SAT考试数学练习题 5

SAT是Scholastic Aptitude Test的缩写，是申请几乎所有美国大学必须参加的考试。通常，希望继续接受高等教育的高中生需要参加SAT考试，并且SAT考试得分是获取奖学金的重要标准之一。大部分美国大学要求SAT考试作为录取的条件并根据SAT得分授予奖学金。 

1. If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?

I 6

II 0

III -6

A. I only

B. I and II only

C. II and III only

D. I and III only

E. I, II and III

Correct Answer: A

解析:

Choice I is correct because f(x) = 6 when x=3. Choice II is incorrect because to make f(x) = 0, x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x² would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)

2. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

A. 48

B. 49

C. 50

D. 51

E. 52

Correct Answer: C

解析:

1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 50

3. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?

A. 23

B. 22

C. 18

D. 16

E. 14

Correct Answer: B

解析:

First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A + BC = 143. A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 22

4. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)

A. 6

B. 8

C. 10

D. 20

E. 40

Correct Answer: B

解析:

Total volume of water = 12 liters = 12 x 1000 cm3. The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 8

5. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?

A. 11/P + 6

B. P/11 +6

C. 17 - P/6

D. 17/P

E. 11.5P

Correct Answer: A

解析:

Let Ben’s age now be B. Anita’s age now is A. (A - 6) = P(B - 6)

But A is 17 and therefore 11 = P(B - 6). 11/P = B-6

(11/P) + 6 = B