### COURSE DESCRIPTION

**The Standardized College Admissions Test** in the United States.

For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work. **(CALCULATOR USE PERMITTED)**

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- Question 1 of 12
##### 1. Question

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?

CorrectIncorrectChoice C is correct. Increasing the sample size while randomly selecting participants from the original population of interest will most likely result in a decrease in the margin of error.

- Question 2 of 12
##### 2. Question

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

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?

CorrectIncorrectChoice B is correct. The people who have first metacarpal bones of length 4.0, 4.3, 4.8, and 4.9 centimeters have heights that are greater than 3 centimeters different from the height predicted by the line of best fit.

- Question 3 of 12
##### 3. Question

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

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

CorrectIncorrectChoice A is correct. The slope is the change in the vertical distance divided by the change in the horizontal distance between any two points on a line. In this context, the change in the vertical distance is the change in the predicted height of a person, and the change in the horizontal distance is the change in the length of his or her first metacarpal bone. The unit rate, or slope, is the increase in predicted height for each increase of 1 centimeter of the first metacarpal bone.

- Question 4 of 12
##### 4. Question

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

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?

CorrectIncorrectChoice C is correct. Students must see that the scale of the

*x*-axis is 0.1, and therefore the*x*-value of 4.45 is halfway between the unmarked value of 4.4 and the marked value of 4.5. The student must then find the*y*-value on the line of best fit that corresponds with an*x*-value of 4.45, which is 170. - Question 5 of 12
##### 5. Question

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 onetime 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?CorrectIncorrectChoice B is correct. The total charge that Aaron will pay is the room rate, the 8% tax on the room rate, and a fixed fee. If Aaron stayed

*x*nights, then the total charge is , which can be rewritten as . - Question 6 of 12
##### 6. Question

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 table below displays a summary of the survey results.

Reported Voting by Age (in thousands) 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 According to the table, for which age group did the greatest percentage of people report that they had voted?

CorrectIncorrectChoice C is the correct answer. The first question asks students to select the relevant information from the table to compute the percentage of self-reported voters for each age group and then compare the percentages to identify the largest one, choice C. Of the 55- to 74-year-old group’s total population (59,998,000), 43,075,000 reported that they had voted, which represents 71.8% and is the highest percentage of reported voters from among the four age groups.

- Question 7 of 12
##### 7. Question

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?

CorrectIncorrectChoice A is correct. A relationship in the data can only be generalized to the population that the sample was drawn from.

- Question 8 of 12
##### 8. Question

The scatterplot above 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?

CorrectIncorrectChoice C is correct. The slope of the line of best fit is the value of the average increase in manatees per year. Using approximate values found along the line of best fit (1,200 manatees in 1991 and 4,200 manatees in 2011), the approximate slope can be calculated as

- Question 9 of 12
##### 9. Question

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?

CorrectIncorrectChoice B is correct. The tracking station can receive 118,800 megabits each day

which is about 116 gigabits each day

If each image is 11.2 gigabits, then the number of images that can be received each day is

Since the question asks for the maximum number of typical images, rounding the answer down to 10 is appropriate because the tracking station will not receive a completed 11th image in one day.

- Question 10 of 12
##### 10. Question

If is a solution to the system of equations above, what is the value of

CorrectIncorrectChoice C is correct. The second equation gives

*y*in terms of*x*, so a student can use this to rewrite the first equation in terms of*x*. Substituting -4*x*for*y*in the equation gives This can be simplified to or Since the question asks for the value of not*x*, dividing both sides of by 17 gives the answer: - Question 11 of 12
##### 11. Question

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.

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.

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.

CorrectIncorrect$9.88 represents the conversion of 602 rupees plus a 4% fee on the converted cost. To calculate the original cost of the item in dollars, x:

Since the original cost is $9.50, to calculate the exchange rate

*r*, in Indian rupees per one U.S. dollar: - Question 12 of 12
##### 12. Question

The function

*f*is defined by where*c*is a constant. In the*xy*-plane, the graph of*f*intersects the*x*-axis at the three points (-4,0), and What is the value of*c*?CorrectIncorrectChoice A is correct. The given zeros can be used to set up an equation to solve for

*c*. Substituting –4 for*x*and 0 for*y*yields or Alternatively, since –4, and*p*are zeros of the polynomial function it follows that Were this polynomial multiplied out, the constant term would be (We can see this without performing the full expansion.) Since it is given that this value is 8, it follows that or rather, Substituting 2 for*p*in the polynomial function yields and after multiplying the factors one finds that the coefficient of the*x*term, or the value of*c*, is –18.

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