SAT data analysis and statistics part 3

Mastering Advanced Math: SAT Test - part 3

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A new fitness class was started at several fitness clubs owned by the same company. The scatterplot shows the total number of people attending the class during the first five months in which the class was offered. The line of
best fit is drawn.
At the beginning of which month did the actual number of people attending the class differ by the greatest amount from the number predicted by the line of best fit?

month 4

month 5

month 2

month 3

None

The table above shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.
If each player’s salary is increased by 10%, which of the following statistics does not increase by 10%?

all increase by 10%

mean

mode

median

None

Chris plans to purchase a car that loses its value at a rate of 14% per
year. If the intial cost of the car is $27,000, which of the following
equations should Chris use to determine the value, v, of the car after 4
years?

$$ v = 27,000 (0.86x4)$$

$$v = 27,000 (1.14)^{4}$$

$$ v = 27,000 (0.86)^{4}$$

$$ v = 27,000 (0.14)^{4}$$

None

The average of a, b, c, d, and e is 28. If the average of a, c, and e is 24,
what is the average of b and d?

None

A new fitness class was started at several fitness clubs owned by the same company. The scatterplot shows the total number of people attending the class during the first five months in which the class was offered. The line of
best fit is drawn.
For month 4, the predicted number of people attending the class was approximately what percent greater than the actual number of people attending the class?

15%

20%

36%

30%

None

The histogram above shows the number of mobile text messages sent
by a randomly selected group of 27 people on a given day. The average
number of text messages sent per person is closest to what whole
number?

None

The table above summarizes the number of people by age group who were included in a survey of driving habits. Which of the following
statements is true?

The survey was biased because individuals 36 and older were underrepresented.

The survey was not biased since different age groups were included.

The survey was not biased since a large number of drivers were polled.

The survey was biased because it did not differentiate between males and females.

None

The graph above shows the number of U.S. households with laptop
computers for the years 2010 to 2014.
What was the percent of increase in the number of households with
laptops from 2010 to 2014?

40%

60%

150%

120%

None

On a test that has a normal distribution of scores, a score of 58 falls
two standard deviations below the mean, and a score of 85 is one
standard deviation above the mean. What is the mean score of this test?

None

10.

The breakdown of a sample of a chemical compound is represented by
the function $p(n) = 300(0.5)^{n}$ , where p(n) represents the number of
milligrams of the substance that remains at the end of n years. Which of
the following is true?
I. 300 represents the number of milligrams of the substance that
remains after the first year.
II. 0.5 represents the fraction of the starting amount by which the
substance gets reduced by the end of each year.
III. Each year the substance gets reduced by one-half of 300.

II only

I only

I and III only

II and III only

None

11.

If 2a + b = 7 and b + 2c = 23, what is the average of a, b, and c?

12.25

7.5

None

12.

The equation above represents the total monthly cost, C, in dollars of a
data plan offered by a cell phone company when the data usage in a
month exceeds a 1 gigabyte limit by d megabytes. According to the
model, what is the meaning of 0.05?

The cost of each additional gigabyte of data after the first megabyte of data is used

The cost per gigabyte of data used

The cost per megabyte of data after one gigabyte of data is used

The cost per megabyte of data used

None

13.

The owner of a small computer repair business has one employee, who
is paid an hourly rate of $22. The owner estimates his weekly profit
using the function P(x) = 8,600 – 22x. In this function, x represents the
number of

employee’s hours worked per week.

computers repaired per week.

customers served per week.

days worked per week.

None

14.

A radioactive substance has an initial mass of 100 grams, and its mass
is reduced by 40% every 5 years. Which equation could be used to find
the number of grams in the mass, y, that remains after x years?

$$y=100(0.4)^{5x}$$

$$y=100(0.4)^{\frac{x}{5}}$$

$$y=100(0.6)^{5x}$$

$$y=100(0.6)^{\frac{x}{5}}$$

None

15.

After a single sheet of paper is folded in half, there are two layers of
paper. The same sheet of paper is repeatedly folded in half. If function
f represents the number of layers of paper that results when the original
sheet of paper is folded a total of x times, then which equation could
represent this function?

$$f(x) = x²$$

$$f(x)= 2x$$

$$f(x)= 2^{\frac{x}{2}}$$

$$f(x)= 2^{x}$$

None

16.

The average of r and s is 7.5, and the average of r, s and t is 11. What
is the value of t?

None

17.

Refer to the above scatterplot, which shows wrist and neck
circumference measurements, in centimeters, for 12 people. The line of best fit is drawn.
What is the predicted neck circumference, in centimeters, for someone whose wrist circumference is 17.0 cm?

None

18.

Susan received grades of 78, 93, 82, and 76 on four math exams. What
is the lowest score she can receive on her next math exam and have an
average of at least 85 on the five exams?

None

19.

The number of hours, H, needed to manufacture X computer monitors
is given by the function H = kX + q, where k and q are constants. If it
takes 270 hours to manufacture 100 computer monitors and 410 hours
to manufacture 160 computer monitors, how many minutes are
required to manufacture each additonal computer monitor?
write answer only in numbers

20.

