sat practice test 6 for assistive technology – … · web viewthe s a t®practice test #6 math...

The S A T®

Practice Test #6

Math Test—Calculator38 Questions

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

DirectionsFor questions 1 through 30, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 31 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 question 31 on how to record your answers in the spaces provided. You may use scratch paper for scratch work.

Notes1. 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.

© 2016 The College Board.

5. Unless otherwise indicated, the domain of a given function f is the set of all

real numbers x for which f of x is a real number.


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 one-half 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 30-degree angle and a 60-degree angle. The side opposite the 30-degree angle is labeled x. The side opposite the 60-degree 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 45-degree 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 four-thirds 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 one-third 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 one-third 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.

Which expression is equivalent to open parenthesis, 2 x squared minus 4, close parenthesis, minus, open parenthesis, negative 3 x squared plus 2 x minus 7, close parenthesis?

A. 5 x squared minus 2 x plus 3

B. 5 x squared plus 2 x minus 3

C. negative x squared minus 2 x minus 11

D. negative x squared plus 2 x minus 11


Question 2 refers to the following figure.

Begin skippable figure description.

The figure presents a graph of 2 lines in the first quadrant in the x y-plane with origin labeled O. The x-axis is labeled “Time, in seconds,” and the numbers 5 and 10 are indicated. The y-axis 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 6 comma 60.

The line labeled “Mark” begins on the y-axis at 18 and moves upward and to the right until reaching a point with the coordinates 10 comma 60.

The lines intersect at approximately the point with coordinates 3 comma 30.© 2016 The College Board.

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 6 seconds, and Mark finished the race in 10 seconds. According to the graph, Mark was given a head start of how many yards?

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 versus time?

Each option presents a graph in the first quadrant 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.


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.



B.


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.


C.


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.



D.


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.


Question 4.A website-hosting service charges businesses a onetime setup fee of $350 plus d dollars for each month. If a business owner paid $1,010 for the first 12 months, including the setup fee, what is the value of d ?

A. 25

B. 35

C. 45

D. 55


Question 5 refers to the following inequality. 6 x minus 9 y is greater than 12

Question 5.Which of the following inequalities is equivalent to the preceding inequality?

A. x minus y is greater than 2

B. 2 x minus 3 y is greater than 4

C. 3 x minus 2 y is greater than 4

D. 3 y minus 2 x is greater than 2


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 1,200 responses 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 dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. 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 dog park.

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

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

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


Question 8 refers to the following table.


The figure presents a 4-column table, with 2 rows of data, titled “Ice Cream and Topping Selections.” There are no headings for columns 1 and 2. The heading for columns 3 and 4 is “Flavor.” The subheading for column 3 is “Vanilla,” and the subheading for column 4 is “Chocolate.” The heading for rows 1 and 2, which is located in column 1, is “Topping.” The subheading for row 1 is “Hot fudge,” and the subheading for row 2 is “Caramel.” The 2 rows 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.



Question 8.The preceding table shows the flavors of ice cream and the toppings chosen by the people at a party. Each person chose one flavor of ice cream and one topping. Of the people who chose vanilla ice cream, 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 92.1 square miles, of which 11.3 square miles is water. If the city had a population of 621,000 people in the year 2010, which of the following is closest to the population density, in people per square mile of land area, of the city at that time?

A. 6,740

B. 7,690

C. 55,000

D. 76,000


Question 10.Between 1497 and 1500, Amerigo Vespucci embarked on two voyages to the New World. According to Vespucci’s letters, the first voyage lasted 43 days longer than the second voyage, and the two voyages combined lasted a total of 1,003 days. How many days did the second voyage last?

A. 460

B. 480

C. 520

D. 540


Question 11 refers to the following system of equations.

7 x plus 3 y equals 8

And

6 x minus 3 y equals 5

Question 11.

For the solution of the ordered pair x comma y to the preceding system of equations, what is the value of x minus y ?

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 height h, in centimeters, of a sunflower t days 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



The figure, which presents a line graph in the first quadrant of a t h-coordinate plane, is titled “Sunflower Height over Time.” The horizontal t-axis is labeled “Time, in days,” and the numbers 0 through 84, in increments of 7, are indicated. The vertical h-axis is labeled “Height, in centimeters,” and the numbers 0 through 260, in increments of 20, are indicated. There are 13 points on the graph that represent the data given in the preceding table. The curve is made up of 12 line segments connecting each of the data points from the table, beginning at the point with coordinates 0 comma 0, moving upward and to the right, and ending at the point with coordinates 84 comma 254.50.



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 function h, defined by h of t equals a, times t plus b, where a and b are constants, models the height, in centimeters, of the sunflower after t days of growth during a time period in which the growth is approximately linear. What does a 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 day 14 to day 35 is nearly constant. On this interval, which of the following equations best models the height h, in centimeters, of the sunflower t days after it begins to grow?

