数学知识点清扫

比较1001^(1/3)和1001/100的大小

[优化思路]两者相除比较商和1的大小

Quadrilateral ABCD is a parallelogram,r=2,and ∠DAB=45,what is the area of the shaded region?

[优化思路]两边相等平行四边形是菱形

The coordinates of three points in an x-y rectangular coordinate system are (0,3), (3,3b) and (b,3) respectively (b is a constant). If the area of the triangle is 18 when connecting the three coordinates, then b equals? A:4 B:2 C:-1 D:-2 E:-3

[优化思路]从选项出发画图，表示出来的面积公式会比较清晰。

The sum of three different positive integers is 11.Which two of the following statements together provide sufficient information to determine the three integers? A：None of those three can be 1 B：None of those three can be 4 C：None of those three can be 7 D：None of those three can be 8

[优化思路]列出所有组合，真的不多，然后对比一下去掉哪两个数字之后只剩一组，就说明是哪两个数字。

The probability that each toss of a certain coin will result in heads is 0.5. If the probability that n tosses of the coin will each result in heads is greater than 0.0002, what is the greatest possible value of n?

[优化思路]即求2^n<5000的最大n值

Point A and point B are the centers of two circles, and their radius are 10 and 3 respectively. Point C and point D and the points of tangency of the two circles and a horizontal line. Point E and point F are the intersections between the two circles and line AB, EF=12, what is the length of CD?

[优化思路]梯形补成四边形是常见辅助线

-1/2p和-1/3p比大小

[优化思路]直接plug in numbers正数负数各来一组就可以。不要思考作商的问题了，除一个负数是要变号的

√7+√11和√3+√15比较

[优化思路]直接计算器

In triangle ABC, the length of side AB is 13, the length of side AC is 15, and the length of side BC is 14. What is the length of the height that corresponds to the base BC?

[优化思路]要对13/15这一类勾股数敏感，即使没有想起来是两个特殊直角三角形，但也可以通过a^2+b^2=13^2，(14-a)^2+b^2=15^2两个式子联立得出ab。

As shown in the following figure, there is a vertical wall surface in the figure. The distance from point P to left edge is 10m, and the distance from point P to bottom edge is 10m. A barrel of pigment can be used to brush 170m2 of the wall`s surface. If the barrel of pigment is used to brush the wall vertically from left edge, the total width of the surface that has been brushed to the left edge is x m, what is the range of x?

[优化思路]首先理解图片即墙面。其次，已知左边的梯形有150了，并且不要求准确答案，那么可以右边切高位1的一小块一小块试探，发现一块比20少，两块比20多，所以在21-22之间

The reciprocal of x-2 is x+3. What is the product of all the possible values of x?

[优化思路，补充]解得x^2+x-7=0。根据韦达定理，两根之积=c/a=-7。复习韦达定理：x₁+x₂=-b/a，x₁x₂=c/a。

There are 4 fiction books and 6 non-fiction ones, while 3 of the non-fiction are biographies. Now choose 3 books from the total 10 books. What is the probability of at least one fiction and no more than 1 biography are selected?

[分类别偷懒]用组合的思路写,0B1F=12,0B2F=18,0B3F=4,1B1F=36,1B2F=18,一共88种可行的，随机组合是C3\10=120，所以88/120=11/15

The number of ordered triples (x1, x2, x3), where x1, x2 and x3 are non-negative integers such that x1+x2+x3=9

[别忘记0]带0的有27种，其他的28种，一共55

Alice weighs a kilograms, and Bob weighs b kilograms less than Alice.ab ≠ 0 Quantity A: The sum of Alice'sweight and Bob'sweight Quantity B: 2a kilograms

[别想多]美国人说b kg less就代表一定是less。别考虑b小于0的情况了。

(y - 1)(y + 5) = 0 Quantity A：y Quantity B：3

[别跳步]得到y=1或-5。不论哪一个都！比！3！小！

1/3<x/y<2/3, y=6, 判断x和3的大小关系

[别跳步！]又没说x为整数，从不等式只能得出范围，所以关系不一定。

What is the sum of all possible solutions of the equation |x+4|^2 -10|x+4|=24

[十字相乘！] k^2-10k-24=(k-12)(k+2)！！！不要拆成别的东西。以及得出的两个解12和-2要舍去后者因为K>0

A hexagon is inscribed in a circle with diameter d.Each of the six sides of the hexagon have the same length, and each of the six angles of the hexagon have the same measure. What is the perimeter of the hexagon in terms of d?

