͑vpef[lQ_
 
 XNlNV_R  a 2 - b 2 = ( a + b ) ( a - b )   a 3 + b 3 = ( a + b ) ( a 2 - a b + b 2 )   a 3 - b 3 = ( a - b ) ( a 2 + a b + b 2 )   ͑vpef[lQ_
 
 	N҉
NI{_  | a + b | d"| a | + | b |   | a - b | d"| a | + | b |   | a | d"b < = > - b d"a d"b   
 
 | a - b | e"| a | - | b |   - | a | d"a d"| a |   
 
  NCQN!kezv  - b + "( b 2 - 4 a c ) / 2 a   - b - b + "( b 2 - 4 a c ) / 2 a   
 
 9hN|pevsQ|  X 1 + X 2 = - b / a   X 1 * X 2 = c / a   l旾[t  
 
 $R+R_  b 2 - 4 a = 0   lez	gvI{v$N[9h  
 
 b 2 - 4 a c > 0   lez	g N*N[9h  
 
 b 2 - 4 a c < 0   lez	gqQm
Ype9h  
 
 	N҉QpelQ_  
 
 $N҉TlQ_  s i n ( A + B ) = s i n A c o s B + c o s A s i n B   s i n ( A - B ) = s i n A c o s B - s i n B c o s A   
 
 c o s ( A + B ) = c o s A c o s B - s i n A s i n B   c o s ( A - B ) = c o s A c o s B + s i n A s i n B   
 
 t a n ( A + B ) = ( t a n A + t a n B ) / ( 1 - t a n A t a n B )   t a n ( A - B ) = ( t a n A - t a n B ) / ( 1 + t a n A t a n B )   
 
 c t g ( A + B ) = ( c t g A c t g B - 1 ) / ( c t g B + c t g A )   c t g ( A - B ) = ( c t g A c t g B + 1 ) / ( c t g B - c t g A )   
 
 
P҉lQ_  t a n 2 A = 2 t a n A / ( 1 - t a n 2 A )   c t g 2 A = ( c t g 2 A - 1 ) / 2 c t g a   
 
 c o s 2 a = c o s 2 a - s i n 2 a = 2 c o s 2 a - 1 = 1 - 2 s i n 2 a   
 
 JS҉lQ_  s i n ( A / 2 ) = "( ( 1 - c o s A ) / 2 )   s i n ( A / 2 ) = - "( ( 1 - c o s A ) / 2 )   
 
 c o s ( A / 2 ) = "( ( 1 + c o s A ) / 2 )   c o s ( A / 2 ) = - "( ( 1 + c o s A ) / 2 )   
 
 t a n ( A / 2 ) = "( ( 1 - c o s A ) / ( ( 1 + c o s A ) )   t a n ( A / 2 ) = - "( ( 1 - c o s A ) / ( ( 1 + c o s A ) )   
 
 c t g ( A / 2 ) = "( ( 1 + c o s A ) / ( ( 1 - c o s A ) )   c t g ( A / 2 ) = - "( ( 1 + c o s A ) / ( ( 1 - c o s A ) )   
 
 T]Sy  2 s i n A c o s B = s i n ( A + B ) + s i n ( A - B )   2 c o s A s i n B = s i n ( A + B ) - s i n ( A - B )   
 
 2 c o s A c o s B = c o s ( A + B ) - s i n ( A - B )   - 2 s i n A s i n B = c o s ( A + B ) - c o s ( A - B )   ؚ-Npef[͑lQ_      pef[lQ_  
 
   
 
 s i n A + s i n B = 2 s i n ( ( A + B ) / 2 ) c o s ( ( A - B ) / 2   c o s A + c o s B = 2 c o s ( ( A + B ) / 2 ) s i n ( ( A - B ) / 2 )   
 
 t a n A + t a n B = s i n ( A + B ) / c o s A c o s B   t a n A - t a n B = s i n ( A - B ) / c o s A c o s B   
 
 c t g A + c t g B s i n ( A + B ) / s i n A s i n B   - c t g A + c t g B s i n ( A + B ) / s i n A s i n B   
 
 gNpeRMRn yT  1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + & + n = n ( n + 1 ) / 2   1 + 3 + 5 + 7 + 9 + 1 1 + 1 3 + 1 5 + & + ( 2 n - 1 ) = n 2   
 
 2 + 4 + 6 + 8 + 1 0 + 1 2 + 1 4 + & + ( 2 n ) = n ( n + 1 )   1 2 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + & + n 2 = n ( n + 1 ) ( 2 n + 1 ) / 6   
 
