Mathematics Grade 11 Paper 1 Eastern Cape November 2017 Memo

Downloaded from hlayiso.com ale basic education wat Department: (GO) Basic Education aw” REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 11 Flannel iinet’ " MATHEMATICS P1/WISKUNDE V1 : NOVEMBER 2017 " " MARKING GUIDELINES/NASIENRIGL YNE : % MARKS/PUNTE: 150 These marking guidelines consist of 19 pages. Hierdie nasienriglyne bestaan uit 19 bladsye. ja\n Jaorq ru 20"7 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde VI 2 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne NOTE: If a candidate answered a question TWICE, mark only the FIRST attempt. If a candidate crossed out an answer and did not redo it, mark the crossed-out answer. e e Consistent accuracy applies to ALL aspects of the marking guidelines. e Assuming values/answers in order to solve a problem is unacceptable. LET WEL: e As 'n kandidaat 'n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na. e As ‘n kandidaat 'n antwoord deurgehaal en nie oorgedoen het nie, sien die deurgehaalde antwoord na. Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing. Dit is onaanvaarbaar om waardes/antwoorde te veronderstel om 'n probleem op te los. _QUESTION/VRAAG 1 Ll (2x-3\Xx+7)=0 3 vy=l x= > or x=-7 * 2 vx =-7 112 Te 43x-2=0 —b+,/b’ -4ac x= 2a ¥ substitution/vervanging ———— _~8)* VG) 4-2) 27) ~3+ 65 NOTE/LET WEL: = 414, Penalty 1 mark for incorrect rounding ¥ answer/antwoord x=-0,79 or x = 0,36 Penalisering 1 punt ¥ answer/antwoord vir verkeerde afronding OR/ OF x? + 3, a 0 7 7 >,3. 9 2.9 2 a oo 3) _ 65 TF" {96 7” 196 v(xe3) = 106 (ale 14 196 3 +65 xt—= 14 14 xe 3+ V65 ¥ answer/antwoord 14 ¥ answer/antwoord x=-0,79 or x= 0,36 Copyright reserved/Kopiereg voorbehou Gs Wu 2) |

Downloaded from hlayiso.com Mathematics/P1/Wiskunde VI 3 CAPS/KABV ~ Grade/Graad 11 — Marking guidelines/Nasienrighyne DBE/November 2017 1.13 vx-14+3=x vx-1l=x-3 Y isolate/isoleer \ sign/teken (ve—1f =(x-3Y ¥ squaring/kwadr both sides/ x-1l=x? -6x+9 beide kante 2 ¥ std form/stand vorm x —7x+10=0 ¥ factors/fakt (x-2)(x-5)=0 vx=5 x#2 orlof x=5 Vx#2 (6) | | 1.1.4 x? >3(x +6) 2 ¥ std form/vorm x° —3x-18>0 ¥ factors/fakt (x-6)(x +3)>0 OR/OF x<-3 or x>6xE(-~%;-3)U6; &) ¥x<-3 OR/OF (-» ; -3) ¥ x>6 OR/OF (6; ~) — (4) 1.2 2y+x=l x=l-2y V x=1-2y +p 43xyt+yp=0 ¥ substitution/verv (l-2y)P +y? +3y0- 2y)+y = 0 1-4y+4y? +y? +3y-6y? +y=0 1-y’=0 (l- y)A+y)=0 y=l or y=-l x=-lor x=3 OR/OF % std form/stand vorm Y factors/fakt vy-values/wrdes vx-values/wrdes Copyright reserved/Kopieregvoorbehou G Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P t/Wiskunde V1 4 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne 2y+x=l l-x V ya lox =—— y= 2 2 x+y? +3xypt+y=0 ¥ substitution/verv 2 wafIc®) 43, oe i120 2 2 2 2 l-2x+x? 3x-3x? 1-x xo $+ +—=0 4 2 2 4x? +1-2x+x7 +6x—6x? +2-2x=0 ~x?