SAT Mathematics : Interpreting Graphs

Study concepts, example questions & explanations for SAT Mathematics

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Example Questions

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Example Question #1 : Interpreting Graphs

In a cross-country race, Lauren started the race as fast as she could, got tired partway through and slowed down a bit while, and then got a cramp toward the end and had to walk on her way to the finish. Which of the following graphs best displays her speed throughout the race in light of the experience outlined in this question?

Possible Answers:

Lauren3

Lauren1

Lauren2

Lauren4

Correct answer:

Lauren1

Explanation:

Some important things to consider from the description in this question are that: 1) Lauren started the race as fast as she could run, meaning that all the way at the left hand side of the graph is where the line for her speed should be at its highest. 2) She slowed during the middle portion of the race and then got even slower toward the end, so there shouldn't be any peaks toward the right half of the graph - everything should be flat or pointed downward. Only one graph starts highest on the left and avoids peaks on the right half, so you have your correct answer.

Example Question #1 : Interpreting Graphs

Charlie got a part-time job to save up money for a new video game console. After several weeks of working and saving, he accidentally broke a neighbor's window playing baseball and had to spend almost all of his money to fix it. After continuing to work just to catch up to his savings total, he asked his boss if he could double his hours to earn money faster, and after doing so for a few weeks he was finally able to purchase the console. Which of the following graphs could represent this situation?

Possible Answers:

Charliebank2

Charliebank3

Charliebank1

Charliebank4

Correct answer:

Charliebank1

Explanation:

Some important things about this situation should stand out to you. For one, there should be a sharp drop in the amount of money in Charlie's account before you see a steeper slope in his increase: he makes money at one job, then loses money on the window, then continues that same increase slope before his slope ever increases. So a graph such as the following that has an increase in slope before it ever decreases is incorrect:

Charliebank4

You then need him to recover his savings slowly at first, and then with a sharp increase in his savings rate as he doubles his hours.  And you need him to have only two decreases in his savings: the window, then after some recovery the video game purchase.

Only one graph accounts for these: a slow growth then a decrease, then a slow growth then a steeper slope, then one big drop. This is your correct answer:

Charliebank1

Example Question #2 : Interpreting Graphs

Screen shot 2020 09 29 at 1.05.40 pm

Kevin is selling cups of lemonade to raise money to buy a bike. If he sells each cup for $0.50, what is the maximum amount of money he made on a single day this week?

Possible Answers:

$2

$10

$11

$22

Correct answer:

$11

Explanation:

The correct answer is $11. He would make the most money on the day he sold the most cups of lemonade. On Thursday, he sold 22 cups. Since each cup costs $0.50, he made $11 that day.

Example Question #4 : Interpreting Graphs

Screen shot 2020 09 29 at 1.05.40 pm

Kevin is selling cups of lemonade to raise money to buy a bike. The number of cups sold on Friday is what fraction of the number he sold on Saturday?

Possible Answers:

Correct answer:

Explanation:

According to the graph, he sold 4 cups on Friday and 13 cups on Saturday. Thus, the fraction of cups sold on Friday compared to Saturday is .

Example Question #3 : Interpreting Graphs

Screen shot 2020 09 29 at 1.05.40 pm

Kevin is selling cups of lemonade to raise money to buy a bike. How many more cups did Kevin sell on his most profitable day than his least profitable day?

Possible Answers:

18

2

22

16

Correct answer:

18

Explanation:

According to the graph, he sold 22 cups on Thursday and 4 cups on Friday.

Example Question #4 : Interpreting Graphs

Screen shot 2020 09 29 at 1.05.40 pm

Kevin is selling cups of lemonade to raise money to buy a bike. Overnight, at some point during the week, Kevin changes the recipe of his lemonade to make it even more tasty, and his sales increase the next day. Which night could this have been?

I) Monday

II) Friday

III) Thursday

 

Possible Answers:

I, II, and III

II and III

I and II

I

Correct answer:

I and II

Explanation:

The graph shows an increase (a positive slope) from Monday to Tuesday and Friday to Saturday. However, there is a sharp decline from Thursday to Friday.

Example Question #5 : Interpreting Graphs

Screen shot 2020 09 29 at 1.14.07 pm

Newland County is tracking the number of public schools in the county from 1920 to 2010. In which years did the county shut down schools?

I) 1940

II) 1970

III) 2010

Possible Answers:

I, II, and III

I

II and III

I and II

Correct answer:

II and III

Explanation:

According to the graph, the number of schools decreased from 1960 to 1970 (13 to 9) and 2000 to 2010 (17 to 15). From 1930 to 1940, a new school was added.

Example Question #6 : Interpreting Graphs

Screen shot 2020 09 29 at 1.14.07 pm

Newland County is tracking the number of public schools in the county from 1920 to 2010. How many more schools were open in 1990 than 1940?

Possible Answers:

15

11

13

14

Correct answer:

13

Explanation:

According to the graph, the number of schools open in 1990 was 15 and in 1940 was 2. Be sure to read the data associated with the data points, not the trendline.

Example Question #7 : Interpreting Graphs

Screen shot 2020 09 29 at 1.14.07 pm

Newland County is tracking the number of public schools in the county from 1920 to 2010. How many more schools were open in 1960 than what would be predicted by the line of best fit?

Possible Answers:

3

4

6

5

Correct answer:

3

Explanation:

According to the graph, the number of schools open in 1960 was 11. The line of best fit for an x-value of 1960 shows a y-value of 8. This question requires you to use both the scatter plot data points as well as the trendline.

Example Question #8 : Interpreting Graphs

Screen shot 2020 09 29 at 1.18.35 pm

Bonnie is conducting a survey in her class to understand how many fruits her peers eat on a daily basis. What is the mode of this graph?

Possible Answers:

0

5

1

2

Correct answer:

1

Explanation:

The mode is the data value that occurs most often. 8 of her peers eat 1 fruit daily.

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