Full Practice Exam 10 — Module 1

Questions in this quiz (22)

1. In 2018, Sofia had $$320$$ books in her personal library. She added $$12$$ books each year from the beginning of 2018 through the end of 2024. Starting in 2025, she began adding $$18$$ books each year. How many books will Sofia have at the end of 2040?

   • $$588$$
   • $$600$$
   • $$612$$
   • $$692$$

2. How many ordered pairs $$(x,y)$$ satisfy both $$2x-y$$ < $$4$$ and $$y$$ > $$2x+7$$?

   • $$0$$
   • $$1$$
   • $$2$$
   • Infinitely many

3. Marcus's yearly salary, $$S$$, is modeled by the equation $$S=4200t+58000$$ where $$t$$ represents the number of years Marcus has worked at the company. Which of the following best describes the number $$58000$$ in this context?

   • The amount Marcus's salary increases each year
   • Marcus's salary after $$58000$$ years
   • Marcus's starting yearly salary
   • The total amount Marcus earns over $$t$$ years

4. Solve for $$x$$.$$2\frac{1}{4}x-\frac{7}{24}=4\frac{1}{2}x-3\frac{5}{6}$$

   • $$\frac{17}{18}$$
   • $$\frac{19}{18}$$
   • $$\frac{7}{6}$$
   • $$\frac{85}{54}$$

5. If $$f(x)=5x-4$$ and $$g(x)=2x+1$$ what is the value of $$f(g(-2))$$?

   • $$-19$$
   • $$-17$$
   • $$-15$$
   • $$-13$$

6. Under a new city ordinance, a restaurant must charge an additional $$8\%$$ tax on all takeout orders. By what factor should the original bill be multiplied to determine the final total cost?

   • $$\frac{8}{100}$$
   • $$\frac{108}{100}$$
   • $$\frac{116}{100}$$
   • $$\frac{8}{10}$$

7. How will the function $$f(x)=3x+7$$ be affected by the following transformation?$$g(x)=f(x+2)-5$$

   • Shifted left $$2$$ units and down $$5$$ units
   • Shifted right $$2$$ units and down $$5$$ units
   • Shifted left $$5$$ units and up $$2$$ units
   • Shifted right $$5$$ units and up $$2$$ units

8. The function $$h(x)=2x^2-8x+5$$ has its minimum value at the point $$(a,b)$$. What is the value of $$a+b$$?

   • $$-1$$
   • $$1$$
   • $$3$$
   • $$5$$

9. Which of the following is equivalent to $$\sqrt[5]{96x^{13}y^{17}}$$ for positive values of $$x$$ and $$y$$?

   • $$2x^2y^3\sqrt[5]{3x^3y^2}$$
   • $$2x^3y^2\sqrt[5]{3x^2y^3}$$
   • $$2xy^3\sqrt[5]{3x^8y^2}$$
   • $$4x^2y^3\sqrt[5]{3x^3y^2}$$

10. $$x-4=\sqrt{45-4x}$$What are the solutions for $$x$$ in the equation above?

    • $$9$$ only
    • $$9$$ and $$-5$$
    • $$2+\sqrt{33}$$ only
    • No solution

11. At what values of $$x$$ does the graph of $$f(x)=12x^2-37x+21$$ intersect the $$x$$-axis?

    • $$\frac{3}{4}$$ and $$\frac{7}{3}$$
    • $$\frac{4}{3}$$ and $$\frac{3}{7}$$
    • $$-\frac{3}{4}$$ and $$-\frac{7}{3}$$
    • $$3$$ and $$7$$

12. The correlation coefficient between two variables is given by $$r=\frac{s_{xy}}{s_xs_y}$$ where $$s_{xy}$$ is the covariance and $$s_x$$ and $$s_y$$ are the standard deviations. If the covariance is doubled, while both standard deviations are also doubled, what happens to the correlation coefficient?

    • It doubles.
    • It is cut in half.
    • It stays the same.
    • It becomes negative.

13. A polynomial function $$p(x)$$ has exactly $$7$$ real zeros. A new function is defined by $$q(x)=-4p(x)$$ How many real zeros does $$q(x)$$ have?

    • $$-7$$
    • $$4$$
    • $$7$$
    • $$28$$

14. A train travels $$180$$ miles at a constant speed. If the speed had been increased by $$15$$ miles per hour, the trip would have taken $$1$$ hour less. What was the original speed of the train, in miles per hour?

    • 45

15. The table below shows the average monthly subscription price, $$p$$, of a streaming service and the corresponding number of subscribers, $$S(p)$$.Which of the following functions best models the relationship between the number of subscribers and the monthly price?

    • $$S(p)=15000-550p$$
    • $$S(p)=15000+550p$$
    • $$S(p)=12400-300(p-8)^2$$
    • $$S(p)=3000+550p$$

16. A restaurant currently has an average customer rating of $$4.1$$ stars based on $$25$$ reviews. What is the minimum number of additional $$5$$-star reviews needed to raise the average rating to at least $$4.4$$ stars?

    • 13

17. On Friday, the price of a stock was $120. On Saturday, the price increased by $$15\%$$. On Sunday, the new price decreased by $$20\%$$ from Saturday's price. What was the difference between Friday's and Sunday's prices?

    • $$4.80$$
    • $$6.00$$
    • $$9.60$$
    • $$12.00$$

18. A circle has equation $$(x+5)^2+(y-2)^2=49$$ What is the equation of the circle after it is reflected across the $$y$$-axis?

    • $$(x+5)^2+(y+2)^2=49$$
    • $$(x-5)^2+(y-2)^2=49$$
    • $$(x-5)^2+(y+2)^2=49$$
    • $$(x+5)^2-(y-2)^2=49$$

19. Given that $$\theta$$ is between $$0^\circ$$ and $$90^\circ$$ and that $$\sin\theta=k$$ what is the value of $$\cos(90^\circ-\theta)$$?

    • $$90-k$$
    • $$1-k$$
    • $$k$$
    • $$\frac{1}{k}$$

20. If the area of an equilateral triangle is $$12\sqrt{3}$$ square units, what is the perimeter of the triangle?

    • $$12$$
    • $$18$$
    • $$12\sqrt{3}$$
    • $$36$$

21. A storage container in the shape of a rectangular prism has dimensions $$24$$ inches by $$18$$ inches by $$15$$ inches. Inside the container are five solid cubes, each with edge length $$3$$ inches. If the remaining space in the container is empty, what is the volume of the empty space, in cubic inches?

    • $$5805$$
    • $$6075$$
    • $$6345$$
    • $$6480$$

22. Triangles $$ABC$$ and $$DEF$$ are similar to one another. If the cosine of $$\angle BAC$$ is $$\frac{8}{17}$$, and the length of $$DE$$ is $$32$$ units, what is the length of $$DF$$?

    • 68