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Math – Calculator Tests

Mathematics Test—Calculator 1

38 Questions. 55 Minutes to Complete.

Directions

Notes

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.

For questions 1 through 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 through 38, solve the problem and enter your answer in the grid on the answer sheet.

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1. Directions

Reference

Begin skippable figure descriptions.

The figure presents information for your reference in solving some of the problems. Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.

A equals pi times the square of r.

C equals 2 pi r.

Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.

A equals ℓ w.

Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.

A equals onehalf b h.

Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.

c squared equals a squared plus b squared.

Special Right Triangles

Reference figure 5 is a right triangle with a 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeled x. The side opposite the 60degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.

Reference figure 6 is a right triangle with two 45degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2. Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.

V equals ℓ w h.

Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.

V equals pi times the square of r times h.

Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.

V equals fourthirds pi times the cube of r.

Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.

V equals onethird times pi times the square of r times h.

Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.

V equals onethird ℓ w h.

End skippable figure descriptions.

Additional Reference Information

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

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

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

Question 1 refers to the following figure.

Begin skippable figure description.

The figure presents a line graph in a coordinate plane. The horizontal axis is labeled “Time” in minutes, and the vertical axis is labeled “Target heart rate” in beats per minute. Numbers 0 through 100, in increments of 10, appear along the horizontal axis, and there are vertical gridlines at those numbers. Numbers 40 to 160, in increments of 40, appear along the vertical axis, and there are three horizontal gridlines at 80, 120, and 160. The line graph is divided into three disjointed pieces over three intervals: 0 to 40 minutes, 40 to 74 minutes, and 74 to 100 minutes.

Over the interval from 0 to 40 minutes, the line graph moves upward and to the right from 65 beats per minute at 0 minute, until reaching 80 beats at 9 minutes. It then moves horizontally, staying at 80 beats per minute until 32 minutes. The graph then moves downward and to the right, ending at 75 beats per minute at 40 minutes.

Over the interval from 40 to 74 minutes, the line graph moves upward and to the right from 95 beats per minute at 40 minutes, until reaching 120 beats per minute at 50 minutes. It then moves downward and to the right, until reaching 95 beats per minute at 62 minutes. The graph then moves upward and to the right, until reaching 120 beats per minute at 66 minutes. The graph then moves horizontally, ending at 120 beats at 74 minutes.

Over the interval from 74 to 100 minutes, the line graph moves upward and to the right from 140 beats per minute at 74 minutes, until reaching 160 beats per minute at 85 minutes. It then moves horizontally, staying at 160 beats per minute until 92 minutes. The graph then moves downward and to the right, ending at 110 beats per minute at 100 minutes.

End skippable figure description.

Question 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?

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

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3. .

The figure presents two horizontal lines ℓ and m with line ℓ above line m, and two lines s and t that are slanted upward and to the right with line s to the left of line t. Lines s and t intersect lines ℓ and m. The angle above line ℓ and to the right of line t is labeled 1, and the angle above line m and to the left of line s is labeled 2.

Question 3.

In the preceding figure, lines ℓ and m are parallel and lines s and t are parallel. If the measure of ∠ 1 is 35°, what is the measure of ∠2?

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

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

Each of the four answer choices presents a scatterplot in the first quadrant of the d t plane. The horizontal axis is labeled d and the vertical axis is labeled t.

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6. Question 6 is based on the following information.

1 decagram = 10 grams

1,000 milligrams = 1 gram

Question 6.

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

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7. Question 7 is based on the following graph.

The figure presents a bar graph titled “Rooftop Solar Panel Installations in Five Cities.” The horizontal axis is labeled “City,” and there are five vertical bars, from left to right, labeled A through E. The numbers 0 through 9, in increments of 1, appear along the vertical axis, and there are horizontal gridlines at those numbers. According to the graph, the numbers for the five bars are as follows.

City A: 9.

City B: 5.

City C: 6.

City D: 4.

City E: 3.5.

Question 7.

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

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8. For what value of n is , equal to 0?

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9. Questions 9 through 10 refer to the following information.

a = 1,052 + 1.08t

The speed of a sound wave in air depends on the air temperature. The preceding formula shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit (°F)

Question 9.

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

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

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11. Which of the following numbers is NOT a solution of the inequality

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12.

The figure presents a histogram titled “Number of Seeds in Each of 12 Apples.” The horizontal axis is labeled “Number of seeds,” and the vertical axis is labeled “Number of apples.” Numbers 3 through 9, in increments of 1, appear along the horizontal axis. There are five vertical bars above the numbers 3, 5, 6, 7, and 9, and there are no bars above numbers 4 and 8. Along the vertical axis are numbers 0 through 5, in increments of 1, and there are horizontal gridlines at those numbers. According to the graph, the number of apples with the corresponding number of seeds is as follows.

