1. In 1977, there were 12,168,450 U.S. households with cable television. In 1997, there were 65,929,420 U.S. households with cable television. Over that time period, what was the average rate of change per year in households with cable television?
- 2,688,048.5
- 5,376,097.0
- 53,760,970.0
- 65,320,997.5
2. Harrison High School has 768 students. In 6 years, it is projected to have 1,157 students. What is the projected average rate of change per year in students over this time period? Round your answer to the nearest student and then enter your solution in the blank below.
- 65
- 389
- 193
- 321
3. A rabbit population grew in the following pattern: 2, 4, 8, 16, ...
If all the rabbits live and the pattern continues, how many rabits will be in the 8th generation?- 32
- 128
- 256
- 512
4. Pedro throws a ball upward at a rate of 20 meters per second from an initial height of 2 meters. The height of the ball above the ground can be approximated by h = -5t2 + 20t + 2, where t represents the amount of time, in seconds, since the ball has been released. What is the maximum height that the ball reaches?
- 5 meters
- 6 meters
- 20 meters
- 22 meters
5. Which of the following graphs shows a function?
-
6. How can the following compound statement be combined into a statement using absolute value?
x < 5 and x > -1- |x + 1| < 5
- |x - 5| < 1
- |x - 2| < 3
- |x - 3| < 2
7. Tickets for a concert cost $15.00 each plus $1.50 each for handling charges. The shipping fee for an order of any number of tickets is $4.00. Which equation could be used to determine the cost, C, of any number of tickets, t?
- C = 15.00t + 5.50
- C = 16.50t + 4.00
- C = 17.00t
- C = 20.50t
8. Yia wrote the equation P = 0.25n - (0.05n + 1) to represent the school store's weekly profit, P, from sales of n pencils. Which equation is equivalent to Yia's equation?
- P = 0.20n - 1
- P = 0.20n + 1
- P = 0.125n2 - 1
- P = 0.0125n2 + 1
9. In an electric circuit, the power dissipated in a load can be modeled by the equation p = iv - i2r. The following chart tells what each variable in the equation represents. In a certain circuit, the voltage supplied is 100 volts and the resistance of the rest of the circuit is 25 ohms. Which of the following currents can be present if the load is expected to use 75 watts of power?
p = power used by a load in watts v = voltage supplied in volts r = resistance of the circuit external to the load in ohms i = current in the circuit in amperes - 3 amperes
- 5 amperes
- 8 amperes
- 10 amperes
10. The yearly growth of a tree is modeled by concentric circles in a cross-sectional cut through the tree trunk as shown. The one-year-old tree has a diameter of 2.5 centimeters. Which equation models the diameter of the tree, d, in terms of the age of the tree in years, n? (use the diagram below to answer the question)
- d = 2.5n + 1
- d = 2.5n + 2
- d = 2.5 + 2n
- d = 2.5 + 2(n - 1)
11. A mathematical diversion sometimes used to amaze and amuse people is the creation of a "black hole" for a certain number. You ask your subjects to take any number, go through some mathematical manipulations, and then you "magically" tell them the remainder. Here is one such "black hole" for the number 3:
Pick any number
Multiply it by 20
Add 15 to your result
Divide that result by 5
Subtract 4 times the number you picked
The answer is always 3.
Show that this will work with any positive number. Explain your answer using algebraic expressions.
Your solution should begin with the following: (20x+15) / 5 - 4x
You should be able to reduce the first fraction and simplify to 3. Try it ... were you able to do this?- Yes
- No
12. Two numbers are written in scientific notation as follows: 7.3x10n and 1.2x10q. What is the product of the two numbers?
- 7.3 x 1.2 x 10n+q
- 7.3 x 1.2 x 100n+q
- 7.3 x 1.2 x 10nq
- 7.3 x 1.2 x 100nq
13. Rosa wants to use $20 to buy games. The inequality 2.50k + 5.50 < 20.00 represents the number of games, k, she can buy with her money. What is the greatest number of games Rosa can buy?
