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两道SAT数学题及解法

  下面为大家介绍的是两道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 stopping distance of a car is the number of feet that the car travels after the driver starts applying the brakes. The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied. If the car’s stopping distance for an initial speed of 20miles per hour is 17feet, what is its stopping distance for an initial speed of 40miles per hour? 

  Answer Choices

  (A) 34feet 

  (B) 51feet 

  (C) 60feet 

  (D) 68feet 

  (E) 85feet 

  2、If kis divisible by 2, 3, and 15, which of the following is also divisible by these numbers? 

  Answer Choices

  (A) k + 5 

  (B) k + 15 

  (C) k + 20 

  (D) k + 30 

  (E) k + 45 

  Explanation:

  1、The correct answer is D

  The stopping distance is directly proportional to the square of the initial speed of the car. If srepresents the initial speed of the car, in miles per hour, and drepresents the stopping distance, you have that the stopping distance is a function of sand that function d of s = c times (s^2), where cis a constant. Since the car’s stopping distance is 17feet for an initial speed of 20miles per hour, you know that 17 = c times 20^2. Therefore, c = 17 over 20^2 = 0.0425, and the car's stopping distance for an initial speed of 40miles per hour is 0.0425 times 40^2 = 68feet. 

  2、The correct answer is D

  Since kis divisible by 2, 3, and 15, kmust be a multiple of 30, as 30is the least common multiple of 2, 3, and 15. Some multiples of 30are 0, 30, 60, 90, and 120

  If you add two multiples of 30, the sum will also be a multiple of 30. For example, 60and 90are multiples of 30and their sum, 150, is also a multiple of 30

  If you add a multiple of 30to a number that is not a multiple of 30, the sum will not be a multiple of 30. For example, 60is a multiple of 30and 45is not. Their sum, 105, is not a multiple of 30

  The question asks which answer choice is divisible by 2, 3, and 15; that is, which answer choice is a multiple of 30. All the answer choices are in the form of "kplus a number." Only choice (D), k + 30, has kadded to a multiple of 30. The sum of kand 30is also a multiple of 30, so the correct answer is choice (D).

  以上就是这两道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。

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