The percent increase in the number of students enrolled in advanced mathematics courses from 2010 to 2011 exceeded the percent increase from 2012 to 2013 by approximately what percent?

133

None

21.

The table above shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.
The team signs an additional player to a contract with an annual salary of 7.5 million dollars per year, which brings the sum of the salaries of the 25 players to 69 million dollars. By what amount, in dollars, does the mean increase?

256,250

It cannot be determined

300,000

197,500

None

22.

The bar graph above shows the verbal and math SAT scores for five students labeled A through E. If a scatterplot of the data in the bar graph is made such that the math SAT score for each student is plotted along the x-axis and their verbal SAT score is plotted along the y-axis, how many of the data points would lie above the line y = x?

None

23.

Which of the following is the best approximation for the decrease in
the number of cars purchased per year between 2011 and 2014? refer to the graph above.

105

140

180

185

None

24.

The diagram above shows a graph of the students’ test scores in Ms. Wedow’s algebra class. Which ten-point interval contains the median?

61–70

71–80

81–90

91–100

None

25.

If there are 72 SAT Math scores between 510 and 600, how many SAT Math scores are above 700? refer to the graph above.

None

26.

The average of a, b, c, and d is p. If the average of a and c is q, what is
the average of b and d in terms of p and q?

2p+q

2q - p

2p-q

2q + p

None

27.

The cumulative histogram above shows the distribution of mistakes 28 students in a French language class made on a test. What is the probability that a student selected at random made more than 10 mistakes?

3/4

1/4

5/4

7/4

None

28.

If the average of x, y, and z is 32 and the average of y and z is 27, what
is the average of x and 2x?

None

29.

A man drove a car at an average rate of speed of 45 miles per hour for
the first 3 hours of a 7-hour car trip. If the average rate of speed for the
entire trip was 53 miles per hour, what was the average rate of speed in
miles per hour for the remaining part of the trip?

None

30.

The greatest percent of increase in the jogger’s heart rate occurred over
what interval of time, in minutes? Refer to the graph above which shows the heart rate, in beats per minute, of a jogger during a 4-minute interval.

0 to 1

3 to 4

1 to 2

2 to 3

None

31.

The yearly growth in the number of fast food restaurants in a certain
retail chain can be modeled by the function f(n) = 5 + 8n. According to
this model which statement is true?

The y-intercept of the graph of function f shows the year in which the retail chain made a zero profit.

8 is the initial number of restaurants; 5 is the number of restaurants added each year after the first year

5 is the starting number of restaurants; 8 is the number of restaurants added each year after the first year.

The retail chain opened with 13 restaurants.

None

32.

Refer to the above table, which summarizes the results of a survey of the student body of a high school about club membership in which each student enrolled in the high school enumerated the clubs in which they were members.

If a student is selected at random, what is the probability that the student does not belong to 3 or more clubs?

7/9

8/9

1/9

2/9

None

33.

The graph above represents a jogger’s speed during her 20-minute jog
around her neighborhood. Which statement best describes what the
jogger was doing during the 9 to 12 minute interval of her jog?

She was jogging at a constant rate.

She was increasing her speed.

She was decreasing her speed.

She was standing still.

None

34.

The accompanying graph illustrates the presence of a certain strain of
bacteria at various pH levels. Between which two pH values is the rate
at which the number of colonies of bacteria increasing at the lowest
rate?

6 to 7

8 to 9

7 to 8

5 to 6

None

35.

The arithmetic mean of a set of 20 test scores is represented by x. If
each score is increased by y points, which expression represents the
arithmetic mean of the revised set of test scores?

$$x+y$$

$$x+20y$$

$$\frac{x+y}{20}$$

$$x+\frac{y}{20}$$

None

36.

Refer to the above scatterplot, which shows wrist and neck
circumference measurements, in centimeters, for 12 people. The line of best fit is drawn.
How many of the 12 people have an actual neck circumference that differs by more than 1 centimeter from the neck circumference predicted by the line of best fit?

None

37.

On January 1, a share of a certain stock costs $180. Each month
thereafter, the cost of a share of this stock decreased by one-third. If x
represents the time, in months, and y represents the cost of the stock, in
dollars, which graph best represents the cost of a share over the
following 5 months?

Graph B

Graph C

Graph A

Graph D

None

38.

Some banks charge a fee on savings accounts that are left inactive for
an extended period of time. The equation $y = 5,000(0.98)^{x}$
represents the value, y, of one account that was left inactive for a period of x
years. What is the y-intercept of this equation and what does it
represent?

5,000, the amount of money in the account initially

5,000, the amount of money in the account after x years

0.98, the percent of money in the account initially

0.98, the percent of money in the account after x years

None

39.

The average of the test scores of a group of x students is 76 and the
average of the test scores of a group of y students is 90. When the
scores of the two groups of students are combined, the average test
score is 85. What is the value of x/y?

7/4

2/3

4/7

5/9

None

40.

The scatterplot above shows the profit, by month, for a new company for the first year of operation. A line of best fit is also shown. Using this line, by what dollar amount did the profit in the 18th month exceed the profit in the 13th month?

$5,000

$12,500

$15,000

$7,750

None

Time's up