May 2026 Int.A Module 2

\(\text{Line }p\text{ in the }xy\text{-plane contains the points }(6,0)\text{ and }(6,6)\text{. Which equation defines line }p?\)

\(\text{The function }f\text{ is defined by }f(z)=8z.\text{ Which of the following is equivalent to }f(z-6)?\)

\(\text{A length of 550 meters is equal to how many }\underline{\text{decimeters}}?\text{ (1 meter = 10 decimeters)}\)

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

\(\begin{aligned}
&\text{The equation }E(t)=5(1.7)^t\text{ gives the estimated number of employees at a certain business,}\\
&\text{where }t\text{ is the number of years since the business opened. Which of the following is the best}\\
&\text{interpretation of the number 5 in this context?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=4x^{2}-24x+38\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y+3=0\\
&\text{How many solutions are there to the given system of equations?}\end{aligned}\)

\(\text{What is an equation of the graph shown?}\)

\(\begin{aligned}
&\mathrm{If~}x\geq-6\text{ represents all solutions to the inequality }ax-18\leq24\text{, where }a\text{ is a constant, }\\&\text{what is the greatest possible value of }a?\end{aligned}\)

\(\begin{aligned}
&\text{A community organization surveyed a random sample of residents of the community to estimate the}\\
&\text{percentage of residents who visit their local library at least once per month. From the survey, the}\\
&\text{organization estimates that }19\%\text{ of residents of the community visit their local library at least once}\\
&\text{per month with an associated margin of error of }3.7\%\text{. The organization repeated the survey with a}\\
&\text{random sample of residents that was double the original sample size. Assuming the margins of error}\\
&\text{are calculated in the same way for both studies, which of the following is true about the margin of}\\
&\text{error associated with the estimate from the larger sample?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(2x-11)(2x+15)\\
&\text{What is the minimum value of the given function?}\end{aligned}\)

\(\begin{aligned}
&\text{A right square prism has a height of 9 units. The volume of the prism is 1,521 cubic units. What is the}\\
&\text{length, in units, of an edge of the base?}\end{aligned}\)

\(\begin{aligned}
&\text{A zoologist observed the nests of wood ducks in an area. Each year, the zoologist recorded the}\\
&\text{number of eggs in each of the first 35 nests that were observed and created a frequency table for}\\
&\text{the data set. Which of the following frequency tables represents the data set with the smallest}\\
&\text{standard deviation?}\end{aligned}\)

\(\text{Which expression is a factor of 64}p^{17}-121p^{15}?\)

\(\begin{aligned}
&\text{Each angle of }\triangle ABC\text{ is congruent to one of the angles of }\triangle QRS.\mathrm{~If~}AB=56,BC=84,\\
&AC=112\text{, and }RS=336,\text{ what is one possible value for the perimeter of }\triangle QRS?\end{aligned}\)

\(\begin{aligned}
&\text{The line shown can be represented by the equation }ax+by=28,\mathrm{where~}a\mathrm{~and~}b\\
&\text{are constants. Which of the following is true about }a\mathrm{~and~}b?\end{aligned}\)

\(\begin{aligned}
&\text{The expression }\frac{kx-17}{2x^2-11x+15}\text{ is equivalent to }\frac{p}{x-3}-\frac{1}{2x-5}\text{, where }k\mathrm{~and~}p\\
&\text{are constants. What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&\text{An artist made 14 pieces of pottery using 64 pounds of clay. The pottery included only bowls and}\\
&\text{vases. Each bowl used 3 pounds of clay and each vase used 5 pounds of clay. How many vases did}\\
&\text{the artist make?}
\end{aligned}\)

\(\begin{aligned}
&\text{The function }f\text{ is defined by }f(x)=41(0.26)^x.\text{ For any positive integer }n,\text{ the value of }f(n)\\
&\text{is }p\%\text{ less than the value of }f(n-1).\text{ What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&\text{For the right circular cone shown, }\overline{OP}\text{ is a radius of the base and }V\text{ is the vertex. The }\\
&\text{cone’s lateral surface area, in square meters, is }rL\pi,\mathrm{~where~}r\text{ is the length, in meters, }\\
&\text{of }\overline{OP}\mathrm{~and~}L\text{ is the length}\text{ in meters, of }\overline{VP}.\text{ The cone has a base area of }81\pi\text{ square}\\
&\text{meters and a lateral surface area of }214\pi\text{ square meters. What is the height of the cone,}\\
&\text{to the nearest meter?}\end{aligned}\)

\(\begin{aligned}
&\text{The function }g\text{ is defined by }g(x)=-2x(x+4)(x-k)^2+r,\mathrm{~where~}k\mathrm{~and~}r\text{ are integer }\\
&\text{constants. ln the }xy\text{-plane, the graph of }y=g(x)\text{ passes through the point }(8,13)\text{, and }\\
&g(0)=13.\text{ What is the value of }r+k?\end{aligned}\)

\(\begin{aligned}&\text{A researcher investigated two species of mites: a predator and its prey. At the start of a week,}\\&\text{there was an equal number of the two species. At the end of the week, the number of prey}\\&\text{had increased by 1900}\%\text{ of the number of prey at the start of the week, and the number of}\\&\text{predators had increased by }220\% \text{ of the number of predators at the start of the week. The}\\&\text{number of predators at the end of the week was }p\%\text{ less than the number of prey at the end}\\&\text{of the week. What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-7x^2+bx-63=0\\
&\text{In the given equation, }b\text{ is a positive integer. The equation has no real solution. What is the }\\
&\text{largest possible value of }b?\end{aligned}\)