# SAT MATH(Calc Allowed) Practice Tests

*65mins*

**You have 55 minutes to finish the task.Your response will be judged on the quality of your writing and on how well your response presentsthe key points presented in the lectures**

00:55:00 |

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) of x is a real number.

**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.

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.

**End skippable figure descriptions.**

For student produced response questions, students will also see the following 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 three and one half must be recorded as three point five or seven slash two. (If three and one half is entered into the grid as , three, one, slash, two, 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 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

Beging skippable figure description.

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

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

End skippable figure description.

Example 3

Beging skippable figure description.

Example 3: Acceptable ways to record two thirds are: two slash three, point six six six, and point six six seven.

End skippable figure description.

Example 4

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

Beging skippable figure description.

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 two in the first space, zero in the second space, and one in the third space. Alternatively, you may record two in the second space, zero in the third space, and one in the fourth space. Spaces not needed should be left blank.

End skippable figure description.

**
Question 1.
The recommended daily calcium intake for a 20 year old is 1,000 milligrams (m g). One cup of milk contains 299 milligrams of calcium and one cup of juice contains 261 milligrams of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20 year old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?**
A. 299 m plus 261 j is greater than or equal to 1,000

B. 299 m plus 261 j is greater than 1,000

C. the fraction 299 over m, plus the fraction 261 over j, is greater than or equal to 1,000

D. the fraction 299 over m, plus the fraction 261 over j, is greater than 1,000

**Question 2.**

A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology degree program read per day?

A. 40 randomly selected undergraduate psychology degree program students

A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology degree program read per day?

B. 40 randomly selected undergraduate students from all degree programs at the college

C. 300 randomly selected undergraduate psychology degree program students

D. 300 randomly selected undergraduate students from all degree programs at the college

**Questions 3 through 5 refer to the following information and figure.**

The first metacarpal bone is located in the wrist. The following scatterplot shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.

Begin skippable figure description.

The figure presents a gridded graph titled “Height of Nine People and Length of Their First Metacarpal Bone” and nine data points. The y axis is labeled “Length of first metacarpal bone,” in centimeters, and the x axis is labeled “Height,” in centimeters. The values 4, 4.5, and 5 are labeled on the x axis with a vertical grid line at every increment of 0.1. The values 155 through 185, in increments of 5, are labeled on the y axis with a horizontal grid line at every increment of one.

The approximate values of the nine data points on the scatterplot are as follows.

4.0 comma 157.

4.1 comma 163.

4.3 comma 175.

4.5 comma 171.

4.6 comma 173.

4.7 comma 173.

4.8 comma 172.

4.9 comma 183.

5.0 comma 178.

A straight line of best fit is drawn for the data points. The approximate coordinates of the line are as follows.

4.0 comma 161.5

4.1 comma 163.

4.2 comma 165.

4.3 comma 167.

4.4 comma 169.

4.5 comma 171.

4.6 comma 172.5.

4.7 comma 174.5.

4.8 comma 176.

4.9 comma 178.

5.0 comma 180.

End skippable figure description.

**Question 3.**

How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

A. 2

How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

B. 4

C. 6

D. 9

**Question 4.**

Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

A. The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone

Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

B. The predicted first metacarpal bone increase in centimeters for every centimeter increase in height

C. The predicted height in centimeters of a person with a first metacarpal bone length of 0 centimeters

D. The predicted first metacarpal bone length in centimeters for a person with a height of 0 centimeters

**Question 5.**

Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?

A. 168 centimeters

Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?

B. 169 centimeters

C. 170 centimeters

D. 171 centimeters

**Question 6.**

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional one time untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights?

A. parenthesis, 99.95 plus 0.08 x, close parenthesis, plus 5

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional one time untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights?

B. 1.08, parenthesis, 99.95 x, close parenthesis, plus 5

C. 1.08, parenthesis, 99.95 x plus 5, close parenthesis

D. 1.08, parenthesis, 99.95 plus 5, close parenthesis, x

Begin skippable figure description.

