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SAT数学选择题精选6道

2013-11-04 18:26:00来源:网络

  参考答案及解析:

  Explanation

  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 ofgrams. Since thesolution ispart alcohol toparts water, it isalcohol. So it containsgrams of alcohol. Similarly, thesolution isalcohol by mass, so it containsgrams of alcohol. Thus, the finalsolution containsgrams of alcohol, so, or, of it is alcohol.

  2.The correct answer is D

  Explanation

  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.)

  3.The correct answer is E

  Explanation

  The quantitycan be expressed as. If, thenand. Since, eitheroror both. Therefore, statementmust be true, but statement,, is not always true. For statement, you can write, and since, it follows that. Therefore, both statementsandmust be true.

  4.The correct answer is D

  Explanation

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

  It follows that.

  5.The correct answer is D

  Explanation

  By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Therefore,, or. Thus,, which eliminates options (A), (B), and (C). Also by the Triangle Inequality,, or, which eliminates choice (E). Therefore, of the given choices, only choice (D),, could be the length of side.

  6.The correct answer is B

  Explanation

  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. Therefore,. Since bothandequal, they are equal to each other. Statementis true.

  Consider statement,. The left 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.

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本文关键字: SAT数学考点 SAT数学难题

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