Unit 3 2025 — Unit Plan

A set of data is graphed on a scatter plot. Which scatter plot of the data shows a line that could be used to best model the relationship of the data?

A. [Image Description: A scatter plot with the $x$-axis from $0$ to $10$ and the $y$-axis from $0$ to $8$. Data points are scattered showing a general downward trend from left to right. A line with a steep negative slope is drawn through the data, declining sharply from the upper-left to the lower-right.]
B. [Image Description: A scatter plot with the same data points as in option A. A roughly horizontal line is drawn through the data, suggesting little to no relationship between $x$ and $y$.]
C. [Image Description: A scatter plot with the same data points as in option A. A line with a moderate negative slope is drawn through the center of the data, closely following the general downward trend of the points.]
D. [Image Description: A scatter plot with the same data points as in option A. A line with a positive slope is drawn through the data, suggesting an upward trend from left to right, which contradicts the downward pattern of the data points.]

A vertical plane intersects a right rectangular pyramid as shown below.

Image Description: A three-dimensional diagram of a right rectangular pyramid with a vertical plane slicing through it from the apex to the base. The plane passes through the apex of the pyramid and cuts vertically down to the rectangular base, creating a triangular cross-section.

What is the resulting two-dimensional shape formed by the intersection of the plane and the pyramid?

A. parallelogram
B. rectangle
C. trapezoid
D. triangle

The diagram below shows a person flying a kite. They let out $20$ feet of string and are holding the end of the string $4$ feet above the ground. The kite is directly above a spot on the ground that is $15$ feet away from where they are standing.

Image Description: A diagram showing a person on the left holding a kite string at $4$ feet above the ground. The string extends $20$ feet to a kite in the upper right. The horizontal distance along the ground from the person to the point directly below the kite is $15$ feet. A dashed vertical line from the ground to the kite's height is shown, with $x$ representing the vertical distance from the person's hand height to the kite, and $4$ ft representing the height from the ground to the horizontal level. A right angle is marked where the vertical meets the horizontal.

Which equation can be used to determine the value of $x$?

A. $x^2 = 20^2 + 15^2$
B. $24^2 = 15^2 + x^2$
C. $20^2 = 19^2 + x^2$
D. $20^2 = 15^2 + x^2$

The graph of a line is shown below.

Image Description: A coordinate plane with the $x$-axis ranging from $-4$ to $6$ and the $y$-axis ranging from $-1$ to $5$. A line with a negative slope passes through the points $(0, 3)$ and $(6, 0)$.

What is the equation of the line?

A. $y = -2x + 3$
B. $y = -2x + 6$
C. $y = -\frac{1}{2}x + 3$
D. $y = -\frac{1}{2}x + 6$

A soccer ball has a diameter of $23$ centimeters. What is the volume, to the nearest cubic centimeter, of the soccer ball?

A. $1{,}593$
B. $6{,}371$
C. $12{,}741$
D. $50{,}965$

An equation is shown below.

$$-6(x - 4) + 5x = -9x$$

Which value of $x$ makes the equation true?

A. $-3$
B. $-2.4$
C. $0.5$
D. $3$

A set of numbers is shown below.

$$\left\{\frac{1}{3},\ 1.1\overline{3},\ \sqrt{5},\ \frac{5}{2}\right\}$$

What number would need to be removed from the set so that the set contains only rational numbers?

A. $\frac{1}{3}$
B. $1.1\overline{3}$
C. $\sqrt{5}$
D. $\frac{5}{2}$

Which expression is equivalent to $3^5$?

A. $\frac{(3^6 \cdot 3^4)}{3^2}$
B. $(3^2)^2 \cdot 3$
C. $(3^3)^2$
D. $\frac{3^{15}}{3^3}$

Rectangle JKLM is graphed on the coordinate plane shown below. Rectangle JKLM will be translated $5$ units right and $2$ units up to produce rectangle J'K'L'M'.

Image Description: A coordinate plane with both axes ranging from $-10$ to $10$. Rectangle JKLM has vertices at $J(1, 4)$, $K(1, 1)$, $L(3, 1)$, and $M(3, 4)$.

Which statement about the line segments of rectangle J'K'L'M' is true?

A. $\overline{J'K'} \parallel \overline{J'M'}$
B. $\overline{J'K'} \parallel \overline{L'M'}$
C. $\overline{K'L'} \parallel \overline{J'K'}$
D. $\overline{K'L'} \parallel \overline{L'M'}$

Figure ABCD is shown on the coordinate plane below. The figure will be dilated by a scale factor of $2$, with the center of the dilation at the origin. The resulting image will be figure A'B'C'D'.

Image Description: A coordinate plane with both axes ranging from $-10$ to $10$. Figure ABCD is a quadrilateral with vertices at approximately $A(-3, 4)$, $B(-3, 0)$, $C(-1, 2)$, and $D(-1, 3)$.

What will be the coordinates of vertex A'?

