sat数学真题及答案解析（6）

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1. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?

A. f(-1)

B. f(0)

C. f(1)

D. f(3)

E. f(4)

Correct Answer: D

解析：

You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.sat

A (-1 + 2) / (-1-2) = -2 / 2 = -1;

B (0 + 2) / (0-2) = 2/ -2 = -1;

C (1 + 2) / (1-2) = 3/-1 = -3;

D (3 + 2) / (3-2) = 5/1 = 5;

E (4+ 2) / (4-2) = 6/2 = 3

If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.

2. 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

解析：

(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

3. 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

解析：

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

4. 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

解析：

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

5. 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

解析：

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