SAT 2016



Math Test – Calculator


Turn to Section 4 of your answer sheet to answer the questions in this section.


For questions 1–30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 31–38, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 31 on how to enter you answers in the grid. You may use any available space in your test booklet for scratch work.


1. The use of a calculator is permitted.

2. All variables and expressions used represent real numbers unless otherwise indicated.

3. Figures provided in this test are drawn to scale unless otherwise indicated.

4. All figures lie in a plane unless otherwise indicated.

5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers for which f(x) is a real number.



The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2π.

The sum of the measures in degrees of the angles of a triangle is 180.


If Images and 2a + 4b = 20, what is the value of b?

A)   2.5

B)   4

C)   5

D)   15



The spinner for a board game has 10 sectors, numbered 1 through 10. It is spun 20 times and the results summarized in the table above. What is the median value of these 20 spins?

A)   2

B)   4

C)   5

D)   6


A 48-gram serving of breakfast cereal contains 8 grams of sugar. How many grams of sugar are there in a 57-gram serving of the same cereal?

A)   9.5

B)   10.5

C)   11.5

D)   12.5



The graph above shows the number of applicants and finalists for a statewide college scholarship program over four consecutive years. For which year was the ratio of finalists to applicants the greatest?

A)   2010

B)   2011

C)   2012

D)   2013


If y3 = 20 and z2 = 10, what is the value of (yz)6?

A)   2 × 105

B)   4 × 104

C)   2 × 105

D)   4 × 105


If the sum of ab, and c is three times the sum of a and b, which of the following expresses the value of a in terms of b and c?

A)   Images

B)   Images

C)   Images

D)   Images



Note: Figure not drawn to scale.

In the figure above, BCDE is a rectangle, AC = 14, BC = 12, and EC = 13. What is the value of tan x?

A)   0.4

B)   0.6

C)   1.3

D)   2.5


Which of the following binomials is a factor of x2 − 6x + 8?

A)   x − 4

B)   x + 4

C)   x + 2

D)   x − 8

Questions 9–11 are based on the graph below.


The pie graph above represents the monthly ad sales for four salespeople—Maria, Eli, Georgia, and Zoe—at a social media website. For the month, Maria’s sales accounted for 25% of the total, Eli had $3,000 in sales, Georgia had $5,000 in sales, and Zoe had $10,000 in sales.


Which sector represents Georgia’s sales for the month?

A)   Sector A

B)   Sector B

C)   Sector C

D)   Sector D


What is the sum of the monthly sales for all four salespeople?

A)   $22,500

B)   $24,000

C)   $25,000

D)   $27,000


If Eli and Georgia both earn 10% commission on their sales, and Maria and Zoe both earn 15% commission on their sales, how much more did Maria earn in monthly commissions than Georgia?

A)   $300

B)   $360

C)   $375

D)   $400


Let the function f be defined by f(x) = 2 − |x − 4| for all real values of x. What is the greatest value of f?

A)   −2

B)   2

C)   4

D)   6


If Images, what is the value of b?

A)   Images

B)   Images

C)   Images

D)   5


For the function ff (1) = 4 and f (2) = 13. Which of the following equations could describe f?

A)   f(x) = x2 + 3

B)   f(x) = x2 + 9

C)   f(x) = 2x2 + 2

D)   f(x) = 3x2 + 1


Which of the following is NOT equivalent to 12b2?

A)   (6b)(6b)

B)   12b(b)

C)   Images

D)   6b2 + 6b2


If m is a number chosen randomly from the set {2, 3, 4, 6} and n is a number chosen randomly from the set {1, 2, 3, 4}, what is the probability that mn is a multiple of 12?

A)   Images

B)   Images

C)   Images

D)   Images


If y = 3x + 4 and x < 3, which of the following represents all the possible values of y?

A)   y > 7

B)   y < 13

C)   7 < y < 13

D)   y > 13


If g(x + 1) = x2 + 2x + 4 for all values of x, which of the following is equal to g(x)?

A)   x2 + 4

B)   x2 + 3

C)   (x − 1)2 + 4

D)   (x − 1)2 + 3


A: 2, 7, 12, 17, 22, . . . 

B: 5, 15, 25, 35, 45, . . . 

Two sequences, A and B, follow the patterns shown above. If the nth term of sequence A is 72, what is the nth term of sequence B?

A)   125

B)   135

C)   145

D)   155


A website received 2,100 visitors in July from both subscribers and nonsubscribers. If the ratio of subscribers to nonsubscribers among this group was 2:5, how many more nonsubscribers visited the site in July than subscribers?

A)   126

B)   630

C)   900

D)   1,260



The figure above shows the locations of quadrants I–IV in the xy-plane. Which of the following represents a pair of linear equations that do NOT intersect in quadrant I?

