The SAT®Practice Test #6

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.

Which expression is equivalent to open parenthesis, 2xsquared minus4, close parenthesis, minus, open parenthesis, negative3xsquared plus 2xminus7, close parenthesis?

A.5x squared minus 2x plus3

B.5x squared plus 2x minus3

C.negativex squared minus 2x minus11

D.negativex squared plus 2x minus11

Question 2 refers to the following figure.

Begin skippable figure description.

The figure presents a graph of 2 lines in the firstquadrant in the xyplane with origin labeledO. The xaxis is labeled “Time, in seconds,”and the numbers 5 and 10 are indicated. The yaxis is labeled “Distance, in yards,” and the numbers 12 through 60, in increments of 12, are indicated. One line is labeled “Paul,” and the other line is labeled “Mark.” The behavior of the 2 lines in the graph is as follows.

The line labeled “Paul” begins at the origin and moves upward and to the right until reaching a point with coordinates 6comma60.

The line labeled “Mark” begins on the yaxis at 18 and moves upward and to the right until reaching a point with the coordinates 10comma60.

The lines intersect at approximately the point with coordinates 3comma30.

End skippable figure description.
Question 2.

The preceding graph shows the positions of Paul and Mark during a race. Paul and Mark each ran at a constant rate, and Mark was given a head start to shorten the distance he needed to run. Paul finished the race in 6seconds, and Mark finished the race in 10seconds. According to the graph, Mark was given a head start of how manyyards?

A.3

B.12

C.18

D.24

Question 3.

Snow fell and then stopped for a time. When the snow began to fall again, it fell at a faster rate than it had initially. Assuming that none of the snow melted during the time indicated, which of the following graphs could model the total accumulation of snow versustime?

Each option presents a graph in the firstquadrant of a coordinate plane. The horizontal axis is labeled “Time,” and the vertical axis is labeled “Accumulation.” There are no scales on either axis.

A.

Begin skippable figure description.

The graph consists of three line segments. The first line segment begins at the intersection of the two axes and moves gradually upward and to the right and ends where a second line segment begins. The second line segment moves horizontally and to the right and ends above the horizontal axis. A third line segment begins where the second line segment ends and moves steeply upward and to the right, ending above the horizontal axis.

End skippable figure description.

B.

Begin skippable figure description.

The graph consists of three line segments. The first line segment begins at the intersection of the two axes and moves steeply upward and to the right and ends where a second line segment begins. The second line segment moves horizontally and to the right and ends above the horizontal axis. A third line segment begins where the second line segment ends and moves gradually upward and to the right, ending above the horizontal axis.

End skippable figure description.

C.

Begin skippable figure description.

The graph consists of three line segments. The first line segment begins at the intersection of the two axes and moves upward and to the right and ends where a second line segment begins. The second line segment moves horizontally and to the right and ends above the horizontal axis. A third line segment begins where the second line segment ends and moves downward and to the right, ending on the horizontal axis.

End skippable figure description.

D.

Begin skippable figure description.

The graph consists of a line that begins at the intersection of the two axes and moves steadily upward and to the right, ending above the horizontal axis.

End skippable figure description.
Question 4.

A websitehosting service charges businesses a onetime setup fee of $350 plusddollars for each month. If a business owner paid $1,010 for the first 12months, including the setup fee, what is the valueofd?

A.25

B.35

C.45

D.55

Question 5 refers to the following inequality.

6x minus 9y is greater than12

Question 5.

Which of the following inequalities is equivalent to the preceding inequality?

A.x minus y is greater than2

B.2x minus 3y is greater than4

C.3x minus 2y is greater than4

D.3y minus 2x is greater than2

Question 6 refers to the following table.

Where Do People Get Most of Their Medical Information?

Source / Percent of those surveyed
Doctor / 63%
Internet / 13%
Magazines or brochures / 9%
Pharmacy / 6%
Television / 2%
Other or none of the above / 7%

Question 6.

The preceding table shows a summary of 1,200responses to a survey question. Based on the table, how many of those surveyed get most of their medical information from either a doctor or the Internet?

A.865

B.887

C.912

D.926

Question 7.

The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dogpark. The council surveyed a sample of 500city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dogpark. Which of the following is true about the city council’s survey?

A.It shows that the majority of city residents are in favor of the dogpark.

B.The survey sample should have included more residents who are dogowners.

C.The survey sample should have consisted entirely of residents who do not owndogs.

D.The survey sample is biased because it is not representative of all cityresidents.

Question 8 refers to the following table.

Begin skippable figure description.

