Full Practice Exams — Exam 2

Questions in this quiz (45)

1. What is the sum of the complex solutions to $$x^2 + 4x + 5 = 0$$?

   • $$2i$$
   • $$2+i$$
   • -4
   • $$-2-i$$

2. What is the value of x if $$3^{x+2} = 81$$?

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

3. If $$\tan(\theta) = 2$$ and $$\sin(\theta)$$ > $$0$$ find $$\sin(2\theta)$$.

   • $$\frac{4}{5}$$
   • $$\frac{1}{2}$$
   • $$\frac{\sqrt{3}}{3}$$
   • $$\frac{\sqrt{3}}{2}$$

4. Daisy set her car's trip odometer to 0 miles before she traveled to visit her aunt. She traveled at an average speed of 60 mph for 3.5 hours and then took a 45-minute break at a rest stop. She then traveled at an average speed of 74 mph until her trip odometer read 395 miles. How many hours did Daisy drive after her break?

   • $$1$$
   • $$1.5$$
   • $$2$$
   • $$2.5$$

5. Jack has 8 identical large cubes and some identical small cubes. He packed all the cubes tightly into a rectangular box such that cubes of the same size are stacked on top of each other. The box is filled to its brim exactly. The figure shows the first layer of cubes packed in the box. The volume of the box is $$4032$$ cm³. The total volume of the 8 large cubes is $$\frac{3}{7}$$ of the volume of the box. What is the length of one edge of the small cube in cm?

   • 4
   • 5
   • 6
   • 7

6. The figure below shows a regular hexagon tangent to circle O at six points. If the area of the hexagon is $$6\sqrt{3}$$, the circumference of circle O?

   • $$6\pi$$
   • $$\frac{12\sqrt{3}}{\pi}$$
   • $$\frac{3\pi\sqrt{3}}{2}$$
   • $$2\pi\sqrt{3}$$

7. If $$3^{100} \cdot 4^{100} \cdot 5^{100} = 2^{20a} \dot 15^{50b}$$, find a + b.

   • 12
   • 50
   • 15
   • 45

8. For what value of k will the graphs of $$3x+4y+5=0$$ and $$kx+6y+7=0$$ not intersect?

   • $$-8$$
   • $$-6$$
   • $$\frac{9}{2}$$
   • $$8$$

9. If $$\log_b 2=x$$ and $$\log_b 3=y$$, what is $$\log_b 72$$?

   • $$3x+2y$$
   • $$2x+3y$$
   • $$2x-3y$$
   • $$2x-2y$$

10. How many positive integers less than 36 are equal to 4 times an odd integer?

    • 3
    • 4
    • 5
    • 6

11. Given $$m$$ > $$n$$ and $$(m-n)$$ > $$(m^2-n^2)$$, determine what $$(m+n)$$ must be.

    • Greater than 1
    • Greater than 2m-n
    • Greater than m-n
    • Less than 2

12. Liam is adding a decorative border around the outside of an elliptical garden. The perimeter of an ellipse is given by the formula $$p=\frac{\pi}{2}\sqrt{2(h^2+w^2)}$$ where $$h$$ is the height and $$w$$ is the width of the ellipse. If the garden has a height of $$6$$ meters and a width of $$8$$ meters, what is its outside perimeter, in meters?

    • $$5\pi\sqrt{2}$$
    • $$5\pi$$
    • $$2\pi\sqrt{2}$$
    • $$\pi\sqrt{5}$$

13. If $$\frac{x}{y}+x=8$$ what is the value of $$\sqrt{\frac{x+xy-3y}{y}}$$?

    • $$2$$
    • $$4$$
    • $$\sqrt{5}$$
    • $$\sqrt{6}$$

14. For all real numbers x and y, the two operations ★ and ♡ are defined as follows:$$x★y=xy+x$$$$x♡y=x-xy$$For all real numbers p and q, what is $$(p♡q)★q$$?

    • $$p+pq^2+q^2$$
    • $$p-pq^2$$
    • $$p-pq^2-q^2$$
    • $$p-2pq^2+q^2$$

15. Vectors u and v are shown in standard position in the standard (x,y) coordinate plane. Which of the following vectors in standard position in the standard (x,y) coordinate plane is v - u?