The figure presents the graph of a circle, a parabola, and a line in the x y plane. The horizontal axis is labeled x, the vertical axis is labeled y, and the origin is labeled O. The integers negative 3 through 3 appear on both axes.

The circle has its center at the origin and radius of approximately 2.2.

The parabola has its vertex on the y axis at negative 3 and opens upward.

The circle and parabola intersect at four points, of which two are below the x axis and two are above the x axis. Of the two points of intersection below the x axis, one is to the left of the y axis and one is to the right of the y axis. Of the two points of intersection above the x axis, one is to the left of the y axis and one is to the right of the y axis.

The line slants upward and to the right, and passes through two of the four points of intersection where the circle and parabola meet, one below the x axis and to the left of the y axis, and one above the x axis to the right of the y axis. In other words, the three graphs intersect at two points.

End skippable figure description.

The following system of three equations is given beneath the figure.

x squared plus y squared equals five.

y equals x squared minus three.

x minus y equals one.

**Question 7.**

A system of three equations and their graphs in the x y plane are shown above. How many solutions does the system have?

A. One

A system of three equations and their graphs in the x y plane are shown above. How many solutions does the system have?

B. Two

C. Three

D. Four

Solids | Liquids | Gases | Total | |

Metals | 77 | 1 | 0 | 78 |

Metalloids | 7 | 0 | 0 | 7 |

Nonmetals | 6 | 1 | 11 | 18 |

Total | 90 | 2 | 11 | 103 |

**Question 8.**

What fraction of all solids and liquids in the preceding table are metalloids?

Question 9.

If the fraction negative 9 over 5 is less than negative 3 t plus 1, and negative 3 t plus 1 is less than the negative of the fraction 7 over 4, what is one possible value of 9 t minus 3?

What fraction of all solids and liquids in the preceding table are metalloids?

Question 9.

If the fraction negative 9 over 5 is less than negative 3 t plus 1, and negative 3 t plus 1 is less than the negative of the fraction 7 over 4, what is one possible value of 9 t minus 3?

**Questions 10 and 11 refer to the following information and table.**

A survey was conducted among a randomly chosen sample of U. S. citizens about U. S. voter participation in the November 2012 presidential election. The following table displays a summary of the survey results.

Reported Voting by Age (in thousands)

Age | Voted | Did Not Vote | No Response | Total |

18 to 34 year olds | 30,329 | 23,211 | 9,468 | 63,008 |

35 to 54 year olds | 47,085 | 17,721 | 9,476 | 74,282 |

55 to 74 year olds | 43,075 | 10,092 | 6,831 | 59,998 |

People 75 years old and over | 12,459 | 3,508 | 1,827 | 17,794 |

Total | 132,948 | 54,532 | 27,602 | 215,082 |

**Question 10.**

According to the table (follow link), for which age group did the greatest percentage of people report that they had voted?

A. 18- to 34-year-olds

According to the table (follow link), for which age group did the greatest percentage of people report that they had voted?

B. 35- to 54-year-olds

C. 55- to 74-year-olds

D. People 75 years old and over

**A. About 123 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.**

Question 11.

Of the 18- to 34 year olds who reported voting, 500 people were selected at random to do a follow up survey where they were asked which candidate they voted for. There were 287 people in this follow up survey sample who said they voted for Candidate A, and the other 213 people voted for someone else. Using the data from both the follow up survey and the initial survey, which of the following is most likely to be an accurate statement?

Question 11.

Of the 18- to 34 year olds who reported voting, 500 people were selected at random to do a follow up survey where they were asked which candidate they voted for. There were 287 people in this follow up survey sample who said they voted for Candidate A, and the other 213 people voted for someone else. Using the data from both the follow up survey and the initial survey, which of the following is most likely to be an accurate statement?