 1 3 + 2 3 + 3 3 + 4 3 + 5 3 + 6 3 + & n 3 = n 2 ( n + 1 ) 2 / 4   1 * 2 + 2 * 3 + 3 * 4 + 4 * 5 + 5 * 6 + 6 * 7 + & + n ( n + 1 ) = n ( n + 1 ) ( n + 2 ) / 3   
 
 ck&_[t  a / s i n A = b / s i n B = c / s i n C = 2 R   l  vQ-N  R   h:y	N҉b_vYcWJS_  
 
 YO&_[t  b 2 = a 2 + c 2 - 2 a c c o s B   l҉B /fa Tc v9Y҉  
 
 WvhQez  ( x - a ) 2 + ( y - b ) 2 = r 2   la , b 	/fW_PWh  
 
 Wv N,ez  x 2 + y 2 + D x + E y + F = 0   lD 2 + E 2 - 4 F > 0   
 
 bir~hQez  y 2 = 2 p x   y 2 = - 2 p x   x 2 = 2 p y   x 2 = - 2 p y   
 
 vhgOby  S = c * h   ehgOby  S = c ' * h   
 
 ckh%Oby  S = 1 / 2 c * h '   ckhSOby  S = 1 / 2 ( c + c ' ) h '   
 
 WSOby  S = 1 / 2 ( c + c ' ) l = p i ( R + r ) l   tvhby  S = 4 p i * r 2   
 
 WgOby  S = c * h = 2 p i * h   W%Oby  S = 1 / 2 * c * l = p i * r * l   
 
 '_lQ_  l = a * r   a /fW_҉v'_^per   > 0   Gbb_bylQ_  s = 1 / 2 * l * r   
 
 %SOSOylQ_  V = 1 / 3 * S * H   W%SOSOylQ_  V = 1 / 3 * p i * r 2 h   
 
 ehgSOy  V = S ' L   lvQ-N, S ' /fv*bbby  L /fOh  
 
 gSOSOylQ_  V = s * h   WgSO  V = p i * r 2 h   
 
 8 7   c  s^LN	N҉b_ Nvv~*bvQN$Nb$Nv^~	@b_v[^~kbkO  
 
 8 8   [t  Yg Nagv~*b	N҉b_v$Nb$Nv^~	@b_v[^~kbkOHNُagv~s^LN	N҉b_v,{	N  
 
 8 9   s^LN	N҉b_v Nv^NTvQN$NvNvv~@b*b_v	N҉b_v	NNS	N҉b_	N[^bkO  
 
 9 0   [t  s^LN	N҉b_ Nvv~TvQN$Nb$Nv^~	vN@bgbv	N҉b_NS	N҉b_v<O  
 
 9 1   v<O	N҉b_$R[[t1   $N҉[^vI{$N	N҉b_v<OA S A 	  
 
 9 2   v҉	N҉b_e
NvؚRbv$N*Nv҉	N҉b_TS	N҉b_v<O  
 
 9 3   $R[[t2   $N[^bkON9Y҉vI{$N	N҉b_v<OS A S 	  
 
 9 4   $R[[t3   	N[^bkO$N	N҉b_v<OS S S 	  
 
 9 5   [t  Yg N*Nv҉	N҉b_veT Nagv҉NS N*Nv҉	N  
 
 ҉b_veT Nagv҉[^bkOHNُ$N*Nv҉	N҉b_v<O  
 
 9 6   '`([t1   v<O	N҉b_[^ؚvk[^-N~vkN[^҉s^  
 
 R~vkI{Nv<Ok  
 
 9 7   '`([t2   v<O	N҉b_hTvkI{Nv<Ok  
 
 9 8   '`([t3   v<O	N҉b_byvkI{Nv<Okvs^e  
 
 9 9   Na҉vck&_<PI{N[vYO҉vYO&_<PNa҉vYO&_<PI{  
 
 N[vYO҉vck&_<P  
 
 1 0 0 Na҉vckR<PI{N[vYO҉vYOR<PNa҉vYOR<PI{  
 
 N[vYO҉vckR<P  
 
 1 0 1 W/f[pvݍyI{N[vpvƖT  
 
