Full Practice Exams — Exam 17

Questions in this quiz (45)

1. A candy shop sells 7 lollipops, 5 chocolate bars, and 6 gummy packs. If Sarah buys 6 candies at random, what is the probability that she gets exactly 2 lollipops, 2 chocolate bars, and 2 gummy packs?

   • $$\frac{1}{12}$$
   • $$\frac{9}{100}$$
   • $$\frac{75}{442}$$
   • $$\frac{3}{20}$$

2. Simplify the following expression:$$\frac{x^{\frac{2}{3}} \cdot x^{-\frac{1}{2}}}{x^{\frac{5}{6}}}$$

   • $$x^{-\frac{2}{3}}$$
   • $$\frac{2}{x^{\frac{3}{2}}}$$
   • $$\frac{1}{x^{\frac{1}{4}}}$$
   • $$\frac{2}{x^{\frac{1}{3}}}$$

3. If $$f(x)=2^{5x+4}$$, determine the value of $$f^{-1}(10)$$.

   • $$\frac{\log_2(10)-4}{5}$$
   • $$\frac{\log(54)}{2}$$
   • $$\frac{\ln(54)}{2}$$
   • $$\frac{\log(2)}{54}$$

4. Which of the following answers is $$y=\sqrt{x}$$ moved down 5 and right 3 and then reflected about the y-axis?

   • $$y=\sqrt{-x+5}+3$$
   • $$y=\sqrt{-x-5}-3$$
   • $$y=\sqrt{x+5}+3$$
   • $$y=\sqrt{-x-3}-5$$

5. Which of these is the intersection point of the asymptotes of $$y=\frac{Ax+B}{Cx+D}$$, where $$A\neq 0$$ and $$C\neq 0$$?

   • $$(-\frac{A}{C},\frac{D}{C})$$
   • $$(\frac{C}{D},\frac{A}{C})$$
   • $$(\frac{D}{A},-\frac{A}{C})$$
   • $$(-\frac{D}{C},\frac{A}{C})$$

6. Determine the domain of $$y=\sqrt{x^3-27}$$.

   • $$(-3,\infty)$$
   • $$[3,\infty)$$
   • $$(-\infty,3)$$
   • $$(-\infty,-3]$$

7. The sum of an infinite geometric series is $$400$$, and the common ratio is $$0.2$$. Determine the fourth term of this series.

   • $$1.80$$
   • $$2.56$$
   • $$3.20$$
   • $$4.08$$

8. a is a positive 2-digit number, and t and u are its tenth and unit digits, respectively. Let b be a 2-digit number formed by reversing the digits of a. Find the equivalent of a-b.

   • $$\frac{t+u}{2}$$
   • $$\frac{9}{t+u}$$
   • $$9(t-u)$$
   • $$\frac{1}{t-u}$$

9. The graph of the function $$f$$ passes through the point $$(x,y)$$. Which of the following is NOT a possible value of $$y$$ if:$$f(x)=(x-4)(x+4)(x+2)$$ and $$-2\leq x\leq 4$$.

   • 0
   • -48
   • 63
   • -45

10. The system of equations below has exactly one solution. If $$c$$ is a constant, which of the following is the value of $$c$$?$$y=3x+7$$$$y=cx+4$$

    • $$c\neq3$$
    • $$c=3$$
    • $$c=-3$$
    • $$c=\frac{1}{3}$$

11. Determine the radius of the circle with the equation:$$x^2+y^2=\frac{199-2x-2y}{2}$$

    • $$10$$
    • $$100$$
    • $$50$$
    • $$5$$

12. The positive number $$x$$ is $$10\%$$ of the sum of the positive numbers $$y$$ and $$z$$, and $$y$$ is $$10\%$$ of $$z$$. What percentage of $$y$$ is $$x$$?

    • $$90%$$
    • $$10%$$
    • $$110%$$
    • $$11%$$

13. In the equation $$Z - Z' = a + bi$$, $$a$$ and $$b$$ are real numbers and $$i$$ is the imaginary unit such that $$i^2 = -1$$. If $$Z = 3 + 2i$$ and $$Z' = 4 - 3i$$, what is the value of $$(Z - Z')^2$$?

    • $$5i$$
    • $$2i$$
    • $$26 + 10i$$
    • $$-24 - 10i$$

14. An enterprise conducted a study on its products and the results showed that when the unit selling price $$P$$ is raised, the number of units sold $$U$$ went down. This result is modeled by the equation $$10P + 2U = 2500$$. Based on this model, the manager decided to decrease the unit selling price from $$50$$ to $$45$$. How many more items did he sell?