A. $(-5, 6)$
B. $(-3, 6)$
C. $(-3, 8)$
D. $(-6, 8)$

A diagram of a right cone is shown below.

Image Description: A right cone with a dashed line showing the height of $8$ yd from the apex to the center of the circular base, with a right angle mark at the base. The diameter of the circular base is labeled $6$ yd.

What is the volume, in cubic yards, of the cone?

A. $14\pi$
B. $24\pi$
C. $72\pi$
D. $96\pi$

A transformation maps $\triangle ABC$ to $\triangle A'B'C'$. If $\triangle A'B'C'$ is similar but not congruent to $\triangle ABC$, which transformation occurred?

A. a rotation about the origin
B. a reflection over the $y$-axis
C. a dilation with a scale factor not equal to 1
D. a translation of 1 unit in both the $x$ and $y$ directions

An equation is shown below.

$$8 - 12x = h(3x - 4)$$

For which value of $h$ will this equation have no solutions?

A. $-4$
B. $-2$
C. $3$
D. $4$

The diagram below shows three intersecting lines.

Image Description: Three lines intersect at a single point. One line is horizontal. Two other lines pass through the same intersection point. The angle on the upper-left side of the horizontal line, between the horizontal line and one of the other lines, is labeled $(6x - 23)°$. The angle on the lower-right side of the horizontal line, between the horizontal line and another line, is labeled $(4x + 11)°$. These two angles are vertical angles.

What is the value of $x$?

A. $6$
B. $10.2$
C. $17$
D. $19.2$

Alex and Taylor are comparing the costs of their gym memberships.

• The total cost, $y$, in dollars, of Alex's gym membership for $x$ months is represented by the equation $y = 15x$.
• The total cost of Taylor's gym membership is represented by the graph shown below.

Image Description: A graph titled "TAYLOR'S GYM MEMBERSHIP" with the $x$-axis labeled "Number of Months" (0 to 10) and the $y$-axis labeled "Cost (dollars)" (0 to 250). A straight line passes through the origin $(0, 0)$ and $(10, 250)$, indicating a rate of $$25$ per month.

Which statement identifies the gym membership with the lower cost per month?

A. Alex's gym membership at a cost of $10.00 per month
B. Alex's gym membership at a cost of $15.00 per month
C. Taylor's gym membership at a cost of $15.00 per month
D. Taylor's gym membership at a cost of $25.00 per month

What is the value of the expression $2^5 \cdot 10^0 \cdot 3^{-2}$?

A. $-288$
B. $-90$
C. $\frac{0}{9}$
D. $\frac{32}{9}$

Trapezoid ABCD was rotated $180°$ about the origin to create trapezoid PQRS, as shown below.

Image Description: A coordinate plane with the $x$-axis from $-9$ to $9$ and the $y$-axis from $-4$ to $4$. Trapezoid ABCD is in the third quadrant with vertices at approximately $A(-6, -1)$, $B(-3, -1)$, $C(-2, -3)$, and $D(-7, -3)$. Trapezoid PQRS is in the first quadrant with vertices at approximately $P(6, 1)$, $Q(3, 1)$, $R(2, 3)$, and $S(7, 3)$.

Which statement about the trapezoids is true?

A. Angle A is congruent to angle S.
B. Angle C is congruent to angle Q.
C. Side BC is congruent to side QR.
D. Side DC is congruent to side RQ.

Brayden and Hannah were asked to calculate the slope of the same line. Brayden calculated the slope to be $\frac{2}{3}$ and Hannah calculated the slope to be $\frac{4}{6}$. Their work is shown below.

Image Description: Two coordinate planes side by side.

• Brayden's Work: A line with a positive slope and a $y$-intercept at $(0, 1)$. A slope triangle is drawn from $(0, 1)$ to $(3, 3)$, with arrows showing a rise of $2$ units up and a run of $3$ units to the right, giving a slope of $\frac{2}{3}$.
• Hannah's Work: The same line with a $y$-intercept at $(0, 1)$. A slope triangle is drawn from $(-3, -1)$ to $(3, 3)$, with arrows showing a rise of $4$ units up and a run of $6$ units to the right, giving a slope of $\frac{4}{6}$.

Which statement is true?

A. Only Brayden calculated the slope correctly.
B. Only Hannah calculated the slope correctly.
C. Both Brayden and Hannah calculated the slope correctly.
D. Neither Brayden nor Hannah calculated the slope correctly.

The table of values shown below represents a relation.

Which statement describes the relation?

A. The table represents a function because each input has only one output.
B. The table represents a function because each output has only one input.
C. The table does not represent a function because each input has only one output.
D. The table does not represent a function because each output has only one input.

On which number line does point P represent the value of the expression $\sqrt{4} + \sqrt{10}$?

A. [Image Description: A number line from $-1$ to $8$. Point P is located just before $3$.]
B. [Image Description: A number line from $-1$ to $8$. Point P is located just before $4$.]
C. [Image Description: A number line from $-1$ to $8$. Point P is located slightly more than $5$.]
D. [Image Description: A number line from $-1$ to $8$. Point P is located at approximately $7$, almost exactly at $7$.]

