Advanced Programme Maths P2 Info Booklet 2019 Afr hlayiso.com

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy i van iv INLIGTINGSBOEKIE Algebra –b ± b2 – 4ac  x ; x 0 x= x = 2a  x ; x < 0 n n n(n + 1) n 2 n  1= n i=1  i=1 i= 2 = + 2 2 n Sn = 2a   n  1 d  Sn =  a 1 r n  2 1 r z = a+ bi z* = a  bi  A ln A + ln B = ln (AB) ln A – ln B = ln   B logb x ln An = n ln A loga x = logb a Calculus b  ba  n b  x n+1    f  xi   x dx =  n + 1 , n   1 n Oppervlakte = lim  n   n  i=1 a  a f(x + h) – f(x) dy dy dt f'(x) = lim = × h 0 h dx dt dx  f'  g(x).g'(x)dx = f(g(x))+ c  f(x).g'(x)dx = f(x).g(x)   g(x).f'(x)dx + c b f(x ) xr +1 = xr  r V =  y 2dx f'(xr ) a IEB Copyright © 2019 BLAAI ASSEBLIEF OM

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy ii van iv Funksie Afgeleide xn nx n 1 sin x cos x cos x sin x tan x sec 2 x cot x cosec 2 x sec x sec x.tan x cosec x cosec x.cot x ex ex 1 ln x x f(g(x)) f'(g(x)).g'(x) f(x).g(x) g(x).f'(x)+ f(x).g'(x) f(x) g(x).f'(x)  f(x).g'(x) g(x) 2 g(x) 1 2 A= r θ s = rθ 2 a b c In ABC: = = sin A sin B sin C a2 = b 2 + c 2 – 2bc.cos A 1 Oppervlakte = ab.sin C 2 sin2 A+ cos2 A = 1 1+ tan2 A = sec 2 A 1+ cot 2 A = cosec 2 A sin  A± B  = sin A.cos B ± cos A sin B cos  A± B  = cos A cos B sin A sin B cos2 A  sin2 A  sin 2A= 2sin A cos A cos 2A = 2cos2 A  1 1  2sin2 A  1 sin A.cos B = sin(A+ B)+ sin(A  B) 2 1 sin A.sin B = cos(A  B)  cos(A+ B) 2 1 cos A.cos B = cos(A  B)+ cos(A+ B) 2 IEB Copyright © 2019

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy iii van iv Matrikstransformasies  cos θ sin θ   cos 2θ sin 2θ       sin θ cos θ   sin 2θ cos 2θ  Finansies & Modellering F = P( 1+ in) F = P( 1 in) F = P( 1+ i)n F = P( 1 i)n  1+ i n  1 1 1+ i  n  k F=x  P=x   r reff =  1+   1  i   i   k  P  Pn+1 = Pn + rPn  1 n   K   R  Rn+1 = Rn + aRn  1 n   bRn Fn Fn+1 = Fn + f bRnFn  cFn  K  Statistiek n(A) P B  A P(A) = P B | A = P(A  B) = P(A)+ P(B) – P(A  B) n(S) P  A n! n n! n nx P  X = x  =   p x 1  p  n n Pr = Cr =   = n  r  !  r   n  r  !r! x  p  N  p      r  n  r  P R = r  = EX= n  p Var  X  = n  p 1 p  N    n  x  y    μ x  μy  X μ xμ z= z= z= σ σ x2 σ y 2 σ n + n x ny x  z σ p 1  p  EX= x P  X  x n p  z n Var  X  = E  X 2    E  X  2 IEB Copyright © 2019 BLAAI ASSEBLIEF OM

