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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
According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?
Some values of the linear function f are shown in the table above. Which of the following defines f ?
3. To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins?
(1 pound = 16 ounces)
4. If 3(c + d) = 5 , what is the value of c + d ?
5. The weight of an object on Venus is approximately 9/10 of its weight on Earth. The weight of an object on Jupiter is approximately 23/10 of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?
6. An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?
7. The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of n businesses per year. There were b businesses in the DBA at the beginning of this year. Which function best models the total number of businesses, y, the DBA plans to have as members x years from now?
8. Which of the following is an equivalent form of (1.5x – 2.4)2 – (5.2x2 – 6.4) ?
9. In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)
10. The density d of an object is found by dividing the mass m of the object by its volume V. Which of the following equations gives the mass m in terms of d and V ?
-2x + 3y = 6
In the xy-plane, the graph of which of the following
equations is perpendicular to the graph of the
The system of equations above has solution (x,y).
What is the value of x ?
y ≤ 3x + 1
x – y > 1
Which of the following ordered pairs (x,y) satisfies
the system of inequalities above?
In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated professional activity is research?
15. A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?
I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the cit .
Questions 16 – 18 refer to the following information
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
16. According to the information in the table, what is the approximate age of an American elm tree with a diameter of 12 inches?
The scatterplot above gives the tree diameter plotted against age for 26 trees of a single species. The growth factor of this species is closest to that of which of the following species of tree?
18. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
In ▲ABC above, what is the length of AD?
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y = d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
In the equation above, if a is negative and b is positive, which of the following must be true?
22. In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?
Questions 23 and 24 refer to the following information.
23. The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?
24. Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?
25. A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?
27. The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?
The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point (0, −4), what is the value of g(9) ?
x2 + 20x + y2 + 16y = -20
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?
y = x2 – a
In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?
31. Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?
2 horsepower = watts
32. The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is 1/3 the corresponding original dimension, what is the height of the reproduction, in inches?
the height of the reproduction is inches.
The length of PS is
34. In the xy-plane, the point (2,5) lies on the graph of the function f. If f(x) = k – x2 , where k is a constant, what is the value of k ?
35. A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?
The length of the garden in feet is
Point P is the center of the circle in the figure above. What is the value of x ?
Questions 37 and 38 refer to the following information.
Ms. Simon drives her car from her home to her workplace every workday morning. The table above shows the distance, in miles, and her average driving speed, in miles per hour (mph), when there is no traffic delay, for each segment of her drive.
37. One morning, Ms. Simon drove directly from her home to her workplace in 24 minutes. What was her average speed, in miles per hour, during her drive that morning?
her average speed, in miles per hour was
38. If Ms. Simon starts her drive at 6:30 a.m., she can drive at her average driving speed with no traffic delay for each segment of the drive. If she starts her drive at 7:00 a.m., the travel time from the freeway entrance to the freeway exit increases by 33% due to slower traffic, but the travel time for each of the other two segments of her drive does not change. Based on the table, how many more minutes does Ms. Simon take to arrive at her workplace if she starts her drive at 7:00 a.m. than if she starts her drive at 6:30 a.m.? (Round your answer to the nearest minute.)
It takes Ms. Simon more minutes.