A scatter plot is shown below.

Image Description: A scatter plot with $x$-axis from $0$ to $60$ and $y$-axis from $0$ to $60$. Approximately 25 data points are plotted showing a general upward trend from lower left to upper right. Points range from roughly $(5, 5)$ to $(45, 55)$, with the data following an approximately linear positive pattern.

Which statement best describes the association between $x$ and $y$?

A. There is a positive, linear association.
B. There is a negative, linear association.
C. There is a positive, nonlinear association.
D. There is a negative, nonlinear association.

This question is worth 1 credit.

A table of values for a linear function is shown below.

What is the rate of change for this function?

This question is worth 1 credit.

A circular dart board has a circumference of $17.75\pi$ inches. What is the radius, in inches, of the dart board?

This question is worth 1 credit.

David and Lisa each earn money by mowing lawns. They both charge a one time maintenance fee and an hourly rate. David's total charges, based on the number of hours he mows a lawn, are shown in the table below. The total charges, $y$, in dollars, for Lisa mowing the lawn for $x$ hours is represented by the equation $y = 6x + 12$.

What is the difference, in dollars, between the one time maintenance fee David charges and the one time maintenance fee Lisa charges?

This question is worth 2 credits.

Classify $\sqrt{1.44}$ as being rational or irrational.

Explain how you know your answer is correct.

This question is worth 2 credits.

The equations of two functions are shown below.

Function A: $y = 3x + 8$

Function B: $y = x^2 + 2$

Classify each function as linear or nonlinear.

Explain how you determined your answer.

This question is worth 2 credits.

The graph shown below represents the time and speed of a roller coaster over the course of the entire ride.

Image Description: A graph titled "ROLLER COASTER SPEED" with the $x$-axis labeled "Time (seconds)" ranging from $0$ to $45$ and the $y$-axis labeled "Speed (mph)" ranging from $0$ to $90$. The curve starts at $(0, 0)$ and increases non-linearly (a curve) up to a peak of approximately $50$ mph around $t = 25$ seconds. From $25$ to $30$ seconds, the speed decreases quickly along a non-linear curve down to $30$ mph. From $30$ to $40$ seconds, the roller coaster travels at a constant speed of $30$ mph (a horizontal line segment). From $40$ to $45$ seconds, the speed decreases at a constant rate (a straight line) from $30$ mph to $0$ mph.

Based on the graph, during what interval of time, in seconds, is the speed, in miles per hour, of the roller coaster constant? Be sure to include what the constant speed is, in miles per hour, for that interval in your answer.

Explain your answer.

This question is worth 2 credits.

An equation is shown below.

$$\frac{2}{3}(3x + 9) = x - 4$$

What value of $x$ will make the equation true?

Show your work.

This question is worth 2 credits.

Triangle ABC is graphed on the coordinate plane shown below. Triangle ABC will be reflected over the $y$ axis to create triangle A'B'C'.

Image Description: A coordinate plane with axes from $-7$ to $7$. Triangle ABC has vertices at $A(-3, 4)$, $B(-5, -1)$, and $C(1, 2)$.

What will be the coordinates of vertex A'?

Explain how you determined your answer.

This question is worth 2 credits.

A student used the diagram shown below to support their work in representing the relationship among the lengths of the sides, in units, of a right triangle.

Image Description: A diagram showing a right triangle with sides labeled $a$, $b$, and $c$. Squares are drawn on each side of the triangle: a square with side length $a$, a square with side length $b$, and a square with side length $c$ (the hypotenuse). The square on side $a$ appears to be a $3 \times 3$ grid (9 unit squares), the square on side $b$ appears to be a $4 \times 4$ grid (16 unit squares), and the square on side $c$ appears to be a $5 \times 5$ grid (25 unit squares).

The student then showed how the diagram relates to the Pythagorean theorem, but made an error as shown below.

$$a^2 + b^2 = c^2$$

$$5^2 + 4^2 = 3^2$$

$$25 + 16 \neq 9$$

$$41 \neq 9$$

What is the error that the student made and what are the correct steps needed to show how the Pythagorean theorem shows the relationship among the lengths of the sides, in units, of the right triangle?

Explain your answer.

This question is worth 3 credits.

Kaley and Mark each tracked their total amount of sleep, to the nearest hour, for a science project and determined that their total hours of sleep is proportional to the total number of nights. The graph and the table shown below represent the sleep times for Kaley and Mark.

Image Description: A graph titled "KALEY'S SLEEP TIME" with the $x$-axis labeled "Total Number of Nights" (0 to 6) and the $y$-axis labeled "Total Time (hours)" (0 to 42). Points are plotted at $(1, 7)$, $(2, 14)$, $(3, 21)$, $(4, 28)$, and $(5, 35)$, showing a proportional relationship with a rate of $7$ hours per night.

Based on the graph and the table, determine who gets more sleep per night.

Explain how you determined your answer.