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy iv van iv NORMAALVERDELINGSTABEL Oppervlaktes onder die Normaalkromme z 1  ½ x2 H(z) = e dx 2 0 H(z) H(–z) = H(z), H() = ½ Inskrywings in die tabel is waardes van H(z) vir z  0. 0 z z ,00 ,01 ,02 ,03 ,04 ,05 ,06 ,07 ,08 ,09 0,0 ,0000 ,0040 ,0080 ,0120 ,0160 ,0199 ,0239 ,0279 ,0319 ,0359 0,1 ,0398 ,0438 ,0478 ,0517 ,0557 ,0596 ,0636 ,0675 ,0714 ,0753 0,2 ,0793 ,0832 ,0871 ,0910 ,0948 ,0987 ,1026 ,1064 ,1103 ,1141 0,3 ,1179 ,1217 ,1255 ,1293 ,1331 ,1368 ,1406 ,1443 ,1480 ,1517 0,4 ,1554 ,1591 ,1628 ,1664 ,1700 ,1736 ,1772 ,1808 ,1844 ,1879 0,5 ,1915 ,1950 ,1985 ,2019 ,2054 ,2088 ,2123 ,2157 ,2190 ,2224 0,6 ,2257 ,2291 ,2324 ,2357 ,2389 ,2422 ,2454 ,2486 ,2517 ,2549 0,7 ,2580 ,2611 ,2642 ,2673 ,2704 ,2734 ,2764 ,2794 ,2823 ,2852 0,8 ,2881 ,2910 ,2939 ,2967 ,2995 ,3023 ,3051 ,3078 ,3106 ,3133 0,9 ,3159 ,3186 ,3212 ,3238 ,3264 ,3289 ,3315 ,3340 ,3365 ,3389 1,0 ,3413 ,3438 ,3461 ,3485 ,3508 ,3531 ,3554 ,3577 ,3599 ,3621 1,1 ,3643 ,3665 ,3686 ,3708 ,3729 ,3749 ,3770 ,3790 ,3810 ,3830 1,2 ,3849 ,3869 ,3888 ,3907 ,3925 ,3944 ,3962 ,3980 ,3997 ,4015 1,3 ,4032 ,4049 ,4066 ,4082 ,4099 ,4115 ,4131 ,4147 ,4162 ,4177 1,4 ,4192 ,4207 ,4222 ,4236 ,4251 ,4265 ,4279 ,4292 ,4306 ,4319 1,5 ,4332 ,4345 ,4357 ,4370 ,4382 ,4394 ,4406 ,4418 ,4429 ,4441 1,6 ,4452 ,4463 ,4474 ,4484 ,4495 ,4505 ,4515 ,4525 ,4535 ,4545 1,7 ,4554 ,4564 ,4573 ,4582 ,4591 ,4599 ,4608 ,4616 ,4625 ,4633 1,8 ,4641 ,4649 ,4656 ,4664 ,4671 ,4678 ,4686 ,4693 ,4699 ,4706 1,9 ,4713 ,4719 ,4726 ,4732 ,4738 ,4744 ,4750 ,4756 ,4761 ,4767 2,0 ,4772 ,4778 ,4783 ,4788 ,4793 ,4798 ,4803 ,4808 ,4812 ,4817 2,1 ,4821 ,4826 ,4830 ,4834 ,4838 ,4842 ,4846 ,4850 ,4854 ,4857 2,2 ,4861 ,4864 ,4868 ,4871 ,4875 ,4878 ,4881 ,4884 ,4887 ,4890 2,3 ,48928 ,48956 ,48983 ,49010 ,49036 ,49061 ,49086 ,49111 ,49134 ,49158 2,4 ,49180 ,49202 ,49224 ,49245 ,49266 ,49286 ,49305 ,49324 ,49343 ,49361 2,5 ,49379 ,49396 ,49413 ,49430 ,49446 ,49461 ,49477 ,49492 ,49506 ,49520 2,6 ,49534 ,49547 ,49560 ,49573 ,49585 ,49598 ,49609 ,49621 ,49632 ,49643 2,7 ,49653 ,49664 ,49674 ,49683 ,49693 ,49702 ,49711 ,49720 ,49728 ,49736 2,8 ,49744 ,49752 ,49760 ,49767 ,49774 ,49781 ,49788 ,49795 ,49801 ,49807 2,9 ,49813 ,49819 ,49825 ,49831 ,49836 ,49841 ,49846 ,49851 ,49856 ,49861 3,0 ,49865 ,49869 ,49874 ,49878 ,49882 ,49886 ,49889 ,49893 ,49896 ,49900 3,1 ,49903 ,49906 ,49910 ,49913 ,49916 ,49918 ,49921 ,49924 ,49926 ,49929 3,2 ,49931 ,49934 ,49936 ,49938 ,49940 ,49942 ,49944 ,49946 ,49948 ,49950 3,3 ,49952 ,49953 ,49955 ,49957 ,49958 ,49960 ,49961 ,49962 ,49964 ,49965 3,4 ,49966 ,49968 ,49969 ,49970 ,49971 ,49972 ,49973 ,49974 ,49975 ,49976 3,5 ,49977 3,6 ,49984 3,7 ,49989 3,8 ,49993 3,9 ,49995 4,0 ,49997 IEB Copyright © 2019