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1.In the xy-plane, line passes through the points and , where . What is the slope of line ?
(A)
(B)
(C)
(D)
(E)
2.Ten cars containing a total of people passed through a checkpoint. If none of these cars contained more than people, what is the greatest possible number of these cars that could have contained exactly people?
Answer Choices
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
3.The cars in a car service use a total of gallons of gasoline per week. If each of the cars uses the same amount of gasoline, then, at this rate, which of the following represents the number of gallons used by 5 of the cars in 2 weeks?
Answer Choices
(A)
(B)
(C)
(D)
E)
4.Read the following SAT test question and then click on a button to select your answer.
If triangle above is congruent to triangle (not shown), which of the following must be the length of one side of triangle ?
Answer Choices
(A)
(B)
(C)
(D)
(E) It cannot be determined from the information given.
5.If the function is defined by , where , for which of the following values of is undefined?
Answer Choices
(A) None
(B) only
(C) only
(D) and only
(E) , , and
6.In the , line is perpendicular to the grAPh of the function . Line could be the grAPh of which of the following functions?
Answer Choices
(A)
(B)
(C)
(D)
(E)
7.A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are seniors, juniors, and sophomores who APplied. Each senior's name is placed in the lottery times; each junior's name, times; and each sophomore's name, time. What is the probability that a senior's name will be chosen?
Answer Choices
(A)
(B)
(C)
(D)
(E)
Explanation
1.The correct answer is A
Choice (A) is correct. Given two points on a line, the slope of the line can be found by dividing the change in the y-coordinates between the points by the corresponding change in the x-coordinates. Hence, since line passes through the points and , its slope is .
2.The correct answer is D
It could not be true that each of the ten cars contained exactly people, as this would give a total of only . If nine of the cars contained exactly people, the remaining car could have no more than people, for a total of only . Continuing in the same way, a pattern develops. If eight of the cars contained exactly people, the remaining two cars could have no more than people each, for a total of only . If seven of the cars contained exactly people, the total number of people could be only . From the pattern, you can see that if four of the cars contained exactly people, and the remaining six cars contained the maximum of people, the total number would be , as given in the question. Therefore, at most four of the ten cars could have contained exactlypeople.
3.The correct answer is E
The car service uses a total of gallons of gasoline per week, and each of the cars uses the same amount of gasoline, so each of the cars uses gallons of gasoline per week. Therefore, of the cars use a total of gallons per week. It follows that of the cars use gallons of gasoline in weeks.
4.The correct answer is D
Triangle is congruent to triangle , so the lengths of the three sides of triangle are the same as the lengths of the three sides of triangle . Triangle is a - - triangle with hypotenuse of length , so the other two sides of triangle have lengths and . Therefore, the lengths of the sides of triangle must be , , and . Of the choices given, only is one of these values.
5.The correct answer is C
If , then . If , then . If , then , which is not defined because division by is undefined. Therefore, of the three values, , , and , the only one for which is undefined is . Thus the correct response is only.
6.The correct answer is B
If two lines are perpendicular, the product of their slopes is equal to . The function is in slope-intercept form, so the slope of the grAPh of is equal to . Therefore, the slope of line must be equal to . The only choice that corresponds to a slope of is .
7.The correct answer is D
To determine the probability that a senior's name will be chosen, you must determine the total number of seniors' names that are in the lottery and divide this number by the total number of names in the lottery. Since each senior's name is placed in the lottery times, there are seniors' names. Likewise, there are juniors' names and sophomores' names in the lottery. The probability that a senior's name will be chosen is .
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