Full Practice Exam 17 — Module 2

Questions in this quiz (22)

1. If $$18ax=54-15bx$$, what is the value of $$\frac{a}{b}$$ such that the equation has no solution?

   • $$\frac{5}{6}$$
   • $$-\frac{5}{6}$$
   • $$\frac{6}{5}$$
   • $$-\frac{6}{5}$$

2. A restaurant sells Chicken Alfredo, $$c$$, and Grilled Salmon, $$s$$. The restaurant makes a profit of $$12$$ dollars on each Chicken Alfredo and $$18$$ dollars on each Grilled Salmon. The restaurant wants to earn a profit of at least $$420$$ dollars from these dishes. Which inequality represents this situation?

   • $$12c+18s$$ < $$420$$
   • $$12c+18s\le420$$
   • $$12c+18s$$ > $$420$$
   • $$12c+18s\ge420$$

3. Sophia has a savings account. At the beginning of the year, the balance is $$2000$$ dollars. By the end of two years, the balance has grown to $$5120$$ dollars. Assume the account earns no interest and Sophia deposits the same amount every week. There are $$52$$ weeks in a year. How much does Sophia deposit each week?

   • 30

4. The function $$y=2x^2+5x-4$$ is shifted $$2$$ units to the right. What is the $$y$$-intercept of the resulting function?

   • $$-6$$
   • $$-2$$
   • $$4$$
   • $$14$$

5. For the function $$f(x)=ax+12$$, where $$a$$ is a constant, the graph passes through the point $$(3,30)$$. What is the value of $$a$$?

   • 6

6. A weather station collected rainfall data over two years.Year 1: 110, 90, 100, 80, 120, 70, 60, 130, 110, 100, 120, 140Year 2: 100, 95, 105, 85, 115, 80, 70, 125, 120, 105, 130, 145What is the difference between the means of the rainfalls in the two years?

   • $$3.75\text{ mm}$$
   • $$5.00\text{ mm}$$
   • $$6.25\text{ mm}$$
   • $$8.50\text{ mm}$$

7. Researchers found that the height $$y$$ of a plant, in centimeters, can be modeled by $$y=0.72x+8$$, where $$x$$ is the number of leaves. If the number of leaves increases by $$25$$, by how many centimeters does the height increase?

   • $$15$$
   • $$18$$
   • $$20$$
   • $$25$$

8. $$5x+2y=31$$$$3x-4y=-11$$Which of the following is a complete description of the solution to the system?

   • The graphs intersect at $$(3,8)$$.
   • The graphs intersect at $$(5,3)$$ and are perpendicular.
   • The graphs intersect at $$(3,8)$$ and are parallel.
   • The graphs intersect at $$\left(\frac{51}{13},\frac{74}{13}\right)$$.

9. The concentration of a medication in the bloodstream decreases over time. Which function could model this situation?

   • $$C(t)=300e^{kt}$$, where $$k$$ > $$0$$
   • $$C(t)=300e^{-kt}$$, where $$k$$ > $$0$$
   • $$C(t)=t^3+300$$
   • $$C(t)=300+t^2$$

10. The height of an object is modeled by $$h(x)=3x^2+6x+4$$, where $$h$$ is measured in meters and $$x$$ is measured in seconds. When the object is $$43$$ meters above the ground, what is the value of $$x$$?

    • $$2-\sqrt{2}$$
    • $$-\sqrt{14}$$
    • $$4$$
    • $$-1+\sqrt{14}$$

11. A rectangular garden has an area of $$60$$ square meters. The length of its diagonal is $$13$$ meters. Which of the following could be the dimensions of the garden?

    • Width $$=6$$ mLength $$=14$$ m
    • Width $$=7$$ mLength $$=12$$ m
    • Width $$=5$$ mLength $$=16$$ m
    • Width $$=5$$ mLength $$=12$$ m

12. Emma bought $$8$$ notebooks, each with the same price. The store offered a $$10\%$$ discount on the total purchase. After applying an $$8\%$$ sales tax, the total cost was $$155.52$$. What was the original price, in dollars, of one notebook?

    • 20

13. Which of the following is the greater solution of $$8|2x-1|=56$$?

    • $$4$$
    • $$5$$
    • $$\frac{9}{2}$$
    • $$\frac{7}{2}$$

14. The functions $$f_1(x)=ka^x$$ and $$f_2(x)=kb^x$$, where $$k$$ is a constant and $$a,\ b$$ > $$0$$, satisfy the condition that the percent change of $$f_1$$ for every increase of $$x$$ by $$3$$ is equal to the percent change of $$f_2$$ for every increase of $$x$$ by $$6$$. What relationship must hold between $$a$$ and $$b$$?

    • $$a=b^2$$
    • $$b=a^2$$
    • $$b=\sqrt[3]{a}$$
    • $$a=\sqrt{b}$$

15. For the equation $$\sqrt{4x+a}=x$$, where $$a$$ is a positive constant, which of the following must NOT be a solution?

    • $$8$$
    • $$5$$
    • $$2$$
    • $$-4$$

16. A polynomial function is defined by $$P(x)=x^3-5x^2-14x+40$$. Which of the following must be the zeros of the polynomial?

    • $$5,\ \pm2$$
    • $$4,\ \pm3$$
    • $$2,\ \pm5$$
    • $$2,\ 5,\ -4$$

17. Triangle $$ABC$$ and triangle $$DEF$$ each have two angles measuring $$35^\circ$$, as shown. Which of the following additional pieces of information is sufficient to prove that triangle $$ABC$$ is congruent to triangle $$DEF$$?

    • The measures of $$\angle ACB$$ and $$\angle DFE$$ are equal.
    • The lengths of $$BC$$ and $$EF$$ are equal.
    • The lengths of $$AC$$ and $$DE$$ are equal.
    • No additional information is necessary to prove that the two triangles are congruent.

18. Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

    • $$y=-1.9x-10.1$$
    • $$y=-1.9x+10.1$$
    • $$y=1.9x-10.1$$
    • $$y=1.9x+10.1$$

19. In the figure above, $$ABCD$$ is a square with sides of length $$2$$. The square contains two semicircles with diameters $$\overline{AB}$$ and $$\overline{CD}$$. What is the sum of the areas of the two shaded regions?

    • $$2-\frac{\pi}{2}$$
    • $$2-\pi$$
    • $$4-\pi$$
    • $$4-2\pi$$

20. Dawson needs to measure the height of a building near his house. He chooses a point $$P$$ on the ground where he can visually align the roof of his car with the edge of the building roof. The height of the car is $$4$$ feet and the distance from point $$P$$ to point $$Q$$ is $$10$$ feet, as shown in the figure. If the distance from point $$Q$$ to point $$R$$ is $$80$$ feet and the height of the building is $$k$$ feet, what is the value of $$k$$?

    • 36

21. The graph of the function $$f$$ is shown in the $$xy$$-plane above. Which of the following is the average rate of change between $$x=-3$$ and $$x=6$$?

    • $$\frac{1}{9}$$
    • $$\frac{2}{9}$$
    • $$\frac{1}{3}$$
    • $$\frac{4}{9}$$

22. The graph above shows the test scores of $$20$$ students. Based on the histogram above, what is the average (arithmetic mean) score on the test?

    • 73