Turn to Section 4 of Your Answer Sheet to Answer the Questions in This Section

Math Test—Calculator

38 Questions

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

Directions

For questions1 through 30, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions31 through 38, solve the problem and indicate your answer, which is to be recorded in the spaces provided on the answer sheet. Please refer to the directions before question31 on how to record your answers in the spaces provided. You may use scratch paper for scratch work.

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 functionfis the set of all real numbersxfor which fofx is a real number.

Reference

Begin skippable figure descriptions.

The figure presents information for your reference in solving some of theproblems.

Reference figure 1 is a circle with radiusr. Two equations are presented below reference figure1.

Aequals pi times the square ofr.

Cequals 2 pir.

Reference figure 2 is a rectangle with lengthℓand widthw. An equation is presented below reference figure2.

Aequalsℓw.

Reference figure 3 is a triangle with baseband heighth. An equation is presented below reference figure3.

Aequals onehalfbh.

Reference figure 4 is a right triangle. The two sides that form the right angle are labeledaandb, and the side opposite the right angle is labeledc. An equation is presented below reference figure4.

csquared equalsasquared plusbsquared.

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 labeledx. The side opposite the 60degree angle is labeledxtimes the squareroot of3. The side opposite the right angle is labeled2x.

Reference figure 6 is a right triangle with two 45degree angles. Two sides are each labeleds. The side opposite the rightangle is labeledstimes the squareroot of2.

Reference figure 7 is a rectangular solid whose base has lengthℓand widthwand whose height ish. An equation is presented below reference figure7.

Vequalsℓwh.

Reference figure 8 is a rightcircularcylinder whose base has radiusrand whose height ish. An equation is presented below reference figure8.

Vequalspitimes the square ofrtimesh.

Reference figure 9 is a sphere with radiusr. An equation is presented below reference figure9.

Vequalsfourthirds pi times the cube ofr.

Reference figure 10 is a cone whose base has radiusrand whose height ish. Anequation is presented below reference figure10.

Vequals onethird times pi times the square ofrtimesh.

Reference figure 11 is an asymmetrical pyramid whose base has lengthℓand widthwand whose height ish. An equation is presented below reference figure11.

Vequalsonethirdℓwh.

End skippable figure descriptions.

Additional Reference Information

The number of degrees of arc in a circle is360.

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

The sum of the measures in degrees of the angles of a triangle is180.

Question 1 refers to the following graph.

Begin skippable figure description.

The figure presents a line graph titled “Number of 3D Movies Released by Year.” The horizontal axis is labeled “Year,” and the years2003 through 2011 are indicated. The vertical axis is labeled “Number of 3D movies released,” and the numbers 0 through 50, in increments of 10, are indicated. The data, represented by 9points on the graph, are as follows. Note that all values are approximate.

2003, 2 movies.

2004, 2 movies.

2005, 6 movies.

2006, 8 movies.

2007, 6 movies.

2008, 8 movies.

2009, 20 movies.

2010, 26 movies.

2011, 46 movies.

End skippable figure description.

Question 1.

According to the preceding line graph, between which two consecutive years was there the greatest change in the number of 3Dmovies released?

A.2003 through2004

B.2008 through2009

C.2009 through2010

D.2010 through2011

Question 2 refers to the following table.

x / fofx
1 / 5
3 / 13
5 / 21

Question 2.

Some values of the linear functionf are shown in the preceding table. Which of the following definesf?

A.f of x equals, 2xplus3

B.f of x equals, 3xplus2

C.f of x equals, 4xplus1

D.f of x equals,5x

Question 3.

To make a bakery’s signature chocolate muffins, a baker needs 2.5ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48signature chocolate muffins? (1pound equals16ounces.)

A.7.5

B.10

C.50.5

D.120

Question 4.

If3 times, open parenthesis, c plus d, close parenthesis, equals 5, what is the value ofcplusd?

A.the fraction 3 over5

B.the fraction 5 over3

C.3

D.5

Question 5.