[可优化思路]圆的内切正六边形，不就是六个等边三角形堆起来嘛，每条边长都等于半径，所以6*d/2=3d就好啦

Set A={9, 13, 4, 2, 7}Set B={9, 13, 4, 2, 9}Set C={9, 13, 4, 2, 4}Set D={9, 13, 4, 2, 6}Which of the following statement illustrates the exact order of standard deviation of these sets of numbers from the lowest to the greatest?

[可优化思路]果断一点算出固定那四个的平均数为7。第五个数离7约近标准差越小

If the probability for each cannon shoots the target is 0.6, how many cannons shoot together can you ensure the overall probability of shooting the target reach 0.99?

[可优化思路]用倒算考虑更快捷。n个人不命中的几率是（0.4）^n，当n>=6时这个几率<0.01，所以六次及以后都可以

Between two similar pentagons, the length of each side of the smaller pentagon is half of the larger one. If the area of the larger pentagon is 1/3, then the area of the smaller pentagon is?

[可优化思路]误打误撞使用的思路就很好，不管它是多少边形，按照四边形的比例算就对了，因为不管多少边形都能分割成三（四）角形

y=2x+1, where x > 0. Quantity A：The percent increase in the value of y when the value of x is increased by 10% Quantity B：10%

[复查选项！]到下一题之前一定要重新check想选的是那个，选上去了哪个！别选错了也太亏了

Each student in a school takes either the French class or Spanish class, but not both. Each class has some male and some female students. The ratio of the number of female students to the number of male students is less for Spanish class than for French class. Quantity A：The ratio of the number of female students to the number of male students in French class Quantity B：The ratio of the number of female students to the number of male students in the school

[审题+优化思路]提供对比的那一句是在说ratio(S)<ratio(F)别看错了，可以按照这样写下来。解题则使用糖水思考，一杯浓糖水跟一杯稀糖水混合，最后的浓度一定在二者之间

If x ≥ 0, y ≥ 0, and x^2+y^2=1, is x+y ≥ 1 must be true? ？

[审题]=1说明点在圆上！圆内就不管了！那个1/4弧是在y=-x+1之外的

In a right circular cylinder, the radius of the base circle is 1, the height is 8. Quantity A: The outside area (top ,down and lateral surface) of a section of the cylinder with a central angle of 100°. Quantity B: 5π.

[审题]QA是包括上下底面积的！

In region A, 17 percent of the acres that are planted with corn are planted with a certain hybrid seed. In region B, which borders region A, 11 percent of the acres that are planted with corn are planted with the same hybrid seed. Quantity A：Of all the acres planted with corn in region A and region B combined, the percent of acres that are planted with the hybrid seed Quantity B：14%

[审题]borders是接壤！不是更宽的意思！所以没有办法比较因为不知RA和RB的面积。

A set of k consecutive integers, including 2. The sum of the integers in the set is -11. Quantity A：k Quantity B：10

[审题]consecutive integers连续整数。那就是哪几个连续负数加起来是-11，其他的都正负抵掉就是

if a is an integer and b = a+6/2, what's the least possible value of a for which b is greater than 20?

[审题]greater than代表大于，不是大于等于。看到这个词就马上提醒自己，边缘不可以。易求出a>34所以a=35。

From 1976 to 1992, the greatest increase in expenditures in millions of dollars occurred during which two-year period?

[审题]greatest increase in expenditures只是问增长的值没有问率或者其他的，读题即可

If the sum of 5 times a number x and 7 is squared, the result is y.

[审题]y=(5x+7)^2

There are a total of 40 red, yellow or blue balls in a box. Each ball is marked with a number out of 1, 2, 3 and 4 on the side. The figure in the shaded area below each shows the number of balls in that category. For example, the number of red balls marked with the number "1" is 12. What is the minimum number of balls to be taken out of the box to ensure that you have at least one ball of each color and at least one ball of each marked number?

