SAT® Practice Test #7
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 table.
Feeding Information for Boarded Pets
Fed only dry food / Fed both wet and dry food / TotalCats / 5 / 11 / 16
Dogs / 2 / 23 / 25
Total / 7 / 34 / 41
Question 1.
The preceding table shows the kinds of foods that are fed to the cats and dogs currently boarded at a pet care facility. What fraction of the dogs are fed only dryfood?
A.the fraction 2over41
B.the fraction 2over25
C.the fraction 7over41
D.the fraction 2over7
Question 2 refers to the following expression.
open parenthesis, xsquared minus 3, close parenthesis, minus, open parenthesis, negative 3xsquared plus 5, close parenthesis
Question 2.
Which of the following expressions is equivalent to the preceding one?
A.4xsquared minus8
B.4xsquared minus2
C.negative2xsquared minus8
D.negative2xsquared minus2
Question 3.
A certain package requires 3centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 6meters of tape? (1meter equals 100centimeters)
A.100
B.150
C.200
D.300
Question 4.
A market researcher selected 200people at random from a group of people who indicated that they liked a certain book. The 200people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?
A.At least 95% of people who go see movies will dislike thismovie.
B.At least 95% of people who read books will dislike thismovie.
C.Most people who dislike this book will like thismovie.
D.Most people who like this book will dislike thismovie.
Question 5.
Which of the following ordered pairsx comma ysatisfies the inequality5x minus 3y is less than4?
1.1 comma 1
2.2 comma 5
3.3 comma 2
A.1 only
B.2 only
C.1 and 2 only
D.1 and 3 only
Question 6.
In the equationopen parenthesis, a, times x plus 3, close parenthesis, squared, equals 36, a is a constant. Ifx equals negative3is one solution to the equation, what is a possible valueofa?
A.negative11
B.negative5
C.negative1
D.0
Questions 7 and 8 refer to the following information.
The following scatterplot shows the densities of 7planetoids, in grams per cubiccentimeter, with respect to their average distances from the Sun in astronomicalunits (AU). The line of best fit is also shown.
Begin skippable figure description.
The figure presents a scatterplot titled “Distance and Density of Planetoids in the Inner Solar System.” The horizontal axis is labeled “Distance from the Sun, in astronomicalunits (AU),” and the numbers 0 through 3.2, in increments of 0.4, are indicated. The vertical axis is labeled “Density, in grams per cubiccentimeter,”and the numbers 3 through 6, in increments of 0.5, are indicated. There are 7data points. The line of best fit is also drawn. The data points are above and below the line of best fit.
The line of best fit begins at the vertical axis approximately at the point with coordinates 0 comma 5.75. It extends downward and to the right, and ends approximately at the point with coordinates 2.9 comma 3. The line of best fit contains the following points with approximate coordinates:
0.8 comma 5
1.6 comma 4.25
2.4 comma 3.5
End skippable figure description.
Question 7.
According to the scatterplot, which of the following statements is true about the relationship between a planetoid’s average distance from the Sun and its density?
A.Planetoids that are more distant from the Sun tend to have lesser densities.
B.Planetoids that are more distant from the Sun tend to have greater densities.
C.The density of a planetoid that is twice as far from the Sun as another planetoid is half the density of that other planetoid.
D.The distance from a planetoid to the Sun is unrelated to its density.
Question 8.
An astronomer has discovered a new planetoid about 1.2AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?
A.3.6
B.4.1
C.4.6
D.5.5
Question 9 refers to the following equation.
9a, times x, plus 9b, minus 6, equals21
Question 9.
Based on the preceding equation, what is the value ofaxplusb?
A.3
B.6
C.8
D.12
Question 10.
Lani spent 15% of her 8hour workday in meetings. How many minutes of her workday did she spend in meetings?
A.1.2
B.15
C.48
D.72
Question 11.
A software company is selling a new game in a standard edition and a collector’s edition. The box for the standard edition has a volume of 20cubic inches, and the box for the collector’s edition has a volume of 30cubic inches. The company receives an order for 75copies of the game, and the total volume of the order to be shipped is 1,870cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, s, and collector’s edition games, c,that were ordered?
A.75 minus s, equals c, and 20s plus 30c, equals1,870
B.75 minus s, equals c, and 30s plus 20c, equals1,870
C.s minus c, equals 75, and 25 times, open parenthesis, s plus c, close parenthesis, equals1,870
D.s minus c, equals 75, and 30s plus 20c, equals1,870
Question 12.
