Mathematics Grade 11 Paper 1 Eastern Cape November 2018 Memo

__Downloaded from hlayiso.com gen Doan oad basic education ) Department: QY HI Basic Education y REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 11 | “a * " MATHEMATICS P1/WISKUNDE V1 . / a M NOVEMBER 2018 : i. u iy u 1 MARKING GUIDELINES/NASIENRIGLYNE : Oo tate stafatetatete ete gtete etete ete a PTREECCOCOT Ere meeans? MARKS/PUNTE: 150 These marking guidelines consist of 18 pages. Hierdie nasienriglyne bestaan uit 18 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne 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. Consistent accuracy applies to ALL aspects of the marking marking guidelines. Assuming values/answers in order to solve a problem is unacceptable. LET WEL: As 'n kandidaat 'n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na. 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 DBE/November 2018 LL x(2x +1) =0 1 =0 ork =-— x or/of x (2) 1.1.2) 5x? +2x-6=0 x ~b+,/b’ —4ac 2(5) _ 5+ V124 10 x=0,91 or/of x= -1,31 2 _2@t oy ~46)-6) 1.1.3 2x? -2> 3x 2x? -3x-2 20 (2x +1(x—2) 20 xs -5 or/of x22 Y substitution into correct formula/ vervanging in korrekte formule v answer/antw. v answer/antw. = G) ¥ std form/stand. vorm ¥ factors or using formula/ Saktore of gebruik formule Y0xs-3 orlof x22 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde VI 3 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne 2x +5 Let J2x+5 =k p-3=-2 ‘ 2k 42 ke 3-0 ¥ changing to quadratic/ ( ket 3) ( k- 1)= 0 verander na kwadraties k=—-3 otlof k=1 ¥ factors or using formula/ Saktore of gebruik formule V¥k=3 orlofk=1 y2x+5 =-3 2x+5 =1 no solution orlof 2x+5=1 . “no solution/ geen oplossing 2x=—4 x=-2 “square both sides/ kwadreer beide kante ¥Y yx=-2 OR/OF Jix+5 -—3—=-2 (6) 2x +5 (lax +5 ) -3=-2,2x +5 (lax +5 } +2(/2x +5 }-3-0 (/2e +5 +3\ (2x +5 -1)<0 —= v changing to quadratic/ af =- 2. = px +5 3 or v r+5 =I verander na kwadraties V2x+5 =-3 2x45 =1 ¥ factors/fakt. or/of iosin he no solution x4+5=1 v 2x +5 =-3or/of\2x +5 =1 2x=-4 . 2 Y¥ no solution/ geen oplossing x= ¥ square both sides/ kwadreer beide kante OR/OF ¥ x=-2 (6) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 4 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne . _ V2x+5—- =-2 v2x+5 2x+5-3=-2V2x+5 2x+2=-2V2x+5 2 2 f (x +2) = (2 2x+ 5) ¥ Multiplying by/ Vermenigy. met 4x? 48x44 =4(2x45) is 4x? + 8x44 =8x +20 oars! 4x? -16=0 x’ -4=0 ¥ square both sides/ (x+2)(x-2)=0 kwadreer beide kante 2 or lof x#2 % std form/ vorm ¥ factors/fakt. ¥ x#2 ¥Y x=-2 (6) 1.2 y+x=2 and/en = x? +3xy+8=0 2 y=2-x x? +3x(2—-x)+8=0 VY y=2-x x? + 