The weight of an object on Venus is approximatelythe fraction 9 over 10of its weight on Earth. The weight of an object onJupiter is approximatelythe fraction 23 over 10of its weight on Earth. If an object weighs 100pounds on Earth, approximately how many more pounds does it weighon Jupiter than it weighs on Venus?

A.90

B.111

C.140

D.230

Question 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 11novels and magazines that have a combined selling price of $20, how many novels did she purchase?

A.2

B.3

C.4

D.5

Question 7.

The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of nbusinesses per year. There were bbusinesses 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 xyears from now?

A.y equals,ntimes x,plusb

B.y equals,ntimes x,minusb

C.y equals,b times,n raised to the powerx

D.y equals,n times,braised to the powerx

Question 8.

Which of the following is an equivalent form ofopen parenthesis, 1.5x minus 2.4, close parenthesis, squared, minus, open parenthesis, 5.2,xsquared, minus 6.4, close parenthesis?

A.negative2.2,xsquared, plus1.6

B.negative2.2,xsquared, plus11.2

C.negative2.95,xsquared, minus 7.2x, plus 12.16

D.negative2.95,xsquared, minus 7.2x, plus 0.64

Question 9.

In the 1908 Olympic Games, the Olympic marathon was lengthened from 40kilometers to approximately 42kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1mile is approximately 1.6kilometers.)

A.1.00

B.1.25

C.1.50

D.1.75

Question 10.

The densityd of an object is found by dividing the massm of the object by its volumeV. Which of the following equations gives the massmin terms ofdandV?

A.m equals,dtimesV

B.m equals, the fraction doverV

C.m equals, the fraction Voverd

D.m equals,Vplusd

Question 11 refers to the following equation.

negative2x plus 3y, equals6

Question 11.

In the xyplane, the graph of which of the following equations is perpendicular to the graph of the preceding equation?

A.3xplus 2y,equals6

B.3xplus 4y,equals6

C.2xplus 4y,equals6

D.2x plus 6y,equals3

Question 12 refers to the following system of equations.

onehalf y equals4,

and

x minus,one halfy,equals2

Question 12.

The preceding system of equations has solutionx comma y. What is the value ofx?

A.3

B.the fraction 7 over2

C.4

D.6

Question 13 refers to the following system of inequalities.

y is less than or equal to, 3xplus1,

and

x minus yis greater than1

Question 13.

Which of the following ordered pairsx comma ysatisfies the preceding system of inequalities?

A.negative2 comma negative1

B.negative1 comma3

C.1 comma 5

D.2 comma negative1

Question 14 refers to the following table.

Begin skippable figure description.

The figure presents a 4-column table, with 3rows of data. The heading for column1 is “Type of surgeon.” The heading for columns2 and 3 is “Major professional activity.” The subheading for column2 is “Teaching,” and the subheading for column3 is “Research.” The heading for column4 is “Total.” The data are as follows.

Row 1. Type of surgeon, General. Major professional activity, teaching, 258. Major professional activity, research, 156. Total,414.

Row 2. Type of surgeon, Orthopedic. Major professional activity, teaching, 119. Major professional activity, research, 74. Total,193.

Row 3. Type of surgeon, Total. Major professional activity, teaching, 377. Major professional activity, research, 230. Total,607.

End skippable figure description.

Question 14.

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the preceding table. 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?

A.0.122

B.0.196

C.0.318

D.0.379

Question 15.

A polling agency recently surveyed 1,000adults 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, 78percent 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?

1. Of all adults in the city, 78percent are satisfied with the quality of air in the city.

2. If another 1,000adults selected at random from the city were surveyed, 78percent of them would report they are satisfied with the quality of air in the city.

3. If 1,000adults selected at random from a different city were surveyed, 78percent of them would report they are satisfied with the quality of air in the city.

A.None

B.2 only

C.1 and 2only

D.1 and 3only

Questions 16 through 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 following tablegives the growth factors for eight species of trees.

