November 2025 Int.D Module 2

\(\begin{aligned}
&\text{The equation }d=27w+100\text{ gives the total amount of money }d,\text{ in dollars, that Janna}\\
&\text{plans to save }w\text{ weeks after she starts to save. What is the total amount of money, in dollars}\\
&\text{she plans to save in 10 weeks?}\end{aligned}\)

\(\begin{aligned}&\text{The function }f(x)=\text{1,400}(0.5)^{\frac{x}{16}}\text{ gives the predicted intensity of a beam }f(x)\mathrm{,in~number}\\&\text{of photons in the beam, }x \text{ millimeters below the surface of a certain material. What is the}\\&\text{best interpretation of }f(16)=700?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\left(x-11\right)\left(x-7\right)=0\\&\text{Which value is a solution to the given equation?}\end{aligned}\)

\(\begin{aligned}
&\text{A survey of the daily commuting times, in minutes, of seven different Chicago-based}\\
&\text{employees at a certain company yielded a data set consisting of the values 32, 14, 44, 31, 5}\\
&24,\mathrm{and~}44.\text{A survey of the daily commuting times, in minutes, of seven different San}\\
&\text{Francisco-based employees at the same company yielded a data set consisting of the values}\\
&46,32,19,34,48,x,\mathrm{and~}38\text{. If the means of the two data sets are equal, what is the value of}\\
&x?\end{aligned}\)

\(\begin{aligned}
&\text{A circle in the }xy\text{-plane has its center at }(6, 9)\text{ and has a radius of length 7 . Which equation}\\
&\text{represents this circle?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g(x)=5(15x-16)\\
&\text{What is the }y\text{-coordinate of the }y\text{-intercept of the graph of }y=g(x)-5\text{ in the }xy\text{-plane?}\end{aligned}\)

\(\mathrm{If}\left|14-2x\right|=42,\text{which of the following is a value of }7-x?\)

\(\begin{aligned}
&\text{Triangle }QRS\text{ is similar to triangle }FGH\text{ such that }Q, R \text{, and }S \text{ correspond to }F, G\text{ and }H\\
&\text{respectively. Each side of triangle }FGH\text{ has }\frac{1}{4}\text{ the length of its corresponding side in}\\
&\text{triangle }QRS.\text{ In triangle }FGH\text{, the measure of angle }F\text{ is 10°, the measure of angle }G \text{ is}\\
&8°\text{, and }FG=a\text{. In triangle }QRS\text{, the measure of angle }Q\text{ is }b°\text{ and }QR=40\text{. What is the}\\&\text{value of }a+b?\end{aligned}\)

\(\begin{aligned}
&\text{Line }h\text{ is defined by }\frac{1}{5}x+\frac{1}{3}y-75=0\text{. Line }j\text{ is perpendicular to line }h\text{ in the }xy\text{-plane.}\\
&\text{What is the slope of line }j?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9x-3y=3y+8\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~hy=6+9x\\
&\text{In the given system of equations, }h\text{ is a constant. If the system has no solution, what is the}\\
&\text{value of }h?\end{aligned}\)

\(\text{The shaded region shown represents the solutions to which inequality?}\)

\(\begin{aligned}&\text{The graph of the equation }y=3^x+k\text{ is shown, where }k\text{ is a constant. What is}\\
& \text{the value of }k?\end{aligned}\)

\(\begin{aligned}&\text{The function }f\text{ gives the product of a number},x,\text{and a number that is 27 more than }x.\\&\text{Which equation defines }f?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}+y^{2}=49\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=mx+\frac{b}{5}\\&\text{In the given system of equations, }m\text{ and }b\text{ are negative constants. In the }xy\text{-plane, the graphs}\\&\text{of the equations in the given system intersect at the point }(-4,y),\text{where }y < 0\text{. Which}\\&\text{expression represents the value of }b?\end{aligned}\)

\(\begin{aligned}&\text{The triangle inequality theorem states that the sum of any two sides of a triangle must be}\\&\text{greater than the length of the third side. If a triangle has side lengths of 8 and 11, which}\\&\text{inequality represents the possible lengths, }x,\text{of the third side of the triangle?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y\geq x+15\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y\leq-5x-15\\&\text{Which point }(x,y)\text{ is a solution to the given system of inequalities in the }xy\text{-plane?}\end{aligned}\)

\(\text{The result of increasing the quantity }x\text{ by }300\%\text{ is 72. What is the value of }x?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9x^2+12=nx\\&\text{In the given equation, }n\text{ is a constant. The equation has exactly one solution. What is the}\\&\text{value of }\frac{n^2}{16}?\end{aligned}\)

\(\begin{aligned}
&\text{The table gives the areas and perimeters of two similar rectangles, where }n\mathrm{~is~a~constant.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|c|}\hline &\text{Area (square inches)}&\text{Perimeter (inches)}\\\hline\text{Rectangle A}&840&280\\\hline\text{Rectangle B}&3,360&n\\\hline\end{array}\\\\&\text{What is the value of }n?\end{aligned}\)

\(\begin{aligned}&\text{In the figure, }\overline{AD}\text{ and }\overline{BC}\text{ intersect at point }D.\text{ The measure of }\angle ABD\text{ is }w{°}\text{, the measure}\\
&\text{of }\angle CAD\text{ is }z{°},\text{ and }AD=178.\text{ If }\cos w{°}=\frac{9}{41},\text{what is the value of }\tan z{°}?\end{aligned}\)

\(\text{Which expression is a factor of }y^2\left(x-8\right)-25\left(x-8\right)^3?\)

\(\begin{aligned}&\text{For a study, a group of coypus will be selected from a habitat consisting of 250 coypus, and a}\\&\text{group of chinchillas will be selected from a habitat consisting of 210 chinchillas. Some of the}\\&\text{coypus and chinchillas will be in a treatment group, and some of the coypus and chinchillas}\\&\text{will be in a control group. Which of the following is necessary for this study to attempt to}\\&\text{establish a cause-and-effect relationship between two variables?}\end{aligned}\)