6x-3x" +8 =0 ¥ substitution/verv. -2x? +6x+8=0 x°~3x-4=0 (x-4)(x+1)=0 ¥ std form/stand. vorm x=4orx=-1 ¥ 5 4 orfof * 3 ~C) ¥ factors or using formula/ y= y= Jaktore of gebruik formule ¥ both x-values/wrdes ¥ both y-values/wrdes OR/OF (6) yrxu=2 and =x? 4+3xy+8=0 “ x=2-y V x=2-y Q _ yy +3(2-y)y+8=0 ¥ substitution/verv. 4-Ayt+y? +6y—3y? +8=0 —2y? +2y+12=0 ¥ std form/stand. vorm vy -y-6=0 (y-3y+2)=0 ¥ factors or using formula/ y=3ory=-2 faktore of gebruik formule x=2-3 or x=2-(-2) both y-values/wrdes x=-l or x=4 ¥ both x-values/wrdes © Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 5 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne 13 4+,/16—4m(—m+5) eee ee 2m For non -real roots/Vir nie-reéle wortels: 16—4m(-m+5)<0 16+4m? —20m<0 m=” —5m+4<0 ¥16—4m(-—m+5) <0 | ¥ factors or using formula/ (m—4\m—1)<0 Saktore of gebruik formule l<m<4 VVleme4 (4) 14 | —x? 44x+412 =-1(x? —4x-12 c x-12) v-1(x? -4x—12) =o vata a1 ¥ ~1(x? 4x 4+4-4-12) =-1(x-2)' +16 Y¥-1(x—2) +16 The maximum value of/Die maksimum waarde van —x? +4x+12 is 16 max value of /—x? +4x+12 is4 ¥ V16=4 (4) OR/OF OR/OF Vx? +4x412 max when y= 2a -4 ¥ subst/verv. ~ 2-1) =2 “x-value/waarde -_(oP max valuey ©) +4(2)4+12 ¥y-value/waarde The maximum value of/Die maksimum waarde van ~x? +4x412 is 16 .. max value of \)—x* +4x+12 is 4 ¥ Vi6 =4 (4) [29] | Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 DBE/November 2018 CAPS/KABV — Grade/Graad 1 — Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1 233 3 91 or? 2824-3242! ~ 2%97 v separate bases/aparte basisse 2*(2°-3.2 = rm 72 ¥ common factor/gemene fakt. a ¥ (23 -3.2) =-6 -8 _ i 4 __ 47 ¥ answer/antw. > (4) 2.2.1 3 16x ? =2 3] x75 g ¥ isolating/isoleer x 2 3)\3 2 : 2 ) = Oe ) 3 v raising both sides by/verhef albei kante met — 2 x4 3 v answer/antw. (3) OR/OF 3 2-16x? =0 -3 2=2' x? ¥ prime base/priembasis 3 27 =x? Y exp law/eksp. wet x=2°> x=4 Yanswer/antw. GB) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne DBE/November 2018 2.2.2 | 4*+8=9.2" | (2? -9.2* +8=0 2* ~9.2* +8=0 ¥ standard form/stand. vorm (2x -8\2* -1}=0 2*=8 or 2*=1 ¥2*=8 or 2°=1 27 =23 2% =2° x=3 x=0 x=3 v x=0 OR/OF (4) 4° +8 =9.2* (2? -9.2" +8 =0 2* -9.27 +8=0 Let 2*=k kh? -9.k +8=0 ¥ standard form/stand. vorm (k-8\Xk-1)=0 k=8 or k=l 2° =8 2*=2° ¥2*=8 or 2*=1 x_ 93 _ 2*=2 x=0 v 3 x=3 v x=0 (4) 2.23 | [9 =243 =Y a(x V3) =(3 2 5 ( ) ) ¥ exp form/eksp. vorm 3* =3 32 35 20 5 OR/OF 2=5x ¥ equating the exp/gelykst van eks x 2 2 x= 5 v answer/aniw. x= (3) 5 5 23 | Vp*-9' x(p+a)? a (p-ap | 3 v difference of 2 s —q\pt+@)xlp+qp quares = Mo~aho+a)xlo+ap verskil van 2 kwadrate (p-ap: v : ay (p + a x (p + q) exponent law/eksponentwet oa 15 =(p+q)22 3 Y answer/antw. =(p+q (p+a) (3) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 8 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne OR/OF 5 vp’ -4 x(p+q)? (p-a: _ |@-aDeraXrtay “y a) —4 = \(p+4q)° v difference of 2 squares verskil van 2 kwadrate 3 = (p + a) ¥ exponent law/eksponentwet v answer/antw. (3) [17] QUESTION/VRAAG 3 3.1.1 7 2 - <5 5 T,=an+b ¥ ~ =-5n+12 (2) 3.1.2 | Ty =-5(20)+12 Y substitution/verv. =-88 ¥ answet/aniw. (2) 3.1.3 | —5n+12=-138 ¥ substitution/very. —5n=-150 " ¥ answer/antw. n=30 (2) 30" term(T,, ) 3.2 6 2x+1 3x-3 \ 4 _~ / 2x-5 x-4 v 2x—5 and/en x-4 2x-5=x- * x4 ¥ equating/verg. x=l ¥ answer/antw. G3) [9] Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 9 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienrighne QUESTION/VRAAG 4 4 p 11 22 oN a ON a oN ™ a p-4 ll-p q-l 22-q -~2p 415 q+p-2 332g 41 1" difference//*® verskil: p-4; ll-p; q-ll; 22-q¢ 2" difference/2® verskil: —2p+153q+ p—22; 33-2q¢ —2p+15=1 —2p=-14 p=7 33-2q=1 q+ p-22=1 -2g=-32 orlof = g+7-22=1 g=16 q=16 OR/ OF —2p+15=1 -2p=-14 p=7 4 7 11 3 4 5 ‘ee ee 1 1 Y p—4;11- ps q-11; 22-4 Y ~2p4153q+ p—22: 33-2q ¥—-2p+15=1 and/en 33—2q=1 3) v p-4;1l-p VY -2p+15=1 ¥ subst. of p in pattern to find q/ vervang p in patroon om q te vind (3) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde VI DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne 4.2 2a=1 aati Vaal 2 2 3at+b=3 {5} r6=3 vb=2 b=3 2 2 at+b+c=4 Lib yecg 2 2 ¥c=2 c=2 i 3 1 3 VT, ==n?+=n+2 T,==n’ +in+2 2 2 2 2 (4) OR/OF T,=c=2 ¥c=2 2a=1 awl 2 Vai T, =an’ +bn+e 2 4S" +b(I)+2 5-2 Vp=5 2 2 14,3 T=5" +5nt2 VT, 21+ 3n42 2 2 (4) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 11 CAPS/KABV — Grade/Graad 11 -— Marking Guidelines/Nasienriglyne DBE/November 2018 43 7, =232 Vin? s3nt2 =232 1,3 2" 3 <n +—n+2 =232 2 2 se +5n -230=0 ” standard form/std. vorm n +3n-460=0 ¥ factors/subst quad. eq. (n+23\n—20)=0 [faktore/ verv kwadr. verg n=—23 orn=20 selecting/kies n=20 (4) 44 1? +3 nsoeh (arty +3 (n41)42=1227 2 2 2 2 Le s3ns2t h(n? 42n41e 3 ne 342 =1227 2 2 2 2 #2 Ly tng 2edntans ty 3ng342=1227 2 2 2 22 2 n? +4n+6=1227 n’ +4n-1221=0 (n+37\n-33)=0 n#-37 n=33 1 3 1 3 Ty —Ts, = 564) +5 G4)+ 2-(40) +5 63)+ 2] Ty, —Ty, = 631-596 Ly, — Ty = 35 ¥ subst into/very, in T, +T,., =1227 ¥ expansion/ontw. ¥ standard form/std. vorm v value off/wrde van n v answer/antw. (G) [16] | Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 12 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1 | x=3 ¥x=3 Vy=2 ye (2) 5.2 4 O= Par es ¥ subst./verv. y= 0 4 -2= 73 ¥ simplification/vereenv. —AUx-3)=4 -2x+6=4 x=1 v answer/antw. Q) OR/OF (1:0) ¥ ¥ ¥ answer/antw 3) 53) 4 ye 03° ¥subst/verv. x =0 2 =3 ¥ answer/antw. (2) OR/OF ¥ ¥ answer/antw 3 5.4 For/Vir f ¥ asymptotes/asimptote ¥ shape/vorm vx- and y- int. /afsnit For/Vir g ¥ x-int/afsnit ¥ y-int /afsnit (5) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 13 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne 8 ——+2=x+2 V4 gaxs2 x= x- Aa x42-2 x-3 4 =, x-3 x(x-3)= 4 ¥ std vorm/stand. vorm x’ ~3x-4=0 ¥ factors/faktore (x—4)(x+1)= 0 ¥ answers/aniw. x=4 or x=-1 (4) 5.6 | -l<x<3 vv answer/antwoord (2) 5.7 | y=xte 2=(3)+e -l=c “.y=x-1 Is an axis of symmetry off simmetrie-as van f v Olv4 +3; +2) [v4 +3;4 +2)= 0(5:4) v5 v4 OR/ OF G) x-l= 4 7) ¥ equating / vergelyk x-3 oe x-3 (x-3) =4 x’? -6x+5=0 (x-5)(x-1)=0 = = v5 x=5 or x=1 VA y=5-1=4 @) O(5;4) [21] Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 14 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1 ya-4 ¥ answer/antwoord Q) 6.2 D(3;25) v3 v 25 2) 6.3 ys25 ¥ answer/antwoord or ye(—0;25] (1) 64 | £(0)=-(x-3) +25 v i = =-(0- 37 425 substitute/verv, x=0 =16 E(0;16) Vf (0) =16 1 O41 2(0)= {3} -4 O75 ¥g(0)=-3 =-3 B(0;-3) v) EB =16—(~3) = 19units/eenhede answealarwWoard @) 6.5 x>3 or/of xE(3;0) ¥ ¥ answer/antwoord Accept/Aanvaar x>3 or/of xe[3;00) (2) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 15 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienrighyne 6.6 | yu O= {>| -4 2 | xl 4= {>| 2 atl 2= (3} 2 2-2" l=-x-1 x=-2 A(-2;0) B(O;-3) OR/ OF ~(x-3)' +25=0 (x-3)' =25 x-3=5 or x-3=-5 x=8 x=-2 A(-2;0) B(O;-3) y27V Ave gradient/Gemid gradiént =—*—+ % — % _ —3-0 0+2 = “2 Hy _ 3-0 042 -3 ~ 2 Ave gradient/Gemid gradiént = aM ¥ substitution/verv, ¥ equating exponent/gelykst. eksp. v answer/antwoord ¥ subst. into correct formula /very, in formule ¥ answer/antwoord ¥ substitution/very. ¥ factors or using formula/ faktore of gebruik formule ¥ answer/antwoord ¥ subst. into correct formula /verv. in formule v answer/antwoord (G) (5) Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 16 CAPS/KABV -- Grade/Graad 11 — Marking Guidelines/Nasienriglyne DBE/November 2018 67 | ae)=-el0) x+l =- {5 4 2 wa yt 2 Range/Waardeversameling:y <4 or y€(—»;4) ¥ y<4 or ye(-00:4) (2) 6.8 | Turning point/ draaipunt ; (3:27) v3 ¥27 (2) 6.9 F(x =-(x—3) +25 f@)= 3) VY —x? +6x416 -x°+6x+16=2x+k ¥ equating/vergelyk -x’ +4x+16-k=0 tangent has one point of intersection thus two equal roots/ raaklyn het een snypunt dus twee gelyke wortels v —~4(- -k)= A=(4)' -4(-1)(16-&) =0 (4f -4-1l6- &)=0 16+64-4k =0 80 =4k k=20 vanswer/antw. (4) [23] Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 