+2x+3=0 x? —~2x-3=0 ¥ std form/stand vorm (x—3)(x+1)=0 ¥ factors/fakt x=3 0 or x=-l vx-values/wrdes y=-l or y=l vy-values/wrdes (6) 13 3-12k? =0 ¥ 3-12k =0 1-4k? =0 a ve =4 4 1 v k=t— k=t5 k 2 (3) 3-12k? =0 ¥3~12k =0 1-4k? =0 (1-24) 2k) = 0 ¥ (I-24Y1+2k)=0 1 ket OR/OF k=-5 Vh=ty @) [24] Copyright reserved/Kopieregvoorbehou G& WW Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde VI DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1 gma 6.3" m2 73 ¥ common factor/gemene fakt 7.3773 3-6 se . =3 ¥ simplification/vereenv. 2 21 =1 ¥ answer/antw. OR/OF am+4 mil arn 6.3 ¥ common factor /gemene fakt 73m _ 3" 3*-6.3) v (3° -63) 3" (7.37) = 3”.63 ¥ simplification/vereenv. 3” .63 =1 Y answer/antw. (4) 2.2.1 3 x4 =8 3 v2 x4 =2° aa “rational exponent/ x=(2°)? rasionele eksp xy=24 Y answer in any form/ antw. 1 in enige vorm 16 (3) OR/OF as xt=8 ¥use of surds/gebr van wortls 4 x? 3 ~1_ 44 xta2" (2 = 4096) vxt=2 x'=2' (2* =16) x=24 vi answer in any form/antw. in 1 enige vorm x=— 3) 16 Copyright reserved/Kopieregvoorbehou 6; \NW Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 6 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne 2.2.2 2?*_9* <2 NOTE/ LET WEL: 22*_2*-2=0 If answer only of x = 1: award 1/4 marks | ~ Slegs antwoord van x = 1: gee 1/4 punte ¥ std vorm/stand vorm io +1)2" - 2)= 0 ¥ factors/fakt | x F If the learner writes 2x — x =1 2" #-1 or 2% =2 Breakdown: 0/4 marks vx=1 x=l1 As die leerder 2x —x =1 skryf Yo Ontleding: 0/4 punte aed 5 (4) . 2 (r+ yy -( 3a, atv “ substitution/very. v2 2 | (7 } 2 _49 ¥ simplification/vereenv. 2 1 = _ | “answer/antw. OR/OF (x+y)? =x? +2xy+ y? 2 2 = 3-Va +2 3-Va (44a + 4+va ¥ substitution/verv. V2 v2 v2 v2 -~6 _Ja— =|? va+a +2) 12-Va-a + 16+8Va +a ¥ simplification/vereenv. 2 2 2 _ # 2ye*28) «(asi = Pa +a+t2-Ja~a 1 | = 24 | Yanswer/antw. | @) 2.4 'Y10 .9/64.10 .4/81.10. /4.10 Y split the surd/ skei wortel ='¥10 9/25 10 .4/3* 10. /2? 10 1 6 1 4 1 a 6 1! 4 Yo2 Lt =10” .2° 10°. 34 104.2? 102 12 =2x3x2x10? =120 OR/OF v prime base/ priem basis ¥ rational exponents/ rasionele eksp 2 v 108 Copyright reserved/Kopieregvoorbehou G Wr Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 7 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne ¥ prime base/ priem basis =¥2s 927s 43°25. \255 P p Joi 7i 4 bois ¥ rational exponents/ = 212,512 2656 34.24, 54,22 5? rasionele eksp wo 4 2 =2? x34 x5? Y exponent law/ eksp. wet =23x3!x5! owe =120 ¥ simpification/ vereenv (4) [18] Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief & \lu

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 8 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1 12 17 N 22 5 5 v 5n T,=5n+7 v47 (2) 3.1.2 Ty =5(12) +7 ¥ subst/verv -67 ¥ answer/antw — (2) 3.1.3. 5n+7=172 ¥ 5n+7=172 5n=165 ¥ answet/antw n=33 (2) 3.2 3 x yo 30 N\ AON 4oO™ a x-3 vrx 30-y x-3=y-x Yx-3=y-x y=2x-3 3=30 30-y=y-x ¥ 30-yay-x 330-2 +3 S04 x=2y x-3=30-2x 3x36 30+x = 2(2x—3) ¥ equating/verg. = OR/OF 36=3x x=12 De y=2l = Y both /beide ye2l x=I2and/en y=21 (4) OR/OF 30-3 =3d Vv 30-3=3d 3d =27 d=9 vd=9 x=3+9=12 Y both /beide y=12+9=21 x=12and/en y=21 (4) _ 0} Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief G \W

