SAT data analysis and statistics part 3

Mastering Advanced Math: SAT Test - part 3

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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?

$$f(x)= 2x$$

$$f(x) = x²$$

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

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

None

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?

1/4

3/4

5/4

7/4

None

In 2012, the number of cars purchased was x percent of the number of
cars leased. What is the best approximation for x? refer the graph above.

None

Vanessa plans to invest $10,000 for 5 years at an annual interest rate of
6% compounded annually. Which equation could be used to determine
the profit, P, Vanessa earns from her initial investment?

$$P = 10,000\times [5(1.06)-1]$$

$$P = 10,000\times [(1.06)^{5}-1]$$

$$P = 10,000\times [(1.06)^{5}+1]$$

$$P = 10,000\times (1.06)^{5}$$

None

The City Tunnel and Bridge Authority in a certain city estimates that
40,000 vehicles currently travel over a certain bridge per year but, due
to highway construction and changing traffic patterns, vehicle traffic
over the bridge will begin to decline by 12% every 5 years. Which of
the following expressions best represents the vehicle traffic projections
for this bridge n years from now?

$$40,000(0.12)^{\frac{n}{5}}$$

$$40,000(0.12)^{5n}$$

$$40,000(0.88)^{\frac{n}{5}}$$

$$40,000(0.88)^{5n}$$

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.
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 3

month 2

month 5

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%?

mode

median

all increase by 10%

mean

None

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?

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.

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

None

A certain drug raises a patient’s heart rate, h, in beats per minute, according to the equation h(x) = 65 + 0.2x, where x is the number of milligrams of the drug in the patient’s bloodstream. After t hours, the level of the drug in the patient’s bloodstream decreases exponentially according to the equation x(t) = 512(0.7)^t . After 5 hours, what is the number of beats per minute in the patient’s heart rate, correct to the nearest whole number?

None

10.

The tables above give the distribution of grades for 21 students in two different college mathematics classes. For purposes of making statistical calculations,
A = 4, B = 3, C = 2, D = 1, and F = 0. Which of the following statements is true about the data shown for these two
classes?
I. The standard deviation of grades is greater for class X.
II. The standard deviation of grades is greater for class Y.
III. The median letter grade is the same for classes X and Y.

I and III only

II and III only

II only

I only

None

11.

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 C

Graph D

Graph A

Graph B

None

12.

Sasha invested $1,200 in a savings account at an annual interest rate of
1.6% compounded annually. She made no further deposits or
withdrawals. To the nearest dollar, how much more money did she
have in the account after 3 years than after 2 years?
write answer only in numbers

13.

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.

185

140

105

180

None

14.

From 2014 to 2015 the number of students enrolled in advanced mathematics courses increased by the same percent that student enrollment in advanced mathematics courses dropped from 2013 to 2014. What was the approximate number of students enrolled in advanced mathematics courses in 2015?

440

480

420

450

None

15.

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

16.

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 it did not differentiate between males and females.

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.

None

17.

In order to compensate for a difficult midterm exam, Danielle’s
mathematics teacher adjusted each of the 25 students’ midterm exam
scores by replacing it by one-half of the original score increased by 50.
If the mean of the revised set of midterm scores is 82, what was the
mean of the original set of scores?

None

18.

Which of the accompanying tables that show how population is changing over time illustrate exponential decay?

Table I

Table IV

Table III

Table II

None

19.

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

20.

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

300,000

197,500

It cannot be determined

None

21.

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.

I and III only

II only

I only

II and III only

None

22.

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?

2/9

8/9

7/9

1/9

None

23.

What percent of the people surveyed saw either an action or a science fiction movie?
Refer to the graph above that summarizes a survey of a
group of 250 people who were randomly selected when leaving a multiplex movie theater and asked what type of movie they had seen.

None

24.

The lowest value in a set of ordered scores is x and the highest value is
y. If each score is increased by k, then which of the following must be
true of the revised set of scores?
I. The mean is increased by k.
II. The range is k.
III. The median remains unchanged.

II and III

I and III

II only

I only

None

25.

The graph above shows the average daily temperature during a particular week in January in a certain city. Which statement best describes the temperature data in the graph above?

mean = mode

median = mean

mean < mode

median = mode

None

26.

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

81–90

91–100

61–70

71–80

None

27.

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?

0.98, the percent 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 after x years

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

None

28.

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

29.

Based on the cumulative histogram above, what percent of the total number of swimmers swam between 200 and 249 yards?

30%

20%

40%

15%

None

30.

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.
During the five-month period, the average increase in the number of people attending the class per month is closest to which of the following?

100

140

120

None

31.

In a set of n data values, m represents the median. If each number in the
set is decreased by 3, which expression represents the median of the
revised set of data values?

(m-3)/n

m-(3/n)

m-3

None

32.

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?

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

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

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

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

None

33.

Two health clubs offer different membership plans. The accompanying graph represents the total yearly cost of belonging to Club A and Club B for one year. The yearly cost includes a membership fee plus a fixed monthly charge. By what amount does the monthly charge for Club A exceed the monthly charge for Club B?

10.00

12.50

7.50

5.00

None

34.

The gas tank in a car holds a total of 16 gallons of gas. The car travels 75 miles on 4 gallons of gas. If the gas tank is full at the beginning of a trip, which graph represents the rate of change in the amount of gas in the tank?

Graph A

Graph B

Graph D

Graph C

None

35.

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

36.

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

2q - p

2p-q

None

37.

If the average of x, y, and z is 12, what is the average of 3x, 3y, and 3z?

None

38.

If $ a_{n}$ represents the nth term of the sequence 54,18,6, ..., and $ a_{1}$
represents the first term, then $ a_{n}$ =

$$54(\frac{1}{3})^{n}$$

$$6(\frac{1}{3})^{n}$$

$$54(\frac{1}{3})^{n-1}$$

$$6(\frac{1}{3})^{n-1}$$

None

39.

The graph above shows how $250,000 is invested.
After 20% of the amount that is invested in technology stocks is
reinvested in health stocks, how much money is invested in health
stocks?

$39,000

$45,000

$77,500

$65,000

None

40.

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

Time's up