[审题]要求的是最坏情况！！其中的最大值肯定是的最小值。

Which of the following is an equation of a line that does NOT contain any points in the xy-plane for which both coordinates are integers? A：y=4 B：y=12x C：y=x+3 D：y=x+12 E：y=12x+3

[审题]这一题在问，是否所有线上的点横纵坐标都不能同时为整数。固定几个x为整数思考y喽举反例，如果能找出y为整数就pass

In the △ABC, AE= 1/3AC, AD=1/3 AB, BF=1/3 BC, what is the ratio of the area of the shaded region to the area of △ABC?Give your answer in fraction.

[审题]问的是阴影面积啊姐姐！

Sara drove from her company to her home at a constant speed of 55 kilometers per hour for two hours, and then drove another 2.2 hours at a constant speed of 65 kilometers per hour. Then how many more minutes did she need to drive from her company to her home at a constant speed of 50 kilometers per hour?

[审题！单位]结论问的是【多】多少【分钟】。所以不可以回答总时间也不可以回答多少小时。记住是先/50（速度）得到总小时数-4.2（原时间）再x60（分钟）

At least how much money will it cost to fill a rectangular solid pit featuring a length, width and height of 12 feet, 8 feet and 4 inches with 3.5-cubic-feet sized concrete bags that cost $6 each? (1 foot=12 inches)______dollars

[应用题常见坑]水泥只能买整袋整袋的，算出来需要9.14袋所以得买10袋，10*6=60元。

(5^3)w+(5^2)x+5y+z=264In the equation shown,w, x, y and z are integers that are no less than 0 and no greater than 5. What is the sum of w+x+y+z? A5 B6 C8 D9 E10 F12

[思路]其实并没有很多wxyz供选择，只有两组而已，point is找出这两组然后明白其他为什么不可能

In a sequence of 700 integers, each term after the first two terms is the sum of the two preceding terms.Which of the following could be the number of odd integers in the sequence? A0 B2 C233 D234 E350 F466 G467 H698

[思路]对于前两项的奇偶一共有四种可能，偶偶，奇奇，奇偶，偶奇。由此可以算出三个答案AFG

If a, b, c are three consecutive positive even integers, which of the following must be an integer? A(a+b+c)/2 B(a+b+c)/4 C(a+b+c)/6 D(a+b+c)/12 E(a+b+c)/15

[思路]很明显可知2和6是可除的，但是既然知道4不行，为什么会觉得12可以呢？

Tickets for a carnival are sold either individually or in packages of 10 tickets or 20 tickets at the costs shown in the table. A group of friends bought n tickets for the least possible total cost. A second group of friends bought more than n tickets for a total cost that was less than the first group`s total cost. Which of the following could be the value of n? A8 B9 C11 D12 E16 F17 G18 H19

[思路]首先要明白有两个临界点。然后 ①x＜10时，11＜1.25x，解得x只能取9 ②10<x<20时，20＜11+(x-10)1.25，解得x只能取18、19

Several parents take their children to the park and need to buy tickets and food. The ticket price for each parent is 20 dollars and the ticket price for each child is 10 dollars. The number of parents is equal to the number of children. The total cost of tickets is 420 dollars. The average cost for food and ticket is 21 dollars, how much do they pay for food?

[思路捋清晰，草稿打清晰]420/30=14人，得出的结果代表大人14小孩14，所以一共【28】人！其他没问题

The remainder is 30 when 6n is divided by 75, which of the following could be the remainder when 7n is divided by 75? A5 B10 C15 D25 E35 F45 G60

[思路真的得好好想明白]设6n除75的商为m, 6n=75m+30, 等式两侧同乘7/6，那么7n=( 175/2)m+35，此处因为7n是整数所以m只能为2的倍数。。。然后多算几个就是发现循环 当m=0, 7n=35，除75的余数为35 当m=2, 7n=210，除75的余数为60 当m=4，7n=385，除75的余数为10 当m=6, 7n=560，除75的余数为35

A machine works at a constant rate and can produce a bolts in 15 minutes and b bolts in c hours. Quantity A:b Quantity B:3ac

[思路要清晰]有两个未知数，效率和时间，两个关系不可以混为一谈。最后a=k,b=4kh,c=h

The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true? A：The price of the book was less than $9.50. B：The price of the book was greater than $6.90. C：The sales tax was less than $0.45.