B. About 76 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

C. About 36 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

D. About 17 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

**A. n is less than 70.**

Question 12.

A company’s manager estimated that the cost C, in dollars, of producing n items is C equals 7 n plus 350. The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?

Question 12.

A company’s manager estimated that the cost C, in dollars, of producing n items is C equals 7 n plus 350. The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?

B. n is less than 84.

C. n is greater than 70.

D. n is greater than 84.

**A. m equals 17.**

Question 13.

At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age m of the combined group of male and female primates at the primate reserve?

Question 13.

At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age m of the combined group of male and female primates at the primate reserve?

B. m is greater than 17.

C. m is less than 17.

D. 15 is less than m, and m is less than 19.

**A. There is a positive association between exercise and sleep for 16 year olds in the United States.**

Question 14.

A researcher wanted to know if there is an association between exercise and sleep for the population of 16 year olds in the United States. She obtained survey responses from a random sample of 2000 United States 16 year olds and found convincing evidence of a positive association between exercise and sleep. Which of the following conclusions is well supported by the data?

Question 14.

A researcher wanted to know if there is an association between exercise and sleep for the population of 16 year olds in the United States. She obtained survey responses from a random sample of 2000 United States 16 year olds and found convincing evidence of a positive association between exercise and sleep. Which of the following conclusions is well supported by the data?

B. There is a positive association between exercise and sleep for 16 year olds in the world.

C. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 year olds in the United States.

D. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 year olds in the world.

**A. P equals 12 plus 50 n.**

Question 15.

A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2014 was estimated to be 50 animals. If P represents the population n years after 2014, then which of the following equations represents the class’s model of the population over time?

Question 15.

A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2014 was estimated to be 50 animals. If P represents the population n years after 2014, then which of the following equations represents the class’s model of the population over time?

B. P equals 50 plus 12 n.

C. P equals 50, parenthesis, 2, close parenthesis, to the power of 12 n.

D. P equals 50, parenthesis, 2, close parenthesis, to the power of the fraction n over 12.

Question 16 is based on the following figure.

Question 16 is based on the following figure.

Begin skippable figure description.

The figure presents line segments A E and B D that intersect at point C. Line segments A B and D E are drawn resulting in two triangles A B C and E D C.

A note under the figure says that the figure is not drawn to scale.

End skippable figure description.

**Question 16.**

In the preceding figure (follow link), triangle A B C is similar to triangle E D C. Which of the following must be true?

A. Line segment A E is parallel to line segment B D.

In the preceding figure (follow link), triangle A B C is similar to triangle E D C. Which of the following must be true?

B. Line segment A E is perpendicular to line segment B D.

C. Line segment A B is parallel to line segment D E.

D. Line segment A B is perpendicular to line segment D E.

Question 17.

The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?

Question 17.

The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?

A. f of t equals 17 minus the fraction 21 over 50 t.

B. f of t equals 17 minus the fraction 50 t over 21.

C. f of t equals the fraction whose numerator is 17 minus 21 t, and whose denominator is 50.

D. f of t equals the fraction whose numerator is 17 minus 50 t, and whose denominator is 21.

**A. x plus y equals 1,338.**

Question 18.

The toll rates for crossing a bridge are $6.50 for a car and $10 for a truck. During a two hour period, a total of 187 cars and trucks crossed the bridge, and the total collected in tolls was $1,338. Solving which of the following systems of equations yields the number of cars, x, and the number of trucks, y, that crossed the bridge during the two hours?

Question 18.

The toll rates for crossing a bridge are $6.50 for a car and $10 for a truck. During a two hour period, a total of 187 cars and trucks crossed the bridge, and the total collected in tolls was $1,338. Solving which of the following systems of equations yields the number of cars, x, and the number of trucks, y, that crossed the bridge during the two hours?

6.5 x plus 10 y equals 187.

B. x plus y equals 187.

6.5 x, plus 10 y, equals the fraction 1,338 over 2.

