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SAT数学练习题(三)

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1. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

 

  A. 2.25

  B. 3

  C. 4

  D. 4.5

  E. 6

 

Correct Answer: D

 

Explanation:

 

(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral 9 - (2 x ? x 3 x 1.5) = 4.5

 

2. If n 0, which of the following must be greater than n?

 

  I 2n

  II n2

  III 2 – n

 

  A. I only

  B. II only

  C. I and II only

  D. II and III only

  E. None

 

Correct Answer: E

 

Explanation:

 

Remember that n could be positive negative or a fraction. Try out a few cases: In case I, if n is -1, then 2n is less than n. In case II, if n is a fraction such as ? then n2 will be less than n. In case III, if n is 2, then 2-n = 0, which is less than n. Therefore, none of the choices must be greater than n

 

3. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?

 

  A. 20

  B. 15

  C. 8

  D. 5

  E. 3.2

 

Correct Answer: C

 

Explanation:

 

If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8

 

4. n and p are integers greater than 1, 5n is the square of a number, 75np is the cube of a number. The smallest value for n + p is

 

  A. 14

  B. 18

  C. 20

  D. 30

  E. 50

  

Correct Answer: A

 

Explanation:

 

The smallest value for n such that 5n is a square is 5. 75np can now be written as 75 x 5 x p. This gives prime factors.... 3 x 5 x 5 x 5 x p To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9 n + p = 5 + 9 = 14


延伸阅读:

SAT语法技巧——完全倒装句

SAT语法技巧——部分倒装句

SAT数学选择题解题技巧


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