Species of tree / Growth factor
Red maple / 4.5
River birch / 3.5
Cottonwood / 2.0
Black walnut / 4.5
White birch / 5.0
American elm / 4.0
Pin oak / 3.0
Shagbark hickory / 7.5

Question 16.

According to the information in the preceding table, what is the approximate age of an American elm tree with a diameter of 12inches?

A.24 years

B.36 years

C.40 years

D.48 years

Question 17 refers to the following graph.

Begin skippable figure description.

The figure presents the graph of a scatterplot, titled “Tree Diameter versus Age.” The horizontal axis is labeled “Tree diameter, in inches,” and the numbers 10 through 16 are indicated. The vertical axis is labeled “Age, in years,” and the numbers 70 through 130, in increments of 10, are indicated.

There are 26data points in the scatterplot. The leftmost data point is at approximately 10.7inches and 73years. The points are clustered, and trend upward and to the right. The rightmost data point is at approximately 16.5inches and 120years.

End skippable figure description.

Question 17.

The preceding scatterplotgives the tree diameter plotted against age for 26trees of a single species. The growth factor of this species is closest to that of which of the following species of tree?

A.Red maple

B.Cottonwood

C.White birch

D.Shagbark hickory

Question 18.

If a white birch tree and a pin oak tree each now have a diameter of 1foot, which of the following will be closest to the difference, in inches, of their diameters 10years from now? (1foot equals 12inches.)

A.1.0

B.1.2

C.1.3

D.1.4

Question19 refers to the following figure.

Begin skippable figure description.

The figure presents triangleABC, where sideAC is horizontal and pointB is above sideAC. PointD lies on sideAC, and line segmentBD is drawn, forming right angleBDC. SideBCis labeled 12. AngleABD is labeled 30degrees, and angleBCDis labeled 60degrees.

End skippable figure description.

Question 19.

In precedingtriangleABC, what is the length ofsegmentAD?

A.4

B.6

C.6 times the square root of 2

D.6 times the square root of 3

Question 20 refers to the following figure.

Begin skippable figure description.

The figure presents a diagram and a graph. The diagram, on the left, is a circle that represents a wheel. The circlelies on a horizontal line. A point is shown in the center of the circle andanother point is shown at the top of the circle directly above the center. Four rightward pointing arrows are shown, to the left of the circle, curved around the top of the circle, and to the right of the circle, indicating the movement of the wheel.

The graph, on the right, presents the graph of a curve labeled “y equals d of t” in a tycoordinate plane. The horizontal taxis is labeled “Time.” The curve begins on the vertical yaxis, high above the horizontal taxis. It curves downward and to the right, touches the horizontal taxis, then turns upward. It continues upward until reaching the same height at which it started, where it then turns back downward. It continues downward and to the right, touches the horizontal taxis for a second time, and then turns upward again. It continues upward until the curve ends at the same height at which it started.

End skippable figure description.

Question 20.

The preceding figure on the left 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 ofy equals d of tin thetycoordinate planeon the right could represent which of the following as a function of time from when the wheel began to roll?

A.The speed at which the wheel is rolling

B.The distance of the wheel from its starting point

C.The distance of the mark on the rim from the center of the wheel

D.The distance of the mark on the rim from the ground

Question 21 refers to the following equation.

the fraction with numerator a minus b, and denominator a, equalsc

Question 21.

In the preceding equation, if a is negative and b is positive, which of the following must be true?

A.cis greater than1

B.cequals1

C.cequals negative1

D.cis less than negative1

Question 22.

In State X, Mr.Camp’s eighthgrade class consisting of 26students was surveyed and 34.6percent of the students reported that they had at least two siblings. The average eighthgrade class size in the state is 26. If the students in Mr.Camp’s class are representative of students in the state’s eighthgrade classes and there are 1,800eighthgrade classes in the state, which of the following best estimates the number of eighthgrade students in the state who have fewer than two siblings?