 1 0 2 WvQSNw\O/fW_vݍy\NJS_vpvƖT  
 
 1 0 3 WvYSNw\O/fW_vݍy'YNJS_vpvƖT  
 
 1 0 4 TWbI{WvJS_vI{  
 
 1 0 5 0R[pvݍyI{N[vpvh/fN[p:NW_[:NJS  
 
 _vW  
 
 1 0 6 T]w~k$N*NzpvݍyvI{vpvh/f@wag~kvWv  
 
 s^R~  
 
 1 0 7 0R]w҉v$NݍyvI{vpvh/fُ*N҉vs^R~  
 
 1 0 8 0R$Nags^L~ݍyvI{vpvh/fTُ$Nags^L~s^LNݍ  
 
 yvI{v Nagv~  
 
 1 0 9 [t  
N(WT Nv~
Nv	Npnx[ N*NW0  
 
 1 1 0 W_[t  WvN&_vv_s^Rُag&_v^Ns^R&_@b[v$Nag'_  
 
 1 1 1 c1   `$s^R&_
N/fv_	vv_WvN&_v^Ns^R&_@b[v$Nag'_  
 
 a$&_vWvs^R~~ǏW_v^Ns^R&_@b[v$Nag'_  
 
 b$s^R&_@b[v Nag'_vv_Wvs^R&_v^Ns^R&_@b[vS Nag'_  
 
 1 1 2 c2   Wv$Nags^L&_@b9Yv'_vI{  
 
 1 1 3 W/fNW_:N[y-N_v-N_[yVb_  
 
 1 1 4 [t  (WTWbI{W-NvI{vW_҉@b[v'_vI{@b[v&_  
 
 vI{@b[v&_v&__ݍvI{  
 
 1 1 5 c  (WTWbI{W-NYg$N*NW_҉0$Nag'_0$Nag&_b$N  
 
 &_v&__ݍ-N	g N~ϑvI{HN[N@b[^vvQYOT~ϑvI{  
 
 1 1 6 [t   Nag'_@b[vWhT҉I{N[@b[vW_҉v NJS  
 
 1 1 7 c1   T'_bI{'_@b[vWhT҉vI{TWbI{W-NvI{vWhT҉@b[v'__NvI{  
 
 1 1 8 c2   JSWbv_	@b[vWhT҉/fv҉9 0  vWhT҉@b  
 
 [v&_/fv_  
 
 1 1 9 c3   Yg	N҉b_ N
Nv-N~I{Nُv NJSHNُ*N	N҉b_/fv҉	N҉b_  
 
 1 2 0 [t  WvQcVb_v[҉Nev^NNUO N*NY҉I{N[  
 
 vQ[҉  
 
 1 2 1 `$v~L T"O vN  d r   
 
 a$v~L T"O vR  d = r   
 
 b$v~L T"O vy  d r   
 
 1 2 2 R~v$R[[t  ~ǏJS_vYzv^NWvNُagJS_vv~/fWvR~  
 
 1 2 3 R~v'`([t  WvR~WvN~ǏRpvJS_  
 
 1 2 4 c1   ~ǏW_NWvNR~vv~_~ǏRp  
 
 1 2 5 c2   ~ǏRpNWvNR~vv~_~ǏW_  
 
 1 2 6 R~[t  NWY Np_Wv$NagR~[NvR~vI{  
 
 W_Tُ Npvޏ~s^R$NagR~v9Y҉  
 
 1 2 7 WvYRVb_v$N~[vTvI{  
 
 1 2 8 &_R҉[t  &_R҉I{N[@b9Yv'_[vWhT҉  
 
 1 2 9 c  Yg$N*N&_R҉@b9Yv'_vI{HNُ$N*N&_R҉_NvI{  
 
 1 3 0 vN&_[t  WQv$NagvN&_NpRbv$Nag~kvy  
 
 vI{  
 
 1 3 1 c  Yg&_Nv_WvvNHN&_v NJS/f[Rv_@bbv  
 
 $Nag~kvkO-Ny  
 
 1 3 2 RrR~[t  NWY Np_WvR~TrR~R~/fُp0RrR  
 
 ~NWNpv$Nag~kvkO-Ny  
 
 1 3 3 c  NWY Np_Wv$NagrR~ُ Np0RkagrR~NWvNpv$Nag~kvyvI{  
 
 1 3 4 Yg$N*NWvRHNRp N[(Wޏ_~
N  
 
 1 3 5 `$$NWYy  d R + r   a$$NWYR  d = R + r   
 
 b$$NWvN  R - r d R + r ( R r )   
 
 c$$NWQR  d = R - r ( R r )   d$$NWQ+Td R - r ( R r )   
 