    • 25
    • 40
    • 55
    • 75

15. The supply function of a product is given by $$f(x)=\frac{1+x}{2}$$ and the demand function of the same product is given by $$g(x)=\frac{2}{x}+1$$ where $$x$$ represents the price in dollars of the product in both functions. What is the market equilibrium of this product given that it is the point of intersection of the two curves of the two functions?

    • $$2.79$$
    • $$1.79$$
    • $$2.56$$
    • $$1.56$$

16. Using the figure below, what is the value of $$y$$? (figure not drawn to scale)

    • -3.5
    • 59
    • 80
    • 65

17. What is the abscissa of the vertex of the parabola defined by the quadratic function $$g(x)=x^2-7x-4$$?

    • $$3.5$$
    • $$1$$
    • $$-7$$
    • $$-4$$

18. What is the area of the figure below?

    • 22.75
    • 14.72
    • 26.75
    • 47.12

19. The bar graph below displays the results of a Math test scored out of 100.What is the median score of the results?

    • 75
    • 55
    • 80
    • 95

20. If $$\cos(x)\sin(x)=\frac{1}{2}$$, what is the value of $$(\cos(x)+\sin(x))^2+16\sin(2x)$$?

    • 1
    • 0
    • $$\frac{1}{4}$$
    • 18

21. What is the value of $$AD^2+DC$$?

    • $$15-\sqrt{26}$$
    • $$45+\sqrt{37}$$
    • $$16+\sqrt{26}$$
    • $$2\sqrt{29}$$

22. A company for renting cars published a summary of the amount they won during the past few years from renting cars and trucks. This company has only one employee who works for $$1650$$ per month. In which year was this company unable to pay his full wage from the amount won from renting cars and trucks?

    • 2015
    • 2016
    • 2017
    • 2019

23. In the figure below, triangle BDC is right angled at D with $$\angle CBD=40^\circ$$. Given that $$\angle CAB=35^\circ$$ and $$AC=10$$ cm, what is the length of segment AB?

    • 8.19
    • 6.48
    • 5.56
    • 1.36

24. In triangle △ABC, the measure of angle B is 90°, AB is a leg with a length of 12, and segment AC contains the point D. Which of the following must be true?I. $$BC=12\tan(\angle CAB)$$II. $$\cos(\angle ABD)-\sin(\angle DBC)=0$$III. $$\angle ABD=\angle BDC$$

    • I and II only.
    • I and III only.
    • II and III only.
    • I, II and III.

25. Two spheres have radii in the ratio $$12:13$$. The difference in their surface areas is $$400\pi$$ square inches. If the volume of the smaller sphere can be written as $$v\pi$$, what is the value of $$v$$?

    • $$200\pi$$
    • $$18432$$
    • $$150\pi$$
    • $$115\pi$$

26. A bird-watching group initially observed 200 birds in a certain area and set a goal of reaching 800 birds. According to their model, the population starts at 200 and increases by 30 birds per week for the first two weeks after the observation. After those two weeks, the population increases by 50 birds per week until the goal of 800 birds is reached. At the end of week $$w$$ (where $$w$$ > $$2$$) after the initial observation, let $$p(w)$$ be the predicted number of birds still needed to reach the 800-bird goal. Which of the following functions correctly represents $$p(w)$$?

    • $$p(w)=150-50w$$
    • $$p(w)=200-50w$$
    • $$p(w)=800-20w$$
    • $$p(w)=640-50w$$

27. If $$b$$ equals $$40\%$$ of $$a$$, then in terms of $$b$$, $$40\%$$ of $$4a$$ is equal to which of the following?

    • $$4b$$
    • $$16b$$
    • $$8b$$
    • $$\frac{b}{4}$$

28. The graph of which of the following equations is parallel to the line with equation $$y=-3x-6$$?

    • $$x-3y=3$$
    • $$x-\frac{1}{3}y=2$$
    • $$x+\frac{1}{6}y=4$$
    • $$x+\frac{1}{3}y=5$$

29. In the figure below, $$x \parallel y$$. What is the value of $$a$$ in terms of $$b$$ and $$c$$?

    • $$2b - c$$
    • $$c-b$$
    • $$90 + b + c$$
    • $$b + c$$

30. If $$f(g(a))=6$$, $$f(x)=\frac{x}{2}+2$$, and $$g(x)=|x^2-10|$$, which of the following is a possible value of $$a$$?