- 5
- 6
- 8
- 10
14. The braking distance of Samir's car can be described by the equation below:
where x is the car's speed in kilometers per hour and y is the braking distance in meters.
How fast is the car traveling when the braking distance is 75 meters?- 30 kilometers per hour
- 50 kilometers per hour
- 55 kilometers per hour
- 120 kilometers per hour
15. Given a1 = 1 and an = an-1 + 2. Find a7.
- 7
- 9
- 11
- 13
16. Dr. Franklin begins an experiment with 100 bacteria in a container. She finds that the number of bacteria present at any given time is modeled by the following recursive formula:
where n is the number of hours after the beginning of the experiment.
How many bacteria are present 5 hours after the beginning of the experiment?- 1,000
- 1,600
- 3,200
- 6,400
17. Use the graph below to answer this question.
All of Tyler's DVDs and videotapes are on a shelf. The inequality d + 1.7v < 34 represents the number of DVDs, d, and videotapes, v, that the shelf can hold. He owns fewer videotapes than DVDs, represented by the inequality v < d. The possible combinations of Tyler's DVDs and videotapes that the shelf can hold are found in which region of the graph?- 1
- 2
- 3
- 4
18. Use the graph below to answer this question:
A contractor wants to lay an underground telephone cable across a field starting at the telephone pole, T. The cable should run parallel to the water line. Which of these is an equation for the line that the telephone cable should lie on?- y = (3/2)x - 13.5
- y = (-4/9)x + 4
- y = (-2/3)x + 4
- y = (-2/3)x + 6
19. The heights, in inches, of the 15 students in Jared's 11th-grade science class are 60, 66, 65, 74, 68, 67, 70, 65, 67, 69, 71, 68, 67, 70, and 68. What is the upper quartile, Q3, of these data?
- 67
- 68
- 69
- 70
20. Use the table below to answer this question.
What conclusion can be made from the above data on six months of accidents?- The median number of accidents is 6.
- On average, more accidents happened in September and October than in January and February.
- On average, more accidents happened in December, January, and February than in September, October, and November.
- More students drive to school as the school year goes on.
21. Use the graph below to answer this question.
The scatter plot shows the time and distance that Aidan rode his bike on several trips. Using the scatter plot and assuming a linear relationship, about how many miles would Aidan travel if he rode for 175 minutes?- 20 miles
- 30 miles
- 40 miles
- 50 miles
22. Use the chart below to answer this question.
Which of the following statements is supported by the data?- More sleep causes a person to have a higher G.P.A.
- A higher G.P.A. allows a person to get more sleep.
- In the sample study, sleep and G.P.A. are positively correlated.
- Schoolwide, sleep and G.P.A. are positively correlated.
23. Use the following graph to answer this question.
Dave drew this graph to give the impression that Minnesota raised a much greater number of turkeys than North Carolina. To the nearest percentage, what is the percentage difference between the number of turkeys raised in Minnesota and North Carolina based on North Carolina's number of turkeys?- 1%
- 2%
- 50%
- 100%
24. Use the information shown below to answer this question:
Ten of the eleven ballots collected for student council representative from Mrs. Rodriguez's homeroom are shown. Using a run-off method of voting, which of the following ballots would need to be cast as the eleventh ballot in order for Jan to win?-
25. There are four performers in a school talent show. In how many ways can the performers be arranged by different order of appearance?
- 12
- 16
- 24
- 256
26. In the high school parking lot 16% of the vehicles are trucks and 8% of the vehicles are painted yellow. If these characteristics are mutually exclusive, what is the probability that a vehicle in the high-school parking lot will be a yellow truck?
- 0%
- 8%
- 24%
- 50%
27. What is the probability that a family with 4 children will have exactly 2 girls and 2 boys? (enter your answer, as a decimal, in the blank below)
- .375
- .5
- .25
- .333
28. Use the table below to answer the question.
Emma rolls a fair, 6-sided number cube, numbered 1 to 6, 18 times as shown in the frequency table. She rolls the number cube 72 more times. What is the range representing the number of times Emma will most likely roll a 3 in her 90 rolls?- From 0 to 10
- From 11 to 20
- From 21 to 30
- From 31 to 40
29. A store has 25 VCRs in stock, but 2 of these are defective. What is the probability that the second person to buy a VCR gets a defective one, given that the first customer's was not defective? Round your answer to the nearest thousandth.