Bar 1, 2 apples, 3 seeds each.

Bar 2, 4 apples, 5 seeds each.

Bar 3, 1 apple, 6 seeds each.

Bar 4, 2 apples, 7 seeds each.

Bar 5, 3 apples, 9 seeds each.

Question 12.

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

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13.

The figure presents a table with the column heading labeled “Course” and column subheadings labeled “Algebra 1,” “Geometry,” “Algebra 2,” and “Total.” The row heading is labeled “Gender” and the row subheadings are labeled “Female,” “Male,” and “Total.” The data in the table are as follows.

Algebra 1: 35 Females; 44 Males; 79 Total.

Geometry: 53 Females; 59 Males; 112 Total.

Algebra 2: 62 Females; 57 Males; 119 Total.

Total: 150 Females; 160 Males; 310 Total.

Question 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 preceding table. Which of the following categories accounts for approximately 19 percent of all the survey respondents?

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14.

Question 14.

The preceding table 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?

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15. Questions 15 through 16 refer to the following information.

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

The figure presents a line graph in a coordinate plane titled “Total Cost of Renting a Boat by the Hour.” The horizontal axis, h, is labeled “Time” in hours, and the vertical axis, C, is labeled “Total cost” in dollars. Numbers 0 through 5, in increments of 1, appear along the horizontal axis, and there are vertical gridlines at the numbers, in increments of a quarter of one. Numbers 0 through 20, in increments of 2, appear along the vertical axis, and there are horizontal gridlines at those numbers, in increments of one. In the figure, there are 6 data points connected by a line segment starting at the point with coordinates 0 comma 5 and ending at the point with coordinates 5 comma 20. The coordinates of the 6 data points are as follows.

Point 1: 0 comma 5.

Point 2: 1 comma 8.

Point 3: 2 comma 11.

Point 4: 3 comma 14.

Point 5: 4 comma 17.

Point 6: 5 comma 20.

Question 15.

What does the C-intercept represent in the graph?

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

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17.

The figure presents the graph of the function f in the x y-plane. The graph is labeled y equals f of x. The horizontal axis is labeled x, the vertical axis is labeled y, and the origin is labeled O. There are evenly spaced horizontal and vertical gridlines, in increments of 1 unit, along each axis. The graph consists of 4 connected line segments. The first line segment slants downward and to the right. It starts at the point that is 5 units to the left of the y axis and 2 units above the x axis, and it ends at the point that is 3 units to the left of the y axis and 2 units below the x axis. The second line segment slants upward and to the right. It starts where the first line segment ends, and ends at the point that is 1 unit to the right of the y axis and 4 units above the x axis. The third line segment slants upward and to the right again. It starts where the second line segment ends, and ends at the point that is 3 units to the right of the y axis and 5 units above the x axis. The fourth line segment slants downward and to the right. It starts where the third line segment ends, and ends at the point that is 5 units to the right of the y axis and 1 unit above the x axis.

Question 17.

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

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18. Question 18 is based on the following system of inequalities.

y < -x + a

y > x + b

Question 18.

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

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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?

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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?

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21.

The figure shows a table titled “Dreams Recalled during One Week.” The table has 3 rows of data and 5 columns. Column 1 is labeled, from top to bottom, Group X, Group Y, and Total. The column headings for columns 2, 3, 4, and 5 from left to right are: None, 1 to 4, 5 or more, and Total, respectively. The information in the table is as follows.

Group X: No dreams recalled, 15; 1 to 4 dreams recalled, 28; 5 or more dreams recalled, 57; Total dreams recalled, 100.

Group Y: No dreams recalled, 21; 1 to 4 dreams recalled, 11; 5 or more dreams recalled, 68; Total dreams recalled, 100.

Total: No dreams recalled, 36; 1 to 4 dreams recalled, 39; 5 or more dreams recalled, 125; Total dreams recalled, 200.

Question 21.

The data in the preceding table 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

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22. .

The figure presents a table titled “Annual Budgets for Different Programs in Kansas, 2007 to 2010.” The table has 6 rows and 5 columns of data. The column heading for column 1 is “Program.” Column 1 has 6 programs from top to bottom, Agriculture/natural resources, Education, General government, Highways and transportation, Human resources, and Public safety. The columns 2 through 5 are under the heading “Year” and are labeled from left to right 2007, 2008, 2009, and 2010. There is a note under the table stating “The table above lists the annual budget, in thousands of dollars, for each of six different state programs in Kansas from 2007 to 2010.” The data in the table are as follows.

