Name:    Alg. II SOL Practice Test

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

1.

Which function has a graph with x-intercepts and ?
 a. c. b. d.

2.

The relationship between the times a and b it will take each of two people to complete a job working alone and the time t it will take them to complete the job working together can be described by the equation . Amir and Hector are students at Shenandoah University in Winchester. They are planning to paint the apartment that they share. If Amir could paint the apartment in 18 hours working alone and Hector could do the job in 15 hours working alone, about how long will it take them to paint the apartment if they work together?
 a. 3 h c. 8 h 11 min b. 7 h 15 min d. 16 h 30 min

3.

Which is a factor of ?
 a. c. b. d.

4.

If b is a real number greater than 1, which equation could be represented by this graph?

 a. c. b. d.

5.

The volume V of a gas varies directly as its temperature T and inversely as its pressure P. Which equation describes this relationship?
 a. c. b. d.

6.

Which is a solution of ?
 a. c. b. d.

7.

What is the simplest form of ?
 a. –2 c. b. 2 d. x

8.

Which equation most closely fits the data in this scatterplot?

 a. c. b. d.

9.

Which function includes the values in the table?

 x 0 1 2 3 4 y –4 –1 0 –1 –4
 a. c. b. d.

10.

Which could be the graph of ?
 a. c. b. d.

11.

A store sells “I Love Virginia: T-shirts in four sizes: small (S), medium (M), large (L), and extra large (XL). Matrix V shows the number of each size sold at the store during three summer months of 2003, while matrix P gives the store’s profit on a T-shirt of each size.

What was the store’s profit from selling these T-shirts just for July?
 a. \$2,651.50 c. \$886.25 b. \$979.75 d. \$785.25

12.

The chart gives the population of a city at the beginning of four 5-year intervals. Assuming an exponential relationship, which is the best estimate of the population of this city in 1980?

 Year 1985 1990 1995 2000 Population 45,250 41,600 38,300 35,400
 a. 49,100 c. 40,200 b. 48,600 d. 32,600

13.

What property is illustrated by 75(34 + 56) = (34 + 56)75?
 a. Associative Property of Multiplication b. Commutative Property of Addition c. Commutative Property of Multiplication d. Distributive Property

14.

Which describes the graph of ?
 a. circle c. hyperbola b. ellipse d. parabola

15.

What are the solutions of ?
 a. and –3 c. and 3 b. 2 and –3 d. 2 and 3

16.

Visitors to Colonial Williamsburg may choose between several ticket plans. Two of these are the Colonial Sampler Ticket and the Freedom Pass. Both plans have one price for adults and another price for youths, ages 6-17. One group of teenagers, all under age 18, paid a total of \$395 for 12 Colonial Sampler Tickets and 10 Freedom Passes. Another group of teenagers, also all under 18, paid a total of \$418 for 8 Colonial Sampler Tickets and 10 Freedom Passes. What is the cost of a youth Freedom Pass?
 a. \$29.00 c. \$16.00 b. \$17.50 d. \$9.50

17.

The children in Ms. Steinberg’s kindergarten class are building block walls that follow the pattern shown in the figure. If they want to make their wall 12 levels high, how many blocks will they need?

 a. 156 blocks c. 78 blocks b. 91 blocks d. 66 blocks

18.

The figure shows the graph of a system of equations. What is the solution set for this system?

 a. c. b. d.

19.

Which is equivalent to ?
 a. –18i c. –18 b. 18i d. 18

20.

Which is the solution set for ?
 a. c. b. d.

21.

If , what is the solution set of f(x) = 0?
 a. c. b. d.

22.

Which equation has solution set ?
 a. c. b. d.

23.

Which is the graph of a logarithmic function?
 a. c. b. d.

24.

Which matrix equation is equivalent to the system of equations below?
 a. c. b. d.

25.

Which statement about matrices M and N is true?

 a. The product N ´ M is a 1 ´ 2 matrix. c. The product M ´ M is a 3 ´ 2 matrix. b. The product M ´ N is a 3 ´ 3 matrix. d. The product N ´ N is a 3 ´ 3 matrix.

26.