A customer paid $53.00 for a jacket after a 6percent sales tax was added. What was the price of the jacket before the sales tax was added?
A.$47.60
B.$50.00
C.$52.60
D.$52.84
Question 13 refers to the following graph.
Begin skippable figure description.
The figure, which presents a graph of 5line segments, is titled “Theresa’s Running Speed and Time.” The horizontal axis is labeled “Time, in minutes,” and the numbers 0through 30, in increments of 5, are indicated. The vertical axis is labeled “Speed, in miles per hour,” and the numbers 0 through 8 are indicated. The first line segment begins at the origin and moves upward and to the right until reaching the point with coordinates 5 comma 7. The second line segment begins where the first line segment ends and moves horizontally to the right until reaching the point with coordinates 10 comma 7. The third line segment begins where the second line segment ends and moves downward and to the right ending at the point with coordinates 20 comma 5. The fourth line segment begins where the third line segment ends and moves steadily upward and to the right, ending at the point with coordinates 25 comma 8. The fifth line segment begins where the fourth line segment ends and moves downward and to the right, ending at the horizontal axis at the point with coordinates 30 comma0.
End skippable figure description.
Question 13.
Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on the preceding graph. According to the graph, which of the following statements is NOT true concerning Theresa’s run?
A.Theresa ran at a constant speed for five minutes.
B.Theresa’s speed was increasing for a longer period of time than it was decreasing.
C.Theresa’s speed decreased at a constant rate during the last five minutes.
D.Theresa’s speed reached its maximum during the last ten minutes.
Question 14 refers to the following figure.
Begin skippable figure description.
The figure presents quadrilateralABCD with horizontal baseAD. Each of the 4angles are labeled. Starting from the bottom left and moving clockwise, angleA is labeled 45degrees, angleB is labeled xdegrees, angleC is labeled xdegrees, and angleD is labeled xdegrees.
End skippable figure description.
Question 14.
In the preceding figure, what is the value ofx?
A.45
B.90
C.100
D.105
Question 15.
If 50onecent coins were stacked on top of eachother in a column, the column would be approximately3 and seveneighthsinches tall. At this rate, which of the following is closest to the number of onecent coins it would take to make an 8inchtall column?
A.75
B.100
C.200
D.390
Question 16.
Ifa, minus b, equals 12and the fraction b over 2, equals 10, what is the value ofa, plusb?
A.2
B.12
C.32
D.52
Question 17 refers to the following equation.
y equals, 19.99 plus 1.50x
Question 17.
The preceding equation models the total cost y, in dollars, that a company charges a customer to rent a truck for one day and drive the truck xmiles. The total cost consists of a flat fee plus a charge per mile driven. When the equation is graphed in the xyplane, what does the yintercept of the graph represent in terms of the model?
A.A flat fee of $19.99
B.A charge per mile of $1.50
C.A charge per mile of $19.99
D.Total daily charges of $21.49
Question 18 refers to the following scatterplot.
Begin skippable figure description.
The figure presents a scatterplot titled “Income and Percent of Total Expenses Spent on Programs for Ten Charities in 2011.” The horizontal axis is labeled “Total income, in millions of dollars,” and the numbers 0 through 7,000, in increments of 1,000, are indicated. The vertical axis is labeled “Percent of total expenses spent on programs,” and the numbers 70 through 95, in increments of 5, are indicated. There are 10data points. The line of best fit is also drawn. The line of best fit begins at approximately the point with coordinates 1,000 comma 80. It extends upward and to the right, and ends at approximately the point with coordinates 6,000 comma90. The line of best fit passes through the points with the following coordinates. Note that all values are approximate.
2,000 comma 82
3,000 comma 84
4,000 comma 86
5,000 comma 88
The data points are scattered above and below the line of best fit. The data presented by the points are as follows. Note that all values are approximate.
1,100 comma 74
1,500 comma 82
1,550 comma 84
1,550 comma 85
3,200 comma 84
3,400 comma 92
4,200 comma 91
4,500 comma 89
4,500 comma 80
6,000 comma 87
End skippable figure description.
Question 18.
The preceding scatterplot shows data for ten charities along with the line of best fit. For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?
A.10%
B.7%
C.4%
D.1%
Questions 19 and 20 refer to the following information.
