Mathematics Grade 12 Paper 1 Gauteng Mock 2016 Memo

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Downloaded from hlayiso.com 1061 1/1 6 GAUTENG DEPARTMENT OF EDUCATION PREPARATORY EXAMINATION MATHEMATICS (First Paper) MEMORANDUM QTTESTTON I 1.1 1. 1.1 3x3 + 5x=2 3x2 + 5x-2=0 / standard form (:r-t)(r+2)=s / factors I x = 1...OR..x = -2 / both x values J (3) L.t.z J;n-r=x J;n=x*l x+7 =(x + tf { x+7:(x+l)2 x*l=x-+'2x+L -a /standard form x2+x-6=0 (x +:)(x - 2)= o /factors x=-3 OR x=2 N/A. /N/A .Jt-./- { x=2 (s) 1.1.3 x' -8"r=10 /standard form x' - 8x - 10:0 x: -brJu'-qac 2a /substitution x- -(-8) r - +(r[- ro) 2Q) .[ = 9,1 OR x=-l.,1 / x :9,1 /x :-1,1 (4)

Downloaded from hlayiso.com 1061 1116 1"t.4 3-t + 3-r*I.5 -8 3'*3-5-B 3' 32' - 9.3" + 15=0 /standard form /lfactors (r' - tXr' - :)= o 3'" =5 OR J =J x=logr5 x=1 / x:l x =1,46 / x:log 5 ORx = 1,46 OR Let 3* =k &*3'5=8 k y'substitute with k2 -8k+15 =o /standard forrn (* -z)(r, - 5)= o y'factors k=3 OR k=5 3* =3 3* =5 { x:l x=l x = log:5 / x:log 5 OR x:1,46 x --1,46 (s) 1.2 22015 + 22013 71006 .+ /factors Zrrrr{2, + t) 2"0r? / 2zotz = z(s) /answer =10 (3) t20l

Downloaded from hlayiso.com 1061 1116 QUESTTON 2 2.1 kxl +Ix+1=0 L,= b2 - 4ac =(k)' - +(r[r) /correct substitution rn ...= kz - 4k A =t(t -+) for non- realroots a<0 / L<A la and4 k(k - 4). o / inequality signs :.a <k <4 gl 2.2 2**r = 4Y.... 2**' = 4Y.......1 x? +2y=3 xz + 2y =3......2 1x+l _ 17y 1.t+l _ e1?y x +l=2y r + 1= 2y-........3 / simplify equation x=2y-1.......3 Substitute in 2 Substitute tu 2 / substitute (zy -tY + 2y =3 xn +x+1=3 4y' -4y +1+ 21t - 3 = 0 x' + x -2=0 4y' -Zy -2=o (x+z)(x-l)=o z{zy + t)(y - t)= o x=-2...OR...J=l / factors Substilute in 3 ...y--LoR '2 v=t / both y values -2+l-Zy...l+L=2y Substitute in 3 ,=-1.........v=l "2 , =,f-1l - r...... x = z(r)- r t2) x= -2. .-..J = I lboth x values OR (s) tel

Downloaded from hlayiso.com 10611116 QUESTTON 3 3.r -8 -28 22 / \to-/\=14/ \a ,/---.-4 ./ 3.1.1 40 /answer (1) 3.12 2a=4 3a+l=6 a+b+c:-8 /second difference :4 a=2 t(z)+b --o 2+c---8 / a=2 {b=0 b=0 c=-10 {c=-lO =2n? -lO "'7, &\ 3.2 3.2.1 a=5 / To=1AT. To =107., a+5d:t0(a +2d) la + 5d =l}(a +2d) 5+5d:lo(5 +tul) /simplification 5d -ZM = 50- 5 d=-3 /d=1 AI 3.2.2 s, =iP, + fu -lal / correct formula /conect substitution S.n =fft ttl+ (zo- rX-r)l =-470 /answer (3)

Downloaded from hlayiso.com 10611116 .. /-\k 3.3 3.3.1 tr{ I ) t4'lt) I \.' = ./ r. 1. 1. '2'4' 1 .l rl y --- 2 2 e-a / correct substitution in,S* -- l-r I I t- ^ 2 -2 (3) 3.3.2 .t,H. ).r. I u2 L) 1 | -- 2 *un-'(" -r) r-L /n=8 ,[f1)' -,] /correct substitution in ,s, =- [(2/ ) 1-1 y'S,,=a "<< 9B3.93 2 64 255 =-64 ..oR...3,99 (3) 3.3.3 ?55 64 t 63 y'answer & OR =--127 64 OR = - 1,98 (1)

Downloaded from hlayiso.com 10611/16 3.4 le: tsl: 5) n?: u,t---- 4 { d =- A' 5 5 Tn = ct + (n -tld ' rfl). /correct substitution in re + (n- o 't5,/ correct formula AA 19--n+-<0 {7,<o 55 -4rr.-Lg! /inequality 55 y'answer .24,75 44 .'.The 25th Tetm /conclusion (6) t2st OUESTION 4 4.t P:4 / P=4 cl=2 { q:2 r(s;3) : y =++2 3=a+2 a=1 { a:l (3) 4.2 &(-r) = I +2 /answer -x-4 OR h(r)=* t') (1) 4.3 y - - x + c........,{q;z) /correct substitution of z: -(+)+ c @;2) C:6 /answer t6t

Downloaded from hlayiso.com ts6t 111s QITESTI{}N 5 f{:,-} :ee" roug}r t}re Point {*4, rf,J * "tr-*ft a /substitution .l }# fl:*: t&u l- $"* d /value of * jift \nJ {4* t" /intercirange:r ancl Y 4! t*I /equation rtJ*46 /shnpe ./" 'rshap* l' ' *'asyrnptotes of br:th graPhs 1 t-rX t4i / / \- l+1 I.ri r.l rit.r7- - -l i -_ II t\i \* / Atrr:ut rhe line V ::.v

