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Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
1., , ,, ...
The first four terms of a sequence are shown above. Which of the following could be the formula that gives the th term of this sequence for all positive integers ?
Answer Choices
(A)
(B)
(C)
(D)
(E)
2.In the figure above, all intersecting sides of the polygon meet at right angles. What is the area of the polygon?
Answer Choices
(A) 108
(B) 104
(C) 102
(D) 98
(E) 96
Choice (D) is correct. Adding shaded rectangles as in the figure above, the given polygon is seen to be a 12-by-9 rectangle with a 2-by-3 and a 2-by-2 rectangle removed. Therefore, the area of the polygon is (12 × 9) – (2 × 3) – (2 × 2), which is equal to 98.
3.The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If represents the median temperature, represents the temperature that occurs most often, and represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of , , and ?
Answer Choices
(A)
(B)
(C)
(D)
(E)
4.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
5.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 E
If a formula gives the th term of the sequence for all positive integers , it must give the th term of the sequence for . If , then and , but the first term of the sequence is , so the general formula cannot be or . Also, if , then and , but the third term of the sequence is , so the general formula cannot be or . However, for , the values of are , , , , respectively. Therefore, the general formula for this sequence could be .
2.The correct answer is D
3.The correct answer is A
To determine the correct order of , , and , it is helpful to first place the seven temperatures in ascending order as shown below.
The median temperature is the middle temperature in the ordered list, which is , so . The temperature that occurs most often, or the mode, is , so . To determine the average, you can add the seven numbers together and divide by . However, you can determine the relationship between the average and the median by inspection. The three numbers greater than are closer to than are the three numbers smaller than . Therefore, the average of the seven numbers will be less than . The correct order of , , and is .
4.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 exactly
people.
5.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 .#p#分页标题#e#
以上就是这五道SAT数学练习题目的全部内容，非常丰富，包括了代数和几何两个部分。大家可以在备考自己的SAT数学考试的时候，根据自己的实际情况进行参考和借鉴。