Interpreting Graphs

1. Interpreting Graphs

2. Slope The slope of a line represents the number of units a line rises or falls vertically for each unit of horizontal change from left to right.

3. (define in your own words) Draw your picture: Slope Understanding Level 1 2 3 4

4. Independent variable: Variable that is manipulated, sometimes experimentally, in order to observe its effects on a dependent variable. For example, in a study of the effects of age on sports participation, age is the independent variable and sports participation the dependent variable. (the x-axis)

5. (define in your own words) Draw your picture: Independent Variable: Understanding Level 1 2 3 4

6. Dependant variable: A variable that is acted on or influenced by another variable. For example, in an investigation of the affects of age on running speed, the independent variable ( the age of the athlete) is manipulated, selected, or otherwise controlled, and the affect of this manipulation can be seen in the change in the dependent variable (running speed). It is, therefore, an aspect of behavior or experience that goes with or depends on the changes in the independent variable. (the y-axis)

7. (define in your own words) Draw your picture: Dependant variable: Understanding Level 1 2 3 4

8. Displacement: The vector quantity that defines the distance and direction between two positions. (sometimes loosely referred to as distance)

9. (define in your own words) Draw your picture: Displacement: Understanding Level 1 2 3 4

10. Time: The difference between two clock readings. Seconds are the metric unit for time.

11. (define in your own words) Draw your picture: Time: Understanding Level 1 2 3 4

12. Velocity: The relationship between displacement and time. (displacement / time)

13. (define in your own words) Draw your picture: Velocity: Understanding Level 1 2 3 4

14. Acceleration: The relationship between velocity and time. (velocity / time)

15. (define in your own words) Draw your picture: Acceleration: Understanding Level 1 2 3 4

16. Origin: The point in a coordinate system at which the variables have a zero value.

17. (define in your own words) Draw your picture: Origin: Understanding Level 1 2 3 4

18. Bar graph: A graph consisting of parallel, usually vertical bars or rectangles with lengths proportional to the frequency with which specified quantities occur in a set of data. Also called bar chart or histogram.

19. (define in your own words) Draw your picture: Bar graph: Understanding Level 1 2 3 4

20. Line graph: Graphical device that displays quantitative information or illustrates relationships between two changing quantities (variables) with a line or curve that connects a series of successive data points. A grouped line graph compares a trend with on or more other trends, and shows if its rate of change is increasing, decreasing, fluctuating, or remaining constant. Line graphs are the most versatile and most extensively used family of graphs. Also called line chart.

21. (define in your own words) Draw your picture: Line graph: Understanding Level 1 2 3 4

22. Pie graph: A circular graph having radii dividing the circle into sectors proportional in angle and area to the relative size of the quantities represented. Also called circle graph.

23. What generalization can be made • from the data in the solubility graph? • 2008 11th -4 obj1 • The volume of a solvent • affects the solubility of • a solute. • B. The volume of a solute affects • its solubility. • Increasing the temperature of a • solution increases the solubility of • a solute. • D. Increasing the mass of a solute decreases its solubility.

24. Of the 800 students at a local high school, 200 students have no siblings, 318 have one sibling, 160 students have two siblings, and the rest of the students have three or more siblings. Use the key below to find the circle graph that best represents this information.

25. A C D B

26. Based on the graph, the reader can conclude that the most likely reason that peeper frogs and tree frogs do not mate and produce fertile offspring is that their mating activity _____. 2008 11th -2 obj3 A. peaks at different times B. fails to reach a maximum rate C. occurs mostly in springtime D. decreases at the same time

27. The graph shows how the cost of using batteries varies depending on the number of hours of battery operation. What economic and environmental factors should be considered when choosing between disposable and rechargeable batteries for a 40-hour use period? 2008 11th -5 obj5 A. Disposable batteries are more expensive and produce less solid waste. B. Rechargeable batteries are more expensive and produce more solid waste. C. Disposable batteries are cheaper and produce more solid waste. D. Rechargeable batteries are cheaper and produce less solid waste.

28. The graph shows how the heart rate of Daphnia, a water flea, is affected by water temperature. • Which statement is best supported by these data? 2008 10th -4 obj1 • A. Daphnia do well in freezing water. • B. Daphnia have healthy hearts. • C. The pulse of Daphnia can double. • D. The rate of mutation in Daphnia varies with temperature.

29. According to the graph, about how much hemoglobin would be saturated at an O2 pressure of 7.3 kPa? Apr'03 10th -49 A. 32% B. 67% C. 89% D. 92%

30. Which graph best shows the comparison of the elements to the total composition of the copper ore? A. C. B. D.

31. The graph best represents which of the following relationships between temperature and time? Math A-04 10th -51 • Oven temperature while a cake is • baking • Temperature of water that is heated • on a stove, removed, and then allowed to cool • Temperature of a container of hot tea after placing several cubes of ice • in it. • Room temperature of a gym after the • air conditioner is turned on.