16. For the real number x, consider the equationsI. $$\frac{|x-2|}{4}=\frac{7\frac12}{25.4}$$II. $$\frac{x-2}{4}=\frac{7\frac12}{-25.4}$$Which statement about their solutions is true?

    • One of the two solutions of I is also a solution of II.
    • One of the two solutions of II is also a solution of I.
    • I and II have the exact same solution.
    • I and II have infinitely many solutions.

17. The population of rabbits R in Clover Field at the beginning of each year can be modeled by the equation $$R(t)=5(3^t),$$ where t represents the number of years after the beginning of the year 2010. For example, t=0 represents the beginning of the year 2010, t=1 represents the beginning of the year 2011, and so forth. According to the model, how many rabbits were in Clover Field at the beginning of the year 2014?

    • 81
    • 162
    • 405
    • 324

18. The stopping distance, in feet, of a certain car can be estimated by multiplying the square of the car's initial speed, in miles per hour, by 0.03. According to this method, what is the estimated initial speed, in miles per hour, of the car if it comes to a stop in 108 feet?

    • 36
    • 60
    • 54
    • 30

19. Each time a spinner is spun, it lands on either red or blue. The probability of landing on red is twice the probability of landing on blue. In a certain game, the player wins 3.00 dollars when the spinner lands on red and 5.00 dollars when the spinner lands on blue. To the nearest cent, what is the expected value of each spin in this game?

    • $$0.67$$
    • $$1.67$$
    • $$2.67$$
    • $$3.67$$

20. Which of the following datasets has the largest standard deviation?

    • 1, 1, 15, 15
    • 0, 5, 10, 15
    • 4, 6, 8, 10
    • 7, 7, 7, 7

21. During a survey, two groups, X and Y, were studied. Groups X and Y have no members in common. Which of the following probabilities must be equal to 0?

    • P(X)
    • P(Y)
    • P(X or Y)
    • P(X and Y)

22. In the standard (x,y) coordinate plane, how many points are both 10 coordinate units from the origin and also 3 coordinate units from the line y=0?

    • 3
    • 4
    • 5
    • 6

23. Let $$g(x)=5e^{2x}-4$$. Which of the following numbers is closest to the value of $$g(4)$$?

    • $$1\times 10^{2}$$
    • $$3\times 10^{3}$$
    • $$2\times 10^{4}$$
    • $$1.5\times 10^{4}$$

24. Which of the following matrices is equal to:

25. Sarah found 10.14 dollars in pennies, nickels, dimes, and quarters. She had 3 times as many nickels as pennies, 2 fewer dimes than pennies, and 5 more quarters than nickels. How many quarters did Sarah have?

    • 32
    • 9
    • 27
    • 7

26. When points P and Q(6, -1) are graphed in the standard (x,y) coordinate plane, the midpoint of line segment PQ is (2,1). What are the coordinates of point P?

    • $$(3, \frac{1}{2})$$
    • $$(3, -\frac{1}{2})$$
    • $$(3, -2)$$
    • $$(-2, 3)$$

27. In the figure below, vertices C and D of triangle ACD lie on line BE. The measure of angle BCA is 160°, and the measure of angle ADE is 150°.What is the measure of angle CAD?

    • $$130^\circ$$
    • $$30^\circ$$
    • $$20^\circ$$
    • $$40^\circ$$

28. At a local bakery, an average of 4 customers are in line when the store closes each day. The probability P that exactly n customers are in line at closing can be modeled by $$P=\frac{4^n\cdot e^{-4}}{n!}$$. Given that $$e^{-4}\approx0.018$$, which value is closest to the probability that exactly 3 customers are in line when the bakery closes?

    • $$0.210$$
    • $$0.192$$
    • $$0.180$$
    • $$0.189$$

29. A biologist estimates that the number of bacteria in a petri dish is $$73.2\times10^n$$. What is the correct scientific notation for this number?