A. h equals 2.1 times t minus 15

B. h equals 4.5 times t minus 27

C. h equals 6.8 times t minus 12

D. h equals 13.2 times t minus 18




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

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







Question 15.Which of the following equations relates y to x for the values in the preceding table?

A. y equals one-half, times, open parenthesis, five-halves, close parenthesis, to the power x

B. y equals 2 times, open parenthesis, three-fourths, close parenthesis, to the power x

C. y equals three-fourths x plus 2

D. y equals seven-halves x minus three-fourths




The figure presents two right triangles, A B C and D E F. In triangle A B C, side A C is horizontal, and side B C is drawn such that it is perpendicular to side A C and point B is above point C. Angle A is labeled 32 degrees, and the right angle symbol is indicated at angle C. In triangle D E F, side D F is horizontal, side E F is drawn such that it is perpendicular to side D F, and point E is above point F. Angle D is labeled 58 degrees, and the right angle symbol is indicated at angle F.


Question 16.Triangles A B C and D E F are shown in the preceding figure. Which of the

following is equal to the ratio B C over A B ?

A. D E over D F

B. D F over D E

C. D F over E F

D. E F over D E© 2016 The College Board.

Questions 17 through 19 refer to the following information. When designing a stairway, an architect can use the riser-tread formula

2 h plus d equals 25, where h is the riser height, in inches, and d 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 5 steps 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.


The figure presents a drawing of the side view of a stairway that has 5 steps. 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.



Question 17.Based on the given information, which of the following expresses the riser height in terms of the tread depth?

A. h equals one-half, times, open parenthesis, 25 plus d, close parenthesis

B. h equals one-half, times, open parenthesis, 25 minus d, close parenthesis

C. h equals negative one-half, times, open parenthesis, 25 plus d, close parenthesis

D. h equals negative one-half, times, open parenthesis, 25 minus d, close parenthesis


Question 18.Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread 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 to 5

B. h is greater than or equal to 5

C. 5 is less than or equal to h, which is less than or equal to 8

D. 8 is less than or equal to h, which is less than or equal to 16

Question 19.An architect wants to use the riser-tread formula (refer to the given information) to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, 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? (1 foot equals 12 inches.)

A. 7.2

B. 9.5

C. 10.6

D. 15


Question 20.

What is the sum of the solutions to open parenthesis, x minus 6, close parenthesis, times, open parenthesis, x plus 0.7, close parenthesis, equals 0 ?

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 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?

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

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

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

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


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

A. 13

B. 15

C. 17

D. 20




The figure presents a graph titled “Height versus Time for a Bouncing Ball.” The horizontal axis is labeled “Time elapsed, in seconds,” and the numbers 0 through 3 are indicated. The vertical axis is labeled “Height, in feet,” and the numbers 0 through 4 are indicated. The graph begins on the vertical axis at 4 feet and curves steeply downward and to the right until it reaches the horizontal axis at 0.5 seconds. It then curves upward and to the right until reaching approximately 2.4 feet at approximately 0.9 seconds and then curves back downward and to the right until it reaches the horizontal axis at approximately 1.3 seconds. The graph then curves upward and to the right until reaching approximately 1.25 feet at approximately 1.6 seconds and then curves back downward and to the right until it reaches the horizontal axis at approximately 1.9 seconds. This pattern is repeated five more times with the height reached by the curve decreasing each time the pattern is repeated.



Question 23.As part of an experiment, a ball was dropped and allowed to bounce repeatedly off the ground until it came to rest. The preceding graph represents the relationship between the time elapsed after the ball was dropped and the height of the ball above the ground. After it was dropped, how many times was the ball at a height of 2 feet?

A. One

B. Two

C. Three

D. Four

Question 24.A customer’s monthly water bill was $75.74. Due to a rate increase, her monthly bill is now $79.86. To the nearest tenth of a percent, by what percent did the amount of the customer’s water bill increase?

A. 4.1%

B. 5.1%

C. 5.2%

D. 5.4%




The figure presents a 2-column table with 3 rows of data. The heading for the first column is “x,” and the heading for the second column is “f of x.” The 3 rows of data are as follows.

Row 1: x, 0; f of x, negative 2.

Row 2: x, 2; f of x, 4.

Row 3: x, 6; f of x, 16.


Question 25.Some values of the linear function f are shown in the preceding table. What is the

value of f of 3 ?

A. 6

B. 7

C. 8

D. 9


Question 26 refers to the following information.A gear ratio r:s (r to s) is the ratio of the number of teeth of two connected gears. The ratio of the number of revolutions per minute of two gear wheels is s:r (s to r). In the following diagram, Gear, A, is turned by a motor. The turning of Gear, A, causes Gears B and C to turn as well.


