Unit 5 August 2025 — Unit Plan

Which expression is equivalent to $100x^2 - 16$?

(1) $(50x - 8)(50x + 8)$
(2) $(50x - 8)(50x - 8)$
(3) $(10x - 4)(10x + 4)$
(4) $(10x - 4)(10x - 4)$

Josie has $2.30 in dimes and quarters. She has two more dimes than quarters. Which equation below can be used to determine $x$, the number of quarters she has?

(1) $0.35(2x + 2) = 2.30$
(2) $0.25(x + 2) + 0.10x = 2.30$
(3) $0.25x + 0.10(x + 2) = 2.30$
(4) $0.25x + 0.10(x - 2) = 2.30$

If $g(x) = -2x^2 + 16$, then $g(-3)$ equals

(1) $-20$
(2) $-2$
(3) $34$
(4) $52$

What are the zeros of $f(x) = x^2 - 8x - 20$?

(1) $10$ and $2$
(2) $10$ and $-2$
(3) $-10$ and $2$
(4) $-10$ and $-2$

Which point lies on the graph of $y = 3x^2 - \frac{1}{4}x + 3$?

(1) $(-2, 15.5)$
(2) $(-1, 5.75)$
(3) $(1, 6.25)$
(4) $(2, 15.5)$

Given $f(x) = x^2$ and $g(x) = 8x - 15$ graphed on the same set of axes, which value(s) of $x$ will make $f(x) = g(x)$?

(1) $3$, only
(2) $9$, only
(3) $3$ and $5$
(4) $9$ and $25$

Which trinomial is written in standard form and has a constant term of five?

(1) $x^5 - 4x^2 + 10$
(2) $2x^2 + 6x^4 + 5$
(3) $5x^4 - 3x^2 + 1$
(4) $4x^5 - 8x^2 + 5$

When solving $x^2 + 6x = -8$ for $x$, a student wrote $x^2 + 6x + 8 = 0$ as their first step. Which property justifies this step?

(1) associative property
(2) commutative property
(3) zero property of addition
(4) addition property of equality

The tables below show the input and output values of four different functions.

Which table represents a linear function?

(1) $f(x)$
(2) $g(x)$
(3) $h(x)$
(4) $j(x)$

What is the solution set to the equation $3x^2 = 24x$?

(1) $\{8\}$
(2) $\{0, 8\}$
(3) $\{0, -8\}$
(4) $\{0, 8, -8\}$

The table below shows the radioactivity level of a substance after the given time, $t$, in seconds.

What is the average rate of change in radioactivity level over the interval $1 \leq t \leq 3$?

(1) $3.75$
(2) $-3.75$
(3) $4.6875$
(4) $-4.6875$

Fred recorded the number of minutes he read each day, from Monday through Friday. His results are shown in the table.

What is the correlation coefficient, to the nearest thousandth, and strength of the linear model of these data?

(1) $0.984$ and strong
(2) $0.968$ and strong
(3) $0.984$ and weak
(4) $0.968$ and weak

Given $f(x) = x^2$, which function will shift $f(x)$ to the left 3 units?

(1) $g(x) = x^2 + 3$
(2) $h(x) = x^2 - 3$
(3) $j(x) = (x - 3)^2$
(4) $k(x) = (x + 3)^2$

A class of 20 students was surveyed to determine the number of pets each student owned. The data are represented in the dot plot below.

Image Description: A dot plot on a number line from 0 to 5, labeled "Number of Pets." The dots are stacked vertically above each value: 0 has 1 dot, 1 has 4 dots, 2 has 6 dots, 3 has 4 dots, 4 has 3 dots, and 5 has 2 dots.

Which statement about the data is correct?

(1) The mean and the median are the same.
(2) The median and the mode are the same.
(3) The mean and the mode are the same.
(4) The mean, median, and mode are all the same.

The range of $f(x) = |x + 2| - 5$ is

(1) $y \geq -5$
(2) $y \geq 2$
(3) $x \geq -5$
(4) $x \geq 2$

Which equation is always correct?

(1) $a^3 \cdot a^x = a^{3x}$
(2) $(a^4)^x = a^{4 + x}$
(3) $(ab)^x = a^x b^x$
(4) $a^x \cdot b^y = ab^{x + y}$

The formula for the area of a trapezoid is $A = \frac{1}{2}h(b_1 + b_2)$. The height, $h$, of the trapezoid may be expressed as

(1) $\frac{2A}{b_1 + b_2}$
(2) $\frac{1}{2}A(b_1 + b_2)$
(3) $\frac{b_1 + b_2}{2A}$
(4) $\frac{1}{2}A - (b_1 + b_2)$

Three functions are given below.

$f(x) = -|x + 2| + 7$

$g(x) = (x - 3)^2 - 4$

Which functions have the same $y$-intercept?

(1) $f(x)$ and $g(x)$
(2) $g(x)$ and $h(x)$
(3) $f(x)$ and $h(x)$
(4) The functions all have different $y$-intercepts.