 1 3 6 [t  vN$NWvޏ_~Wvs^R$NWvlQqQ&_  
 
 1 3 7 [t  bWRbn ( n e"3 ) :   
 
 t$O!kޏ~TRp@b_vYb_/fُ*NWvQcckn b_  
 
 u$~ǏTRp\OWvR~NvR~vNp:NvpvYb_/fُ*NWvYRckn b_  
 
 1 3 8 [t  NUOckYb_	g N*NYcWT N*NQRWُ$N*NW/fT_W  
 
 1 3 9 ckn b_vk*NQ҉I{Nn - 2 	 1 8 0  n   
 
 1 4 0 [t  ckn b_vJS_T_ݍbckn b_Rb2 n *NhQI{vv҉	N҉b_  
 
 1 4 1 ckn b_vbyS n = p n r n 2   p h:yckn b_vhT  
 
 1 4 2 ck	N҉b_by"3 a 4   a h:y  
 
 1 4 3 Yg(W N*NvphTV	gk *Nckn b_v҉1uNُN҉vT^:N  
 
 3 6 0  Vdkk  ( n - 2 ) 1 8 0  n = 3 6 0  S:Nn - 2 	( k - 2 ) = 4   
 
 1 4 4 '_{lQ_L = n @QR 1 8 0   
 
 1 4 5 Gbb_bylQ_S Gbb_= n @QR ^ 2 3 6 0 = L R 2   
 
 1 4 6 QlQR~=   d - ( R - r )   YlQR~=   d - ( R + r )   
 
 ؏	g NN'Y[.^eEQ'T	  
 
 
 
 [(u]wQ: 8^(upef[lQ_  
 
 
 
 
 
 lQ_R{|  lQ_h_  
 
 
 
 XNlNV_R  a 2 - b 2 = ( a + b ) ( a - b )   a 3 + b 3 = ( a + b ) ( a 2 - a b + b 2 )   a 3 - b 3 = ( a - b ( a 2 + a b + b 2 )   
 
 
 
 	N҉
NI{_  | a + b | d"| a | + | b |   | a - b | d"| a | + | b |   | a | d"b < = > - b d"a d"b   
 
 
 
 | a - b | e"| a | - | b |   - | a | d"a d"| a |   
 
 
 
  NCQN!kezv  - b + "( b 2 - 4 a c ) / 2 a   - b - "( b 2 - 4 a c ) / 2 a   
 
 
 
 9hN|pevsQ|  X 1 + X 2 = - b / a   X 1 * X 2 = c / a   l旾[t  
 
 
 
 $R+R_  
 
 b 2 - 4 a c = 0   lez	g$N*NvI{v[9h  
 
 b 2 - 4 a c > 0   lez	g$N*N
NI{v[9h  
 
 b 2 - 4 a c < 0   lezl	g[9h	gqQm
Ype9h  
 
 
 
 	N҉QpelQ_  
 
 
 
 $N҉TlQ_  
 
 s i n ( A + B ) = s i n A c o s B + c o s A s i n B   s i n ( A - B ) = s i n A c o s B - s i n B c o s A   
 
 c o s ( A + B ) = c o s A c o s B - s i n A s i n B   c o s ( A - B ) = c o s A c o s B + s i n A s i n B   
 
 t a n ( A + B ) = ( t a n A + t a n B ) / ( 1 - t a n A t a n B )   t a n ( A - B ) = ( t a n A - t a n B ) / ( 1 + t a n A t a n B )   
 
 c t g ( A + B ) = ( c t g A c t g B - 1 ) / ( c t g B + c t g A )   c t g ( A - B ) = ( c t g A c t g B + 1 ) / ( c t g B - c t g A )   
 
 
 
 
P҉lQ_  
 
 t a n 2 A = 2 t a n A / ( 1 - t a n 2 A )   c t g 2 A = ( c t g 2 A - 1 ) / 2 c t g a   
 
 c o s 2 a = c o s 2 a - s i n 2 a = 2 c o s 2 a - 1 = 1 - 2 s i n 2 a   
 
 
 
 JS҉lQ_  
 
 s i n ( A / 2 ) = "( ( 1 - c o s A ) / 2 )   s i n ( A / 2 ) = - "( ( 1 - c o s A ) / 2 )   
 
 c o s ( A / 2 ) = "( ( 1 + c o s A ) / 2 )   c o s ( A / 2 ) = - "( ( 1 + c o s A ) / 2 )   
 
 t a n ( A / 2 ) = "( ( 1 - c o s A ) / ( ( 1 + c o s A ) )   t a n ( A / 2 ) = - "( ( 1 - c o s A ) / ( ( 1 + c o s A ) )   
 
 c t g ( A / 2 ) = "( ( 1 + c o s A ) / ( ( 1 - c o s A ) )   c t g ( A / 2 ) = - "( ( 1 + c o s A ) / ( ( 1 - c o s A ) ) 
 
 