The figure presents a diagram of 3 gears of three different radii arranged side by side such that Gear , A, is interlocked with Gear B and Gear B is interlocked with Gear C. The gears are labeled, from left to right, as follows. “Gear , A, 20 teeth,” “Gear B, 60 teeth,” and “Gear C, 10 teeth.”



Question 26.If Gear, A, is rotated by the motor at a rate of 100 revolutions per minute, what is the number of revolutions per minute for Gear C?

A. 50

B. 110

C. 200

D. 1,000

Question 27.

In the x y-plane, the graph of 2 x squared minus 6 x, plus 2 y squared plus 2 y, equals 45 is a circle. What is the radius of the circle?

A. 5

B. 6.5

C. the square root of 40

D. the square root of 50


Question 28.Two different points on a number line are both 3 units from the point with coordinate negative 4. The solution to which of the following equations gives the coordinates of both points?

A. the absolute value of x plus 4, end absolute value, equals 3

B. the absolute value of x minus 4, end absolute value, equals 3

C. the absolute value of x plus 3, end absolute value, equals 4

D. the absolute value of x minus 3, end absolute value, equals 4

Question 29.A motor powers a model car so that after starting from rest, the car travels s inches

in t seconds, where s equals 16 t, times the square root of t. Which of the following gives the average speed of the car, in inches per second, over the first t seconds after it starts?

A. 4, times the square root of t

B. 16, times the square root of t

C. the fraction 16 over the square root of t

D. 16 t


Question 30 refers to the following information.The following scatterplot shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a 10-year period.


The figure presents a scatterplot in the x y-plane titled “Electric Energy Generated by Nuclear Sources.” The x-axis is labeled “Time, in years,” and the numbers 0 through 12, in increments of 2, are indicated. The y-axis is labeled “Energy, in million megawatt-hours,” and the numbers 700 through 820, in increments of 20, are indicated. There are 10 data points scattered in the form of a curve. The first data point begins approximately at the point with coordinates 1 comma 764. The points follow a path varying upward and downward and to the right, until reaching the point with coordinates of approximately 8 comma 806. The points then move downward and to the right, ending at the point with coordinates of approximately 10 comma 768.


The data represented by the points are as follows. Note that all values are approximate.

Point 1: 1 year, 764 million mega-watt hours.

Point 2: 2 years, 788 million mega-watt hours.











Question 30.Of the following equations, which best models the data in the preceding scatterplot?

A. y equals 1.674 x squared, plus 19.76 x, minus 745.73

B. y equals negative 1.674 x squared, minus 19.76 x, minus 745.73

C. y equals 1.674 x squared, plus 19.76 x, plus 745.73

D. y equals negative 1.674 x squared, plus 19.76 x, plus 745.73


DirectionsFor questions 31 through 38, solve the problem and record your answer in the spaces provided on the answer sheet, as described in the following directions and examples.

1. Although not required, it is suggested that your answer be recorded in the boxes at the top of the columns to help 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, indicate only one answer.

5. Mixed numbers such as three and one half must be recorded as 3.5 or

seven slash two. (If three, one, slash, two, is recorded in the spaces

provided on the answer sheet, it will be interpreted as thirty one halves, not

three and one half.)

6. Decimal answers: If you obtain a decimal answer with more digits than the spaces on the answer sheet can accommodate, it may be either rounded or truncated, but it must fill all four spaces.


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 seven-twelfths, 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 two-thirds 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.A group of friends decided to divide the $800 cost of a trip equally among themselves. When two of the friends decided not to go on the trip, those remaining still divided the $800 cost equally, but each friend’s share of the cost increased by $20. How many friends were in the group originally?

Question 32 refers to the following equation.

2 times, open parenthesis, 5 x minus 20, close parenthesis, minus, open parenthesis, 15 plus 8 x, close parenthesis, equals 7

Question 32.What value of x satisfies the preceding equation?

Question 33.A laboratory supply company produces graduated cylinders, each with an internal radius of 2 inches and an internal height between 7.75 inches and 8 inches. What is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?


Question 34.

In the x y-plane, the graph of y equals 3 x squared minus 14 x

intersects the graph of y equals x at the points with coordinates 0

comma 0 and a, comma, a. What is the value of a ?

Question 35.

The line with the equation four-fifths x plus one-third y equals 1 is graphed in the x y-plane. What is the x-coordinate of the x-intercept of the line?

Question 36 refers to the following table.Masses (kilograms)

Andrew 2.4 2.5 3.6 3.1 2.5 2.7

Maria x 3.1 2.7 2.9 3.3 2.8

Question 36.Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the preceding table. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of x ?


Question 37.Jeremy deposited x dollars in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 dollars in his investment account on January 1, 2005. What is the value of x ?

Question 38.A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?

Stop.If you finish before time is called, you may check your work on this section only. Do not go on to any other section.


sat practice test 6 for assistive technology – … · web viewthe s a t®practice test #6 math...

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