The sum of $(x + 7)^2$ and $(x - 3)^2$ is

(1) $2x^2 + 58$
(2) $2x^4 + 58$
(3) $2x^2 + 8x + 58$
(4) $2x^4 + 8x^2 + 58$

The product of $2\sqrt{10}$ and $3\sqrt{2}$ is

(1) $12\sqrt{5}$
(2) $5\sqrt{20}$
(3) $24\sqrt{5}$
(4) $5\sqrt{12}$

When $6x^3 - 2x + 8$ is subtracted from $5x^3 + 3x - 4$, the result is

(1) $x^3 - 5x + 12$
(2) $x^3 + x + 4$
(3) $-x^3 + 5x - 12$
(4) $-x^3 + x + 4$

Three relations are shown below.

I. $\{(0,1), (1,2), (2,3), (3,4)\}$

II.

Image Description: A mapping diagram with two ovals. The left oval contains the numbers 3, 4, 5, 6. The right oval contains the numbers 3, 4, 5, 6. Arrows show: 3→3, 4→4, 5→5, 6→6.

III.

Image Description: A coordinate plane showing a step function. Horizontal line segments are drawn at different y-levels, each with an open circle on one end and a closed circle on the other, forming a staircase pattern going upward from left to right. The function passes the vertical line test.

Which relations represent a function?

(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III

The method of substitution was used to solve the system of equations below:

$$4x - 7y = 7$$

$$x - y = -1$$

Which equation is a correct first step when using this method?

(1) $x = y - 1$
(2) $y = x - 1$
(3) $3x - 6y = 8$
(4) $5x - 8y = 6$

In 2009, Usain Bolt, a sprinter from Jamaica, set the world record in the 100-meter dash with a time of 9.58 seconds. His approximate speed, in kilometers per hour, can be found using which conversion?

(1) $\frac{9.58 \text{ sec}}{100 \text{ m}} \cdot \frac{1000 \text{ m}}{1 \text{ km}} \cdot \frac{1 \text{ min}}{60 \text{ sec}} \cdot \frac{1 \text{ hr}}{60 \text{ min}}$

(2) $\frac{100 \text{ m}}{9.58 \text{ sec}} \cdot \frac{60 \text{ sec}}{1 \text{ min}} \cdot \frac{1000 \text{ m}}{1 \text{ km}} \cdot \frac{60 \text{ min}}{1 \text{ hr}}$

(3) $\frac{100 \text{ m}}{9.58 \text{ sec}} \cdot \frac{1 \text{ km}}{1000 \text{ m}} \cdot \frac{1 \text{ min}}{60 \text{ sec}} \cdot \frac{1 \text{ hr}}{60 \text{ min}}$

(4) $\frac{100 \text{ m}}{9.58 \text{ sec}} \cdot \frac{60 \text{ sec}}{1 \text{ min}} \cdot \frac{1 \text{ km}}{1000 \text{ m}} \cdot \frac{60 \text{ min}}{1 \text{ hr}}$

Solve the equation $\frac{1}{6}(4x + 12) = 9$ algebraically.

Is the sum of $3\sqrt{2}$ and $5$ rational or irrational? Explain your answer.

Graph $h(x) = |x - 2|$ over the domain $-4 \leq x \leq 4$.

Image Description: A blank coordinate grid with axes labeled $x$ (horizontal) and $h(x)$ (vertical). The grid extends from approximately $-8$ to $8$ on both axes.

A survey was given to 180 cell phone owners about the brand of phone they owned. The results showed that 59 adults owned Brand B and 32 teenagers owned Brand A. Of all the people surveyed, 40% owned Brand A. Complete the two-way frequency table below.

Determine the 8th term of a geometric sequence whose first term is 5 and whose common ratio is 3.

Using the method of completing the square, express $x^2 + 14x - 28 = 0$ in the form $(x - p)^2 = q$.

Graph $f(x) = -\frac{1}{3}x^2 + 4$ on the set of axes below.

Image Description: A blank coordinate grid with axes labeled $x$ (horizontal) and $f(x)$ (vertical).

State the vertex of this function.

State the equation of the axis of symmetry of this function.

Vince wants to rent a canoe while he is on vacation. The canoe rental company charges $18 for the first hour and $7.50 for each additional hour, $x$. If Vince has $78 to spend on renting a canoe, write an inequality in terms of $x$ that models this situation.

Algebraically determine the maximum number of hours that Vince could rent a canoe.

Graph the following system of inequalities on the set of axes below.

$$y \geq -\frac{1}{2}x - 3$$

$$y - 2x < 5$$

Image Description: A blank coordinate grid with axes labeled $x$ (horizontal) and $y$ (vertical).

State the coordinates of a point that is in the solution to this system. Justify your answer.

Using the quadratic formula, solve $x^2 - 6x + 3 = 0$.

Express the answer in simplest radical form.

Cameron sold hot dogs and sodas at a concession stand. He sold a total of 25 items for $45.00. A hot dog sold for $2.25 and a soda sold for $1.50. All prices include tax.

If $x$ represents the number of hot dogs sold and $y$ represents the number of sodas sold, write a system of equations that models this situation.

Determine algebraically the number of hot dogs Cameron sold and the number of sodas he sold.

A customer has $20 to spend at the concession stand. Determine and state the maximum number of hot dogs he can purchase if he buys four sodas.