November 2025 Int.D Module 1

\(\begin{aligned}&\text{A carnival charges \$2 for each ride ticket and \$5 for each game ticket. A family purchased}\\
&\text{ride tickets and game tickets worth a total of \$35. Which equation represents this situation}\\&\text{where }x\text{ is the number of ride tickets and }y\text{ is the number of game tickets that this family}\\&\text{purchased}?\end{aligned}\)

\(\mathrm{If~}8x+2=74,\text{what is the value of }80x+20?\)

\(\text{The function }g\text{ is defined by }g(x)=2x+7.\text{ What is the value of }g(x)\mathrm{~when~}x=7?\)

\(\begin{aligned}
&\text{The measure of angle }G\text{ is }\frac{\pi}{9}\text{ radians. If the measure of angle }G\text{ is }2n\textbf{ degrees}\text{, where }n\text{ is a}\\
&\text{constant, what is the value of }n?\end{aligned}\)

\(\begin{aligned}&\text{A jar has 490 marbles, and }20\%\text{ of these marbles are blue. How many marbles in the jar are}\\&\mathrm{blue?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x+y=125\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x+y+y=185\\&\text{The solution to the given system of equations is }(x,y).\text{ What is the value of }y?\end{aligned}\)

\(\begin{aligned}&\text{During a trip, Bill drove his car for 25.0 miles and then began driving at a constant speed of}\\&\text{70.0 miles per hour. After 2 hours of driving at this speed, what is the total distance, in miles,}\\&\text{Bill has traveled during this trip?}\end{aligned}\)

\(\begin{aligned}&\text{The length of a side of square X is 9 centimeters. The area of rectangle Y is 14 square}\\
&\text{centimeters. What is the total area, in square centimeters, of square X and rectangle Y?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~v(t)=6t+50\\&\text{The function }v\text{ gives the volume of water, in liters, in a tank being filled by a hose }t\mathrm{~minutes}\\&\text{after the hose was turned on. Which of the following is the best interpretation of }50\mathrm{~in~this}\\&\mathrm{context?}\end{aligned}\)

\(\begin{aligned}&\text{In the figure shown, lines }\ell\mathrm{~and~}k\text{ are parallel and line }t\text{ intersects both lines. If }x>132,\\&\text{which of the following must be true?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~13,17,23,6,4,8,17,15,16\\&\text{The list gives the low temperatures, in degrees Fahrenheit, for 9 days in December in a}\\&\text{certain city, According to the list, what is the median low temperature, in degrees}\\&\text{Fahrenheir, for these 9 days?}\end{aligned}\)

\(\begin{aligned}&\text{A group of 10 gardeners recorded data on the germination rates of their tomato crop for one}\\&\text{growing season. The scatterplot shows the relationship between the number of tomato seeds}\\&\text{planted, }x,\text{and the number of tomato seeds that germinated, }y,\text{for each of the gardeners. A}\\&\text{line of best fit is also shown.}\end{aligned}\)

\(\begin{aligned}&\text{Which of the following is the best interpretation of the slope of the line of best fit in this}\\&\text{context?}\end{aligned}\)

\(\begin{aligned}&\mathrm{Line~}t\text{ in the }xy\text{-plane has a slope of }\frac{1}{7}\text{ and passes through the point }(35,-8).\mathrm{~Which}\\&\text{equation defines line }t?\end{aligned}\)

\(\begin{aligned}&\text{During a physics experiment, the speed of an object was determined to be 172.0 inches per}\\&\text{second. What is this speed in }\textbf{feet}\text{ per second? (12 inches =1 foot)}\end{aligned}\)

\(\begin{aligned}&\text{The graph of a polynomial function }y=f(x)\text{ in the }xy\text{-plane passes through the point }(9,7).\\&\text{What is the value of }f(9)?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2-\frac{4}{25}=0\\&\text{How many distinct real solutions does the given equation have?}\end{aligned}\)

\(\begin{aligned}&\text{The area of a triangle is 224 square inches. The length of the base of the triangle, in inches, is}\\
&\text{the sum of 15 and a positive number }d\text{ , and the height, in inches, is 3 less than }d\text{. What is the}\\&\text{value of }d?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{|3x-24|+3}{4}=6\\&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\text{In triangle }QRS\mathrm{~shown,~}QR<RS.\text{ Which expression represents the length of }\overline{QS}?\)

\(\begin{aligned}&\text{A certain town has an area of 3.71 square miles. What is the area, in }\underline{\text{square yards}}\text{, of this}\\
&\text{town? (1 mile=1,760 yards)}\end{aligned}\)

\(\begin{aligned}&\text{The function }h\text{ is defined by }h(x)=a^x+b,\mathrm{where~}a\mathrm{~and~}b\text{ are positive constants. The graph}\\&\mathrm{of~}y=h(x)\text{ in the }x\text{y-plane passes through the points }(0,8)\mathrm{~and~}(2,11).\text{ What is the value of}\\&ab?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r(x)=5(x-2)\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s(x)=x^3+nx^2+2nx+8\\
&\text{For the given functions }r\mathrm{~and~}s,n\text{ is a constant. If }r(x)\cdot s(x)=5(x^4-16)\text{, what is the}\\&\text{value of }n?\end{aligned}\)