December 2025 Int.D Module 1

\(\begin{aligned}&\text{The function }h\text{ is defined by }h(x)=100x-40.\text{ What is the value of }\\
&h(x)\text{ when }x=5?\end{aligned}\)

\(\begin{aligned}
&\text{A teacher is creating an assignment worth 42 points. The assignment will consist of }\\
&\text{questions worth 1 point and questions worth 2 points. Which equation represents this }\\
&\text{situation, where }x\text{ represents the number of 1-point questions and }y\text{ represents the}\\
&\text{number of 2-point questions?}\end{aligned}\)

\(\begin{aligned}&\text{A triangle has a base length of 60 centimeters and a height of 40 centimeters. }\\
&\text{What is the area, in square centimeters, of the triangle?}\end{aligned}\)

\(\text{Which expression is equivalent to }x^3+2x^2+9x+18?\)

\(\begin{aligned}&\text{Line }j\text{ is shown in the }xy\text{-plane. Line }k\text{ (not shown) is parallel to line }j.\\
&\text{What is the slope of line }k?\end{aligned}\)

\(\text{If }\sqrt{x-3}=5\text{, what is the value of }(x-3)?\)

\(\begin{aligned}
&\text{The graph of a system of an absolute value function and a linear function is shown.}\\
&\text{What is the solution }(x,y)\text{ to this system of two equations?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{Week}&\text{Number of dogs walked}\\\hline1&6\\\hline2&18\\\hline 3&30\\\hline\end{array}\\
&\text{The table shows the number of dogs walked by a dog walker each week for 3 weeks. }\\&\text{What is the mean number of dogs walked per week for these 3 weeks?}\end{aligned}\)

\(\text{The ratio 54 to }m\text{ is equivalent to the ratio 2 to 18. What is the value of }m?\)

\(\begin{aligned}
&\text{As part of a science experiment on evaporation, Ella measured the height of water in a glass }\\
&\text{over a period of time. The function }f(x)=32-0.21x\text{ gives the estimated height, in centimeters}\\
&\text{(cm), of the water in the glass }x\text{ days after the start of the experiment. Which of the following}\\&\text{is the best interpretation of 32 in this context?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline x&y\\\hline1&10\\\hline2&16\\\hline3&a\\\hline\end{array}\\&\text{The table shows three values of }x\text{ and their corresponding values of }y\text{ for the equation}\\&y=3(2)^x+4.\text{ In the table, }a\text{ is a constant. What is the value of }a?\end{aligned}\)

\(\begin{aligned}
&\text{The figure shows the }xy\text{-plane with the quadrants labeled. The graph of a linear function}\\
&h\text{ (not shown), where }y=h(x),\text{ is a line completely contained in only quadrants I and II}\\
&\text{of the }xy\text{-plane. Which of the following could define the function }h?\end{aligned}\)

\(\begin{aligned}&\text{A real estate company offers a series of three webinars. }3,125\text{ people attended the}\\&\text{first webinar. }48\%\text{ of the people who attended the first webinar attended the}\\&\text{second webinar, and }37\%\text{ of the people who attended the first and second webinars}\\&\text{attended the third webinar. How many people attended all three webinars?}\end{aligned}\)

\(\text{What is the value of }\tan{X}\text{ in the triangle shown?}\)

\(\begin{aligned}&~~~~~~~~~~~~-3(4v-1)(v+6)^{2}-(v+6)^{2}=0\\&\text{What is the positive solution to the given equation?}\end{aligned}\)

\(\begin{aligned}
&\text{The number }f\text{ is }130\%\text{ greater than a positive number }g\text{. A number }h\text{ is }20\%\text{ less than}\\
&\text{the number }f\text{. The number }h\text{ is how many times the number }g?\end{aligned}\)

\(\begin{aligned}4x^2-12x+4=0\\\text{What is a solution to the given equation?}\end{aligned}\)

\(\text{If }12+\frac{1}{4}(7x-5)=\frac{3}{4}(7x-5),\text{what is the value of }7x-5?\)

\(\begin{aligned}&\mathrm{Triangle~}ABC\text{ is similar to triangle }XYZ\text{, where }A\mathrm{~and~}B\text{ corresponding to }X\mathrm{~and}\\&Y,\text{ respectively. The length of each side of triangle }XYZ\mathrm{~is~}k\text{ times the length of its}\\&\text{corresponding side in triangle }ABC\text{, where }k\text{ is an integer greater than }1.\text{ The measure},\\&\text{in degrees, of angle }Z\text{ can be represented by the expression }9x+29\text{, where }x\text{ is an integer}\\&\text{Which of the following expression represents the measure, in degrees, of angle }C\text{ for all }\\&\text{possible values of }x?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=x+3\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g(x)=7x^{2}-rx+63\\&\text{The function }f\mathrm{~and~}g\text{ are given. In function }g,r\text{ is a constant. If }f(x)\cdot g(x)=7x^{3}+189,\\&\text{what is the value of }r?\end{aligned}\)

\(\begin{aligned}&\text{A conservation specialist hung artificial nesting structures each in the shape of a right}\\&\text{rectangular prism for a species of native duck. Each structure has a height of 18 inches.}\\&\text{The length of each structure’s base is }x\text{ inches, which is 1 inch more than the width of the}\\&\text{structure’s base. Which function }V\text{ gives the volume of each structure, in cubic inches,}\\&\text{in terms of the length of the structure’s base?}\end{aligned}\)

\(\text{Which system of equations has no solution?}\)