[思路要清晰，可优化]首先10/1.04确定P上界，7/1.04确定P下界，tax的范围就用P范围确定即可

p and n are positive integers less than 30. p is a prime number, while n is not a prime number.Which of the following CANNOT be the sum of n and p?Indicate all such numbers. A48 B50 C52 D54 E56

[整理思路]首先列出30内所有质数。然后根据答案往回退，48可以是19+29但这俩质数之间有个23，所以也可以是23+25所以得排除。50，54,56可以任意一个质数去凑。52只能23+29,两者中间没有别的质数了并且29也是最大的因此这一项没别的选择，凑不出。选它。

给出函数图象判断函数表达式的题

[明确思路]①x=0看y轴交点。②从x轴交点判断十字分解拆出来的两个解，记住-5代表有（x+5）而不是，，，

In the square above, the side is 10, and points, P, Q, O, and R are all midpoints of each side. What is the area of the shaded region?

[易错知识点]勾股数12√5，一定要对1的那一边做称的基础。所以这边斜边是5√5，不是10哦。

Each student in a school takes either the French class or Spanish class, but not both. Each class has some male and some female students. The ratio of the number of female students to the number of male students is less for Spanish class than for French class. A：The ratio in French class。B：The ratio in the school

[检查答案]确定选择的答案跟自己想的答案是一样的，不能再选错啦

Machine A and machine B, working simultaneously and independently at their respective constant rates, processed 34 of the shipment of a certain product in 4.5 hours. Then machine A, working alone at its constant rate, processed the rest of the shipment in 6 hours. How many hours would it have taken machine B, working alone at its constant rate, to process the entire shipment of the product?_____hours

[理清楚思路]一定要在【同一个时间长度内】由总效率和A效率推B效率

What is the remainder when 223^4−223^3+223^2−223 is divided by 221?

[理解一下思路]

n, k and r are all positive integersIf n^k=10r+3, then k could be? A11 B12 C13 D15 E17 F19

[理解一下思路]10r+3这种形式就说明了个位数确定是3。然后从n的某个幂要得到3为个位的数字，推出n的个位一定是3或者7

40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. How many ways can these DVDs be arranged?

[理解题意+思路]chronological按照时间顺序的。理解这40张DVD可以随机排列所以是40!但是对于每一个排列中的History只会有一种排序但我们算了9!次所以要除掉，答案是40!/9!

Among Event A, Event B and Event C, Event B and Event C are mutually exclusive.0 < P(A) < 1, P(A)=2P(B)=3P(C). Compare 2/3P(A) and P(B or C)

[理解题意+思路]mutually exclusive互斥。别被互斥这个条件干扰了，假设A=0.6，得到B=0.3，C=0.2即可完成比较，互斥仅用于计算P(B or C)=0.5而已

All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid certification?

[理解题意] all but 4 of the counselors have certification意思是有4个人啥证书也没有。属于non类。以及重复的只需要减一遍就可以

If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members?

[理解题意]S集合包含n个数字，一共有6个包含两个元素的子集 即n!/2!=6得n=4

The median of 7 positive integers is 10, and the average of these 7 numbers is 9. The only mode is 2. What is the greatest possible number in the set?

[理解题意]mode众数。可以直接购造出2,2,2,10,10,11,26的数列

Which of the following numbers satisfy their sum of reciprocals is either less than 1/3 or greater than 1/2 ? A：1 and 14 B：3 and 12 C：5 and 10 D：7 and 8

[理解题意]reciprocal倒数。所以这题求倒数和。

For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the measurement 17.5 is 3.0 deviations above the mean. What is the mean of the of distribution?

[理解题意]standard deviations和deviations都是指标准差。所以别想复杂，就是让你设标准差为x，从题目数据得出3x+1.5x= 17.5-12.1，得出x=1.2，平均数等于17.5-3*1.2=13.9

What is the tens digit of 21^(3^50)?

[理解题意]tens digit个位数字。

|1-|x-250||=1 What`s the number of all the possible values of x?

