Advanced Programme Maths P2 Info Book 2018 Afr hlayiso.com

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy i van iv INLIGTINGSBOEKIE Algebra –b ± b 2 – 4ac  x as x ≥ 0 x= x = 2a − x as x < 0 n n n(n + 1) n 2 n ∑ 1= n i=1 ∑ i=1 i= 2 = + 2 2 n n ( n + 1)( 2n + 1) n 3 n 2 n ∑ i=1 2 i = 6 = + + 3 2 6 n 2 ( n + 1) n 2 n 4 n3 n2 ∑ i=1 i 3 = 4 = + + 4 2 4 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 ) ∫ n Oppervlakte = lim  x dx =   n →∞  n  i=1 a  n + 1 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 = π∫ y 2dx f'(xr ) a IEB Copyright © 2018 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 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 a 2 = 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 = 2 sin A cos A cos 2 A = 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 © 2018

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy iii van iv 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   r k F=x  P=x  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 bRn Fn − 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 n Pr = n Cr =   = P ( X = x ) =   p x (1 − p ) (n - r ) !  r  ( n − r ) !r! x  p  N − p      r  n − r  X −μ x−μ P (R = r ) = z= z= σ N  σ n   n x −y n ∑ (xy) − ∑ x ∑ y ∑ xy − nxy ∑ (x − x)(y − y) z= b= b= b= σ x2 σ y 2 n( ∑ x ) − ( ∑ x) 2 2 ∑ x − n(x) 2 2 ∑ (x − x) 2 + n x ny p (1 − p ) x ± z σ p ± z n n Matrikstransformasies  cos θ −sin θ   cos 2θ sin 2θ       sin θ cos θ   sin 2θ −cos 2θ  IEB Copyright © 2018 BLAAI ASSEBLIEF OM

Downloaded from hlayiso.com GRAAD 12-EKSAMEN: GEVORDERDEPROGRAM-WISKUNDE: VRAESTEL II – INLIGTINGSBOEKIE Bladsy iv van iv Normaalverdelingstabel Oppervlaktes onder die Normaalkromme 1 z e − ½ x 2 dx 2π ∫ 0 H(z) = H(–z) = H(z), H(∞) = ½ H(z) 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 © 2018