-axis ranging from $-1$ to $7$. Quadrilateral FGHJ has vertices at $F(0, 0)$, $G(4, 0)$, $H(6, 5)$, and $J(2, 5)$. Quadrilateral F'G'H'J' has vertices at $F'(0, 0)$, $G'(0, 4)$, $H'(-5, 6)$, and $J'(-5, 2)$. The rotation appears to be $90°$ counterclockwise about the origin.

Which two sides are equal in length?

A. $\overline{FG}$ and $\overline{F'J'}$
B. $\overline{JF}$ and $\overline{H'J'}$
C. $\overline{GH}$ and $\overline{H'G'}$
D. $\overline{HG}$ and $\overline{H'J'}$

A manufacturer makes cylindrical cans in two sizes. The dimensions of each can are shown in the diagram below.

Image Description: Two cylinders are shown side by side.

• Large Can: Radius of $3.5$ cm and a height of $10$ cm.
• Small Can: Diameter of $7$ cm and a height of $6$ cm.

What is the difference between the volumes, in cubic centimeters, of the large can and the small can in terms of $\pi$?

A. $4\pi$
B. $49\pi$
C. $73.5\pi$
D. $155.5\pi$

An equation is shown below.

$$2(3x + 1) = x + 1 + 5x$$

Which statement about the equation is true?

A. It has no solutions.
B. It has exactly one solution.
C. It has exactly two solutions.
D. It has an infinite number of solutions.

Which statement best describes the value of $\sqrt{2}$?

A. between $0.5$ and $1.0$
B. between $1.5$ and $2.0$
C. between $1.0$ and $1.5$ but closer to $1.0$
D. between $1.0$ and $1.5$ but closer to $1.5$

A set of ordered pairs is shown below.

$$\{(-3, 3),\ (1, 1),\ (4, 2),\ (-1, -1),\ (-2, -1),\ (3, 1),\ (-2, 3)\}$$

Which ordered pair should be removed to make the set a function?

A. $(-3, 3)$
B. $(4, 2)$
C. $(-2, -1)$
D. $(3, 1)$

A movie theater sells popcorn in cone shaped containers as shown below.

Image Description: A cone with the point facing down, labeled "POPCORN CONTAINER." The radius of the circular opening at the top is labeled $3$ in. (shown as a dashed line from the center to the edge). The height of the cone is labeled $5$ in.

What is the volume, in cubic inches, of the popcorn container? Round your answer to the nearest tenth.

The area of a square shaped garden is $324$ square feet. What is the length, in feet, of each side of the garden?

Line segment AB is graphed on the coordinate plane shown below.

Image Description: A coordinate plane with the $x$-axis and $y$-axis each ranging from $-10$ to $10$. A line segment is drawn from point $A(2, -4)$ to point $B(7, 8)$. Point A is in quadrant IV and point B is in quadrant I.

What is the length, in units, of line segment AB?

In the figure below, line $p$ is parallel to line $q$ and lines AD and AF are transversals.

Image Description: Two horizontal parallel lines $p$ (upper) and $q$ (lower) are shown with arrows on both ends. Two transversal lines cross both parallel lines, meeting at point $A$ above line $p$. The left transversal passes through point $B$ on line $p$ and continues down through line $q$ to point $D$ below. The right transversal passes through point $C$ on line $p$ and continues down through line $q$ to point $F$ below. At the intersection of the left transversal with line $q$, the angle between the transversal going down to $D$ and line $q$ going right is labeled $110°$. At the intersection of the right transversal with line $q$, the angle between the transversal going down to $F$ and line $q$ going left is labeled $105°$.

What is the measure, in degrees, of $\angle BAC$?

Show your work.

The equation $y = 1.5x + 29$ is used to model the yearly salary, $y$, of an employee, in thousands of dollars, where $x$ is the number of years the employee has worked for the company. What does the slope of the line represent in this situation?

Explain your answer.

A dog owner collected data to see which of his two dogs runs at the greater speed. The graph and the table below show the relationship between the time, in seconds, and the distance, in feet, each dog ran.

DOG A

DOG B

Image Description: A graph with the $x$-axis labeled "Time (seconds)" ranging from $0$ to $10$ and the $y$-axis labeled "Distance (feet)" ranging from $0$ to $200$. A straight line passes through the origin and through the point $(8, 200)$, showing a constant speed of $25$ feet per second.

What is the difference, in feet per second, between the speeds of the two dogs?

Show your work.

Two ordered pairs of a linear function are shown below.

$$\left(2, 4\frac{1}{2}\right), \left(3, 5\frac{1}{4}\right)$$

What is the rate of change for the function?

Show your work.

What value of $x$ makes the equation shown below true?

$$\frac{1}{4}(3x - 8) + 4 = 2(x - 4)$$

Show your work.

A list of numbers is shown below.

• $\sqrt{49}$
• $1.\overline{3}$
• $\sqrt{32}$
• $\frac{7}{2}$
• $1.234$

Classify each number as either rational or irrational. Be sure to include how you know a number is rational.

Explain your answer.

Store A and Store B sell fabric for different prices. The equation $y = 3.5x$ represents the price, $y$, in dollars, for $x$ yards of fabric at Store A. The graph below represents the price for the same type of fabric at Store B.

STORE B

Image Description: A graph with the $x$-axis labeled "Fabric Length (yards)" ranging from $0$ to $10$ and the $y$-axis labeled "Total Price (dollars)" ranging from $0$ to $30$. A straight line passes through the origin and through the labeled points $(2, 5.5)$ and $(6, 16.5)$.

What is the unit rate for the price of fabric, per yard, at each store?

Store A $$$ _____ per yard of fabric

Store B $$$ _____ per yard of fabric