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 9 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne QUESTION/VRAAG 4 41 ae y, 193 \ y, Me y, 109 -51 -45 \ y, -39 6 NOTE/LET WEL: T,=76 Calc. differences 1/2 marks ¥ ¥answer/antw. bereken verskille: 1/2 punte 2) 42 2a=6 a=3 Vaz=3 3a+b=-51 4 33)+b=-S1 =-60 vb=-60 at+b+c=244 | 3+-60+c¢=244 ¥c=301 c=301 _ 3,2 T, =3n’ -60n+301 YT, =3n’ —60n+301 4) 43 3n* —60n+ 301 =508 ¥ equating/verg. 2 = 3n' — 60n— 207 =0 ¥ std form/stand vorm Ww —20n-69=0 (n+3) (n—23) =0 ¥ factors/fakore n=23or n#—3 ¥select/ kies n= 23 (4) 44 using first diff./ gebruik eerste versk T, =6n-5S7 ¥ 6n-57 453 = 6n—57 ¥453=6n—57 510=6n n=85 between 7,, and T,, inthe quadratic pattern Y between T,, and T,, tussen T,, en T,, indie kwadratiese patroon tussen Ty, en Ty, OR/OF @) In the quadratic pattern / in die kwadratiese patroon Tau ~T, = 453 3(n+ 1)? — 60(n-+1)+301 - (Bn? - 60n +301)= 453 y 3n* + 6n-+3— 60n— 60—3n? + 60 = 453 | (01° —60(n-+1)+ 301 ~ (Gn? ~ 60m +301) = 453 6n=510 n=85 v¥n=85 between 7,, and Ty, ¥ between 7,, and Ty. tussen Ty, en Tye tussen Ts en Ty, G3) Copyright reserved/Kopieregvoorbehou & \KW Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde VI 10 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrigiyne DBE/November 2017 45 T, =3n? -60n+300+1 =3(n-10) +1 (n-10) = 0 fortvir neN 3(n-10) >0 3(n-10) +1>0 All terms in the pattern are positive/al die terme in die patroon is positief OR/OF Tn =3n? - 60n+301 = 3(n-10) +1 T is a minimum valued function with minimum value | Range of T: y 21 All terms in the pattern are positive. T is funksie met minimum waarde van I Waardeversameling van T; y>1 al die terme in die patroon is positief q = 3(10)? — 60(10)+ 301 =1 T is a minimum valued function with minimum value 1 Range of T: y2>1 All terms in the pattern are positive. | T is funksie met minimum waarde van | Waardeversameling vanT,; y 21 al die terme in die patroon is positief (vVT, =3(n-10) +1 | | ¥ V argument | YVT, =3(n-10) +1 ¥ ¥ argument ¥ p=10 ¥qz=l v “argument (4) (4) [17] Copyright reserved/Kopieregvoorbehou 6 WN Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde VI DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1 - f= 3 5H =4 ¥ answer/antw. |_ Q). 5.2} 4=2*-4 v¥4=2"-4 8=2* | B=27 x=-3 ¥ answer /antw. Q) 53 |x=2 Vy=2 y=l vy=l Q 5.4 | y>-4 ¥ answer/antw. q) OR/OF ye (4 ; 00) ¥ answer/antw. q) Copyright reserved/Kopieregvoorbehou & WN Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Copyright reserved/Kopieregvoorbehou @ WW Please turn over/Blaai om asseblief Mathematics/P 1/Wiskunde V1? 12 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne 5.5 | y-intercept/afsnit: =<—_ 3 1 y= 0+2 ¥ subst/verv -1 x=0 ys -l . _. 1 Vv y= y-intercept/afsnit is | 0; — 3 2 x-intercept/afsnit: 0-4 ¥ subst/verv x+2 y=0 -l= =3 x+2 —~x-2=3 ¥ simplification/vereenv. taal ¥x=l x=1 (3) x-intercept/afsnit is (1 ; 0) 5.6 | ya-x+e 1=-(-2)+e ¥ subst/verv —l=c ya-xl ¥ answer/antw. (2) OR/OF y-l=-(x-(-2)) ¥ subst/verv y= -x-2+1 yarxed ¥ answer/antw. L _ = (2)

