Advanced Programme Maths P1 Info Book 2018 hlayiso.com

Downloaded from hlayiso.com GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER I – INFORMATION BOOKLET Page i of iv INFORMATION BOOKLET Algebra –b ± b 2 – 4ac  x if x ≥0 x= x = 2a − x if 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 Area = 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 PLEASE TURN OVER

Downloaded from hlayiso.com GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER I – 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 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 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 = 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 GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER I – INFORMATION BOOKLET Page iii of iv 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   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  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 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 Matrix Transformations  cos θ −sin θ   cos 2θ sin 2θ       sin θ cos θ   sin 2θ −cos 2θ  IEB Copyright © 2018 PLEASE TURN OVER

Downloaded from hlayiso.com GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER I – INFORMATION BOOKLET Page iv of iv Normal Distribution Table Areas under the Normal Curve 1 z e − ½ x 2 dx 2π ∫ 0 H(z) = H(–z) = H(z), H(∞) = ½ H(z) 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 © 2018