A1.2.3.2.1: Estimate Or Calculate to Make Predictions Based on Graphs and Charts

MODULE 2 KEYSTONE PREP QUESTIONS

A1.2.3.2.1: Estimate or calculate to make predictions based on graphs and charts.

Anchor Descriptor

A1.2.2.1 Describe, compute, and/or use the rate of change (slope) of a line

Eligible Content

A1.2.2.1.1 Identify, describe, and/or use the constant rates of change

1.)Jeff’s restaurant sells hamburgers. The amount charged for a hamburger ( h) is based on the cost for a plain hamburger plus an additional charge for each topping (t ) as shown in the equation below.

h = 0.60t + 5

What does the number 0.60 represent in the equation?

A. the number of toppings

B. the cost of a plain hamburger

C. the additional cost for each topping

D. the cost of a hamburger with 1 topping

2.)Tara buys two items that cost d dollars each. She gives the cashier $20. Which expression represents the change she should receive?

A.)20-2d

B.)20-d

C.)20+2d

D.)2d-20

3.)In the coordinate plane, the points (2,2) and (2,12) are the endpoints of a diameter of a circle. What is the length of the radius of the circle?

A.)5

B.)6

C.)7

D.)10

4.)The coordinate of the midpoint of the line AB are (2, 4), and the coordinates of point B are (3, 7). What are the coordinates of the point A? [The use of a grid is optional.]

5.)Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail?

A.)15 ft

B.)36 ft

C.)60 ft

D.)100 ft

Eligible Content

A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems

1.)A ball rolls down a ramp with a slope of 2/ 3. At one point the ball is 10 feet high, and at another point the ball is 4 feet high, as shown in the diagram below.

What is the horizontal distance (x), in feet, the ball traveled as it rolled down the ramp from 10 feet high to 4 feet high?

A.) 6

B.) 9

C.) 14

D.) 15

2.)The graph shown below is that of the linear function that relates the value V (in $) of a car to its age t, where t is the number of years after 2000. .

A.)Find the slope and interpret it.

B.) What will be the value of the car in the year 2010?

3.)A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P grows as a linear function of time t, where t is the number of years after 2003.

A) How many students will be enrolled in the school in 2010?
B) Find a linear function that relates the student population to the time t.

4.)A 50-meter by 70-meter rectangular garden is surrounded by a walkway of constant width x meters.

A) Find the slope of the graph of P.
B) What is the meaning of the slope found in in the previous question?

5.)The following data shows the amount of money that John placed in his savings account over a 12 month period.

A.)Find, on average, how much John has saved per month by finding the rate of change.

DOMAIN & RANGE

Make predictions using lines of best fit.

4. A teacher made the following graph showing the number of hours that a student studied for an exam versus their exam grade.

Predict the grade of a student if they studied for 3.5 hours.

/ A. / 80
/ B. / 95
/ C. / 90
/ D. / 100

11. A teacher made the following graph showing the number of hours her students spend playing video games per week versus their grade point average.

Predict the GPA of a student who plays video games for 9 hours every week.

/ A. / 1.8
/ B. / 3.0
/ C. / 2.5
/ D. / 1.0

5. A teacher made the following graph showing the number of hours her students spend playing video games per week versus their grade point average.

Predict the GPA of a student who plays video games for 8 hours every week.

/ A. / 1.0
/ B. / 3.0
/ C. / 2.0
/ D. / 2.5

8. The graph below shows a line of best fit for data collected on the amount of time teenagers spend on the computer and watching television.

Based on the line of best fit, how much time does a teenager spend watching television if they spend 30 minutes on the computer?

/ A. / 180 minutes
/ B. / 195 minutes
/ C. / 225 minutes
/ D. / 210 minutes

14. A teacher made the following graph showing absences vs. final grades.

Predict the grade of a student that has 8 absences.

/ A. / 55
/ B. / 65
/ C. / 45
/ D. / 40

Calculate probabilities for compound events

5. Mark has a standard deck of 52 cards and a fair two-sided coin. What is the probability that he will pull a jack from the deck of cards and toss the coin to land on heads?

/ A. /
/ B. /
/ C. /
/ D. /

7. Katie is trick or treating. The man answering the door holds out two bags. In one bag, there are 3 bars of dark chocolate and 1 bar of white chocolate. In the other bag, there are 3 pieces of strawberry licorice, 1 piece of cherry licorice, and 1 piece of orange licorice. If Katie gets to randomly draw one piece of candy from each bag, what is the probability that she will get a bar of white chocolate and a piece of strawberry licorice?

/ A. /
/ B. /
/ C. /
/ D. /

18. June is making a necklace for her friend out of beads. There is a one jar containing 1 blue bead and 5 green beads, and another jar containing 1 yellow bead and 3 brown beads. If she reaches in without looking and draws a bead from each jar, what is the probability that she will draw one green bead and one yellow bead?