    • $$\sqrt{3}$$
    • $$3$$
    • $$3\sqrt{2}$$
    • $$18$$

31. The table below shows some values for the function $$N$$. If $$N(t)=k\cdot 2^{-at}$$ for positive constants $$k$$ and $$a$$, what is the value of $$a$$?

    • 3
    • -1
    • -3
    • 1

32. If $$5-\frac{3}{2}x\ge3$$, what is the highest value of $$\frac{9}{8}x+1$$?

    • $$\frac{5}{2}$$
    • $$\frac{7}{2}$$
    • $$\frac{9}{2}$$
    • $$\frac{11}{2}$$

33. In the xy-plane, the circle has center $$(h,k)$$ and radius 10. It passes through the points $$(4,0)$$ and $$(20,0)$$. What is the value of $$k$$?

    • 10
    • 7
    • 6
    • 5

34. How many square meters per minute is equivalent to a rate of 130 square centimeters per hour?(Note: 1 meter = 100 centimeters)

    • $$1.3\cdot10^{-3}$$
    • $$1.3\cdot10^{-4}$$
    • $$2.17\cdot10^{-4}$$
    • $$1.3\cdot10^{-5}$$

35. If $$7^k=100$$, what is the value of $$7^{\frac{k}{2}+1}$$?

    • 58
    • 52
    • 70
    • 51

36. A factory produces two products: product A and product B. The production manager sets the constraints shown in the graph below. The shaded region represents the combinations of product A and product B that meet all the constraints. Which of the following statements correctly describes the shaded region?

    • The number of product A exceeds 20, and the number of product B exceeds 20.
    • The number of product A is at least 20, the number of product B is at most 80, and the total does not exceed 100.
    • The number of product A is at least 20, and the number of product B is at most the number of product A.
    • The total number of products A and B exceeds 100, and the number of product B is less than 80.

37. Eight hundred people registered to participate in a charity cycling event. Each person paid one of the registration fees shown in the table below.Eighty-five percent of all registered participants started the event, and 90 percent of those who started also completed it. There were 250 people who paid the early registration fee, 350 people who paid the standard fee, and the rest paid the late fee. What is the total revenue from entry fees, in dollars, written in scientific notation?

    • $$3.55\times10^3$$
    • $$25.5\times10^3$$
    • $$35.5\times10^4$$
    • $$2.55\times10^4$$

38. When $$\frac{y}{5}-3=-\frac{11}{10}$$ which of the following is the value of y?

    • $$\frac{19}{2}$$
    • $$\frac{14}{50}$$
    • $$\frac{15}{11}$$
    • $$\frac{13}{5}$$

39. Of 4800 residents, one fourth are college students. The number of college students is reduced by one third, with no other changes. What portion of the total remaining residents are college students?

    • $$\frac{2}{11}$$
    • $$\frac{1}{8}$$
    • $$\frac{1}{5}$$
    • $$\frac{1}{6}$$

40. What is the value of $$(\sqrt{5+\sqrt{17}}-\sqrt{5-\sqrt{17}})^2$$?

    • $$10+2\sqrt{2}$$
    • 0
    • 10
    • $$10-4\sqrt{2}$$

41. A triangular flower bed has one side 10 feet long that makes a 45° angle with an east-west walkway. A second side is parallel to the walkway, and the third side makes a 30° angle with the walkway. Find the perimeter of the triangle in feet.

    • $$5(2+\sqrt{2}+\sqrt{6})$$
    • $$10(2+\sqrt{8})$$
    • $$10(2+\sqrt{2}+\sqrt{3})$$
    • $$5(\sqrt{2}+\sqrt{3})$$

42. If there are 16 people to choose from, what is the ratio of the number of possible 7-person committees to the number of possible 8-person committees?

    • 8:7
    • 8:9
    • 7:9
    • 7:8

43. The greatest common factor (GCF) of 48 and 72 is:

    • 6
    • 12
    • 24
    • 48

44. In the standard (x,y) coordinate plane, what is the vertex of the parabola with the equation $$y=-2(x+3)^2+1?$$

    • $$(-3,1)$$
    • $$(3,1)$$
    • $$(-3,-1)$$
    • $$(3,-1)$$

45. In the standard (x,y) coordinate plane, triangle ABC is a triangle with vertex B at (-2,2) and vertex C at (4,2). If AB is congruent to AC, which of the following points could be the coordinates of vertex A?

    • $$(2,5)$$
    • $$(3,4)$$
    • $$(10,2)$$
    • $$(1,6)$$