[理解题意]the number of问的是个数。易得x=248,252,250。所以答案是3。

Evelyn invests $5,000 in a savings account that pays interest at a rate of 6.7% compounded annually. If she withdraws half the interest earned at the end of the third year, approximately how much additional interest does she earn during the fourth year?

[理解题意]在第三年结束的时候她取出的是之前【三年获得的利息总和】的一半。

Which of the following shaded regions represents the set of all points (a,b) in the xy-plane above such that (a+1, b+1) is in quadrant 1? (note that a point lies on axis is not in any quadrant)

[理解题意]是想问能让哪些ab能让（a+1,b+1）的点落在第一象限，所以ab都可以有一点小于1的地方

（部分题目）For how many of the four incentives listed does each of the companies surveyed that offers this incentive also offer a health-insurance benefit?

[理解题意]这个长难句的主句是How many (I) that each of the companies offers (b)。提供Bonus plan的公司中有一家不提供健康保险，提供其他I的公司都提供健康保险，所以是3家

Alice and Eddie are each flying a kite on level ground. A taut string extends from Alice's hand to her kite so that the length of the string between the end A in her hand and the end X attached to her kite is 105 meters and A is 2 meters above the ground. A taut string extends from Eddie's hand to his kite so that the length of the string between the end B in his hand and the end Y attached to his kite is 110 meters and B is 1 meter above the ground. At a certain moment, when X and Y are directly above each other, the point on the ground directly below X and Y is 5 meters and 45 meters, respectively, from the points on the ground directly below A and B. Which of the following statements is true about the relative heights of X and Y above the ground at that moment?

[理解题意]这句话At a certain moment, when X and Y are directly above each other, the point on the ground directly below X and Y is 5 meters and 45 meters, respectively, from the points on the ground directly below A and B.意思是在这时刻风筝落点到两个人的位置距离分别是5和45。理解之后就是辅助线+勾股定理算就对了

How many digits lie between the decimal point and the first even digit after the decimal point in the decimal equivalent of 1/(2^8*5^3)?

[理解题意]问小数点后面的第几位是偶数。0也是偶数。①有计算器可以按一下②分子只要大于10第一位就一定是0

The ratio of the number of companies offering both a stock-options incentive and one of the benefits listed to the number of companies offering that benefit is greatest for which of the five benefits?

[理解题意]问题问，提供SO和某种I的公司/提供某种I的公司总数，这个比例，哪种I大。以及看好SO在哪一行 [服了自己，黄豆流汗]

A group of 10 couples plans to rent bayside summer houses on Island X from Realtor M for a certain week. The total rental cost for the houses will be evenly distributed among the 10 couples, and each couple will have their own bedroom. If Realtor M has at least three bayside summer houses of each type available that week, what is the least possible rental cost per couple? A$400 B$300 C$240 D$220 E$190

[理解题意]题目问的是【possible rental cost中最小的】，不是最不可能的cost。

Quantity A：The number of tenths equal to 1.4 Quantity B：The number of hundredths equal to 1.3

[理解题意]题目问：A几个0.1合在一起等于1.4。B几个0.01合在一起等于1.3。显而易见14<130。

n is an integer greater than 10. Quantity A：The sum of the reciprocals of the first 2n positive integers Quantity B：1 more than the sum of the reciprocals of the first n positive integers

[理解题意]首先理解，reciprocal是倒数。那么就很简单，去掉相同的部分比较A和B，

A certain benefits and incentives package consists of 2 benefits to be chosen from the benefits offered by more than 1/2 of all the companies surveyed and 1 incentive to be chosen from the incentives offered by more than 1/3 of all the companies surveyed. How many such packages are possible?

[理解题意]首先，一共调查了600家公司（这个要理解啊！）B超过1/2即300的4家，I超过1/3即200的2家，4选2和2选1组合=6*2=12种

Set R={x, y, z, 2.7, 3.8, 5.5}Set S={x, y, z, -2.7, -3.8, -5.5}If the average (arithmetic mean) of the 6 numbers in list R is r and the average of the 6 numbers in list S is s, then r-s is the average of which of the following lists?