The figure presents a 4column table, with 2rows of data, titled “Ice Cream and Topping Selections.” There are no headings for columns1 and2. The heading for columns3 and4 is “Flavor.” The subheading for column3 is “Vanilla,” and the subheading for column4 is “Chocolate.” The heading for rows1 and2, which is located in column1, is “Topping.”The subheading for row1 is “Hot fudge,” and the subheading for row2 is “Caramel.” The 2rows of data are as follows.

Row 1, hot fudge and vanilla,8; hot fudge and chocolate,6.

Row 2, caramel and vanilla,5; caramel and chocolate,6.

End skippable figure description.

Question 8.

The preceding table shows the flavors of icecream andthe toppings chosen by the people at a party. Eachperson chose oneflavor of icecream and onetopping. Of the people who chose vanilla icecream, what fraction chose hot fudge as a topping?

A.8 over 25

B.5 over 13

C.13 over 25

D.8 over 13

Question 9.

The total area of a coastal city is 92.1square miles, of which 11.3square miles is water. If the city had a population of 621,000people in the year2010, which of the following is closest to the population density, in people per square mile of land area, of the city at thattime?

A.6,740

B.7,690

C.55,000

D.76,000

Question 10.

Between 1497 and 1500, AmerigoVespucci embarked on twovoyages to the NewWorld. According to Vespucci’s letters, the firstvoyage lasted 43days longer than the secondvoyage, and the twovoyages combined lasted a total of 1,003days. How many days did the secondvoyage last?

A.460

B.480

C.520

D.540

Question 11 refers to the following system of equations.

7x plus 3y equals 8

And

6x minus 3y equals 5

Question 11.

For the solution of the ordered pair xcommayto the preceding system of equations, what is the value ofxminusy?

A.the negative fraction 4 over 3

B.the fraction 2 over 3

C.the fraction 4 over 3

D.the fraction 22 over 3

Questions 12 through 14 refer to the following information.

In 1919, H.S.Reed and R.H.Holland published a paper on the growth of sunflowers. Included in the paper were the following table and graph, which show the heighth, in centimeters, of a sunflowertdays after the sunflower begins to grow.

Sunflower Growth

Day / Height (centimeters)
0 / 0.00
7 / 17.93
14 / 36.36
21 / 67.76
28 / 98.10
35 / 131.00
42 / 169.50
49 / 205.50
56 / 228.30
63 / 247.10
70 / 250.50
77 / 253.80
84 / 254.50

Begin skippable figure description.

The figure, which presents a line graphin the first quadrant of a thcoordinate plane, is titled “Sunflower Height over Time.” The horizontal taxis is labeled “Time, in days,” and the numbers 0 through 84, in increments of 7, are indicated. The vertical haxis is labeled “Height, in centimeters,” and the numbers 0 through 260, in increments of 20, are indicated. There are 13points on the graph that represent the data given in the preceding table. The curve is made up of 12line segments connecting each of the data points from the table, beginning at the point with coordinates 0comma0, moving upward and to the right, and ending at the point with coordinates 84comma254.50.

End skippable figure description.

Question 12.

Based on the given information, over which of the following time periods is the average growth rate of the sunflower least?

A.Day 0 to Day 21

B.Day 21 to Day 42

C.Day 42 to Day 63

D.Day 63 to Day 84

Question 13.

In respect to the given information, the functionh, defined by hoft equals a, times t plusb, wherea andb are constants, models the height, in centimeters, of the sunflower aftertdays of growth during a time period in which the growth is approximately linear. What doesa represent?

A.The predicted number of centimeters the sunflower grows each day during the period

B.The predicted height, in centimeters, of the sunflower at the beginning of the period

C.The predicted height, in centimeters, of the sunflower at the end of the period

D.The predicted total increase in the height of the sunflower, in centimeters, during the period

Question 14.

Based on the given information, the growth rate of the sunflower from day14 to day35 is nearly constant. On this interval, which of the following equations best models the heighth, in centimeters, of the sunflowertdays after it begins togrow?

A.h equals 2.1 times t minus15

B.h equals 4.5 times t minus27

C.h equals 6.8 times t minus12

D.h equals 13.2 times t minus18

Question 15 refers to the following figure.

Begin skippable figure description.

The figure presents a 2row table with 5columnsof data. The heading for the first row is “x.” The heading for the second row is“y.” The 5columns of data are as follows.

Column1:x, 1; y, the fraction 11 over 4.

Column2:x, 2; y, the fraction 25 over 4.

Column3:x, 3; y, the fraction 39 over 4.

Column4:x, 4; y, the fraction 53 over 4.

Column5:x, 5; y, the fraction 67 over 4.

End skippable figure description.

Question 15.

Which of the following equations relatesy toxfor the values in the precedingtable?

A.y equals onehalf, times, open parenthesis, fivehalves, close parenthesis, to the powerx

B.y equals 2 times, open parenthesis, threefourths, close parenthesis, to the powerx

C.y equals threefourthsx plus2

D.y equals sevenhalvesx minusthreefourths

Question 16 refers to the following figure.

Begin skippable figure description.

The figure presents two right triangles, ABC andDEF. In triangleABC, sideAC is horizontal, and sideBC is drawn such that it is perpendicular to sideAC and pointB is above pointC. AngleA is labeled 32degrees, and the right angle symbol is indicated at angleC. In triangleDEF, sideDF is horizontal, sideEF is drawn such that it is perpendicular to sideDF, and pointE is above pointF. AngleD is labeled 58degrees, and the right angle symbol is indicated at angleF.

End skippable figure description.

Question 16.

Triangles ABC andDEF are shown in the preceding figure. Which of the following is equal to the ratio BCoverAB?

A.DE over DF

B.DF over DE

C.DF over EF

D.EF over DE

Questions 17 through 19 refer to the following information.

When designing a stairway, an architect can use the risertread formula 2hplus d equals25, whereh is the riser height, in inches, andd is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.

The number of steps in a stairway is the number of its risers. For example, there are 5steps in the stairway in the following figure. The total rise of a stairway is the sum of the riser heights as shown in the figure.

Begin skippable figure description.

The figure presents a drawing of the sideview of a stairway that has 5steps. The height of the stairway is labeled “total rise.” The height of each step is labeled “riser height,h,”and the width of each step is labeled “tread depth,d.” Note: the figure is not drawn to scale.

End skippable figure description.

Question 17.

Based on the given information, which of the following expresses the riser height in terms of the tread depth?

A.h equals onehalf, times, open parenthesis, 25plusd, close parenthesis

B.h equals onehalf, times, open parenthesis, 25minusd, close parenthesis

C.h equals negative onehalf, times, open parenthesis, 25plusd, close parenthesis

D.h equals negative onehalf, times, open parenthesis, 25minusd, close parenthesis

Question 18.

Some building codes require that, for indoor stairways, the tread depth must be at least 9inches and the riser height must be at least 5inches. According to the risertread formula (refer to the given information), which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?

A.0 is less than or equal to h, which is less than or equal to5

B.h is greater than or equal to5

C.5 is less than or equal to h, which is less than or equal to8

D.8 is less than or equal to h, which is less than or equal to16

Question 19.

An architect wants to use the risertread formula (refer to the given information) to design a stairway with a total rise of 9feet, a riser height between 7 and 8inches, and an odd number of steps. With the architect’s constraints, which of the following must be the tread depth, in inches, of the stairway? (1footequals12inches.)

A.7.2

B.9.5

C.10.6

D.15

Question 20.

What is the sum of the solutions to open parenthesis, xminus6, close parenthesis, times, open parenthesis, xplus0.7, close parenthesis, equals0?

A.negative 6.7

B.negative 5.3

C.5.3

D.6.7

Question 21.

A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150largemouth bass, of which 30% weighed more than 2pounds. Which of the following conclusions is best supported by the sampledata?

A.The majority of all fish in the pond weigh less than 2pounds.

B.The average weight of all fish in the pond is approximately 2pounds.

C.Approximately 30% of all fish in the pond weigh more than 2pounds.

D.Approximately 30% of all largemouth bass in the pond weigh more than 2pounds.

Question 22 refers to the following table.

Number of States with 10 or More Electoral Votes in 2008

Electoral votes / Frequency
10 / 4
11 / 4
12 / 1
13 / 1
15 / 3
17 / 1
20 / 1
21 / 2
27 / 1
31 / 1
34 / 1
55 / 1

Question 22.

In 2008, there were 21states with 10or more electoral votes, as shown in the preceding table. Based on the table, what was the median number of electoral votes for the 21states?

A.13

B.15

C.17

D.20

Question 23 refers to the following figure.

Begin skippable figure description.

The figure presents a graph titled “Height versus Time for a Bouncing Ball.” The horizontal axis is labeled “Time elapsed, in seconds,” and the numbers0 through3 are indicated. The vertical axis is labeled “Height, in feet,” and the numbers0 through4 are indicated. The graph begins on the vertical axis at 4feet and curves steeply downward and to the right until it reaches the horizontal axis at 0.5seconds. It then curves upward and to the right until reaching approximately 2.4feet at approximately 0.9seconds and then curves back downward and to the right until it reaches the horizontal axis at approximately 1.3seconds. The graph then curves upward and to the right until reaching approximately 1.25feet at approximately 1.6seconds and then curvesback downward and to the right until it reaches the horizontal axis at approximately 1.9seconds. This pattern is repeated five more times with the height reached by the curve decreasing each time the pattern is repeated.