May 2026 Int.A Module 1

\(\begin{aligned}
&\text{The function }f\text{ is defined by }f(x)=\frac{5}{7}x+\frac{15}{7}.\text{ What is the slope of the graph of }\\&y=f(x)\text{ in the }xy\text{-plane?}\end{aligned}\)

\(\text{What is }20\%\text{ of 480?}\)

\(\text{Which expression is equivalent to}\left(8x^4+x^2\right)+\left(x^4+10x^2\right)?\)

\(\mathrm{If~}\frac{x}{2}+17=17\left(\frac{x}{2}\right)\text{,what is the value of }\frac{x}{2}?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=5x+400\\
&\text{The function shown gives the total cost }f(x),\text{in dollars, for making }x\text{ units of a certain }\\
&\text{product. What is the total cost, in dollars, for making 100 units of this product?}\end{aligned}\)

\(\begin{aligned}
&\text{A soccer team’s goal is to earn at least \$1,650 by selling coupon books. The team earns \$15 from}\\
&\text{selling each coupon book. Which of the following inequalities describes all possible values for the}\\
&\text{number of coupon books, }n\text{, the team can sell to meet the goal?}\end{aligned}\)

\(\begin{aligned}
&\text{A polygon with 24 sides has a perimeter of 193 inches. The length of one side is 9 inches. The}\\
&\text{other 23 sides have equal length. What is the length, in inches, of one of the 23 sides with equal}\\
&\text{lengths?}\end{aligned}\)

\(\begin{aligned}
&\text{A chef made 42 cups of sauce. The chef then filled }x\text{ small jars and }y\text{ large jars with }\\
&\text{all the sauce he made. The equation }2x+7y=42\text{ represents this situation. Which is }\\
&\text{the best interpretation of }7y\text{ in this context?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~11x^2+2x-6=0\\&\text{What is one of the solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x+13=y(z+8)\\
&\text{The given equation relates the distinct positive variables }x,y\text{, and }z.\text{ Which equation correctly}\\
&\text{represents }z\text{ in terms of }x\mathrm{~and~}y?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(x^2-8)(x^2-2)\\
&\text{The given expression can be written in the form }x^4+bx^2+16\text{, where }b\text{ is a constant. }\\&\text{What is the value of }b?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~n(x)=2(x+5)+(x-5)\\
&\text{The function }n\text{ is defined as shown. For what value of }x\mathrm{~is~}n(x)=56?\end{aligned}\)

\(\begin{aligned}
&\text{A circle in the }xy\text{-plane has a diameter with endpoints }(7,-12)\text{ and }(7,-24)\text{. Which }\\
&\text{equation represents this circle?}
\end{aligned}\)

\(\begin{aligned}&\text{The graph shows the estimated boiling point }y,\text{in degrees Celsius, of a straight-chain alkane}\\&\text{with a molecular weight of }x\text{ grams per mole, where }1\leq x\leq280.\text{ Which statement is the best}\\&\text{interpretation of the point }(144.63,178.26)?\end{aligned}\)

\(\begin{aligned}&\text{The table gives the distribution of flavor and type of topping for customer orders}\\
&\text{at an ice cream shop.}\end{aligned}\)

\(\begin{aligned}&\text{If a customer order is selected at random, what is the probability of selecting an order}\\&\text{with sprinkles, given the flavor of ice ream is vanilla?}\end{aligned}\)

\(\begin{aligned}
&\text{A linear function }g\text{ is defined by }g(x)=ax+b,\mathrm{~where~}a\mathrm{~and~}b\text{ are constants. If }\\
&g(-5)=-8\mathrm{~and~}g(2)=6,\text{what is the value of }a?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4|x-4|=28\\
&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\text{In the triangle shown, what is the value of }\sin x°?\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~18x+8=k(9x+8)+9x\\
&\text{In the given equation, }k\text{ is a constant. The equation has exactly one solution. Which value}\\&\text{CANNOT be the value of }k?\end{aligned}\)

\(\begin{aligned}
&\text{An exponential function }f\text{ gives the estimated amount of an X-ray beam’s initial intensity}\\
&\text{remaining after passing through a }w\text{-centimeter-thick window made of beryllium. The function}\\
&\text{estimates that after passing through a 1.2-centimeter-thick window, the amount of the X-ray}\\
&\text{beam’s initial intensity remaining is 0.75. Which equation could define }f?\end{aligned}\)

\(\begin{aligned}
&\mathrm{Triangle~}ABC\text{ is similar to triangle }XYZ\text{ such thet }A,B,\mathrm{and~}C\text{ correspond to }X,Y,\mathrm{and~}Z,\\
&\text{respectively. The length of each side of triangle }ABC\mathrm{~is~}n\text{ times the length of its corresponding}\\
&\text{side in triangle }XYZ,\mathrm{where~}n\text{ is an integer greater than }1.\text{ The measure of angle }C\mathrm{~is~}58\\
&\text{degrees, and }YZ=72.\text{ Which of the following must be true?}\end{aligned}\)

\(\begin{aligned}
&\text{The table shows values of }x\text{ and their corresponding values of }y\text{ for three points on }\\&\text{line }j\mathrm{~in~the~}xy\text{-plane.}\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline x&y\\\hline0&-10\\\hline1&-4\\\hline
2&2\\\hline\end{array}\\
&\text{Line }k\text{ also lies in the }xy\text{-plane and is defined by the equation }y=4x.\text{ At what point }\\
&(x,y)\text{ do lines }j\mathrm{~and~}k\text{ intersect?}\end{aligned}\)