C. x plus y equals 187.

6.5 x, plus 10 y equals 1,338.

D. x plus y equals 187.

6.5 x, plus 10 y equals 1,338 times 2.

Question 19.

When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

Question 19.

When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

A. p equals 0.44 d plus 0.77.

B. p equals 0.44 d plus 14.74.

C. p equals 2.2 d minus 1.1.

D. p equals 2.2 d minus 9.9.

**Question 20 is based on the following figure.**

Begin skippable figure description.

The figure, titled “Count of Manatees,” presents the graph of a scatterplot with a line. The horizontal axis is labeled “Year,” and the vertical axis is labeled “Number of Manatees.” The years 1990 through 2015 are labeled on the horizontal axis, in increments of 5 years. The numbers 1,000 through 6,000 are labeled on the vertical axis, in increments of 1,000. Grid lines extend from the labeled increments of both axes.

There are 24 data points on the graph. The data points range horizontally from years 1991 to 2011 and vertically from approximately 1,300 manatees to approximately 5,100 manatees.

A line of best fit is drawn for the range of years represented by the data points. The line begins at year 1991 with approximately 1,200 manatees and ends at year 2011 with approximately 4,200 manatees. The line of best fit intersects four vertical grid lines, which represent 5 year increments, at the following approximate values.

Year 1995: 1,800 manatees.

Year 2000: 2,600 manatees.

Year 2005: 3,300 manatees.

Year 2010: 4,100 manatees.

End skippable figure description.

**Question 20.**

The preceding scatterplot (follow link) shows counts of Florida manatees, a type of sea mammal, from 1991 to 2011. Based on the line of best fit to the data shown, which of the following values is closest to the average yearly increase in the number of manatees?

A. 0.75

B. 75

C. 150

D. 750

**Question 21 is based on the following figure.**

Begin skippable figure description.

The figure, titled “Bacteria Growth,” presents a graph of two curved lines. The horizontal axis is labeled “Time” in hours and the vertical axis is labeled “Area covered” in square centimeters. Both axes are labeled from 0 to 10 in increments of one with grid lines extending from each labeled increment.

The curved line labeled “Dish 1” begins on the vertical axis at 1 and curves steeply up and to the right passing through the point with coordinates 2 comma 4, and the point with coordinates 3 comma 8. The curved line labeled “Dish 2” begins on the vertical axis at 2 and moves to the right before curving gradually up and to the right passing through the point with coordinates 3 comma 3, and the point with coordinates 5 comma 6. The two curved lines intersect at a point with approximate coordinates 1.2 comma 2.1.

End skippable figure description.

**A. At time t equals zero, both dishes are 100% covered by bacteria.**

Question 21.

A researcher places two colonies of bacteria into two petri dishes that each have area 10 square centimeters. After the initial placement of the bacteria parenthesis, t equals zero, close parenthesis, the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown in the figure (follow link), where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the preceding data?

Question 21.

A researcher places two colonies of bacteria into two petri dishes that each have area 10 square centimeters. After the initial placement of the bacteria parenthesis, t equals zero, close parenthesis, the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown in the figure (follow link), where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the preceding data?

B. At time t equals zero, bacteria covers 10% of Dish 1 and 20% of Dish 2.

C. At time t equals zero, Dish 2 is covered with 50% more bacteria than Dish 1.

D. For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1.

Question 22. A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?

Question 22. A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?

A. 3

B. 10

C. 56

D. 144

**Question 23.**

x squared plus y squared equals 153.

y equals negative 4 x.

**If parenthesis, x comma y, close parenthesis, is a solution to the preceding system of equations, what is the value of x squared?**

A. negative 51

B. 3

C. 9

D. 144

**Question 24 is based on the following figure.**

Begin skippable figure description.

The figure presents a metal nut with two hexagonal faces and six sides. The thickness of one side, from one hexagonal face to the other hexagonal face of the nut, is labeled as 1 centimeter.

