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Mathematical Symbols and FormulasTITLE Formatting Mathematical Expressions TITLE Examples of Mathematical NotationTITLE Basic Arithmetic OperationsTITLE Algebraic Expressions and EquationsTITLE Solving Simple EquationsTITLE Working with Variables TITLE Evaluating ExpressionsTITLE Simplifying ExpressionsTITLE Order of OperationsTITLE Fractions and Rational ExpressionsTITLE Exponents and RadicalsTITLE FunctionsTITLE Graphing FunctionsTITLE

  • 1. ! " # $ # ! % & ' ( # ) ! # * # & # # + # ' ,- ! # # # #) $ + # # # ! # & ! # . # # # ) . # # # # ' -)/, # & & 0 1 2 3 4 5 6 3 0 & 0 7 3 /& 0 7 0 8& 0 7 3 9& 0 7 : /& 0 : 3 0 03 0 3 1 0 0 3 ; 0 0 < 0 2 & : = /& = 8& 0 3 0 : = 9& > = 8& ? @ : 7 : = 2 0 4 =3 :0 A 3 0 0B & # 2 =: 0 /& # 2 8& 9& * 9& => 0 10 0 3 20 < 0 = : 0 7 0 : 0 & " 2 3 0 ) ;0 0 ) 1 0 5 0 ) 1 0 5 0 0 /& 2 3 0 ) ;0 0 ) 1 0 5 0 0 ) 1 0 5 0 8& 2 3 0 ) 1 0 5 0 0 ) 1 0 5 0 ) ;0 0 9& " 2 3 0 ) ;0 0 ) 1 0 5 0 0 ) 1 0 5 0 ,& 2 & 0 03 0 03 A03 = 0:0 2 /& 0 0 4 0 0 <= 0 8& 0 0 9& 0 0 : 3 0 3 0 7 6 3 0 6 0 C& ? @ 0 : 0 A 20 @ 3 0 6 0B & 2 1 0 /& D 03 0 : @ 0 8& @ 0 0 : @ 2 9& # 1 E E 0 0 04 0 2 3 5 1 0
  • 2. / F& # 0 ; : 03 0 3 0 & 10 03 ) 2 7 3 0 0 /& 2 0 ! 0 : ) 2 7 10 03 8& 2 0 ! 0 : ) 10 03 7 3 0 0 9& 0 02 0 ) 3 3 1 7 3 0 0 G& :D 0 4 0 = H ) 2 5 2 0 < 2 = 1 A 1 & * 4 5 /& 3 0 : 0: @6 0 8& " = : ; 9& 0: I& 3 0 201 = 2 3 & ) 3 0 ) 3 : = /& ) 0 ) 2 0 = 3 0 8& 3 0 ) 0 ) 3 : = 9& ) 2 0 = 3 0) 3 : = -& 0 3 0 D1 0 @ 2 & 3 0 0 ) 0 0 02 0 ) 0 0 0 /& 3 0 0 ) 0 6 : 0 ) 0 A 0 3 = 0 8& 0 0 02 0 ) 0 0 ) 0 A 0 3 = 0 9& 0 0 ) 0 6 : 0 ) 0 0 0 & ? @ : 4 3 0 3 20 : 0 20B & : /& 0 0 2 8& 9& # 20 : /& ? @ 0 : ; 3 0 0 =: 0 7 0 6 0 1 = 0 03 0 1 = 0 B & A@1 /& 201 = 8& 03 9& 0 3 8& ) 60 & 0 = 0 /& 0 : 2 0 8& 0 6 : 7 ; 9& 0 0 : 0 20 9& 0 6 2 0 3 2 3 2 J 3 @ 2 6 K) 6= 0 0 L : 2 ) 6= @ 0 L 2 J 3 @ 2 06 K) 2 1 2 01 & 2 01 1 5 6 1 2 0 0 & : ; /& 0 = 0 : 8& 0 = : 9& = 0 =:
