5道SAT数学难题.

　　下面为大家搜集了5道SAT数学难题，供大家在备考的时候进行适当的准备。解答SAT数学难题可以比常规的题目更加容易了解SAT数学考试的出题思路和方法。下面我们来看看详细内容吧。

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　　1.Which of the following statements must be true of the lengths of the segments on lineabove?

　　.

　　.

　　.

　　(A)only

　　(B)only

　　(C)only

　　(D)andonly

　　(E),, and

　　2.Ifismore than, then

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　3.In the figure above, the circle with center and the circle with center are tangent at point . If the circles each have radius , and if line is tangent to the circle with center at point , what is the value of ?

　　Answer Choices

　　(A)

　　(B)

　　(C)

　　(D)

　　(E) It cannot be determined from the information given.

　　4.A manager estimates that if the company chargesdollars for their new product, where, then the revenue from the product will bedollars each week. According to this model, for which of the following values ofwould the company’s weekly revenue for the product be the greatest?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　5.The length of rectangle is percent longer than the length of rectangle , and the width of rectangle is percent shorter than the width of rectangle . The area of rectangle is

　　Answer Choices

　　(A) greater than the area of rectangle

　　(B) greater than the area of rectangle

　　(C) equal to the area of rectangle

　　(D) less than the area of rectangle

　　(E) less than the area of rectangle

　　Explanation

　　1.The correct answer is B

　　Consider each statement separately. For example, consider statement,. From the figure, you can see that segmentis made up of the segments,, and. This tells you thatcannot equal, sincecannot equal zero. Statementis not true.

　　Consider statement,. Sinceis betweenand, it follows that. Sinceis betweenand, it follows that. Therore,. Since bothandequal, they are equal to each other. Statementis true.

　　Consider statement,. The lt side of the equation,, is equivalent to. The right side of the equation,, is equivalent to. Sincecannot equal zero,is not equal to. Statementis not true.

　　Statementis the only one that is true.

　　2.The correct answer is D

　　The statement given in words translates into the equation. This simplifies to. Then, and so.

　　It follows that.

　　3.The correct answer is B

　　The circles each have radius , so . Since the circles are tangent at point , segment contains and . Also, and are perpendicular because a line tangent to a circle forms a right angle with the radius at the point of tangency. Therore, is a right triangle with hypotenuse and side of length . A right triangle with one side of length one-half that of its hypotenuse is a triangle. The angle is opposite side , so .

　　4.The correct answer is D

　　The graph ofis a downward-facing parabola that intersects the-axis atand at. Parabolas are symmetric, so the maximum value ofoccurs at, which is halfway betweenand. (When, the value ofis.)

　　5.The correct answer is D

　　Represent the length and width of rectangle as and . Then the area of is . The length of rectangle is longer than , which is , or . Similarly, the width of is , or . The area of

is, which simplifies to . From this it follows that the area of rectangle is less than the area of rectangle .

　　以上就是这5道SAT数学难题的全部内容，后面附有详细的答案解析。大家可以在备考自己的SAT数学考试的时候，进行适当的参考和借鉴之用。