SAT data analysis and statistics part 3

Mastering Advanced Math: SAT Test - part 3

  • The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experience
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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. 


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?

2. 

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?

3. 

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

4. 

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.

5. 

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?

6. 

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?

7. 

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?

8. 


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?

9. 

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?

10. 

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

11. 

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?

12. 

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.

13. 


The table above can be used to approximate the circumference of the head, in centimeters, during the first 5 years after birth. At 5 years of age, Jacob’s head circumference was 81 cm. Based on the table, what was his approximate height, in centimeters, at 1 years old?

14. 

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?

15. 


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?

16. 


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.

17. 

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?

18. 

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

19. 


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?

20. 


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

21. 


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?

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?

23. 

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?

24. 

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

25. 

The breakdown of a sample of a chemical compound is represented by
the function where \(p(t) = 300(\frac{1}{2})^{t}\)represents the number of
milligrams of the substance, and t represents the time, in years. If t = 0
represents the year 2015, what will be the first year in which the
amount of the substance remaining falls to less than 5 milligrams?

26. 

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?

27. 


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.

28. 


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?

29. 

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

30. 

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?

31. 


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?

32. 


The graph above shows how $250,000 is invested.
How much money is invested in municipal bonds?

33. 


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?

34. 


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?

35. 

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?

36. 


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

37. 

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?

38. 


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?

39. 


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 28% of the students who are enrolled in this school belong to at least two clubs, how many students who are enrolled in this school did not participate in the survey?

40. 

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?

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