A)   3x + 5y = 15y = 4

B)   5x + 3y = 15y = 4

C)   5x − 3y = 15y = 4

D)   3x − 5y = 15y = 4


During a 40-minute session at a 220 volt charging station, the charge on an electric car battery increases from an initial charge of 50 power units to a final charge of 106 power units. If this charge increases linearly with time, which of the following best describes the charge, q, in power units, on this same battery after charging for t hours from an initial charge of 20 power units? (1 hour = 60 minutes)

A)   q = 55t + 50

B)   q = 84t + 50

C)   q = 55t + 20

D)   q = 84t + 20

Questions 23 and 24 are based on the graph below.



The scatterplot above shows the length and weight of a group of 20 salmon and the line of best fit for the data. According to this line of best fit, which of the following best approximates the weight, in kilograms, of a salmon that is 95 centimeters long?

A)   7.6

B)   7.8

C)   8.3

D)   8.8


Which of the following equations best describes the relationship between w, the weight in kilograms of each salmon, and l, its length in centimeters?

A)   Images

B)   Images

C)   Images

D)   Images


The average size of a compressed image file is 750 kB. If Ronika’s data plan allows her to send 2 GB of data each month before she pays any overage charges, but she plans to use 85% of that data for texting, approximately how many compressed images can she send each month before she incurs any overage charges? (1 GB = 1,000 MB; 1 MB = 1,000 kB)

A)   227

B)   400

C)   2,267

D)   4,000


Perfectioner’s Chocolate Company makes two varieties of truffles: dark chocolate and milk chocolate. Each dark chocolate truffle requires 0.65 ounces of cocoa powder, and each milk chocolate truffle requires 0.45 ounces of cocoa powder. If cocoa powder costs c dollars per pound, and Perfectioner’s Chocolate Company has budgeted $200 per week for cocoa powder, which of the following inequalities indicates the restrictions on the number of dark chocolate truffles, d, and the number of milk chocolate truffles, m, the company can make in one week? (1 pound = 16 ounces)

A)   Images

B)   Images

C)   Images

D)   Images


If n is a positive integer and m = 2n + 2 + 2n, what is 2n + 3 in terms of m?

A)   m

B)   Images

C)   Images

D)   3m2


For how many values of x between 0 and 2π does sin Images?

A)   Two

B)   Three

C)   Four

D)   Six



The figure above shows the graphs of functions f and g in the xy-plane. Which of the following equations could express the relationship between f and g?

A)   f(x) = g(x − 2)

B)   f(x) = g(x + 2)

C)   f(x) = g(x) + 2

D)   f(x) = g(x) − 2


A researcher is trying to estimate the daily amount of time undergraduate computer science majors spend on nonrecreational computer activities. She surveys 120 students from among the computer science majors at a large state university and asks them, “How much time do you spend in nonrecreational computer activities each day?” The mean of these responses is 210 minutes per day, with a standard deviation of 16.5 minutes. If another researcher wishes to present the same question to a new set of subjects at the same university, which of the following subject groups would most likely yield a data set with a smaller margin of error for the estimated daily amount of time undergraduate computer science majors spend on nonrecreational computer activities?

A)   240 randomly selected computer science majors

B)   240 randomly selected liberal arts majors

C)   80 randomly selected computer science majors

D)   80 randomly selected liberal art majors


Student-Produced Response Questions


For questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.

1.  Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.

2.  Mark no more than one circle in any column.

3.  No question has a negative answer.

4.  Some problems may have more than one correct answer. In such cases, grid only one answer.

5.  Mixed numbers such as Images must be gridded as 3.5 or Images.

(If Images is entered into the grid as Images, it will be interpreted as Images, not Images.)

6.  Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.




What number is 40% greater than the sum of 40 and 80?



The table above shows a set of ordered pairs that correspond to the function Images. What is the value of k?


hx + 4y = −3

The equation above is the equation of a line in the xy-plane, and h is a constant. If the slope of this line is −13, what is the value of h?


The sum of two numbers is four times their difference. The smaller of these numbers is 15. What is the greater number?


If 0 < x < 2π andImages, what is the value of Images



Note: Figure not drawn to scale.

In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?

Questions 37 and 38 are based on the scenario described below.

An Internet service provider offers three different plans for residential users. Plan A charges users $500 for the first year of service, and $80 per month thereafter. Plan B charges users $68 per month. Plan C is a “high speed” plan that offers 200% higher speeds for $92 per month.


Isabelle has been using Plan A for over a year. She recently reviewed her plan and realized that if she had been using Plan B for same amount of time, she would have saved $104 for Internet service over the entire period. At the time of her review, how many months had Isabelle been on Plan A?


Isabelle is now considering switching to either Plan B or Plan C for her home business, but she calculates that having the “high speed” plan will save her only approximately 45 minutes of work each month. At what minimum hourly rate, in dollars per hour, would she have to value her work (that is, how much more would she have to value one hour of free time over one hour of work time) for Plan C to be worth the extra cost over Plan B?


If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test.