Important Rules You Must Know For The SAT

With Real Sat Problems

Mr.Mohamed Abdallah 3/7/13 01119686808

Important rules you must know for the SAT

Prime numbers ¿{2 ,3 ,5 ,7 ,11 ,13 ,17 ,19 ,23 ,29 ,31 ,37 ,41 ,43 ,47 ,53 ,59 ,61 ,…}

2491

Slope of a line ¿y2− y1x2−x1

=riserun

D

1.9<x<2

1 | Page

Coins

$1 = 1 dollar = 100 cents

1 quarter = 25 cents

1 dime = 10 cents

1 nickel = 5 cents

1¢ = 1 penny = 1 cent

A

Page | 2

A

E

3 | Page

8.5

D

Page | 4

B

E

5 | Page

E

Page | 6

Distance between 2 points ¿√ (x2−x1)2+( y2− y1 )2

3, 25

Midpoint¿( x1+x22,y1+ y22 )

E

D

7 | Page

A

E

Nth term of an Arithmetic sequence an=a1+(n−1 ) ∙d

117

C

Page | 8

B

E

E

Nth term of a Geometric sequence an=a1 rn−1

1024

9 | Page

C

1/45

E

Page | 10

B

11 | Page

Volume of a cube ¿ L3

1000

E

Area of Cuboid ¿2 ∙ (L ∙W+W ∙H+H ∙L )→ Area of Cube ¿6 ∙ L2

D

D

Page | 12

D

A

C

Diagonal of Cuboid ¿√L2+W 2+h2→

Diagonal of Cube¿ L√3

13 | Page

E

D

D

Page | 14

Area of Trapezoid ¿ 12 (b1+b2 )h

B

Area of the right circular cylinder ¿2πr (h+r )

The largest possible area of a triangle with sides a ,b is ¿ a ∙b2

E

Area of equilateral triangle ¿ L2∙√34

15 | Page

In a circular sector θ°

360°= L2πr

= Aπ r2

{θ° isthemeasure of theCENTRAL angle

Lis thelengthof itsarcA the areaof the sector }

D

D

Page | 16

A

A

17 | Page

D

C

Page | 18

E

19 | Page

Sum of interior angles of a polygon¿ (n−2 ) ∙180°

Measure of each angle of a regular polygon ¿ (n−2 ) ∙180°

n

105

C

Page | 20

36

B

Sum of exterior angles of a polygon ¿360°

21 | Page

E

D

Page | 22

E

In any triangle with sides a ,b , c the following inequality must take place a−b<c<a+b

A

B

23 | Page

E

E

13, 14, 15

E

The valid values of x in the inequality a< x<b can be expressed as

|x−a+b2 |<b−a

2

Page | 24

A

Dv

A

25 | Page

C

C

The Average of values ¿ The∑ of valuesThenumber of values

Page | 26

D

1020

C

D

1/20, .05

3/8, .375

27 | Page

E

E

E

Page | 28

D

The Median of values ¿Themiddle value of ordered values

The order of Median of n values ¿ {( n2 )th

,( n2+1)th

if n is even

( n+12 )th

if nis odd }

29 | Page

A

A

109

Page | 30

D

D

1600

31 | Page

2

B

The Mode ¿The value ( s ) that most repeated

A

E

Page | 32

D

33 | Page

The Range of n values ¿Maximumvalue−Minimum value

D

In any arithmetic sequences: Median ¿Average ¿ Last term+First term2

Page | 34

B

B

35 | Page

QUADRATIC FUNCTION:

1-General Form: f ( x )=a x2+bx+c , a≠0 , Vertex¿(−b2a

, f (−b2a ))

B

E

Page | 36

A

37 | Page

B

2

Page | 38

2-Vertex Form: f ( x )=a(x−h)2+k ,a≠0 , Vertex ¿(h , k)

f ( x )=a(bx+c )2+d ,a≠0 , Vertex ¿(−cb

,d)

70

A

B

39 | Page

E

3-Factorized Form:f ( x )=a ( x−m ) ( x−n ) , a≠0 , Vertex ¿(m+n2

, f (m+n2 ))

C

2.73<X<3.45

E

Page | 40

E

7

E

41 | Page

TRANSFORMATIONS OF FUNCTION:

y=f (x )Reflection on the X−axis⇒

y=−f (x )

( x , y ) Reflectionon the X−axis⇒

( x ,− y )

y=f (x )Reflection on theY−axis⇒

y=f (−x)

( x , y ) Reflectionon the Y−axis⇒

(−x , y )

y= f ( x )Reflection on the X−axis followed by theY−axis⇒

y=− f (−x ) {some׿called abouttheOrigin }

( x , y ) Reflectionon the X−axis followed by the Y−axis⇒

(−x ,− y )

y=f ( x )Reflection on theline y=x⇒

x=f ( y )

(x , y )Reflection on theline y=x⇒

( y , x )

y=f (x )Reflection on theline y=−x⇒

x=−f (− y )

(x , y )Reflection on theline y=−x⇒

(− y ,−x )

Page | 42

E

E

43 | Page

A

D

Page | 44

A

45 | Page

A

A

Page | 46

A

C

47 | Page

A

A

Page | 48

y=f ( x )Translation3up⇒

y=f ( x )+3 ↑

y=f ( x )Translation3 down⇒

y=f ( x )−3↓

y=f ( x )Translation3¿ ¿⇒y=f ( x−3 )→

y=f (x )Translation 3¿⇒y=f ( x+3 )←¿

B

49 | Page

A

D

Page | 50

E

51 | Page

C

Page | 52

y=f ( x )Stretching∈directionof y⇒

y=af ( x ){|a|<1 wider|a|>1 narrower }

y=f (x )Stretching∈directionof x⇒

y=f (ax ) {|a|<1 wider|a|>1 narrower}

B

53 | Page

D

Page | 54

Even Function means f (−x )=f (x ), ie. The function is symmetric about the Y-axis

Like f ( x )=x2+5 x4+|x|+7

D

Odd Function means f (−x )=−f ( x), ie. The function is symmetric about the Origin, looks the same when turned upside-down.

Like f ( x )=x3−4 x+ 1x

E

Prepared By

Mr. Mohamed Abdallah

01119686808

01005670499

0122227550955 | Page