32. The graph shows h, the height in meters of a model rocket, versus t, the time in seconds after the • rocket is launched. From the graph, what conclusion can be made about the flight of the rocket? • The rocket reached its • maximum height after 2.5 seconds. • At 0 seconds the rocket was 2 • meters off the ground. • The height of the rocket was 0 • meters when it was launched. • The rocket was in flight for 5 • seconds.

33. The graph shows the distance traveled by a vehicle over a certain period of time. Which segment of the graph shows the vehicle moving with the greatest speed? Apr'04 10th -39 A. L B. M C. N D. O

34. The graph shows the percentage of hemoglobin that combines with carbon monoxide (CO) at various concentrations. Exposure to 400 parts per million of CO in air can cause people to experience nausea and a throbbing headache. According to the graph, about what percentage of hemoglobin is bound to CO at a CO concentration of 400 parts per million? Apr'04 10th -55 A. 25% B. 35% C. 40% D. 55%

35. The graph shows the height of a baseball from the time it is thrown from the top of a building to the time it hits the ground. How much time elapses while the baseball is 80 meters or more above the ground? MathA04 11th -4 A. 1 sec B. 9 sec C. 7 sec D. 6 sec

36. The graph shows the decrease in the value of a personal computer over a period of 60 months. • Which is a reasonable conclusion about the value of this personal computer during the time shown • on the graph? Apr'04 11th -47 • Its value at 18 months was • twice its value at 36 months. • Its value at 36 months was half • its value at 54 months. • It depreciated $200 every 12 • months. • It depreciated $400 every 18 • months.

37. The graph shows the results of a study testing chemical pesticides on a pest species common to cotton plants. Different chemical pesticides were used in five different areas. According to these results, which of the following is the most effective chemical for controlling this pest species? Apr'04 11th -11 A. R B. S C. T D. V

38. Which of these conclusions can be made based on the graphs shown above? Apr'04 11th -15 • Larger mosquitoes have migrated into • the area. • Smaller mosquitoes are being eaten by larger mosquitoes. • A mosquito length of 2 cm has • become a disadvantage in this environment. • Mosquitoes with a body length of 3 cm • have the longest life span.

39. According to the graph, what is the approximate half-life of carbon-14? Apr'04 11th -49 A. 5.7 years B. 5,700 years C. 23,000 years D. 1,000,000 years

40. The graph shows metabolic rates for two types of fish at different environmental temperatures. Which of the following conclusions can be drawn from these data? Apr'04 11th -50 • Fish metabolism responds to • temperature changes. • Metabolic rates decrease as • environmental temperatures increase. • Fish body temperature results from • high metabolism. • D. Metabolic rates are independent of • environmental temperature.

41. The graph shows the distance a certain motorbike can travel at a constant speed with respect to time. Which of the following best describes the meaning of the slope of the line representing this situation? Math A06 10th -12 • The motorbike travels at a speed • of about 8 miles per hour. • The motorbike travels at a speed • of about 2.5 miles per hour. • The motorbike travels at a speed • of about 5 miles per hour. • The motorbike travels at a speed • of about 10 miles per hour.

42. An object was dropped from a height of 250 meters and fell to the ground. The graph below shows the change in h, the object’s height in meters, with respect to t, the time in seconds. According to the graph, which time interval best represents when the object was at 140 meters above the ground? Apr'06 Math 10th -22 A. Between 3 seconds and 3.25 seconds B. Between 3.75 seconds and 4 seconds C. Between 3.5 seconds and 3.75 seconds D. Between 3.25 seconds and 3.5 seconds

43. A student prepared this graph of tornadoes reported over a 50-year period in a midwestern state. Which statement is supported by these data? Apr'06 10th -1 • Tornadoes are less frequent in the • morning. • Darkness increases the strength of • tornadoes. • Tornadoes occurring at night are brief. • The probability of a tornado is the • same throughout the day.

44. The graph shows data for botulism, a form of food poisoning. The conclusion in the box is based on these data. Which of the following is the best reason this conclusion may be unreliable? Apr'06 10th -23 Conclusion: Food poisoning by botulism is increasing in the United States. A. The greatest number of reported botulism cases was 50. B. The number of reported botulism cases remained relatively constant from 1988 to 1995. C. More botulism cases were reported in the 1980s than in the 1990s. D. The number of reported botulism cases decreased after 1994.

45. The graph shows mercury levels found in sediments, prey animals, and adult shorebirds in a bay along the Gulf Coast. Which inference can best be drawn from these data? Apr'06 10th -50 A. Mercury levels are elevated by the presence of shorebirds. B. Mercury concentrations are highest in shorebirds. C. Mercury is produced by sediments. D. Mercury assures the survival of prey animals.

46. The graph shows how the momentum of a given mass changes during a period of motion. According to the information, what is the momentum in kg m/s at 2.75 seconds? Apr'06 11th -20 Record and bubble in your answer to the nearest whole number on the answer document.