[看清楚问题+可优化思路]r-s=(R-S)/6=4, 然后在选项里找平均数是4的即可

What is the value of 0.9999999/1.0001-0.99999991/1.0003 ?

[知识点+优化思路]分子可以通过平方差公式拆成两个数相乘，正好可以跟分母约掉

How many positive factors does 1,575 have?

[知识点+优化思路]求因数个数方法：化简成质因数的幂次方形式，每个指数+1相乘就是因数个数。如1575=5^2 x 3^2 x 7^1。乘积=(2+1)(2+1)(1+1)=18。

The number 24 has the property that it is divisible by its units digit, 4. How many of the integers between 10 and 70 are divisible by their respective units digits?

[知识点+审题]首先。0不能做分母。其次，范围是10-70。因此从1-9各个结尾对应能被整出的数量为662362010

a/b=1/3, b/c=15/4, the relationship between a and c.

[知识点] a,c的比例是12a=15c易知，但负数和整数下大小比较是不同的

Which of the following must be a factor of the product of 5 consecutive positive integers?Indicate all such numbers. A2 B3 C4 D5 E6 F8 G9 H10

[知识点]2345没话说，当时第一反应其实是对的。这个数是这五个连续整数的【乘积】所以肯定足够大。23都有说明6有，24-8，25-10...

x is a positive integer. When x is divided by 2, 4, 6 or 8, the remainder is 1. Quantity A：x Quantity B：24

[知识点]25没问题。但是以后遇到这种余数题要把一句话敲进脑子里1（余数本身）除以任何大于它的数也是1啊

For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize?

[知识点]3σ原则：±σ=0.6827，±2σ=0.9545，±3σ=0.9973。以及换成百分数的时候也要小心一点位数。

比较77^7/7^77和11^7/7^70大小

[知识点]77^7拆出来是（11*7）^7，不要漏掉括号，两个项都有七次方

Anne pays 150 percent more for a wholesale widget than Bart pays. Anne's retail price per widget is 15 percent greater than the wholesale price she paid. Bart`s retail price per widget is 185 percent greater than the wholesale price he paid. Quantity A：Anne's retail price Quantity B：Bart's retail price

[知识点]A的第二个115%是在250%基础上再乘的！一定要用超过100%的标识不然很容易就加上去了！

The boxplot above summarizes a list of 240 numbers. Which of the following statements must be true?Indicate all such expressions. A：The list contains the number 60. B：The range of the numbers in the list is less than 4 times the intequartile range of the numbers. C：There were more numbers in the list that are less than 40 than there are numbers that are greater than 70.

[知识点]intequartile四分位数。箱型图从左到右的五个点是：下边缘，下四分位数，中位数，上四分位数，上边缘。5个点把所有数据分成4块，每一块的数据量为全部的1/4。

What is the maximum possible number of interior angles that are right angles of a convex decagon (10-sided polygon)?

[知识点]凸多边形有以下性质：①锐角不超过三个②所有角的外角（补角）和为360°

The ratio of the length of three sides of a triangle is 3:5:7. Quantity A: The degree of the largest angle in the triangle. Quantity B:84°.

[知识点]可以余弦定理cosA=(b^2+c^2-a^2)/2bc。或者直接简单判断3和5得出的直角边小于7，因此为钝角，必大于84°

How many integers from 1 to 2,000, inclusive, are both the square of an integer and the cube of an integer?

[知识点]同时是平方数和立方数即，是六次方数，所以从1^6开始算到哪个超2000。或者改进原本思路，平方数的立方也可以那就是1,4,9,16。一定一定要平方数，12是不可以的！

The probability distribution function f of a continuous random variable x is defined by f(x) = (2/13)*|x| for −3 ≤ x ≤ 2. Quantity A: The median of the distribution of X. Quantity B: -9/5

[知识点]横轴范围从-3到2，纵轴为f(x)，画出的两块三角形求总面积。在x=-9/5处画一条竖线分割成左右两块，两侧面积不相等，左边的梯形比总面积1/2小，说明分割点在-9/5右侧，因此A>B.

The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively. Quantity A：The value at the 75th percentile of the distribution of X. Quantity B：750.