17 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 TA - \m L lt+ig = [: + ‘us Y formula/form. | 011s)” 0,15 Mig =[1+ = yj — ls 12 12 O15)" i, =|1l+-—| -1 ‘f ( 12 i =12,13% ¥ answer/antw. (3) 72 | A=P(f-i)" ¥ formula/form. v. aie =4700(1-0,18 )* substitution/verv. =R2124,97 ¥ answer/antw. Q) 7.3.1 | A=P(1+i)" Y formula/form. 2x4 =20 ooo + 1 ¥ substitution/verv. 4 =R23 068,12 ¥ answer/antw. (3) 73.2) A =P(1 +i)" 0.078 2x12 = 23068,12{1+ 2078) 0078 sno = R26 949,12 R26 949,12—R2500 =R24.449,12 ¥ A(after 2 years) — R2 500 A =P(1 +i)" 0. 078 3x12 =24 449.12{11 3 } Vn=36 =R30871,61 ¥ answer/antw. (4) OR/OF 0,078 1x8 1293 vi =—— and n= 60 A =23 vos. + or -2500{1+ | bs ° ° vv ~2500{ 14.9078 =R30871,48 12 | v answer/antw. (4) [13] Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P 1/Wiskunde V1 18 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 81 Given/Gegee: P(G) = 0,25 . Let x be the total number of balls P(G)= g_1 y S.1 x 4 x 4 x =32 n(S) = 32 a) OR/OF Let x be the number of yellow balls +. x+14 be the total number of balls 8 1 P(G)= == (6) x+14 4 V gol x+14=32 x+14 4 n(S)=32 (1) 8.2 R (RR) R G (RG) $ Y (®/Y) R (G;R £ (GR) ¥18 (number of yellow balls/ ES < aantal geel baile) G G (G;G) Ss v branches/takke 3D GY ayy 18 y ¢ ) ¥ probabilities/waarskynlikhede 2 R (y;R) ¥ outcomes/uitkomste Y G (¥:6) y (Y¥;Y) (4) 83 | P(G,G)+P(R,R)+P(Y, Y) “ED 8 7) (6 5) (1817 | a2 > =) —x—|+] —x— [+] —x— v( 65 32 31 32 31 32 31 32 31 49 v (2) = 32 31 Io4 ¥answer/ antw (4) [9] Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde V1 19 DBE/November 2018 CAPS/KABV — Grade/Graad 11 — Marking Guidelines/Nasienrigiyne QUESTION/VRAAG 9 9.1 PCV) x P(M) | 32, = x = = 0,095 Lo. P(V and/en M)= cap 08 130 P(V and/en M) # P( V) x P(M) v P(-V)xP(M)=0,095 The events are not independent/Die gebeurtenisse is nie onafhanklik | Y PCV and/en M)=0,08 ¥ conclusion/gevolgtr. OR/OF () vy 22 P(V)xP(F) 150 32 83 v 83 =A x5 = 0,118 — 150” 150 "150 «) P(-V)x P(F) =0,118 P(V andF)= ap 70133 P(VandF) # P( V) x P(F) YPC and F) = 0,133 v . The events are not independent/Die gebeurtenisse is nie onafhanklik vonclusion/gevolgt 5) 92.1 | P(Aand/enB)=0,12 40 vy P(A and B)# 0 ¥ conclusion/gevolgtr. Events are not mutually exclusive/ Gebeurtenisse nie onderling (2) uitsluitend nie 9.2.2 | P(Aor B)=P(A)+P(B)— P(A and B) 0,83 = P(A)+ 4P(A)- 0,12 , formal formule 0,95 = 5P(A) substitution/very. P(A)= 0,19 v P(A) P(B)= 4(0,19) = 0,76 vP(B) | (4) 9.2.3 | P(notA)=1-P(A) v P(not A)=1-P(A) =1-0,19 =0,81 v answer/antw. 2) [13] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou