SAT数学练习题精选（附解析）

　　下面是6道

　　

 

　　1.The histogram above shows the distribution of 31 black cherry trees, by height. For example, the leftmost bar represents the black cherry trees that are at least 60 feet, but not less than 65 feet, in height. Based on the histogram, which of the following can be the average (arithmetic mean) height of the 31 black cherry trees?

　　Answer Choices

　　(A) 70 feet

　　(B) 72 feet

　　(C) 74 feet

　　(D) 78 feet

　　(E) 80 feet

　　

 

　　2.In the figure above, O is the center of the circle and triangle A B O is equilateral. If the sides of triangle A B O are of length 6, what is the length of line B C?

　　(A) 3 times square root 3

　　(B) 4 times square root 3

　　(C) 6 times square root 3

　　(D) 9

　　(E) 12

　　3.When the positive integer n is divided by 5, the remainder is 0. What is the remainder when 3n is divided by 5?

　　(A) 0

　　(B) 1

　　(C) 2

　　(D) 3

　　(E) 4

　　4.A 6-sided number cube, with faces numbered 1 through 6, is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll?

　　(A) 1 over 4

　　(B) 1 over 3

　　(C) 5 over 12

　　(D) 7 over 12

　　(E) 1 over 2

　　

 

　　5.The quadratic function

is graphed in the -plane above. If for all values of , which of the following could be the coordinates of point ?

 

　　(A)

 

　　(B)

 

　　(C)

 

　　(D)

 

　　(E)

 

　　6.In a certain lawn-mower factory, 0.06 percent of all mowers produced are defective. On the average, there will be 3 defective mowers out of how many produced?

　　(A) 500

　　(B) 1800

　　(C) 5000

　　(D) 18000

　　(E) 50000

　　Explanation

　　1.The correct answer is C

　　The histogram does not give the recorded heights for each cherry tree, but rather the intervals in which the heights lie. Thus, to find possible values for the average (arithmetic mean) height, one can find lower and upper bounds for the average height by calculating the averages of lower and upper interval bounds of the histogram with the frequencies given. A lower bound for the average, found by using the value at the left endpoint of the interval, is

feet, and so feet would be an upper bound for the average height. Therefore, the average height of the 31 black cherry trees can be between 72.74 feet and 77.74 feet. Of the choices given, only 74 feet can be a possible value for the average height of the 31 black cherry trees.

 

　　2.The correct answer is C

　　Choice (C) is correct. Since triangle A B O is equilateral, each of its angles has measure

　　60 degrees. It follows that angle B O C has measure 120 degrees. Since line O B and line O C are radii of the same circle, they are of equal length, and so delta O C B is isosceles. Hence angle O B C and angle O C B each have measure 30 degrees. Thus angle A B C has measure 60 degrees + 30 degrees = 90 degrees, and so triangle A B C is a 30 degrees minus 60 degrees minus 90 degrees right triangle. Since line A B, the side opposite the 30 degrees angle in triangle A B C, is of length 6, it follows that line B C, the side opposite the 60 degrees angle, is of length 6 times square root 3

　　3.The correct answer is A

　　Choice (A) is correct. When the positive integer n is divided by 5, the remainder is 0. It follows that n is a multiple of 5. Therefore, 3n is also a multiple of 5, and so the remainder when 3n is divided by 5 is likewise 0.

　　4.The correct answer is C

　　The outcome space for this experiment is the set of all ordered pairs

where represents the first number that comes up, and represents the second one. Since and can take all the values through , there will be a total of possible outcomes. The outcomes can be represented in a table as shown:　　 　　Among all the pairs , are pairs for which . So remaining pairs will have . Notice that the number of pairs for which

 

　　is the same with the number of pairs

for which . Therefore the number of pairs for which , is (half of ). Then the probability that is equal to .

 

　　5.The correct answer is C

　　The fact that

for all values of #p#分页标题#e# means that the point is the maximum of the quadratic function , so must be the vertex of the parabola. The parabola intersects the -axis at the points and , so must be halfway between and . Therefore, . Of the choices, the only one with -coordinate equal to is . Therefore, could be the coordinates of point .

 

　　6.The correct answer is C

　　Recall that 0.06 percent means 0.06 out of every 100, or 6 out of every 10000. The question asks for an equivalent ratio: 3 out of how many. The ratio 6 out of 10000 can be reduced (by dividing both members by 2) to 3 out of 5000.

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