7道SAT数学题及解法.

2017-08-06 作者： 282阅读

　　下面为大家介绍的是7道SAT数学题及其解法的相关内容。这两道SAT数学题都是关于代数方面的，有一些难度，需要大家在解答的过程中适当的注意一下。下面是详细内容，大家一起来看看吧。

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　　1.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)

　　2.In an solution of water and alcohol, the ratio by mass of water to alcohol is to . If grams of a solution consisting of grams water for each gram of alcohol is added to the solution, what fraction by mass of the new solution is alcohol?

　　Answer Choices

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　3.In the figure above, which quadrants contain pairsthat satisfy the condition?

　　(A)only

　　(B)andonly

　　(C)andonly

　　(D)andonly

　　(E),,, and

　　4.In a class ofseniors, there areboys for everygirls. In the junior class, there areboys for everygirls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　5.Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?

. Three　

. Four　　

. Five

　　Answer Choices

　　(A) only

　　(B)only

　　(D) and only

　　(E) , , and

　　6.If the graph of the functionin the-plane contains the points,, and, which of the following CANNOT be true?

　　(A) The graph ofhas a maximum value.

　　(B)for all pointson the graph of.

　　(D) The graph ofis a line.

　　(E) The graph ofis a parabola.

　　7.All numbers divisible by both and are also divisible by which of the following?

　　Answer Choices

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　Explanation

　　1.The correct answer is D

　　Letandbe the original length and width of the rectangle, respectively. If we denote byandthe 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.

　　2.The correct answer is B

　　To find what fraction by mass of the new solution is alcohol, you can find how many grams of alcohol are in the final solution of grams. Since the solution is part alcohol to parts water, it is alcohol. So it contains grams of alcohol. Similarly, the solution is alcohol by mass, so it contains grams of alcohol. Thus, the final 20-gram solution contains grams of alcohol, so , or , of it is alcohol.

　　3.The correct answer is C

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

　　In quadrant, all thevalues are negative and all thevalues are positive, so inquadrant,andcannot be equal. For example, the pairdoes not satisfy the condition, since, not.

　　In quadrant, thevalues and thevalues are both negative, so it is possible forandto be equal. For example, the pairis in quadrantand.

　　In quadrant,andcannot be equal because thevalues are positive and thevalues are negative. For example, the pairdoes not satisfy the condition, since.

　　The quadrants that contain pairsthat satisfy the given condition are quadrantsandonly.

　　4.The correct answer is D

　　Among theseniors, there areboys for everygirls, soof the seniors, or, are boys and, or, are girls. Among the juniors,are boys andare girls. Ifstands for the total number of juniors, thenare boys andare girls. The total number of senior and junior boys is. The total number of senior and junior girls is. The question states that these quantities are equal, so. Solving this gives, or　

　　5.The correct answer is D

　　Since exactly two of the four lines are parallel, the other two lines are not parallel. If the two non-parallel lines intersect at a point that is not on either one of the parallel lines, then the configuration of lines will give a total of points of intersection. (The best way to verify this is by drawing the two parallel lines and then putting in the other two lines.) If, on the other hand, the two non-parallel lines intersect at a point that is on one of the parallel lines, then there will be a total of points of intersection in the figure. (Again, a sketch is the best way to verify this.) Any arrangement of the four lines will again yield either or points of intersection. Since you can’t obtain four points of intersection, the correct answer is and only.

　　6.The correct answer is D

　　If the graph of the function, which contains the points,, and, were a line, then the slope of the segment connecting the pointsandwould be the same as the slope of the segment connecting the pointsand. However, the slope of the segment connecting the pointsandis, and the slope of the segment connecting the pointsandis. Therore, the graph ofcannot be a line.

　　The statements in the other four options could be true. For example, if the equation ofwere, then the graph ofwould contain the points,, and. The graph ofwould be a parabola symmetric with respect to the line with equation. The maximum value ofwould occur at the point, andwould be true for all pointson the graph of.

　　7.The correct answer is A

　　All numbers divisible by both and are the multiples of and . Since and have no prime factor in common , then the least common multiple of and is equal to their product, namely . Every other multiple of and is divisible by . Thus, if is divisible by a number then all the multiples of and are divisible by that number. Therore, it is enough to check by which number in the given options is divisible. Only dividesand none of the other do. The answer must be

　　以上就是这7道SAT数学题的全部内容，后面的题目解答方法非常详细。大家可以在备考SAT数学考试的时候，利用题目对自己掌握的知识点进行适当的检查和测试，以找出不足之处进行更改。