SAT data analysis and statistics part 3

Mastering Advanced Math: SAT Test - part 3

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  • Each question is meticulously crafted to mirror the complexity and diversity of problem-solving you'll encounter in the SAT.
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1. 


Which of the following statements is true about the data in the tables above?
I. The mean salaries for both companies are greater than $35,000.
II. The mean age of workers in Company 1 is greater than the mean
age of workers in Company 2.
III. The salary range in Company 2 is greater than the salary range in
Company 1.

2. 

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?

3. 

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?

4. 

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?

5. 

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?

6. 


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?

7. 

Which survey is most likely to have the least bias?

8. 

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?

9. 


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?

10. 


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?

11. 


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.

12. 

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.

13. 

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.

14. 


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.

15. 

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

16. 


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?

17. 

Given a starting population of 100 bacteria, the formula b(t) = 100(2^t)
can be used to determine the number of bacteria, b, after t periods of
time. If each time period is 15 minutes long, how many minutes will it
take for the population of bacteria to reach 51,200?
write answer only in numbers

18. 

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

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. 

Jacob begins painting at 12:00 noon. At 12:30 P.M. he estimates that 13
gallons of paint are left, and at 3:30 he estimates that 4 gallons of paint
remain. If the paint is being used at a constant rate, how many gallons
of paint did Jacob have when he started the job?

21. 


The cumulative histogram above shows the distribution of scores that
24 students received on an English test. If a student is selected at
random, what is the probability that the student will have a score
between 71 and 80?

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?

23. 


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?

24. 

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?

25. 


The partially completed table above describes the distribution of 200 subjects in a study involving eye color in which there were 4 times as many males with brown eyes as with blue eyes and 7 times as many females with brown eyes as with blue eyes. What percent of the subjects were either male with blue eyes or female with brown eyes?

26. 


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 average increase in neck circumference per centimeter increase in wrist circumference, correct to the nearest tenth?

27. 


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?

28. 

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

29. 

The number of square units, A, in the area covered by a bacteria culture
is increasing at a rate of 20% every 7 days. If the bacteria culture
initially covers an area of 10 square centimeters, which equation can be
used to find the number of square units in the area covered by the
bacteria culture after d days?

30. 


Over what interval of time, in minutes, was the jogger’s heart rate
changing at a constant rate?
Refer to the graph above which shows the heart rate,
in beats per minute, of a jogger during a 4-minute interval.

31. 


If 20% of the students with SAT Math scores from 610 to 700 received
college scholarships, how many students with SAT Math scores from
610 to 700 received college scholarships? refer to the graph above.

32. 


The graph above shows the number of U.S. households with laptop
computers for the years 2010 to 2014.
The greatest percent of increase in the number of households with
laptops occurred in which two consecutive years?

33. 

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

34. 


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.

35. 


If a total of 1,700 tickets were sold for the five types of movies
represented in the histogram, what is the best estimate for the number
of tickets sold to the Romance 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.

36. 

The average (arithmetic mean) of a set of seven numbers is 81. If one
of the numbers is discarded, the average of the remaining numbers is
78. What is the value of the number that was discarded?

37. 


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?

38. 


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?

39. 


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?

40. 

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?

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