[知识点]正态分配越靠近平均数的地方数据越多，已知750①750在平均数右侧②在650和850的正中间。可知<750的部分比>750的数据多,所以75%的地方会是比750小的数，A<B。

The probability that Event A occurs is 0.63, while the probability that Event B occurs is 0.58. What is the greatest probability that Event A and B both occurs?

[知识点]若AB独立，P(AB)=0.63*0.58=0.3654，若AB不独立，P(AB)最小0互斥，最大包含0.58。因此最大的可能性为0.58。

一个89°的角，对边和邻边比长短

[知识点]角越大对边越大，但89°有可能并不是最大角哦

The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length X and 5 circular arcs of length Y. What is the perimeter of the figure?

[知识点]连接五个圆的圆心，得到正五边形，每个内⻆∠MNO为108° ，而∠PON与∠QOM均为直⻆90°，以O为圆心一周360° ，倒推得每个圆弧b所对的圆心⻆为72° ，故五段圆弧b拼起来正好是一个半径为2的圆周 b 5b=2π·2=4π 。因此，5a+5b=4π+20。注意：1）面对多圆图形务必连接辅助线；2）切线与切点处半径垂直；3）弧长公式=(心角/360)*2πR

During which of the following two-year periods did Company X's total expenditures increase by at least 20% ?Indicate all such two-year periods.

[草稿写清楚]把算式和结果都写下来就不容易错了

In a water tank of 72 fishes, 1/3 are blackfin, 2/3 are whitefin. 1/2 have orange dots, while the rest 1/2 have brown dots. If 2/3 of whitefin have brown dots, then how many fishes in the water tank are orange-dotted blackfins?

[要看清楚问什么]72=24B+48W=36BR+36OR，WOR=48*1/3=16，BOR=36-16=20

Set T consists of the integers from 11 through 100, inclusive. Quantity A:4 times the number of integers in set T that are multiples of 4 Quantity B:5 times the number of integers in set T that are multiples of 5

[计算]5的倍数个数算错了，应该是18个。这样4x23>5x18没问题了

In the xy-plane, triangular region R is bounded by the lines x = 0, y = 0, and 4x + 3y = 60. Which of the following points lie inside region R ?Indicate all such points A(2, 18) B(5, 12) C(10, 7) D(12, 3) E(15, 2)

[计算]要么计算器要么手算就写完整步骤，3*18不要再算错了

Greg's weekly salary is $187,which is 15 percent less than Karla's weekly salary.If Karla's weekly salary increases by 10 percent,by what percent must Greg's weekly salary increase in order to equal Karla's new weekly salary?Give your answer to the nearest tenth of a percent.

[计算！]已知G=(1-0.15)K=0.85K,因此要求增长率a使得(1+a%)G=1.1K。

The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches. Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class?

[误打误撞写对]Range这里指极差。通过A项中知道男生最高比女生最高的高5.8inches，可知最矮在女生中并且可知男女生身高范围分布相对关系。其他项对极值判断都没有帮助。

In a distribution of 850 different measurements, x centimeters is at the 73rd percentile. If there are 68 measurements in the distribution that are greater than y centimeters but less than x centimeters, then y is approximately what percentile in the distribution?

[误打误撞写对]percentile百分位。850*73%=620.5,即621个数小于x，用68/850=8%可知y比x小8个百分位及73-8=65位

In 1991, of the revenue from grants went toward artist salaries, and of the remainder went toward administrative costs. How much more grant revenue, in dollars, went toward artist salaries than toward administrative costs?

[货币单位]$million要换成$

There are n positive integers. The sum of the numbers is greater than 48, while the arithmetic average of the numbers is 1.2. What is the least value of n?

[面对陷阱要头脑清晰！]不等式列出1.2n>48易知n>40，此处最小值为41。但是得记得此处的1.2n是n个整数的和所以一定得为整数。因此不可以为41，最小取到45.。

A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?

[题意理解]$1 for every 3即3:1。因此第一阶段机构筹9000，公司另外补贴9000*1/3=3000一共12000。第二阶段（x-9000）+(2/5)(x-9000)。两阶段加起来一共68000。因此最后得出x=49000

一定看清楚给的是diameter还是radius

很重要！

第二轮

第二轮