Full Practice Exams — Exam 5

Questions in this quiz (45)

1. A manufacturer produces six hundred plastic bottles a day. The number of defective bottles is recorded daily. Given the table below, find the expected value of defective bottles that are produced each day:

   • $$E(X)=0.65$$
   • $$E(X)=0.70$$
   • $$E(X)=0.85$$
   • $$E(X)=1.20$$

2. The volume of a sphere is expressed as $$V=\frac{4}{3}\pi r^3$$. If the volume of a sphere is $$\frac{\pi}{6}ft^3$$. Find the diameter of the sphere in inches.

   • $$8$$
   • $$12$$
   • $$4$$
   • $$6$$

3. How many diagonals does an octagon have?

   • $$80$$
   • $$40$$
   • $$60$$
   • $$20$$

4. Determine the coordinates $$(x,y)$$ of the intersection point of the lines: $$3y+4x-6=0$$ and $$3y-x=0$$.

   • $$\left(\frac{3}{5},\frac{6}{5}\right)$$
   • $$\left(\frac{6}{5},\frac{2}{5}\right)$$
   • $$\left(\frac{4}{5},\frac{6}{5}\right)$$
   • $$\left(\frac{3}{5},\frac{2}{5}\right)$$

5. Determine the area of the parallelogram $$ABCD$$.Given: The base of the parallelogram $$AB = 9$$.The perpendicular height $$DH = 3$$.

   • $$45$$
   • $$18$$
   • $$9$$
   • $$27$$

6. A triangle with a perimeter of $$5$$ feet has one side that is $$12$$ inches long. The two other sides have a ratio of $$1:2$$. Find the length in inches of the longest side of the triangle.

   • $$32$$
   • $$60$$
   • $$12$$
   • $$16$$

7. A ramp for wheelchairs to access a building has a slope of $$4\%$$, which means that for each $$100$$ feet traveled horizontally, the ramp rises by $$4$$ feet. If the entrance of the building is $$3$$ feet above the base, find the horizontal distance between the extremities of the ramp.

   • $$55$$
   • 40$$75$$
   • $$75$$
   • $$50$$

8. Find the area of the two shaded triangles in the trapezoid below:

   • $$6$$
   • $$10$$
   • $$4$$
   • $$9$$

9. The table below contains the number of rows and columns of 4 different matrices. Determine which product is not possible.

   • $$M \cdot N$$
   • $$N \cdot M$$
   • $$T \cdot H$$
   • $$H \cdot M$$

10. Considering today is Saturday, what day will it be after 14 days?

    • Friday
    • Saturday
    • Sunday
    • Thursday

11. A manufacturer produces plastic bottles for sale. The graph below shows the revenue $$R(x)$$ and cost $$C(x)$$ as functions of the number of bottles sold.Determine the number of bottles sold when the manufacturer broke even.

    • $$5$$
    • $$7$$
    • $$5,000$$
    • $$7,000$$

12. Mr. Blue invested 12000 at 6% interest compounded monthly. Which of these is an expression for how much his investment will be worth after 15 years?

    • $$12000\left(1+\frac{0.06}{12}\right)^{180}$$
    • $$12000(1+0.06)^{15}$$
    • $$12000\left(1+\frac{0.06}{12}\right)^{15}$$
    • $$12000\left(1+\frac{0.06}{12}\right)^{15}$$

13. If $$- |y| = y$$, which of the following statements must be true?

    • $$y \geq 0$$
    • $$y = 0$$
    • $$y \leq 0$$
    • $$y \neq 0$$

14. If $$-2\leq x\leq 3$$ and $$-5$$ < $$y$$ < $$6$$, what is the maximum value of $$|y-3x|$$?

    • $$11$$
    • $$14$$
    • $$15$$
    • $$22$$

15. Suppose $$y$$ is inversely proportional to the cube of $$x$$. If $$y=8$$ when $$x=3$$, what does $$y$$ equal when $$x=6$$?

    • $$216$$
    • $$\frac{1}{27}$$
    • $$\frac{1}{216}$$
    • $$1$$

16. At a craft store, small baskets sell for $$3.00$$ each and large baskets sell for $$4.50$$ each. Jamie wants to buy at least one basket of each size and must spend exactly $$60.00$$. What is the maximum number of large baskets Jamie can buy?

    • $$8$$
    • $$10$$
    • $$12$$
    • $$16$$

17. A parabola passes through the point $$(6,-24)$$ and has $$x$$-intercepts at $$2$$ and $$10$$. What is the vertex of the parabola?

    • $$(6,-24)$$
    • $$(-6,-20)$$
    • $$(-6,-36)$$
    • $$(6,-16)$$

18. In the standard $$(x,y)$$ coordinate plane, how many times does the graph of $$y=x(x-2)^2(x+4)$$ intersect the $$x$$-axis?