End skippable figure description.

Question 24.

The preceding figure (follow link) shows a metal hex nut with two regular hexagonal faces and a thickness of 1 centimeter. The length of each side of a hexagonal face is 2 centimeters. A hole with a diameter of 2 centimeters is drilled through the nut. The density of the metal is 7.9 grams per cubic centimeter. What is the mass of this nut, to the nearest gram? (Density is mass divided by volume.)

**An international bank issues its Traveler credit cards worldwide. When a customer makes a purchase using a Traveler card in a currency different from the customer’s home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost.**

Questions 25 and 26 refer to the following information.

Questions 25 and 26 refer to the following information.

Sara lives in the United States, but is on vacation in India. She used her Traveler card for a purchase that cost 602 rupees (Indian currency). The bank posted a charge of $9.88 to her account that included the 4% fee.

**Question 25.**

What foreign exchange rate, in Indian rupees per one U. S. dollar, did the bank use for Sara’s charge? Round your answer to the nearest whole number.

What foreign exchange rate, in Indian rupees per one U. S. dollar, did the bank use for Sara’s charge? Round your answer to the nearest whole number.

**Question 26. A bank in India sells a prepaid credit card worth 7,500 rupees. Sara can buy the prepaid card using dollars at the daily exchange rate with no fee, but she will lose any money left unspent on the prepaid card. What is the least number of the 7,500 rupees on the prepaid card Sara must spend for the prepaid card to be cheaper than charging all her purchases on the Traveler card? Round your answer to the nearest whole number of rupees.**

**Question 27. If k is a positive constant different from 1, which of the following could be the graph of y minus x equals, k, parenthesis, x plus y, close parenthesis, in the x y plane?**

Each of the four answer choices presents a graph in the x y plane. The numbers negative 6 through 6 appear along both axes, and the origin is labeled O.

Begin skippable figure description.

Choice A. The graph shows a line that goes up from left to right and intersects the x axis at negative 2, and the y axis at 2.

End skippable figure description.

**Question 28.**

The function f is defined by f of x equals 2 x cubed, plus 3 x squared, plus c x, plus 8, where c is a constant. In the x y plane, the graph of f intersects the x axis at the three points parenthesis, negative 4 comma 0, close parenthesis, parenthesis, one half comma 0, close parenthesis, and parenthesis, p comma 0, close parenthesis. What is the value of c?

The function f is defined by f of x equals 2 x cubed, plus 3 x squared, plus c x, plus 8, where c is a constant. In the x y plane, the graph of f intersects the x axis at the three points parenthesis, negative 4 comma 0, close parenthesis, parenthesis, one half comma 0, close parenthesis, and parenthesis, p comma 0, close parenthesis. What is the value of c?

A. negative 18

B. negative 2

C. 2

D. 10

**Question 29.**

If the expression the fraction whose numerator is 4 x squared, and whose denominator is 2 x minus one, is written in the equivalent form the fraction whose numerator is one, and whose denominator is 2 x minus one, plus A, what is A in terms of x?

A. 2 x plus one.

If the expression the fraction whose numerator is 4 x squared, and whose denominator is 2 x minus one, is written in the equivalent form the fraction whose numerator is one, and whose denominator is 2 x minus one, plus A, what is A in terms of x?

B. 2 x minus one.

C. 4 x squared.

D. 4 x squared minus one.

Question 30 is based on the following information and figure.

**An architect drew the following sketch while designing a house roof. The dimensions shown are for the interior of the triangle.**

Begin skippable figure description.

The figure presents a triangle with a horizontal base. Labels are given to two sides and to two angles. The left side of the triangle is labeled 24 feet. The base of the triangle is labeled 32 feet. The two lower interior angles are labeled x degrees. A note under the figure says that the figure is not drawn to scale.

End skippable figure description.

**Question 30.**

What is the value of cosine x?

What is the value of cosine x?