    • $$7.32\times10^{n-1}$$
    • $$73.2\times10^{n+2}$$
    • $$7.32\times10^{n+1}$$
    • $$73.2\times10^{n-2}$$

30. In the complex numbers where $$i^2=-1$$, given the equation $$x(2-i)-4=6$$, find x.

    • $$4+2i$$
    • $$2+2i$$
    • $$2+i$$
    • $$2-i$$

31. What is the least common multiple of 28, 36, 45, and 60?

    • $$1260$$
    • $$210$$
    • $$252$$
    • $$250$$

32. Two similar triangles have perimeters in the ratio 3:4. The sides of the larger triangle are 12 in, 9 in, and 7 in. What is the perimeter, in inches, of the smaller triangle?

    • $$12$$
    • $$15$$
    • $$21$$
    • $$18$$

33. For all x>5, evaluate $$\frac{(x^2+4x+3)(x-1)}{(x^2-9)(x+3)}$$

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

34. In the rhombus ABCD, diagonal AC=10 and diagonal BD=24. What is the length of each of the four sides?

    • $$10$$
    • $$13$$
    • $$12$$
    • $$5$$

35. Triangles ABC and KLM are similar. Segment AB corresponds to KM and segment AC corresponds to KL. Given AB=15, AC=18, BC=24, and ML=12. Find KM and KL.

    • 9 , 7.5
    • 10 , 8
    • 8 , 10
    • 7.5 , 9

36. The circle graph shows the distribution of 2000 workers (ages 25–34) by total savings and investments. How many workers have at least 50,000 dollars in savings and investments?

    • $$160$$
    • $$260$$
    • $$320$$
    • $$210$$

37. At what value of x does the function $$y=\frac{(x-2)^2(x+3)}{(x-2)^3(x+3)}$$ have a vertical asymptote?

    • $$-3$$
    • $$2$$
    • $$3$$
    • $$-2$$

38. In a certain school, every student is either left-handed or right-handed. If left-handed students make up $$\frac{3}{10}$$ of the total student population, what is the ratio of right-handed students to left-handed students?

    • $$8:5$$
    • $$5:3$$
    • $$3:8$$
    • $$7:3$$

39. Consider the two functions $$f(x)=x^2+4$$ and $$g(x)=f(x+2)$$. Which of the following correctly describes the graph of $$g(x)$$ relative to the graph of $$f(x)$$ in the standard (x,y) coordinate plane?

    • Shifted right by 2 units
    • Shifted left by 2 units
    • Shifted up by 2 units
    • Shifted down by 2 units

40. You run an online granola business. Your special blend consists of 6 parts oats, 2 parts almonds, and 2 parts dried fruit. If a customer places an order for 250 pounds of granola mix, how many pounds of almonds will be needed to fulfill the order?

    • 25
    • 40
    • 50
    • 62

41. A circle graph is to be created based on the data of student enrollment in different majors. What is the angle (in degrees) that should be used to represent students majoring in Engineering?

    • $$36^\circ$$
    • $$32^\circ$$
    • $$40^\circ$$
    • $$44^\circ$$

42. The side lengths of a triangle are 6, 8, and 10 centimeters. Which description best classifies this triangle?

    • Scalene acute.
    • Scalene obtuse.
    • Isosceles right.
    • Scalene right.

43. A company is creating new employee ID numbers. Each ID number must begin with the digits 246, and the remaining 5 digits can each be any digit from 0 through 9. How many different ID numbers are possible?

    • $$3^2\cdot10^5$$
    • $$5^3\cdot10^5$$
    • $$10^5$$
    • $$3\cdot10^5$$

44. A bakery sells muffins for 4 dollars each. At this price, 60 muffins are sold per day. For every 0.50 dollar decrease in price, the bakery will sell 10 more muffins per day. The bakery will adjust the price to maximize its daily revenue. What will be the maximum possible revenue for 1 day?

    • $$245\text{ dollars}$$
    • $$320\text{ dollars}$$
    • $$260\text{ dollars}$$
    • $$360\text{ dollars}$$

45. We are given the expression $$E(x)=(x-5)^2+(x-5)(2x+1)$$. Determine the value of $$E(\sqrt2+1).$$

    • $$5+3\sqrt{2}$$
    • $$-5+3\sqrt{2}$$
    • $$5-3\sqrt{2}$$
    • $$10-13\sqrt{2}$$