A.16,200

B.23,400

C.30,600

D.46,800

Question 23 and 24 refer to the following information.

The Townsend Realty Group invested in the five different properties listed in the following table. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

Begin skippable figure description.

The figure presents a 3column table with 5rows of data that is titled “Townsend Realty Group Investments.” The heading for column1 is “Property address.” The heading for column2 is “Purchase price, in dollars.” The heading for column3 is “Monthly rental price, in dollars.” The data are as follows.

Row 1, Clearwater Lane:purchase price, 128,000dollars; monthly rental price, 950dollars.

Row 2, Driftwood Drive:purchase price, 176,000dollars; monthly rental price, 1,310dollars.

Row 3, Edgemont Street:purchase price, 70,000dollars; monthly rental price, 515dollars.

Row 4, Glenview Street:purchase price, 140,000dollars; monthly rental price, 1,040dollars.

Row 5, Hamilton Circle:purchase price, 450,000dollars; monthly rental price, 3,365dollars.

End skippable figure description.

Question 23.

The relationship between the monthly rental pricer, in dollars, and the property’s purchase pricep, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

A.r of p equals, 2.5p minus870

B.r of p equals, 5pplus165

C.r of p equals, 6.5pplus440

D.r of p equals, 7.5pminus10

Question 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 GlenviewStreet property?

A.$350,000

B.$291,700

C.$233,300

D.$175,000

Question 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, 300people 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 150participants, 36chose the first picture in the set. Among the remaining 150participants, ppeople 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 ofp?

A.p is greater than, 0.20 times, open parenthesis, 300 minus 36, close parenthesis, wherepis less than or equal to150

B.p is greater than, 0.20 times, open parenthesis, 300 plus 36, close parenthesis, wherepis less than or equal to150

C.p minus 36 is greater than, 0.20 times 300, wherep is less than or equal to150

D.p plus 36 is greater than, 0.20 times 300, wherepis less than or equal to150

Question 26.

The surface area of a cube is6 times, open parenthesis, the fraction a over 4, close parenthesis, squared, where a is a positive constant. Which of the following gives the perimeter of one face of thecube?

A.the fraction aover4

B.a

C.4a

D.6a

Question 27.

The mean score of 8players in a basketball game was 14.5points. If the highest individual score is removed, the mean score of the remaining 7players becomes 12points. What was the highest score?

A.20

B.24

C.32

D.36

Question 28 refers to the following figure.

Begin skippable figure description.

The figure presents the graph of a line, labeled y equals f of x, in the xyplane with the origin labeledO. The number1 is indicated on both axes. The graph begins in the second quadrant slightly above the xaxis. It moves upward and to the right, passing through the point with coordinates negative4 comma 1. The line crosses the yaxis at the point with coordinates 0 comma 3 and ends in the first quadrant.

End skippable figure description.

Question 28.

The graph of the linear functionf is shown in the preceding xyplane. The slope of the graph of the linear functiong is 4 times the slope of the graph off. If the graph of g passes through the pointwith coordinates 0 comma negative4, what is the value ofgof9?

A.5

B.9

C.14

D.18

Question 29 refers to the following equation.

xsquared, plus 20x, plus ysquared, plus 16y,equals negative20

Question 29.

The preceding equationdefines a circle in the xyplane. What are the coordinates of the center of the circle?

A.negative20 comma negative16

B.negative10 comma negative8

C.10comma8

D.20comma16

Question 30 refers to the following equation.

y equals xsquared minusa

Question 30.

In the preceding equation, a is a positive constant and the graph of the equation in the xyplane is a parabola. Which of the following is an equivalent form of the equation?

A.y equals, open parenthesis, x plus a, close parenthesis, times, open parenthesis, x minus a, close parenthesis

B.y equals, open parenthesis, x plus the square root of a, close parenthesis, times, open parenthesis, x minus the square root of a, close parenthesis