If an object is thrown upward from a height of h0 feet at an initial velocity of h0 feet per second, its height h (in feet) after t seconds is given by the equation . The Federal Reserve Bank Building in Richmond is 393 feet tall. If a ball is thrown upward from the top of this building at an initial velocity of 50 feet per second, about how long will it take the ball to hit the ground?
 a. 6.8 s c. 5.0 s b. 5.6 s d. 3.6 s

27.

Which equation describes a circle with center at (5, 3) and radius 6?
 a. c. b. d.

28.

Let A and B be 2 ´ 2 matrices such that A ¹ B, let I be the 2 ´ 2 multiplicative identity matrix, and let O be the 2 ´ 2 zero matrix. Which statement is not always true?
 a. AI = IA c. AB = BA b. A + O = O + A d. A + B = B + A

29.

Which are the zeros of ?
 a. , 0, and 1 c. , 0, and 1 b. –1 and d. and 1

30.

Kitchen canisters are cylindrical and come in a variety of sizes. For a given volume, the height of a cylinder varies inversely as the square of the radius. Tricia has two canisters in her kitchen that have the same volume. The one she uses to store spaghetti is 12 inches tall and has a radius of inches. The one she uses to store flour has a radius of 3 inches. How tall is the flour canister?
 a. 9 in. c. in. b. in. d. 3 in.

31.

The VBU Company makes beach chairs and beach umbrellas. The company’s profit is \$5 on each chair and \$8 on each umbrella. To use linear programming to maximize profit, the company’s financial officer developed this feasible region from the constraints on the company’s equipment and the number of hours of employee time available. The number of chairs to be made each day is represented by x. The number of umbrellas to be made each day is represented by y. How many chairs and how many umbrellas should the company make each day in order to maximize the profit?

 a. 10 chairs, 20 umbrellas c. 20 chairs, 20 umbrellas b. 10 chairs, 0 umbrellas d. 40 chairs, 0 umbrellas

32.

Which graph shows the solution set for ?
 a. c. b. d.

33.

Which could be an equation for this graph?

 a. c. b. d.

34.

Which equation has exactly one real solution?
 a. c. b. d.

35.

Which expression is equal to ?
 a. c. b. d.

36.

What are the vertices of the feasible region determined by the constraints ?
 a. (0, 0), (0, 80), (40, 0) c. (10, 0), (10, 60), (30, 20), (30, 0) b. (10, 0), (10, 40), (30, 40), (30, 0) d. (10, 0), (10, 60), (40, 0)

37.

Which is the solution set for the system given below?
 a. b. c. d.

38.

Which function is represented by the graph?

 a. c. b. d.

39.

Which is equivalent to ?
 a. c. b. d.

40.

What is the value of ?
 a. c. b. d.

41.

Which has the set of all real numbers as its solution set?
 a. c. b. d.

42.

This is the graph of a polynomial function g. Which is not a solution of ?

 a. –2 c. 2 b. 0 d. 4

43.

If and , which is the value of ?
 a. –169 c. 3 b. –9 d. 9

44.

Which is the completely factored form of ?
 a. c. b. d.

45.

Which type of function would best fit the data in this scatterplot?

 a. exponential c. logarithmic b. linear d. quadratic

46.

How many real solutions does have?
 a. 0 c. 2 b. 1 d. 3

47.

Which is another way to write ?
 a. c. b. d.

48.

Which is equivalent to ?
 a. 26 + 2i c. 26 b. 22 + 2i d. 22

49.

Brett likes to purchase concert tickets online for himself and his friends. The ticket service he uses charges a service fee that is a fixed percentage of the price of the tickets purchased. The chart shows the purchase prices and service fees for Brett’s last three transactions. If the service fee on Brett’s next purchase is \$10.14, what is the purchase price for this transaction?

 Purchase Price \$48 \$124 \$86 Service Fee \$3.12 \$8.06 \$5.59
 a. \$169 c. \$150 b. \$156 d. \$145

50.

The table lists the seven Presidents of the United States who are buried in Virginia, in the order in which they served, and their ages at death. If this information is considered as a function made up of ordered pairs (President, Age at Death), how should the range of the function be written?

 President Age at Death George Washington 67 Thomas Jefferson 83 James Madison 85 James Monroe 73 John Tyler 71 William Howard Taft 72 John Kennedy 46
 a. 7 c. {46, 67, 71, 72, 73, 83, 85} b. 39 d. {x|46 £ x £ 85}