一、概率论
以下对SAT数学概率论部分的常用解题技巧进行了总结，供大家参考。
(1)In the integer 3589 the digits are all different and increase from left to right. How many integers between 4000 and 5000 have digits that are all different and that increased from left to right?
比较题目：
(2)In the integer 3589 the digits are all different and increase from left to right. How many integers between 30000 and 50000 have digits that are all different and that increased from left to right?
(3)If p, r, m are three different prime numbers greater than 2, and n=p*r* m, how many positive factors, including 1 and n, does n have?
比较题目：
(4)If p, r, m, n, t and s are six different prime numbers greater than 2, and n=p*r*s*m*n*t, how many positive factors, including 1 and n, does n have?
(5)If someone throws a dice twice, on the first time he gets a points, and on the second he gets b points, what is the probability a/b>1?
比较题目：
(6)If someone throws a dice twice, what is the probability that the point he gets on one throw is bigger than the other?
(7) Mr. Jones must choose 4 of the following 5 flavors of jellybean: apple, berry, coconut, kumquat, and lemon, How many different combinations of flavors can Mr. Jones choose?
二、代数
ARITHMETIC
A. Whole numbers
1. Operations—addition, subtraction, multiplication, division
2. Prime and composite numbers
3. Factors and divisors
B. Fractions
1 Types—proper, improper, mixed numbers
2 Operations
C. Decimals
1 Operations
2 Conversions
a) Decimals to fractions
b) Fractions to decimals
3 Rounding and approximation
4 Powers of 10
a) Multiplication
b) Division
c) Scientific notation
D. Percent
1 Conversions
a) Percent to decimal
b) Decimal to percent
2 Percent problems
E Ratio and proportion
F Square roots
G. Averages
H Metric measurement
三、几何
1. 椭圆(很少用到，知道就可以了)
1)周长公式：L=2πb+4(a-b)
椭圆周长定理：椭圆的周长等于该椭圆短半轴长为半径的圆周长(2πb)加上四倍的该椭圆长半轴长(a)与短半轴长(b)的差。
2)面积公式 ：S=πab
椭圆面积定理：椭圆的面积等于圆周率(π)乘该椭圆长半轴长(a)与短半轴长(b)的乘积。
2. 菱形面积=对角线乘积的一半，即S=(a×b)÷2
3. 三角形面积：
1)已知三角形底a，高h，则S=ah/2
2)已知三角形三边a,b,c,半周长p,则
S= √[p(p - a)(p - b)(p - c)] (海伦公式)
3)已知三角形两边a,b,这两边夹角C，则S=absinC/2
4)已知三角形半周长p，内接圆半径r，则S=pr
4.扇形面积：
圆心角为n°，半径为r的扇形面积为(n/360)×π(r^2)
如果其顶角采用弧度单位，则可简化为1/2×弧度×半径平方。
扇形还与三角形有相似之处，上述简化的面积公式亦可看成：1/2×弧长×半径，与三角形面积：1/2×底×高相似。
5.梯形面积：[(上底+下底)×高] / 2
6.矩形面积：长×宽
7. 梯形体积
V=〔S1+S2+√(S1*S2)〕/3*H )
(V：体积;S1：上表面积;S2：下表面积;H：高)
8. 圆柱体体积：V圆柱=S底×h
9.长方体体积：V=长×宽×高
10.正方体体积：V=棱长^3
11.圆锥体体积: V=1/3×S底×h
四、三角函数
1)两角和公式
sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan(A-B)=(tanA-tanB)/(1+tanAtanB)
cot(A+B)=(cotAcotB-1)/(cotB+cotA) cot(A-B)=(cotAcotB+1)/(cotB-cotA)
2)倍角公式
tan2A=2tanA/[1-(tan^2)A]
cot2A=[(cot^2)A-1]/2cotA
cos2A=cos^2A-sin^2=2(cos^2)A-1=1-2(sin^2)A
sin2A=2sinAcosA
3)半角公式
sin(A/2)=√((1-cosA)/2) sin(A/2)=-√((1-cosA)/2)
cos(A/2)=√((1+cosA)/2) cos(A/2)=-√((1+cosA)/2)
tan(A/2)=(+&-)√((1-cosA)/((1+cosA))=√(sinA/(1+cosA)) =√((1-cosA)/sinA)
cot(A/2)=(+&-)√((1+cosA)/((1-cosA))
4)和差化积
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)-sin(A-B) -2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB=2sin((A+B)/2)cos((A-B)/2)
cosA+cosB=2cos((A+B)/2)cos((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB tanA-tanB=sin(A-B)/cosAcosB
cotA+cotBsin(A+B)/sinAsinB -cotA+cotBsin(A+B)/sinAsinB
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