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 13 DBE/November 2017 CAPS/KABV ~ Grade/Graad 11 - Marking guidelines/Nasienriglyne 5.7 tf ¥ asympt/asimpt v Shape / vorm vx and/eny intercepts / afsnitte & ¥ asymptote/asimpt v x-intercept/afsnit (-2 ; 0) v y-intercept/afsnit (0 ; -3) ’ H CG) ' ' Hy ' : : ' ' ' H ‘ eae ee eae we nessa co 1 H ‘ H t 5.8 | x<-3 or -2<x<-l V¥xs-3 ¥-2<x<-l OR/OF (2) xe(-0;-3)U (-2;-1] v¥ (-~ ;-3) ¥(-2;-1] (2) (21) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief G Wl

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 14 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne DBE/November 2017 QUESTION/VRAAG 6 6.1 O=-x? -x+6 vy=0 2 ¥-6=0 ¥ standard form/vorm ( Ns ») ¥ factors/faktore x+3}x-2)=0 x=-3 or/of x=2 “ both answers/beide antw B(3;0) and C(2;0) @) 62 | = - ; ~ - ar NOTE/ LET WEL: ( 1) If answer only: award 2/2 marks x= a) Slegs antwoord : gee 2/2 punte ¥ method/metode _!1 ¥ answer/antw. 2 2) OR/ OF _ x t+% a) ¥ method/metode _ ©3)+() 2 1 | Wanswer/antw 2 @) 6.3 1 A-3) ly (1 1 a v 64 TP/ DP (-}: 63] 2 4 Range/waardeversameling ye (- 0 56 ] ¥ Answer/antw. OR/OF y< 65 @) 6.4 DO; 6) ¥ coordinates/kodrdinate D — 6-4 Map = 0- C 2) 1 ¥ gradient. - v Equation of/vergelyking van g: g(x)=x+6 answer/antw @) Copyright reserved/Kopieregvoorbehou G& \Wd Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V2 15 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne [6.5 Average/Gemid. gradient = gradientof/van g =1 v answer/antw. ql) 6.6 1)? 25 ¥ in the form/ in die vorm sts)=-{x+) +> Ly 25 2 4 se)={x+4) +— 14) 25 4 i(a)=[+-3) -— 2 4 5)? 5) 25 Y (+ - 5) nfs)-[+-3] -— 2 2 4 ve. 25 4 OR/OF (3) J (x)= -x? -x+6 A(x) = (x-3) +(x-3)-6 V h&x)=(x~-3) + (x-3)-6 h(x) = x? —5x 5 2 Vlx | wa) =(x-3) _25 [ 2 2 4 25 vs 4 (3) 6.7 -3<x<2 ¥ v answer/antw. (2) OR/OF xe (33 3 2) ¥ ¥ answet/antw. | = _ 2) 6.8 r=-2 Yr=-2 By symmetry/deur simmetrie p=l ¥vp=1 p-r=3 ¥ answet/antw. OR/OF (4) -x-x+6=4 =x? -x+2=0 x 4+x-2=0 (x + 2x - 1) =0 x=-2 orlof x=1 r=-2 vr=2 p=l ¥vp=1 p-r=3 ¥ answer/antw. (4) [22] Copyright reserved/Kopieregvoorbehou G \NW Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 16 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne QUESTION/VRAAG 7 71 A =P(l-i)' 20000= 80000(1— i) ¥ substitution into correct 0,25 =(1-i) formula/ verv.in korrekte vorm 4/0,25=1-i i=1-4/0,25 ¥ simplification/vereenv £=0,24214417 i= 24,21% ¥ answer/antw. @) 72 _Y Itig = ( vs ¥ vorm/vorm eg, af 14.2295 ’ Fhe HEE ¥ subst/verv ig = 0,050945336... Effective rate = 5,09 % p.a. Y answer/antw. (3) 73°) A=P(1+i)" vom 2x12 4x2 ¥ 300061 02) -s000({1+°) [1.0) “2 12 2 y (1-202) =R58 017,51 12 4x2 v [: + an 08 } OR/OF ¥ answer/antw. \n (4) A=P(1+i) 0,12)" ony? =30 ooo +) “30 oo{ + 0) =R38092,04 Y¥ R38092,04 co Y 38092,04 [« 2108) 0,108 4x2 2 A =38092,04{14°0°8) v answer/antw. 2 (4) =R58 017,51 Copyright reserved/Kopieregvoorbehou G& \Nl/ Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 17 DBE/November 2017 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrigiyne _ 74 5x12 Bld 1,512 0,18 A=25000 14018 — 800! 