Advanced Programme Maths P2 Info Booklet 2019 hlayiso.com

Downloaded from hlayiso.com GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II – INFORMATION BOOKLET Page i of iv INFORMATION BOOKLET 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 Area = 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 PLEASE TURN OVER

Downloaded from hlayiso.com GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II – INFORMATION BOOKLET Page ii of iv Function Derivative 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 Area = 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 GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II – INFORMATION BOOKLET Page iii of iv Matrix Transformations  cos θ sin θ   cos 2θ sin 2θ       sin θ cos θ   sin 2θ cos 2θ  Finance & Modelling 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  Statistics 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 PLEASE TURN OVER

Downloaded from hlayiso.com GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II – INFORMATION BOOKLET Page iv of iv NORMAL DISTRIBUTION TABLE Areas under the Normal Curve z 1  ½ x2 H(z) = e dx 2 0 H(z) H(-z) = H(z), H() = ½ Entries in the table are values of H(z) for 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