Agriculture/natural resources: 373,904 thousand dollars for 2007; 358,708 thousand dollars for 2008; 485,807 thousand dollars for 2009; 488,106 thousand dollars for 2010.

Education: 2,164,607 thousand dollars for 2007; 2,413,984 thousand dollars for 2008; 2,274,514 thousand dollars for 2009; 3,008,036 thousand dollars for 2010.

General government: 14,347,325 thousand dollars for 2007; 12,554,845 thousand dollars for 2008; 10,392,107 thousand dollars for 2009; 14,716,155 thousand dollars for 2010.

Highways and transportation: 1,468,482 thousand dollars for 2007; 1,665,636 thousand dollars for 2008; 1,539,480 thousand dollars for 2009; 1,773,893 thousand dollars for 2010.

Human resources: 4,051,050 thousand dollars for 2007; 4,099,067 thousand dollars for 2008; 4,618,444 thousand dollars for 2009; 5,921,379 thousand dollars for 2010.

Public safety: 263,463 thousand dollars for 2007; 398,326 thousand dollars for 2008; 355,935 thousand dollars for 2009; 464,233 thousand dollars for 2010.

Question 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?

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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?

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24. Which of the following is an equation of a circle in the x y-plane with center (0,4), and a radius with endpoint

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25. Question 25 is based on the following equation.

h = -4.9t² + 25t

Question 25.

The preceding equation 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?

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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?

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27. Question 27 is based on the following information.

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 following table.

Question 27.

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?

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28. Question 28 is based on the following graph.

The figure presents the four quadrants of the x y-plane. The horizontal axis is labeled x and the vertical axis is labeled y. In the figure, quadrant 1 is above the x axis and to the right of the y axis, quadrant 2 is above the x axis and to the left of the y axis, quadrant 3 is below the x axis and to the left of the y axis, and quadrant 4 is below the x axis and to the right of the y axis.

Question 28.

If the system of inequalities y ≥ 2x + 1, and , is graphed in the preceding x yplane, which quadrant contains no solutions to the system?

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

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30. Question 30 is based on the following graph.

The figure presents the graph of a curve in the x y-plane. The horizontal axis is labeled x, the vertical axis is labeled y, and the origin is labeled O. There are equally spaced tick marks on the x axis labeled, from left to right, negative 5 through 7, in increments of 1. There are equally spaced tick marks on the y axis labeled, from bottom to top, negative 20 through 20, in increments of 5. The curve is labeled y equals, x squared minus 2 x, minus 15. The curve is symmetric with respect to a vertical line. It opens up with its lowest point, labeled A, that is to the right of the y axis and below the x axis. The curve starts above the x axis and to the left of the y axis, and moves downward and to the right, crossing the x axis at the tick mark labeled negative 3. The curve continues to go downward and to the right, crossing the y axis at the tick mark labeled negative 15, until reaching the lowest point, A. Then the curve moves upward and to the right, crossing the x axis at the tick mark labeled 5, and extends upward and to the right symmetrically.

Question 30.

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

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31. Directions

For questions 31 through 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 must be gridded as 3.5 or 7/2 (If is entered into the grid, it will be interpreted as not )

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.

The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.

Examples 1 and 2

Example 1: If your answer is a fraction such as seventwelfths, it should be recorded as follows. Enter 7 in the first space, the fraction bar (a slash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.

Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the second space, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in this example.

Example 3

Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.

Example 4

Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.

Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.

Question 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?

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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?

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33.

The figure presents a line graph titled “Number of Portable Media Players Sold Worldwide Each Year from 2006 to 2011.” The horizontal axis is labeled “Year,” and the vertical axis is labeled “Number sold in millions”. Numbers 0 through 180, in increments of 20, appear along the vertical axis, and there are horizontal gridlines at those numbers. Six years from 2006 through 2011 appear from left to right along the horizontal axis. According to the graph, the approximate number of portable media players sold in each of the six years is as follows.

2006, 50 million.

2007, 60 million.

2008, 100 million.

2009, 123 million.

2010, 150 million.

2011, 160 million.

Question 33.

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

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

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35. Question 35 is based on the following circular cylinder.

The figure presents a right circular cylinder. The bases of the cylinder are horizontal and the distance between the two bases is labeled 8 yards.

Question 35.

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

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36. Question 36 is based on the following expression.

Question 36.

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

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37. Questions 37 through 38 refer to the following information.

Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression to find the value of the account after t years.

Question 37.

What is the value of x in the expression?

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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.)

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