March 2026 Int.A Module2

\(\begin{aligned}
&\text{A cable company charges new customers a onetime installation fee and a monthly service}\\
&\text{fee for cable service. The equation }y = 50x + 120\text{ gives the total amount }y,\text{in dollars, the cable}\\
&\text{company charges new customers for }x\text{ months of cable service. What is the amount, in }\\
&\text{dollars, of the onetime installation fee the cable company charges new customers?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set X}: 13,16,19, 21, 24, 25, 25, 26, 38\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set Y}: 13,16,19, 21, 24, 25, 25, 26, 33\\
&\text{Data set Y is created by replacing the number 38 in data set X with the number 33. Which of }\\
&\text{the following statements is true about the means and medians of data set X and data set Y?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=4x+36\\
&\text{One of the two equations in a system of linear equations is given. The system has infinitely}\\
&\text{many solutions. Which equation could be the second equation in this system?}\end{aligned}\)

\(\text{If }x+3y=29\text{ and }7x-12y=-61\text{, what is the value of }y?\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~R=\frac{0.36l}{A}\\
&\text{The given equation relates the resistance }R\text{, in ohms, of a wire to its length }l\text{, in meters, and }\\
&\text{its cross-sectional area }A\text{, in square meters. Which equation correctly expresses the length,}\\
&\text{in meters, of the wire in terms of its resistance, in ohms, and its cross-sectional area, in}\\
&\text{square meters?}\end{aligned}\)

\(\begin{aligned}
&\text{For the polynomial function }f\text{, the graph of }y = f(x)\text{ in the }xy\text{-plane passes through }\\
&\text{the points }(-5,0),(3,0)\text {, and }(7,0)\text{. Which of the following must be a factor of }f(x)?\end{aligned}\)

\(\text{Which shaded region represents the solutions to the inequality }4x+5y < 9?\)

\(\begin{aligned}&\text{In the }xy\text{-plane, line }k\text{ has a slope of }\frac{6}{13},\text{an }x\text{-intercept of }(-6,0)\text{, and a }\\&y\text{-intercept of }(0, p)\text{. What is the value of }p?\end{aligned}\)

\(\text{If }\frac{x+6}{5}=\frac{x+6}{13},\text{ the value of }x+6\mathrm{~is~between~which~of~the~following~pairs~of~values?}\)

\(\text{The price of an item increased by }p\%\text{ from \$90 to \$93. What is the value of }p?\)

\(\begin{aligned}
&\text{The measure of angle }S\text{ is }\frac{8\pi}{11}\text{ radians. The measure of angle }T\mathrm{~is~}2\text{ times the measure of }\\
&\text{angle }S\text{. Which expression represents the measure, in }\textbf{degrees}\text{, of angle }T?\end{aligned}\)

\(\begin{aligned}&\text{The ratio }x\text{ to }y\text{ is equivalent to the ratio 4 to 7. If }x = 11t\text{, what is the value of }\\&y\text{ in terms of }t?\end{aligned}\)

\(\begin{aligned}
&\text{What is the }x\text{-intercept of the graph of }y=\frac{45-x}{ax+b}\text{ in the }xy\text{-plane, where }a\text{ and }b\\
&\text{are positive constants?}\end{aligned}\)

\(\begin{aligned}&\text{A research manager selected 2 random samples of ovens of a certain type to estimate the}\\&\text{average amount of time this type of oven takes to preheat to 350 degrees Fahrenheit( F).}\\&\text{The research manager recorded the amount of time, in minutes, each oven takes to preheat}\\&\text{to 350°F. Based on the first sample, the research manager estimated that this type of oven}\\&\text{takes an average of 14.2 minutes to preheat to 350°F, with an associated margin of error of}\\&\text{1 minute. Based on the second sample, the research manager estimated that this type of}\\&\text{oven takes an average of 14.4 minutes to preheat to 350°F, with an associated margin of}\\&\text{error of 2.2 minutes. Assuming the margins of error were calculated the same way, which of}\\&\text{the following best explains why the first sample obtained a smaller margin of error than the}\\&\text{second sample?}\end{aligned}\)

\(\text{The scatterplot shows the relationship between two variables, }t\text{ and }d.\)

\(\text{Which of the following equations is the most appropriate linear model for the data shown?}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=23(1.20)^{\frac{x}{4}}\\
&\text{For the given function }f\text{, the value of }f(x) \text{ increases by }p\%\text{ for every increase of }x\text{ by }8.\\
&\text{What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&\text{A model estimates that in a particular forest, the number of trees with any given diameter }\\
&\text{measured at shoulder height is }21\%\text{ less for each 1-inch increase in tree diameter measured}\\
&\text{at shoulder height. The model can be written in the form }f(x)=ab^{x},\text{ where }a\text{ and }b\text{ are}\\
&\text{constants and }x\text{ is the tree’s diameter, in inches, measured at shoulder height, and }x\geq5.\\
&\text{The model estimates that 3,100 trees in this forest have a diameter of 13 inches measured }\\
&\text{at shoulder height. Which function best represents this model?}\end{aligned}\)

\(\begin{aligned}
&\text{The function }f\text{ is defined by }f(x)=a^x-b\text{, where }a\text{ and }b\text{ are constants. In the }\\
&xy\text{-plane, the graph of }y=f(x)\text{ passes through the points }(c, 11)\text{ and }(2c,221),\\
&\text{where }c\text{ is a constant. Which of the following could be the value of }b?\end{aligned}\)

\(\begin{aligned}
&\text{In triangle }ABC\text{, the measure of angle }A\text{ is 56° and }\overline{AC}=30\text{. In triangle }PQR\text{, the }\\
&\text{measure of angle }P\text{ is 56° and }\overline{PR} = 90\text{. Which additional piece of information is }\\
&\text{sufficient to prove that triangle }ABC\text{ is similar to triangle }PQR?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{5}{9}(5x+9)(x+\sqrt{5k+9})(x-\sqrt{5k+9})=0\\
&\text{In the given equation, }k\text{ is a positive constant. The product of the solutions to the equation is 81.}\\&\text{What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4x^{2}+px+w=-86\\
&\text{In the given equation, }p\mathrm{~and~}w\text{ are integer constants. The equation has exactly one real}\\
&\text{solution. Which is }\textbf{NOT}\text{ a possible value of }w?\end{aligned}\)

\(\begin{aligned}&\text{The expression }6x^4+17x^2+5\text{ can be rewritten as }(3x^2+a)(2x^2+b),\text{where }a\text{ and }b\\
&\text{are positive integers, or as }(3x^2+c)(2x^2+d)\text{, where }c\text{ and }d\text{ are positive non integers.}\\&\text{What is the value of }a+c?\end{aligned}\)