/ A. /
/ B. /
/ C. /
/ D. /

19. Bobby is taking a multiple-choice history test. He has decided to randomly guess on the first two questions. On each question there are 4 answer choices. What is the probability that he answers the first question incorrectly and the second question incorrectly?

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/ D. /

16. Julia conducting an experiment. Every time she flips a fair two-sided coin, she also rolls a six-sided die. What is the probability that the coin will land on heads and the die will land on a number?

/ A. /
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/ D. /

Module 2: Functions - Create, interpret, and/or use the equation, graph, or table of a linear function.

Module 2: Functions - Translate from one representation of a linear function to another (i.e., graph, table, and equation).

Calculate range, quartile, interquartile range

1. The daily high temperatures, in degrees Fahrenheit (°F), of a town are recorded for one year. The median high temperature is 62°F. Theinterquartile range of high temperatures is 32.

Which is most likely to be true?

A. Approximately 25% of the days had a high temperature less than 30°F.

B. Approximately 25% of the days had a high temperature greater than 62°F.

C. Approximately 50% of the days had a high temperature greater than 62°F.

D. Approximately 75% of the days had a high temperature less than 94°F.

2. What is the lower quartile, Q1, of the following data set?

47, 47, 40, 49, 54, 62, 36, 60, 45, 58, 47, 32, 46, 48, 34

/ A. / 47
/ B. / 40
/ C. / 59
/ D. / 56

3. Angela recorded the ages of the people in sales and the people in accounting at her company below.

Sales: / 26, 25, 23, 30, 34, 31, 28
Accounting: / 32, 35, 33, 30, 36, 40, 38

How does the interquartile range of the ages of the people in sales compare to the interquartile range of the ages of the people in accounting?

/ A. / The interquartile range for sales is 7 years greater than the interquartile range for accounting.
/ B. / The interquartile range for sales is 6 years less than the interquartile range for accounting.
/ C. / The interquartile ranges for sales and accounting are both 7 years.
/ D. / The interquartile ranges for sales and accounting are both 6 years.

4. Mike, Shannon, Layla, and Rachel each recorded the grades they received on five tests in their math class in the table below.

Student / Test Scores
Test 1 / Test 2 / Test 3 / Test 4 / Test 5
Mike / 86 / 76 / 73 / 96 / 78
Shannon / 92 / 80 / 79 / 84 / 88
Layla / 79 / 85 / 84 / 77 / 78
Rachel / 83 / 61 / 56 / 62 / 66

What is the range of Shannon's scores?

/ A. / 23
/ B. / 8
/ C. / 14
/ D. / 13

5. What is the upper quartile, Q3, of the following data set?

52, 51, 46, 54, 58, 65, 43, 65, 50, 61, 53, 39, 51, 53, 39

/ A. / 60
/ B. / 63
/ C. / 58
/ D. / 59

Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations.

1. Mrs. Moises, the school counselor, keeps a candy jar in her office for students. During one week, she kept count of how many students came to visit her and the number of candies in the jar, as shown in the scatter plot below.

Based on the trend line, what is the best prediction for the number of candies in the jar when 30 students visit her?

/ A. / 180
/ B. / 135
/ C. / 150
/ D. / 90

2. Halle planted mint and basil plants in her herb garden. She measured the height of each herb plant at the end of each week for six weeks. The results are shown in the line graph below.

What is the difference in the ranges for both herbs during the six weeks shown in the graph?

/ A. / 2 cm
/ B. / 6 cm
/ C. / 4 cm
/ D. / 7 cm

3. A group of band instructors answered a survey about hours of rehearsal per week and number of competitions won. The graph shows the results of this survey.

Based on these results, if a band practices 5 hours per week next season, which is the best estimate of the number of competitions the band can expect to win?

/ A. / 38
/ B. / 24
/ C. / 31
/ D. / 36

4. Crystal's grandmother planted a tree on the farm in 1920. She measured the tree trunk's diameter every 10 years and recorded the measurements. The scatter plot below shows the progress of the diameter. (The year 1930 is equivalent to 10 on the graph.)

y = 0.507x + 5.543

Looking at the line of best fit equation shown below the graph, what will be the approximate diameter of the tree in 2010?

/ A. / 45.63 in
/ B. / 46.103 in
/ C. / 51.173 in
/ D. / 56.243 in

5. Jeff has been saving money to send his son to college. He created the following line graph to track his progress.

Use the graph to predict how many more years it will take him to save enough money to meet his goal of 45,000 dollars.

/ A. / 4
/ B. / 6
/ C. / 7
/ D. / 5

Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.