8道SAT数学选择题练习(二).

　　下面是为大家准备的8道SAT考试数学选择题练习题。同学们在备考SAT数学的过程中，一定要加强习题的练习，熟练到能充分理解题意，争取得到满分。

　　1.

　　In the figure above, which quadrants contain pairs that satisfy the condition ?

　　(A) only

　　(B) and only

　　(C) and only

　　(D) and only

　　(E) , , , and

　　2.

　　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.

　　3.The length of a rectangle is increased by , and the width of the rectangle is increased by . By what percentage will the area of the rectangle be increased?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　4.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)

　　5.Which of the following CANNOT be the lengths of the sides of a triangle?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　6.In the xy-plane, line passes through the points and , where . What is the slope of line ?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　7.for all integers

　　If is a function dined for all positive integers , and satisfies the two conditions above, which of the following could be the dinition of ?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　8.If is the set of positive integers that are multiples of , and if is the set of positive integers that are multiples of , how many integers are in the intersection of and ?

　　(A) None

　　(B) One

　　(C) Seven

　　(D) Thirteen

　　(E) More than thirteen

　　参考答案及解析：

　　1.The correct answer is C

　　Explanation

　　In order for to satisfy , it must be true that and are equal to each other and not equal to zero. An example of such a pair is , which is in quadrant .

　　In quadrant , all the values are negative and all the values are positive, so inquadrant , and cannot be equal. For example, the pair does not satisfy the condition, since , not .

　　In quadrant , the values and the values are both negative, so it is possible for and to be equal. For example, the pair is in quadrant and .

　　In quadrant , and cannot be equal because the values are positive and the values are negative. For example, the pair does not satisfy the condition, since .

　　The quadrants that contain pairs that satisfy the given condition are quadrantsand only.

　　2.The correct answer is D

　　Explanation

　　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 . Therore, the lengths of the sides of triangle must be , , and . Of the choices given, only is one of these values.

　　3.The correct answer is D

　　Explanation

　　Let and be the original length and width of the rectangle, respectively. If we denote by and the new length and width of the rectangle, respectively, then we have:

and

　　So, the new area will be:

　　where () is the original area of the rectangle.

　　So the area is increased by .

　　4.The correct answer is E

　　Explanation

　　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. Therore, of the cars use a total of gallons per week. It follows that of the cars use gallons of gasoline in weeks.

　　5.The correct answer is B

　　Explanation

　　The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Four of the answer choices can be eliminated because each set of three numbers can be the lengths of three sides of a triangle. For example, in the third choice, the sum of any two numbers is greater than the third number. However, the second choicecannot be the lengths of the sides of a triangle, sinceis not greater than. This choice is the correct answer, since the question asked which set of numbers could NOT be lengths of the sides of a triangle.

　　6.The correct answer is A

　　Explanation

　　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 .

　　7.The correct answer is B

　　Explanation

　　If, then, so the second condition fails. If,then, so the second condition fails for this function also. The other three options satisfy, so it remains to check whether they satisfy the first condition.

　　If, and, thenand, so it is not true thatfor all integers. This means that the functiondoes not satisfy the first condition. If, and, thenand, so it is not true thatfor all integers. This means that the functiondoes not satisfy the first condition.

　　However, if, then, for all integers. Also,.Therore, the functionis the only option that satisfies both conditions.

　　8.The correct answer is E

　　Explanation

　　The intersection of setsandis the set of integers that are inand also in. Setconsists of all positive integers that are multiples of, and setconsists of all positive integers that are multiples of, so the intersection ofandis the set of positive integers that are multiples of bothand. This is the set of all positive integers that are multiples of. There are an infinite number of positive integers that are multiples of, so there are more than thirteen integers in the intersection ofand.

　　以上就是关于8道SAT考试数学选择题练习题及其答案和解析，非常详细。同学们在备考阶段，一定要加强习题的练习以及题意的理解，争取SAT数学满分。

　　下面是为大家准备的8道SAT考试数学选择题练习题。同学们在备考SAT数学的过程中，一定要加强习题的练习，熟练到能充分理解题意，争取得到满分。

　　1.

　　In the figure above, which quadrants contain pairs that satisfy the condition ?

　　(A) only

　　(B) and only

　　(C) and only

　　(D) and only

　　(E) , , , and

　　2.

　　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.

　　3.The length of a rectangle is increased by , and the width of the rectangle is increased by . By what percentage will the area of the rectangle be increased?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　4.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)

　　5.Which of the following CANNOT be the lengths of the sides of a triangle?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　6.In the xy-plane, line passes through the points and , where . What is the slope of line ?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　7.for all integers

　　If is a function dined for all positive integers , and satisfies the two conditions above, which of the following could be the dinition of ?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　8.If is the set of positive integers that are multiples of , and if is the set of positive integers that are multiples of , how many integers are in the intersection of and ?

　　(A) None

　　(B) One

　　(C) Seven

　　(D) Thirteen

　　(E) More than thirteen

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