14.018 +400 14 018 v 12 12 12 12 Sx12 60 36 18 v O18 =25000{ 14228) — good 1+248} + a00014 248 25000( 1+ 12 12 12 sas =R52636,74 v ~ aoo0{ +238) 18 v + ao0o( 1-938) 12 v¥ Vanswer/antw. OR/OF 2x12 018 4 -25000(1+°28 are 12 = R35 737,57 Amount in the account after the withdrawal:/Bedrag in rekening na onttrekking R35 737,5703—R 8000 = R 27737,5703 Amount in the account just before the deposit/bedrag in rekening voor die deposito 1,5«12 A, = R27737,3703 [: + “3) =R36262,45279 Amount in the account just after the deposit/Bedrag in rekening na onttrekking R 36262,45279 + R4000 =R 40262,45279 Amount in the account at the end of 5 years/Bedrag in rekening aan die einde van 5 jaar 1,542 = 40262,45279(1 + 8) 12, =R52636,74 2x12 v 25000 14 218 12 ¥ 27737,57 13x12 ¥ 27737,5703 ( + 1) v 40262,45 ¥ answer/antw. (6) [16] Copyright reserved/Kopieregvoorbehou & Ww Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 18 DBE/November 2017 CAPS/KABV - Grade/Graad 11 - Marking guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1.1 | : | 3 (BB) ¥ branches/takke ¥ probabilities/waarskynlikhede | | R (@;R) ¥ outcomes/uitkomste B (R;B) | | 3 R (R;R) 8 8.1.2 = P(R,B) = 2,3 NOTE/ LET WEL: 23 5 4 If answer only: award 2/2 marks Vv 7x 3 Slegs antwoord : gee 2/2 punte 5 4 =T07 0,3 v answer/antwoord Q) 8.2.1 | P(A) =0,4 P(B) = 0,3 P(A or B) = 0,58 P(A or B)= P(A) + P(B) — P(A and B) 0,58 =0,4+0,3 —P(A and B) P(A and B) =0,12 +0 Events A and B are not mutually exclusive/Gebeurtenis A en B is nie onderlinguitsluitend nie ¥0,58 = 0,4 +.0,3— P(A and B) Y P(A and B) =0,1220 YNot mutually exclusive/ nie onderling uitsluitend nie @G) 8.2.2 P(A andB) = 0,12 P(A) x P(B)=0,4 x 0,3 =0,12 ..P(A and B) = P(A) x P(B) Y P(A) x P(B)=0,4 x 0,3 v¥ P(A and B) = P(A)x P(B) A and B are independent events/is onafhanklik vA and B are independenvis onafhanklik (3) [11] Copyright reserved/Kopieregvoorbehou G& WWW Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 19 CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne DBE/November 2017 QUESTION/VRAAG 9 9.1 n(S) = 80 _ _ ¥ 14 or/of 12 or/of 15 R aa Vv v 26— | 26-x (14) 13-x 26x {o> ¥ 13—x x | 12 15 v5 | 5 3 3 | Cc — (5) 9.2 26-x4+144x+1245+415+13-x+3= 80 v 88-80 =x 26—x+144x4+12454154+13-x4+3 x=8 ¥ equating to/gelyk aan 80 _ 2) | 9.3 Number who chose Rugby only/aantal wat net rugby kies =26-8 =18 ¥ answer/antw. | (1) 94 P(At least 2 types of sports /ten minste 2 sportsoorte) 1241441548 ¥ numerator/Noemer = a a ¥ denominator/Teller NOTE/ LET WEL: = 49 If answer only: award 3/3 marks ¥ answer/antw. 80 | Slegs antwoord : gee 3/3 punte GB) OR/OF P(at least 2 types of sport/ten minste 2 sportsoorte) 18454543 vy 18454543 a 80 ¥ method/metode 31 =]-2 80 _ 49 ~ 80 ¥ answer/antw. (3) [13] | Copyright reserved/Kopiereg voorbehou G yi TOTAL/TOTAAL: 150