    • 3
    • 4
    • 2
    • 0

19. The statement "Maria goes jogging every Saturday" is always true. Which of the following statements is also true?

    • If Maria does not go jogging, then it is not Saturday.
    • If it is Saturday, it is impossible to determine if Maria goes jogging.
    • If it is not Saturday, then Maria does not go jogging.
    • If it is Saturday, then Maria does not go jogging.

20. The sum of the roots of a cubic polynomial $$g(x)=ax^3+bx^2+cx+d$$ is $$10$$. If $$g(x)$$ can be expressed as $$(x^2-6x+9)(x+m)$$, what is the value of $$a+b+c+d$$?

    • 10
    • -12
    • 36
    • -4

21. The length $$L$$, in meters, of a rod is given by the equation $$L=\frac{3}{5}F+0.08$$, where $$F$$ is the applied force in newtons. Approximately what force, in newtons, must be applied for the rod’s length to be $$0.29$$ meters?

    • $$0.45$$
    • $$0.60$$
    • $$0.29$$
    • $$0.35$$

22. A motorcycle is traveling at $$50$$ m/s when the rider applies the brakes, causing a constant deceleration of $$200$$ m/s². Using the kinematic equation: $$v=v_0+at$$. How long does it take for the motorcycle to come to a complete stop?

    • $$0.45$$
    • $$0.25$$
    • $$0.30$$
    • $$0.50$$

23. In the diagram below, lines A and B are parallel. Which of the following pairs of angles does NOT have a sum of $$180^\circ$$?

    • $$\angle a + \angle b + \angle f$$
    • $$\angle a + \angle d$$
    • $$\angle b + \angle e + \angle f$$
    • $$\angle d + \angle e$$

24. From the figure below, determine the measure of $$\angle CAB$$, if $$\angle BOC = 15^\circ$$.

    • $$10^\circ$$
    • $$15^\circ$$
    • $$30^\circ$$
    • $$7.5^\circ$$

25. A student in an industrial technology class slices a solid wooden cube into two identical parts by cutting along the diagonals of opposite faces. The cube has a surface area of 54 square inches. What is the surface area, in square inches, of each resulting prism?

    • $$18 + \sqrt{2}$$
    • $$36$$
    • $$18 + 9\sqrt{2}$$
    • $$27$$

26. A total of 140 students took part in a spelling competition. The graph illustrates the relationship between the number of students $$n$$ who correctly spelled words and the number of letters $$s$$ in each word. Which equation most closely approximates the line of best fit?

    • $$n=20s+165$$
    • $$n=-11s+150$$
    • $$n=-20s+150$$
    • $$n=11s+165$$

27. What are the solutions to the equation $$|2x+4|=12-|x-5|$$?

    • $$\frac{13}{3}, 3, -\frac{11}{3}$$
    • $$\frac{13}{3}, -\frac{11}{3}$$
    • $$ 3, -\frac{11}{3}$$
    • $$\frac{13}{3}, 3$$

28. A bookstore sells paperback and hardcover versions of a popular novel. During a weekend promotion, a paperback sells for $$8$$ and a hardcover sells for $$20$$. Over the course of the weekend, the bookstore sells $$150$$ copies in total and collects $$1920$$ in revenue. Which system of equations would determine the number of paperback books $$p$$ and hardcover books $$h$$ sold during the promotion?

    • $$p+h=8$$, $$150p+h=20$$
    • $$p+h=1920$$, $$8p+h=150$$
    • $$20p+h=1920$$, $$p+1500h=20$$
    • $$p+h=150$$, $$8p+20h=1920$$

29. Mercury is a naturally occurring element that can be toxic to humans in large amounts. Health guidelines suggest limiting daily mercury intake to no more than 0.1 microgram per kilogram of body weight. Different fish species contain varying levels of mercury, as shown in the bar graph below. According to the chart, snapper contains an average of 0.165 micrograms of mercury per gram. If a person weighs 82 kilograms, what is the maximum number of grams of snapper they can safely eat in a day? Round your answer to the nearest gram.

    • 40
    • 30
    • 20
    • 50

30. In a local school board election, three candidates ran: one Independent, one endorsed by the Teachers' Union, and one supported by the Parent Association. The ratio of votes received by the Independent candidate to the Union-endorsed candidate to the Parent-backed candidate was approximately 21:17:12. If a total of 600,000 votes were cast in the election, how many more votes did the Independent candidate receive than the Parent Association candidate?

    • 108000
    • 144000
    • 252000
    • 12000

31. Which of the following functions has a domain of $$x \ge 2$$?

    • $$p(x) = -\sqrt{x + 2}$$
    • $$m(x) = -x^2 + 2$$
    • $$q(x) = -|x - 2|$$
    • $$n(x) = -\sqrt{x - 2}$$

32. Simplify$$\frac{(1+\sin\theta)^2+(1-\sin\theta)^2}{\cos^2\theta}.$$

    • $$2+4\tan^2\theta$$
    • $$1$$
    • $$\frac{2+\sin^2\theta}{\cos^2\theta}$$
    • $$\frac{1+\sin^2\theta}{2\cos^2\theta}$$

33. Verify that $$a_1, a_2, \ldots, a_n$$ form an arithmetic progression where $$a_n = 5 + 6n$$, and then find the sum of the first 12 terms.

    • 11
    • 66
    • 22
    • 528

34. Vector $$u$$ terminates at the point $$(6,3)$$ and vector $$v$$ terminates at the point $$(3,-4)$$. What is the length of the vector resulting from the sum of $$u$$ and $$v$$?

    • $$9$$
    • $$\sqrt{82}$$
    • $$8$$
    • $$2\sqrt{2}$$

35. Between which two consecutive months did Carla experience the greatest percentage increase in her test score?

    • Apr to May
    • Jan to Feb
    • Feb to Mar
    • Mar to Apr

36. The solution set for $$x$$ of the equation $$(x + 4)^2 = k$$ consists of the complex numbers $$-4 + 3i$$ and $$-4 - 3i$$. What is the value of $$k$$?

    • -9
    • 9
    • 3
    • -3

37. Which of the following is an equation of the ellipse shown in the $$x,y$$ coordinate plane below?

    • $$\frac{x^2}{9} + \frac{y^2}{4} = 1$$
    • $$\frac{x^2}{3} + \frac{y^2}{2} = 1$$
    • $$\frac{-x^2}{3} + \frac{y^2}{2} = 1$$

38. In the figure, lines $$AB$$ and $$CD$$ are parallel. Two angles are marked: $$\angle EIB = 140^\circ$$ and $$\angle GKC = 55^\circ$$. Find the measure of $$\angle IKJ$

    • $$85^\circ$$
    • $$55^\circ$$
    • $$140^\circ$$
    • $$95^\circ$$

39. Jamie went for a jog on Saturday morning. The graph below shows Jamie's distance from the park (on the y-axis) versus the elapsed time (on the x-axis). Which of the following statements best describes Jamie’s movement?

    • Jamie jogged at a constant speed toward the park.
    • Jamie jogged at a decreasing speed toward the park.
    • Jamie jogged at an increasing speed away from the park.
    • Jamie jogged at an increasing toward the park.

40. A scatterplot consisting of 10 data points is shown in the standard $$x,y$$ coordinate plane below. Which of the following equations best fits the data in the scatterplot?

    • $$y=4$$
    • $$y=x+4$$
    • $$y=-x-4$$
    • $$y=-x+4$$

41. Bruce and Denise left for work at their homes at the same time, cycling towards each other’s homes. Bruce starts at Town P and cycles towards Town Q. Denise starts at Town Q and cycles towards Town P. The graph below shows their respective bike rides to work, with time into bike ride (in minutes) on the x-axis and distance from Town A (in miles) on the y-axis. How far apart, in miles, are Town P and Town Q?

    • $$22$$
    • $$25.5$$
    • $$24$$
    • $$22.4$$

42. A diameter of a circle in the standard $$(x,y)$$ coordinate plane has endpoints at $$(2,3)$$ and $$(8,9)$$. Which of the following is an equation of the circle?

    • $$(x+2)^2 + (y-9)^2 = 9$$
    • $$(x-5)^2 + (y-6)^2 = 18$$
    • $$(x+2)^2 + (y+3)^2 = 9$$
    • $$(x-8)^2 + (y-9)^2 = 18$$

43. A number is randomly chosen from the set $$\{-4,-1,0,2\}$$ and another number is randomly chosen from the set $$\{-2,3,4\}$$. What is the probability that the product of the two chosen numbers is positive?

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

44. Each number in a list is tripled, and then each resulting number is increased by 6. If $$m$$ is the mean of the final list, which of the following expressions gives the mean of the original list in terms of $$m$$?

    • $$3m+6$$
    • $$\frac{m-6}{3}$$
    • $$3m-6$$
    • $$\frac{3m+2}{6}$$

45. The members of a data set are listed below. A new data set is created from the original data set by adding integers $$x$$, $$y$$, and $$z$$, where $$x\leq 10$$, $$y\leq x$$, and $$z\geq 40$$. What is the median of the new data set?Original data set: $$\{12,\ 16,\ 22,\ 26,\ 30,\ 30,\ 36\}$$

    • 22
    • 24
    • 26
    • 30