Name:    Alg. II SOL Diagnostic Test

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

1.

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

2.

Vicki works in a store at the Valley View Mall in Roanoke. She started her job on November 1, 2002, at an hourly wage of \$6, and receives a 3% raise every 6 months. If she keeps this job, what will be her hourly wage on July 1, 2006?
 a. \$6.96 c. \$7.38 b. \$7.16 d. \$7.60

3.

If a, b, and c are positive real numbers, which equation could be represented by this graph?

 a. c. b. d.

4.

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

5.

Which could be an equation for this graph?

 a. c. b. d.

6.

Which is equivalent to ?
 a. 13 – c. 13 b. 37 – d. 37 –

7.

What is the solution set for this system of equations?
 a. {1, 5} c. {(0, 1), (4, 5)} b. {0, 4} d. {(1, 0), (5, 4)}

8.

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

9.

Which function is the inverse of ?
 a. c. b. d.

10.

Matrix P shows the admission prices at the Science Museum of Virginia in Richmond.

Suppose matrix F gives the number of people in each age category for two family groups that are visiting the museum today.

If the Jones family bought tickets to see the exhibits only and the McKay family bought tickets to see both the exhibits and the film, what is the total amount that these two families spent on admission?
 a. \$78.00 c. \$126.50 b. \$116.50 d. \$144.00

11.

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

12.

Which equation has no real solutions?
 a. c. b. d.

13.

The time needed to remove litter from a park varies directly as the area of the park and inversely as the number of workers. If it takes 4 hours for 5 workers to remove litter from a 120-acre park, how long will it take for 8 workers to remove litter from a 200-acre park?
 a. 2 h 30 min c. 5 hr 36 min b. 4 h 10 min d. 6 h 40 min

14.

Which is the graph of a polynomial function with no real solutions?
 a. c. b. d.

15.

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

16.

What is the value of ?
 a. 110 c. 70 b. 85 d. 50

17.

Which function has a graph with x-intercepts and 4?
 a. c. b. d.

18.

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

19.

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

20.

Which represents in the standard form a + bi?
 a. c. b. d.

21.

If , , and , which product is not possible?
 a. P ´ R c. P ´ P b. S ´ P d. R ´ P

22.

Which equation describes a hyperbola with vertices and asymptotes ?
 a. c. b. d.

23.

What property is illustrated by the following statement?
If x = y and y = z, then x = z.
 a. Distributive Property c. Symmetric Property of Equality b. Reflexive Property of Equality d. Transitive Property of Equality

24.

Which inequality has the empty set as its solution set?
 a. c. b. d.

25.

If the domain of is {3, 1, 1, 3}, what is the range?
 a. {16, 36} c. {0, 4, 16, 36} b. {4, 16, 36} d. {0, 4, 14, 18}

26.

By simply examining , which set includes all of the numbers that cannot be solutions of the equation?
 a. {–5, 0, 5} c. {0} b. {–5, 5} d. {5}

27.

What is the simplest form of ?
 a. c. b. d. –1

28.

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

29.

Which equation shows that f is directly proportional to the square of d and inversely proportional to the square root of e?
 a. c. b. d.

30.

Ashley and Marita went shopping at the Spotsylvania Mall in Fredericksburg. Their favorite store was having a sale where all sweaters were one price and all jeans were another price. Not including sales tax, Ashley paid \$102 for 3 sweaters and 2 pairs of jeans, while Marita paid \$96 for 4 sweaters and 1 pair of jeans. If x represents the price of a sweater and y represents the price of a pair of jeans, which matrix equation can be used to find the price for each sweater and the price for each pair of jeans?
 a. c. b. d.

31.

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

32.

Which is a factor of ?
 a. (2x – 3) c. (4x + 3) b. (4x + 1) d. (4x – 1)

33.

A parking garage charges \$5 for the first hour and \$1.75 for each additional half-hour or portion of a half-hour. Which graph best represents this situation?
 a. c. b. d.

34.

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

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

35.

Which system of inequalities best represents this graph?

 a. c. b. d.

36.

Which is equal to ?
 a. 1 c. i b. –1 d. –i

37.

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

38.

If an object is dropped from a height of h0 feet, its height h (in feet) after t seconds is given by the equation . The Sun Trust building in Richmond is 400 feet tall. If a ball is dropped from the top of this building, how long will it take the ball to hit the ground?
 a. 25.0 s c. 2.5 s b. 5.0 s d. 2.2 s

39.

This is the graph of a polynomial function h. Which appears to be the solution set of h(x) = 0?

 a. {–2} c. {3} b. {–2, 3} d. Æ

40.

The figure shows the graph of a system of equations. How many real-number solutions does the system have?

 a. 0 c. 2 b. 1 d. 4

41.

Since 2000, Virginia’s population has been increasing by about 1.3% per year. What type of function best models this situation?
 a. exponential c. logarithmic b. linear d. quadratic

42.

If a, b, c, and d are distinct real numbers, which matrix is the additive inverse of ?
 a. c. b. d.

43.

The chart shows the number of students enrolled in mathematics classes at Northwest High School in September for several recent years. Assuming a linear relationship, which is the best estimate of the number of students who were enrolled in mathematics classes in September, 2004?

 Year 2000 2001 2002 2003 Number of Students 1,250 1,322 1,405 1,483
 a. 1,170 students c. 1,510 students b. 1,200 students d. 1,560 students

44.

Which type of function is shown here?

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

45.

If and , which is ?
 a. c. b. d.

46.

The function models the cost C, in thousands of dollars, to remove x% of the pollutants from a lake. What percentage of the lake’s pollutants can be removed if \$50,000 is budgeted?
 a. 25% c. 50% b. 30% d. 75%

47.

Which function is represented by the graph?

 a. c. b. d.

48.

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

49.

Which equation most closely fits the data in this scatterplot?

 a. c. b. d.

50.

The VHR Company makes replicas of historic sites in Virginia. Its two best selling replicas are of Mount Vernon and Monticello. The company makes a profit of \$8 on each replica of Mount Vernon and \$10 on each replica of Monticello. To use linear programming to maximize profit, the company’s financial officer developed this feasible region from the constraints on the company’s resources and the pattern of demand for these replicas. The number of Mount Vernon replicas to be made each week is represented by x and y represents the number of Monticello replicas to be made each week. How many of each replica should the company make each week in order to maximize the profit?

 a. 200 Mount Vernon replicas, 0 Monticello replicas b. 150 Mount Vernon replicas, 50 Monticello replicas c. 100 Mount Vernon replicas, 100 Monticello replicas d. 50 Mount Vernon replicas, 100 Monticello replicas