SAT 09/16/23 Math Test – Calculator

Math Test – Calculator
55 MINUTES, 38 QUESTIONS

Directions: 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 your 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 x for
which f(x) is a real number.

1. John runs at different speeds as part of his training program. The graph shows his target heart rate at different times during his workout. On which interval is the target heart rate strictly increasing then strictly decreasing?

2. If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ? 

3.

4. If 16 + 4x is 10 more than 14, what is the value of 8x ? 

5. Which of the following graphs best shows a strong negative association between d and t ?

6. 1 decagram = 10 grams
1,000 milligrams = 1 gram

A hospital stores one type of medicine in 2-decagram containers. Based on the information given in the box above, how many 1-milligram doses are there in one 2-decagram container?

7.

The number of rooftops with solar panel installations in 5 cities is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph?

8. For what value of n is |n −1| + 1 equal to 0 ? 

9. Which of the following expresses the air temperature in terms of the speed of a sound wave?

10. At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?

11. Which of the following numbers is NOT a solution of the inequality 3x − 5 ≥ 4x −3 ? 

12. 

Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?

13.

A group of tenth-grade students responded to a survey that asked which math course they were currently enrolled in. The survey data were broken down as shown in the table above. Which of the following categories accounts for approximately 19 percent of all the survey respondents?

14. 

The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data?

The graph above displays the total cost C, in dollars, of renting a boat for h hours.

15. What does the C-intercept represent in the graph?

16. Which of the following represents the relationship between h and C ?

17.

The complete graph of the function f is shown in the xy-plane above. For what value of x is the value of f(x) at its minimum?

18. y < –x + a
y > x + b

In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?

19. A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?

20. Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ?

21.

The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y ?

22. Which of the following best approximates the average rate of change in the annual budget for agriculture/natural resources in Kansas from 2008 to 2010 ?

23. Of the following, which program’s ratio of its 2007 budget to its 2010 budget is closest to the human resources program’s ratio of its 2007 budget to its 2010 budget?

24. Which of the following is an equation of a circle in
the xy-plane with center (0, 4) and a radius with
endpoint (4/3 , 5) ?

25. h = -4.9t² + 25t

The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?

26. Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina’s observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?

27. A square field measures 10 meters by 10 meters. Ten students each mark off a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground’s surface in each region. The results are shown in the table below. 

Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the ground’s surface in the entire field?

28.

If the system of inequalities y  ≥ 2x +1 and y > (1/2)x – 1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?

29. For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x) ? 

30. 

Which of the following is an equivalent form of the equation of the graph shown in the xy-plane above, from which the coordinates of vertex A can be identified as constants in the equation?

31. Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?

32. The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge’s posted weight limit?

33. 

According to the line graph above, the number of portable media players sold in 2008 is what fraction of the number sold in 2011 ?

34. A local television station sells time slots for programs in 30-minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30-minute time slots the station can sell for Tuesday and Wednesday?

35.

A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?

36.

For what value of x is the function h above undefined?

37. What is the value of x in the expression?

38. Jessica’s friend Tyshaun found an account that earns 2.5 percent interest compounded annually. Tyshaun made an initial deposit of $100 into this account at the same time Jessica made a deposit of $100 into her account. After 10 years, how much more money will Tyshaun’s initial deposit have earned than Jessica’s initial deposit? (Round your answer to the nearest cent and ignore the dollar sign when gridding your response.)