The following formulas are used in medicine to estimate the body surface areaA, in squaremeters, of infants and children whose weightw ranges between 3 and 30kilograms and whose heighth is measured in centimeters.
Mosteller’s formula: A, equals the fraction with numerator the square root of hw, and denominator60
Current’s formula: A, equals the fraction with numerator 4 plus w, and denominator30
Question 19.
Based on Current’s formula, what is w in terms ofA?
A.w equals, 30A, minus4
B.w equals, 30A, plus4
C.w equals, 30 times, open parenthesis, A, minus 4, close parenthesis
D.w equals, 30 times, open parenthesis, A, plus 4, close parenthesis
Question 20.
If Mosteller’s and Current’s formulas give the same estimate for A, which of the following expressions is equivalent tothe square root ofhw?
A.the fraction with numerator 4 plus w, and denominator2
B.the fraction with numerator 4 plus w, and denominator1,800
C.2 times, open parenthesis, 4 plus w, close parenthesis
D.the fraction with numerator, open parenthesis, 4 plus w, close parenthesis, squared, and denominator2
Question 21 refers to the following scatterplot.
Begin skippable figure description.
The figure presents a scatterplot titled “Total Protein and Total Fat for Eight Sandwiches.” The horizontal axis is labeled “Total protein,” in grams, and the numbers 0 through 50, in increments of 10, are indicated. The vertical axis is labeled “Total fat, in grams,” and the numbers 0 through 80, in increments of 10, are indicated. There are 8data points. The line of best fit is also shown. The data points are scattered above and below the line of best fit. The line of best fit begins at the point with coordinates approximately at 9 comma 17. It extends upward and to the right, and ends at the point with coordinates approximately at 49 comma 75. The line of best fit passes through the points with the following coordinates. Note that all values are approximate.
10 comma 19
20 comma 33
30 comma 48
40 comma 64
End skippable figure description.
Question 21.
The preceding scatterplot shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1gram in total protein?
A.2.5
B.2.0
C.1.5
D.1.0
Question 22 refers to the following information.
Percent of Residents Who Earned a Bachelor’s Degree or Higher
State / Percent of residentsState A / 21.9%
State B / 27.9%
State C / 25.9%
State D / 19.5%
State E / 30.1%
State F / 36.4%
State G / 35.5%
Question 22.
A survey was given to residents of all 50states asking if they had earned a bachelor’s degree or higher. Theresults from 7 of the states are given in the precedingtable. The median percent of residents who earned a bachelor’s degree or higher for all 50states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7states and the median for all 50states?
A.0.05%
B.0.95%
C.1.22%
D.7.45%
Question 23.
A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of75centimeters squared, and the height of the can is 10centimeters. If110centimeters cubedof syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?
A.7.5centimeters cubed
B.185centimeters cubed
C.640centimeters cubed
D.750centimeters cubed
Question 24 refers to the following function.
h of t equals, negative 16tsquared, plus 110t, plus72
Question 24.
The preceding function models the heighth, in feet, of an object above ground tseconds after being launched straight up in the air. What does the number 72 represent in the function?
A.The initial height, in feet, of the object
B.The maximum height, in feet, of the object
C.The initial speed, in feet per second, of the object
D.The maximum speed, in feet per second, of the object
Questions 25 and 26 refer to the following information.
The following table gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the threemacronutrients in food.
Energy per Gram of Typical Macronutrients
Macronutrient / Food calories / KilojoulesProtein / 4.0 / 16.7
Fat / 9.0 / 37.7
Carbohydrate / 4.0 / 16.7
Question 25.
If xfood calories is equivalent to kkilojoules, of the following, which best represents the relationship between x andk?
A.k equals0.24x
B.k equals4.2x
C.x equals4.2k
D.xk equals4.2
Question 26.
If the 180food calories in a granola bar come entirely from pgrams of protein,fgrams of fat, and cgrams of carbohydrate, which of the following expressesf in terms of p andc?
A.f equals, 20 plus the fraction 4 over 9, end fraction, times, open parenthesis, p plus c, close parenthesis
B.f equals, 20 minus the fraction 4 over 9, end fraction, times, open parenthesis, p plus c, close parenthesis
C.f equals, 20 minus the fraction 4 over 9, end fraction, times, open parenthesis, p minus c, close parenthesis
D.f equals, 20 plus the fraction 9 over 4, end fraction, times, open parenthesis, p plus c, close parenthesis