【小站教育】GMAT数学笔记(2)

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a1

当∣q∣<1 时， s ?? ? 1 ? q

1 11 1例： ? 2 ? 3 ? ? ? ? ? ？

2 2

2 2

例： 0．373737…=? (将其转换成一个分数) 7．Sets: 集合 例 1：全班 50 个人，选音乐课的有 20 人，选体育课的有 18 人，两课都选的有 5 人，问两课都没选的几人？ 例 2： A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B sop. How many of the 200 households surveyed used both brands of soap? (A) 15 (B)20 (C)30 (D)40 (D)45 例 3：五个人排队，甲不能在首位，乙不能在末位，有几种不同的排法？

第三章 几何

1． Lines & planes 直线与平面

* 两直线平行并为第三条直线所截后，相应角的关系。 * 直线与平面的关系。

例：If n distinct planes intersect in a line, and another line L intersects one of these planes in a single point, what is the least number of these n planes that L could intersect?

(A) n (B) n－1 (C) n－2 (D) n/2 (E)(n－1)/2 2. Triangles 三角形 * 勾股定理：a2+b2=c2

* 构成三角形的条件：两边之和大于第三边。 * 三角形内部边和角的关系：大边对大角。 3. Quadrilaterals 四边形

* parallelogram(平行四边形) : 面积=a×h; 周长=2（a+b） * rectangle(矩形) : 面积=a×h; 周长=2（a+b） * square(正方形) : 面积=a2 ; 周长=4a * trapezoid(梯形) : 面积=（a+b）×h/2

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4. Circles 圆 * 面积=πR2 * 周长=2πR

5. Polygons 多边形 * 多边形内角和：（n-2）180o

6. Rectangular Solids 长方体 * 体积=a×b×c * 表面积=2（a×b+b×c+c×a） 7. Cubes 正方体 * 体积=a3

* 表面积=6a2

8. Cylinders 圆柱 * 体积=πR2h

* 表面积=2πR2+2πR×h 例：一个圆锥内接于一个半球，圆锥的底面与半球的底面重合，则圆锥的高与半 球的半径的比是多少？

9. Coordinate Geometry 解析几何

* 直线的标准方程：y=kx+b ；即斜截式，其中 k 为斜率 slope，b 为 y 轴截距

y-intercept

* 斜率的计算：K= (Y2-Y1)/( X2-X1) * 两点或一点加斜率确定一条直线。 * 两直线垂直，其斜率的乘积为－1。

第四章 统计

1. arithmetic mean (average) 算术平均值 1 n E= ? ai

n i ?1

2. median 中位数

* The median is the middle value of a list when the numbers are in order. * 先排序，后取中。 3. mode 众数

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* The mode of a list of numbers is the nmuber that occurs most frequently in the list.

* A list of numbers may have more than one mode. 4. expectation 期望 * 期望就是算术平均值。 5. deviation 偏差

di=ai-E 6. variance 方差

1 n 2D ?? ? ?ai ? E ??n i ?1

7. standard deviation 标准差

? ?? D

例：Ⅰ.72,73,74,75,76

Ⅱ.74,74,74,74,74 Ⅲ.62,74,74,74,89

The data sets Ⅰ, Ⅱ,and Ⅲ above are ordered from greatest standard deviation to least standard deviation in which of the following ? (A) Ⅰ,Ⅱ, Ⅲ (B) Ⅰ, Ⅲ,Ⅱ (C) Ⅱ, Ⅲ, Ⅰ (D) Ⅲ, Ⅰ,Ⅱ Ⅱ, Ⅰ

8. range 范围

* 最大数减去最小数所得的差就是该组数据的范围。 例 1：150, 200, 250, n

(E) Ⅲ,

Which of the following could be the median of the 4 integers listed above?

Ⅰ. 175 Ⅱ. 215 Ⅲ. 235

(A) Ⅰonly (B) Ⅱonly (C) Ⅰand Ⅱonly (D) Ⅱand Ⅲ only (E) Ⅰ,Ⅱ,and Ⅲ 例 2：The least and greatest numbers in a list of 7 real numbers are 2 and 20,respectively. The median of the list is 6,and the number 3 occurs most often in the list. Which of the following could be the average of the numbers in the list?

Ⅰ. 7 Ⅱ. 8.5 Ⅲ. 10.5

(A)Ⅰonly (B) ⅠandⅡonly (C) Ⅰand Ⅲ only (D) Ⅱand Ⅲ only (E) Ⅰ,

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Ⅱ,and Ⅲ

第五章 数据充分性题

*每道 DS 题的选项都是固定的：

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C BOTH statements TOGETHER are sufficient, but NEITHER statement

ALONE is sufficient.

D Each statement ALONE is sufficient.

E Statement (1) and (2) TOGETHER are not sufficient.(additional data are

needed).

* DS 题的本质是一种判断型的选择题，并非判断正误，而是判断根据条件给的信 息能否回答主题干里提出的问题。 *要注意的几大问题： <1> 唯一性 例：x=?

（1）x=2 （2）x2=4 <2> 否定性 例：x>0? （1）x2>0 （2）x3<0

<3> 不矛盾性 例：A，B 两车在长直道路上相对行驶，现距离为 500 英里，问多长时间后相遇？ (1) 其中一辆速度为 200 英里每小时。 (2) 其中一辆速度为 300 英里每小时。

<4> 独立性 例：x>0? （1）√x=5

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（2）x3<0

<1> If n is an integer, is n+1 odd? (1) n+2 is an even integer. (2) n-1 is an odd integer.

<2> In △PQR,if PQ=x, QR=x+2, PR=y, which of the three angles of △PQR

has the greatest degree measure?

(1) y=x+3 (2) x=2

<3> Tom, Jane, and Sue each purchased a new house . The average (arithmetic mean )price of the three houses was $120,000.What was the median price of the three houses?

(1) The price of Tom’s house was $110,000. (2) The price of Jane’s house was $120,000. <4> 3.2□△6, □=?

(1) 3.2□△6 四舍五入到十分位后是 3.2。

(2) 3.2□△6 四舍五入到百分位后是 3.24。

<5>If °represents one of the operations +, -,and ×,is k°(l +m)=(k°l)+(k°m)for all numbers k, l , and m?

(1) k°1 is not equal to 1°k for some numbers k. (2) °represents subtraction.

<6>On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average of the daily balances at the end of each of 30 days. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane’s account for the billing cycle?

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