  • 3. 8 ,& 0 3 ) 2 0 2 & 3 0A@1 2 M /& 0 3 0 0 8& 6 :4 5 43 2 0 3 0 2 3 0 9& 6 0 2 0 3 0 0 C& < = <3 0 & 3 = :4 = /& 2 0 2 2 4 0 8& 3 0 6 = 3 0 9& 0 : = 20 3 @ /9 A0 F& 0 0 0 7 0 0 0 6 03 0 : 20 0 : 3 0 5 2 & 3 3 0 0 /& 3 3 0 0 7 2A7 3 0 3 8& 3 3 0 0) 2A7 3 7 0 3 9& 3 3 0 0) 2A7 3 ) 7 0 G& 3 = 0 & 0 ; : 0 α 7 β /& 0 ; : 0 β 8& 0 ; : 0 α 9& 0 ; : 0 7 6 0 I& @ 0 0 0 7 @ 0 @ 0 0 0 @ 0 0 0 J: 0 K) 5 G @ 03 0 10 0 0& @ 0 0 0 0 0) 3 5 @ 0 0& 3 0 ; @ 0 6 3 0 ; 0 0 5 & # 3 @ @ 03 0 A =: 0 /& 2 03 1 0 : 0 8& # 3 0 @ 03 0 A =: 0 9& # 3 6 A 0 1 0 /-& 2 1 0 =: 2 3 1 0 2 020 0 < 7 0 0 /9 A0 0 0 03 0 & 0 0 1 /& 0 0 8& 0 02 0 9& 0 0 E / & ? @ 0 : 0 01 = @ 2 3 = 7 6 3 0 0B & 3 0 0 0 @ 2 3 = /& = 0 6 3 : 0 0 0 0 5 @ 2 2 0 0 @ 2 3 = 8& 3 3 0 1 3 :0 2 @ 2 3 = 9& 2 0 5 6 3 01 5 0 2 0 ) 01 :0 2 @ 2 3 = //& : 2 2 0 = ) 2 0 0 > 3 03 0 60 3
  • 4. 9 & # 0 7 4 0 3 /& 4 7 A0E 0 3 8& # 0 ) 4 7 A0E 9& # 0 ) 4 ) A0E 7 3 3 0 /8& 2 0 6 3 E0 03 0 2 & 0 3 A0 M0 /& 0 0 6 2 3 A0 3 20 8& 0 3 A0 6; 5 01 2 2 0 9& = 6 /9& ? @ E) 2 2 03 4B & 2 3 0 0>4: 0 20 6 = /& 2 3 0 : 20 6 = 8& 2 03 3 @ => 0 10 0 20 0 A 9& 2 2 3 @ 0>4: 0 20 0 A /,& ? @ 0 : 2 0 0 E 3 2 0 A 1 = 2 46 B & < A03 0 :0 3 3 0 A03 0 :0 6 3 3 /& = : 3 0 2 0 0 20 3 3 1 0 2 5 0 @ 0 0 : ; 3 8& # 6 : A 3 1 9& < = 0 A 0 >7 0 2A 20 2 3 >7 E3 /C& ?. ; 20 3 3 < = 0 5 0 : 2 =: 0 3 0B & 3 7 6 /& 3 7 8& 3 2 7 6 9& 3 2 7 /F& ? 5 ; 2 M= 0 :03 ; 0 B & ; /& 0 < 8& ; 9& /G& ?. ; 6 = < 2 0 ! 0 :B & 0 6 = 2 0 4 2 = /& 4 2 0 4 8& : = 2 0 4 9& 0 0 /I& ?. ; 2 0 20 3 0 B & 0 D 0 : ; 3 ; 0 /& 0 D 0 : ; 3 ; 0 8& 0 D 0 : ; 3 6 9& 0 D 0 : ; 3 6 8-& ? @ 01E 0 2 07 0 : 03 A 3 0B
  • 5. , & : 0 : 0 A 3 0 0 : /& 0 1 0 0 3 : ; 0 A 3 0 8& 0 @ 0 : @ 2 0 A 3 0 9& = : ; 0 A 3 0 8 & ? @ : 3 6 0 0B & 0 0 5 0 0 0 @ 2 3 0 /& # 0 3 20 1 0 7 0 0 8& 3 5 0 3 A0 0 0 03 20 : : 5 3 0 9& 0 03 1 1 2 20 0 ) 3 0 0 8/& = @ 3 0 0 201 = : ?. ; 0 = 2 01 B & 3 M0 201 = : /& > : = 3 8& 0 0 3 : 9& 201 = 0 6 2 88& 0 = 3 @> 3 3 0 02 0 =2 0 /-- 3 ?. ; : 6 0B & 3 2 = 3 @> 3 /-- 3 /& 3 2 = 3 4 3 /-- 3 8& 0 01E 0 3 @ 2 5 M0 5 /-- 3 0 2 9& 0 01E 0 3 @ 0 5 /-- 3 0 2 : 03 0 2 0 89& ? @ 6 = 4 0 02 3 @ 0 :0 0B & 020 0 0 2 2 = /& 020 0 2 6 2 0 0 N 1 8& 2 : 20 7 : ; 9& 020 0 0 2 4 2 0 4 8,& ? @ 0 : 0 0 7 3 E < ; 0 7 2 0 0 B & 3 1 03 0 03 D 0 /& 3 1 20 0 : 0 3 3 1 8& 3 1 < 03 0 3 : ; 0 9& 3 1 3 0 0 2 2 0 # 8C& ? 5 ; 0 J = 20 3 KB & A 3 A 02 3 0 ; /& 0 1 2 46 8& 6 :3 0 2 60 3 2 @ 3 0 9& 2 2 < 6 :3 0 0 : 7 3 M0 8F& O200 O J 20 2 0K 0 2 2 0 0 0 : 0 03 01 0 2 2 0 0 0 1 0&
