31. In the xy-plane, the point with coordinates (-6,-7) is the center of circle C. The point with coordinates (-6,5) lies inside C, and the point with coordinates (8,-7) lies outside C. If m is the radius of C and m is an integer, what is the value of m ?
m= ?
Ans: 13
解析：
点(-6.-7)与点(-6，-5)之间的距离
为7+5=12
点(-6,-5)在圆C内，所以圆半径
必须大于12
点(-6,-7)与点(8，-7)之间的距离为8+6=14
点(8,-7)在圆C外，所以圆半径必须小于14
圆C半径为整数，所以只能为13
解题要点：做几何题方法之一是尽可能精确的依照题意画出图形
32. If -m/19 is an even integer, which of the following must be true?
A. m is a negative number
B. m is a positive number
C. m is a prime number
D. m is an odd integer
E. m is an even integer
Ans: E
解析： -m/19=2k m=-38k=2(-19k) 为2的倍数，为偶整数
反例：A: k=-1，m=38为正数
B: k=1，m=-38为负数
C: A、B中m都不是质数
D: A、B中m都是偶整数
解题要点：善于将文字转化为数学形式，even integer=2k
33. The integer v is greater than1. If v is the square of an integer, which of the following numbers must also be the square of an integer?
Indicate all such numbers.
A 81v
B 25v+10√v+1
C 4v2+4√v+1
Ans: AB
解析： v=x2>1，x为整数，x=√v
A项：81v=92x2=(9x)2? B项：25v+10√v+1=(5√v+1)2=(5x+1)2
C项：4v2+4√v+1不可以化成 一个完全平方式，找反例
取v=4,4v2+4√v+1=73不是任何数的平方
解题要点：会画完全平方式
34. What is the least positive integer that is not a factor of 25! And is not a prime number?
A 26
B 28
C 36
D 56
E 58
Ans: E
解析： 25!=1*2*3……*24*25
A项：26=2*13
B项：28=2*14
C项：36=2*18
D项：56=2*28=4*14
E项：58=2*29
解题要点：将一个数分解成恰当的两个数的乘积
35. If 0
A 1<1/a<1/b
B 1/a<1<1/b
C 1/a<1/b<1
D 1/b<1<1/a
E 1/b<1/a<1
Ans: D
解析： 0
即01
b>1, 1/b<1
1/b<1<1/a
解题要点：倒数的概念和性质
36. Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?
Give your answer as a fraction.
Ans: 153/190
解析： 方法一
概率为C218 /C220 = 153/190
方法二
取第一个灯泡且该灯泡没坏的概率18/20
取第二个灯泡时，剩余灯泡共19个，从17个没坏的里面选1个
概率为17/19
根据乘法法则，所要求的概率为18/20*17/19=153/190
37. What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?
A 112
B 152
C 224
D 256
E 304
Ans: E
解析： 设矩形一长为x,矩形一面积为24x
矩形二的面积为64*48
24x=64*48 x=128
矩形一周长为2*128+2*24=304
解题要点：文字形式转化为代数关系，熟悉几何名词
38. In year Y, the population of Colorado was approximately half that of New Jersy, and the land area of Colorado was approximately 14 times that of New Jersy. The population density (number of persons per unit of land area) of Colorado in year Y was approximately how many times the population density of New Jersy?
A 1/28
B 1/14
C 1/7
D 1/4
E ?
Ans: A
解析： 设New Jersy (NJ) 的population为x, land area为y?
Colorado (C) 的population为0.5x, land area为14y?
Cpd : NJpd=0.5x/14y:x/y=1/28
解题要点：文字题理解题意，找到列出代数式的关键语句
涉及到比较时，选择合适的基准量
39. In the figure above, line k is parallel to line m. What is the value of y?
y=( )
Ans: 17.5°
解析： ∵ k∥m
∴ 2y°=35°
∴ y=17.5°
解题要点：方法——将题干信息添加到图中，根据几何关系列代数式
知识点——两直线平行，内错角相等
40. If , which of the following could be the value of y?
A 4
B 1
C -1
D -3
E -5
Ans: D
解析： 2(2y-3)=y(3-y)
4y-6=3y-y2
y2+y-6=0
(y+3)(y-2)=0
y=-3或2
解题要点：十字相乘法解分式方程，注意移向变号