- 0.003
- 0.042
- 0.080
- 0.083
30. A survey shows that 55% of the registered voters in Plainville voted on the school budget proposal. Of those who voted, 62% voted to pass the school budget. What is the probability that a registered voter chosen at random voted to pass the school budget?
- 0.171
- 0.209
- 0.279
- 0.341
31. The height of a right cylindrical can of peas is greater than the diameter of the base of the can. The can is sliced into two equal parts through its bases. Which figure best describes the cross section of the cylinder?
- Circle
- Triangle
- Rectangle
- Semicircle
32. Use the diagram below to answer the question:
An engineer models a bridge crossing a river using two parallel lines to represent the riverbanks and two parallel lines to represent the bridge in the aerial view shown. The bridge is not perpendicular to the riverbanks. Which of the following statements about the angles formed between the bridge and the riverbanks must be true?- <5 is congruent to <3
- <1 is congruent to <2
- <2 is congruent to <8
- <1 is congruent to <8
33. Use the diagram below to solve this question:
Jeremy is the set designer for the school play. the center of the circular stage he is designing is at the point P. Walls of the set are reepresented by segments PS, PT, RS, and RT. Using the angle and arc measurements in the diagram, what is the measure, in degrees, of <RTP?- 17 degrees
- 19 degrees
- 21 degrees
- 38 degrees
34. Use the figure below to answer this question:
Find the area of the figure. (Use 3.14 for pi)- 67.71 square feet
- 70.07 square feet
- 72 square feet
- 91.26 square feet
35. Elena inherited 3 small spherical gold beads from her grandmother. They had radii of 2 mm, 3 mm, and 4 mm. She wanted to have them melted and recast to form one larger sphere. Its radius would be closest to which of the following:
- 3 mm
- 5 mm
- 6 mm
- 9 mm
36. Use the diagram below to answer this question.
At a certain time of day, the length of the shadow of the Eiffel Tower to the center of its base was 225 meters when the sun's angle of elevation was 53 degrees. What is the approximate height of the Eiffel tower?- 135 meters
- 180 meters
- 300 meters
- 375 meters
37. Use the graph below to answer this question:
The point A is translated to the left 4 units and up 3 units. How far is image A from the original point A?- 3 units
- 4 units
- 5 units
- 7 units
38. A small plane needs to refuel approximately halfway to its destination. It takes off from its base located at (7, -2) on a coordinate grid and its destination is located at (-3, 6). Which of the following locations is closest to halfway?
- (2.2, 2)
- (2.5, 1.5)
- (4, 1.5)
- (5, -4.5)
39. Ashley connected the following points to form a triangle:
A(-2, 2), B(2, 1), and C(5, 5). She claims that the triangle is isosceles. Draw the triangle on a piece of graph paper. Then use your knowledge of geometry to prove or disprove her claim.
Try this on your own.
To correctly solve this problem, you need to be able to plot all three points on a graph and connect them to make a triangle. After making the triangle you need to be able to show that two of the sides of the triangle are the same length. Try it ... were you able to do it?- Yes
- No
40. A commercial artist has a sketch of a rectangular logo that is 7 inches high. She needs to proportianally reproduce the logo on a sign that is 8 feet high. The sketch of the logo contains a letter M that is 5 inches tall. To the nearest tenth of a foot, how tall will the letter M be on the larger sign?
- 4.4 feet
- 5.7 feet
- 6.0 feet
- 11.2 feet
41. A family is carpeting two rectangular rooms. They have chosen carpeting that costs the same amount per square yard for each room. A 12-foot by 15-foot carpet for the bedroom costs $600. If the dimensions of the living room are 20 feet by 28 feet, which amount is closest to what it will cost carpet the living room?
- $700
- $1,200
- $1,500
- $1,900