  • 6. C 2 O200 O < ) 0 A03 0 :0 0 2 0 0 2 0 7 0 0 A 0 :0 0) ? @ 6 2 01 1 2 0 1 0 0 B & - /& -)/, 8& -),- 9& )- 8G& ? @ 4 0 4: 0 B & 0 2 0 0 20 0 0 6 :0 4 0 /& 2 0 3 ; = 8& 0 3 0 :=1 0 1 0 : 9& 3 60 3 = 20 8I& ?. ; 2 0 0 < 2 B & 0>4: 0 2 : 6 3 /& 3 1 3 : 6 7 3 8& : 3 0 : 6 9& : 3 20 0 = 3 1 9-& ?. ; 0 20 3 = 7 2 5 2 0 < 0 = B & E0 0 0 : 3 0 /& 0 8& A 20 > 9& " = 9 & 03 2 0 0 ; 2 0 ) ? @ 0 3 : ; 0 0 D 0 ; A 2 0 3 3 0 0 : 3 0B & 0 /& 01 8& 3 9& 3 3 9/& ?. ; 0 B & 0 0 3 @ 0 : 3 0 0 : 0 20 ; 0 /& 0 : 3 0 A03 0 :0 0 2 0 0 : 8& 0 : 3 0 A 0 :0 0 2 0 0 : 9& : 20 ; 20 0 7 6 = 3 E 98& ? 0 5 ; 3 0 A 3 B & 0 3 0@ 0 5 20 2 < < 2 0 0 2 2 0 2 0 4 /& ! < 0 3 0 6 3 0 6 7 6 8& 20 2 2 0 2 5 M ) 3 1 :0 1 0 5 0 20 <3 ) :0 0 3 9& 0 2 3 A 0 1 05 43 2 0 20 0 2 2 0 99& ? 0 5 ; E 0 2 0 0 = 3 0 2 0 0B & 0 5 3 0 = => 0 10 0 : ) 20 0 5 3 7 2*
  • 7. F /& 0 5 3 0 = => 0 10 0 : ) 20 0 5 3 2* 8& 0 5 3 7 0 = 0>4: 0 : ) 20 0 5 3 2* 9& 0 5 3 0 = 0>4: 0 : ) 20 0 5 3 7 2* 9,& ? =3 0 < 0 <3 B & 0 6 :4 = /& # 60 3 :4 20 :4 ; 8& # 60 3 :4 ; :4 = 9& 3 7 :4 = 7 3 :4 = 9C& ?. ; < 2 ; 6 0 " * B & 2 0 = 2 /& 2 0 = 2 ; A ; 2 8& 2 0 = 2 9& 2 0 = 2 ; A ; 2 9F& 0 0 A0E 2 0 6 : 0 : & @ 2 = 0 6 0 ? =3 0 := 2 2 B & 0 3 0 3 0 1 0 : 20 : /& 0 = 6 < 2 = > 3 8& 0 0 = 60 3 9& 0 6 = ; 2 0 9G& " * & 0 /& 0 8& 2 =: 9& = 9I& 2 0 0 6 : 0 & ! 0 /& ! =: 0 8& 0 9& A 0> 0 60 6 0 ,-& ?. ; :0 5 2 3 : = 03 B & 05 43 /& 0 0:4 8& 9& #0 2 0 0 &
  • 8. G ! # & # # ! # ! # # & & 0 0 3 3 0 M 0 A03 1 > 0 0 & 1 1 3 0000 60 3 5 3 =3 0 A03 1 ) 03 0 0 ) M 0 0 3 &
  • 9. I /& 0 @ 10 0 0 5 1 0 = 2 3 0 03 0 03 0 03 0 0 2 02 0 0 = A 3 & 0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 Hacemillonesdeaños I II III H. sapiens sapiens H. sapiens sapiens H. sapiens sapiens H. sapiens neardentalensis Australopitecus H. erectus H. erectus H. erectus H. sapiens H. habilis A. africanus A. boisei A. robustus H. habilis A. africanus A. afarensis A. robustus J K 5 @ 0 3 20 A 5 > : => : => : => : = 02 01 & J1K < 0 = 0 0 0 0 3 0 0 ) ; : 5 ; 3 0 0 0 = 3 @3 @3 @3 @ & ? 0 5 ;B
  • 10. - 8& : : 3 3 0 <= A 3 00 <= A 3 00 <= A 3 00 <= A 3 0& IV I II III J K 5 0 03 1 ) 7 4 2 04 2 04 2 04 2 0 2 0 & J1K 1 E 6 A : 3 5 5 3 0 5 0 : 0> : 2 20 0 <= & J K >2 5 5 6 = " : 3 &
  • 11. 9& 1 E0 0 ; 0 3 ) 03 1 0 03 20 &