SAT2数学Level_2常用公式

2 2
Ax1 By1 C A2 B 2
Tan =
m1 m2 （m is the slope of l.） 1 m1m2
x
b b2 4ac 2a
b a c Product of zeros (roots)= a
Sum of zeros (roots)= TRIGONOMETRIC FUNCTIONS Graphs:
10.sin 2 A 2sin A cos A 11.cos 2 A cos 2 A sin 2 A 12.cos 2 A 2 cos 2 A 1 13.cos 2 A 1 2sin 2 A 2 tan A 14.tan 2 A 1 tan 2 A 1 1 cos A 15.sin A 2 2 1 1 cos A 16.cos A 2 2 1 1 cos A A 2 1 cos A 1 cos A 18. sin A sin A 19. 1 cos A 17.tan

sine
6 1 2
or 30

4
or 45

3
or 60
2 2 2 2
1
3 2
cosine
3 2 3 3
3
1 2
3
tangent
cotangent
1
3 2
secant
2 3 3
2
2
2
cosecant
2
2 3 3
Formulas:
1.sin 2 x cos 2 x 1 2.tan x 2 1 sec2 x 3.cot 2 x 1 csc 2 x 4.sin( A B) sin A cos B cos A sin B 5.sin( A B) sin A cos B cos A sin B 6.cos( A B) cos A cos B sin A sin B 7.cos( A B) cos A cos B sin A sin B tan A tan B 8.tan( A B) 1 tan A tan B tan A tan B 9.tan( A B) 1 tan A tan B
Circular permutation (e.g., beads on a bracelet) of n elements=
n
Pr
n! n r !
n n Pr the product of the largest r factors of n! r! r r!
y A f ( Bx C ) A is the amplitude f is the period of the graph B C is the phase shift B
sin csc 1 cos sec 1 tan cot 1 sin tan cos cos cot sin
Parabola: if C=0, ( x h) 4 p( y k ) opens up and down---axis of symmetry is vertical
2
if A=0, ( y k ) 4 p( x h) opens to the side---axis of symmetry is horizontal
SAT II 数学 Level II 常用公式
MATH LEVEL II
INTRODUCTION TO FUNCTIONS (f+g)(x)=f(x)+g(x) (f·g)(x)=f(x)·g(x) (f/g)(x)=f(x)/g(x) (f g)(x)=f(x) g(x)=f(g(x)) POLYNOMIAL FUNCTIONS Linear Functions Distance= (x1 -x 2 ) +(y1 -y2 ) Distance=
Greatest Integer Functions:
x i, where i is an interger and i x i 1
Polar Coordinates:
x r cos y r sin x2 y 2 r 2
MISCELLANEOUS TOPICS
*The correct sign for Formulas 15 through 17is determined by the quadrant in which angle Triangles Law of sines:
1 A lies. 2
sin A sin B sin C a b c
MISCELLANEOUS RELATIONS AND FUNCTIONS The general quadratic equation
Ax 2 Bxy Cy 2 百度文库Dx Ey F 0
If B 4 AC 0 and A C , the graph is a circle.
Probability: Independent events: P( A B) P( A) P( B) Mutually exclusive events:
P( A B) 0 and P ( A B ) P ( A) P ( B )
Sequences and Series In general, an arithmetic sequence is denoted by
Sn t1 (1 r n ) 1 r
lim Sn
n
t1 1 r

Geometry and Vectors If V (v1 , v2 ) and U (u1 , u2 ) ,

U V (u1 v1 , u2 v 2 )
2
Equation of axis of symmetry: x=h if vertical y=k if horizontal Focus: p units along the axis of symmetry from vertex Equation of directrix: y=-p if axis of symmetry is vertical x=-p if axis of symmetry is horizontal Eccentricity=
n ! n(n 1)(n 2)...3 2 1
Permutations: Circular permutation (e.g., around a table) of n elements= (n 1)!
(n 1)! 2 n! Permutations of n elements with a repetitions and with b repetitions= a !b !
Vertices: a units along major axis from center Foci: c units along major axis from center Length=2b Eccentricity=
c <1 a
2b 2 Length of latus rectum= a
2
If B 4 AC 0 and A C , the graph is an ellipse.
2
If B 4 AC 0 , the graph is a parabola.
2
If B 4 AC 0 , the graph is a hyperbola.
2
Circle:
( x h) 2 ( y k ) 2 r 2
Quadrant Function: sin,csc cos,sec tan,cot Arcs and Angles I + + + II + III + IV + -
s r 1 A r 2 2
Special Angles 0 sine cosine tangent cotangent secant cosecant 0 1 0 und 1 und
The number of combinations of n things taken r at a time is denoted by
n
n Cr or C(n,r) or . r
n n r nr
Binomial Theorem:
Tr 1 n Cr a nr br
a 2 b 2 c 2 2bc cos A
Law of cosines: b a c 2ac cos B
2 2 2
c 2 a 2 b 2 2ab cos C
1 Area bc sin A 2 1 Area of a : Area ac sin B 2 1 Area ab sin C 2
Ellipse:
( x h) 2 ( y k ) 2 if C>A, 1 , transverse axis horizontal a2 b2
if C<A,
( x h) 2 ( y k ) 2 1 , transverse axis vertical, where a 2 b2 c 2 2 2 b a
a b (vertical)or (horizontal). b a
the slopes of the asymptotes are
Exponential and Logarithmic Functions
x a x b x a b x0 1 xa x a b b x 1 xa a x a b ( x ) x ab x a y a ( xy ) a log b ( p q ) log b p log b q log b 1 0 b logb p p p log b log b p log b q q log b b 1 log b ( p x ) x log b p log b p log a p log a b
2
1 0 und 0 und 1

0 -1 0 und -1 und
3 2
-1 0 und 0 und -1
2 0 1 0 und 1 und
*und: means that the function is undefined because the definition of the function necessitates division by zero.
t1 , t1 d , t1 2d , t1 3d ......t1 (n 1) d
Sn or
n (t1 tn ) 2
n Sn [2t1 (n 1)d ] 2
In general, a geometric sequence is denoted by
t1 , t1r, t1r 2 , t1r 3 ,..., t1r n1
Vertices: a units along the transverse axis from center Foci: c units along the transverse from center Length of latus rectum= Eccentricity=
2b 2 a
c >1 a
c =1 a
Length of latus rectum=4p Hyperbola:
( x h) 2 ( y k ) 2 1 , transverse axis horizontal a2 b2 ( y k ) 2 ( x h) 2 1 , transverse axis vertical, where c 2 a 2 b2 a2 b2