Downloaded from hlayiso.com 1061 1116 QUESTTON 6 f 6.1 !=a{ /substitution (i; -4) -4= a(L)z -4=a ;x>0 lvalue of a /equation h(x)= 4*z (3) 62 ! = -4xz -9 = -4xz 9 "9 /simplification x2 =- 4 4 ,=*{otr lo \ x>o ..rll)'1:-91 /answer I / (2) vz-!' Gradient of ST = !- 6_3 xz -Jt - (-4) /substitution =-91,5-l /answer = -10 (2\ 6.4 /interchange x artdy x = -4t-' ;y >-A /restriction -.: x v ---- "4 y'the value of y' t-.. II v ='i- z -1 l"\ t- h'=-l-- /equation \l4 (4) 6-5 /shape inverse /point on inverse /axis of symmetry (s) IT4I

Downloaded from hlayiso.com 1 061 1116 QUESTTON 7 7.1 l+0.164:lt*l=,..l rrv,rw_L^, /correct substitution into D) correct fonnulae ; ,"{troq - 11'nont r, 12 /ld.:,rp inon = 15,28o/o /answer (3) - r' 2 300 000 7.2 [(, - 9/2)" -,] .Y) -, L( 4) l { n:32 0,r2 4 /answer x = R43 807,22 (4) 7.3 7.3.1 A= P(r+ i)' r'substitution ( o.t+ts\' A=Rr35000[. o ) / A: ft138 339,15 I = .R138 339,15 (2) 7.3.2 /correct formula (P) -[,.T) '-] /correct substitution {n=L8 aJ475 12 /answer x = R8 613"99 (4) l13l {o

Downloaded from hlayiso.com 10611/16 QUESTTON 8 8.1 .f(x)=4-3x? f(x+h)=4-3(x+h)z /simplification of =4-3x? -6xh-3hz .f(x+h) f (x) /formula J,,$) _r*"f(x+h)- Ir+0 h = lim (4 - 3x2 - 6xh - 3h2 ) - (+ - 3x2) h-+A - 6xh-3hz /simplific ation - 6xh th? = lim h-+O h h(-6x -3h) = lim /common factor i-+0 = lim(-6.r- 3i) = -6x / answer-6x {5) 8.2.t { 4x3 o.l *' -2* * 11 /-2 L J-J / -z)i-l =4x3 -2-2x-3 (3) 8.2.2 1r:- 2x-3 Vx 1_1 /simplification =2xa -3x a dv 3+ 3-: /both values of derivatives dx2 4 (2\ 8.3 -f(x):x'-7x' { f'{x) f'(x):3x2 -l4x f'(x) =5 / J-'k) = s 3x2 -L4x = 5 3x2 -14x-5=0 /factors (:x + t)(x - 5): o *=-1 oR J x=5 /both answers NOTE NO PENALTY IF CANDIDATE COMMITS AN ERROR IN WRITING AN ANSWER WITH POSITIVE EXPONENTS. (41 It4t 11

Downloaded from hlayiso.com 1061 1116 QUESTTON e 9.1 /y-intercept /y-intercept /shape (3) 9.2 J'$)=a(x+?Xx-1){x-6) /corect f,ormulae /substitution 12= alo + \{a - 1}t0 - 6) { a:L c=l .', .f(x) = (r + ?X, - 1)(.:r - 6) /expansion =.r3-5x2-8x+12 (4) 9.3 f'(x) = o /equating to zero .'.3x?-10x-8=0 /factors (3x+2){x-4J=0 y'ansrvers.x *:-Z3 oR r=4 /ansrvers y ,,-ooo oR v=-i6 "27 rurningpoints ** f- ,A ,#) AND (a; --36) r'TPs (s) 9.4 2 /answer ---<x<4 3 (r) 9.5 l'" t-*1: 6x - 1o /second derivative 6x-10>0 /6x-10>0 jf>- 5 /ansrver 30 (3) II6I 12

Downloaded from hlayiso.com t CIst 1116 *ITESTION le f ff Y 4s 10 I Fl .= 128 /substirution 4.u-.r.lr = 128 .ft---- l?8 /ansrver 4-r- f2'! t{}"2 = 4..t:..r+ Zxh+&xh /fonnula =,,$yi 110rft aa 'I otal surf*ce &rea /siniplilication = 4xz + 10x.{ x- . ?i 320 ,il.v' y'answer - -- x {s} / trn\ Dxl 4x'* --- l = 0 1*"3 t .rl ^ ,320 /derivative 6J ---- ::::: U --r'' /equate lo zero {3x'*320=* 8x3 =32* 32! ''t = x /sirnplific.ati*n '11EoI 1. = r i_ 1"=ffi *.- - e..li ri,r / answer t? "l; Fleight: : :2,74 1' 1\- l"-' tk{ I \ )/ {4} I9t 13

Downloaded from hlayiso.com 10611I16 QI]ESTION 11 11"1 Let S represert the participants for swinrming; G represent the gynuastics ,/6 participants and A for the athletics parlicipants. /21-x /14-x / all other values in the Venn diagram correct (CA } AI n.2 2l- x+x + l4-.r+ 9+14+ 1 0+ 6+ I I = B0 y'equation 85-x = 8O /answer -r=5 0\ I 1.3 5+14+10+9 u'equation P (Particip*nts in at least 2 events) 80 /clivision by 80 /answer = 4,47 5 (s) tel 14

Downloaded from hlayiso.com 10611116 QUESTION 12 9! = 362 880 of the answer /gt. rzfiz { 5t, /aRswer =3024 OR !.x 84Jx,6. 9x8x7x6 :3 024 /answer {5