SAT Mathematics : SAT Math

Study concepts, example questions & explanations for SAT Mathematics

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Example Questions

Example Question #1 : Interpreting Graphs & Tables

Which of the following would be the most appropriate label for the y-axis of this graph if the total number of farmed animals in 2002 was closest to 9 billion?

Screen shot 2020 09 30 at 2.19.01 pm

Possible Answers:

Number of animals (in billions)

Number of animals (in millions)

Number of animals (in thousands)

Number of animals (in hundred thousands)

Correct answer:

Number of animals (in millions)

Explanation:

If we use some relative math to draw conclusions, we can see that adding the totals for each month gets us to around 9,000. However, the prompt tells us that the total consumption of farmed animals was 9 billion. So, we need to multiply each of our values by one million (1,000,000) to achieve this total. Thus, the y axis gives us the number of animals in millions.

Example Question #3 : Interpreting Graphs & Tables

Screen shot 2020 09 30 at 2.20.47 pm

The table above gives the weight change measurements of 9 laboratory rats that were fed different diets under a variety of conditions over 30 days. 

After all of the measurements were taken for the nine rats, researchers discovered that the scale used to measure the rats at the close of the experiment under weighed all of them by exactly 5 grams. Which of the following statistical values would change after 5 grams are added to each of the measurements above?

 

Possible Answers:

Range

Standard deviation

It cannot be determined from the information given.

Mean

Correct answer:

Mean

Explanation:

In this case, if we add 5 to each of the numbers in the table above, the dispersion of the set remains the same (all values remain the same distance from one another that they started out at, and just shift 5 up on the number line). However, if I add 5 to each value, the sum of my values will increase, and thus the average/mean (the sum of numbers/number of numbers) will also increase. Thus, “mean” is our correct answer.

Example Question #6 : Interpreting Graphs & Tables

Screen shot 2020 09 30 at 2.23.05 pm

The graph above displays the charge “C” in dollars of riding a taxi for “M” miles. 

According to the graph, what does the C-intercept represent?

 

Possible Answers:

The cost per quarter-mile driven

The initial fee of the taxi, regardless of miles driven

The total number of miles driven

The cost per mile driven

Correct answer:

The initial fee of the taxi, regardless of miles driven

Explanation:

Since the “C” intercept refers to the constant in the linear equation expressed by this graph, it doesn’t make sense for the intercept to refer to a charge “per” any other unknown, whether that unknown is miles or quarter miles. We know that the intercept cannot refer to miles driven, as that has been expressed to us as “M” in this linear relationship. The “C” intercept can, however, refer to an up-front fee assessed regardless of miles driven, as is expressed in our correct answer, “The initial fee of the taxi, regardless of miles driven.”

Example Question #11 : Interpreting Graphs & Tables

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:

Lauren2

Lauren4

Lauren1

Lauren3

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 #12 : Interpreting Graphs & Tables

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:

Charliebank4

Charliebank2

Charliebank1

Charliebank3

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 #1 : 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:

$11

$10

$2

$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 #1 : 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 #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. How many more cups did Kevin sell on his most profitable day than his least profitable day?

Possible Answers:

2

22

18

16

Correct answer:

18

Explanation:

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

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. 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:

II and III

I, II, and III

I

I and II

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 #2 : 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

I and II

I, II, and III

II and III

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.

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