Mathematics Grade 12 Paper 1 Limpopo Prelim 2024 Memo

Downloaded from hlayiso.com PROVINCIAL GOVERNMENT REPUBLIC OF SOUTH AFRICA +, LIMPOPO DEPARTMENT OF EDUCATION NATIONAL SENIOR CERTIFICATE/NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 SPREE RRR, MATHEMATICS P1/WISKUNDE V1 MARKING GUIDELINES/NASIENRIGLYNE SEPTEMBER 2024 o PCP eee | ®ummumneent PUPP POPP RPE REPU CUP POORER ECU RUPE REPRE REE Pee © ia MARKS/PUNTE: 150 This marking guidelines consists of 17 pages/Hierdie nasienriglyne bestaan uit 17 bladsye Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 2 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne NOTE/NOTA: e If a candidate answers a question TWICE, only mark the FIRST attempt/ As ‘n kandidaat 'n vraag twee keer beantwoord, merk slegs die EERSTE poging. e Consistent Accuracy applies in all aspects of the marking guidelines/ Konsekwente akkuraatheid is van toepassing in alle aspekte van die nasienriglyne QUESTION/VRAAG 1 11 [111 | y~3x4+2=0 Hh actorization/faktore (x-2)(x-1) =0 Vx=2 x22 orlof 2=1 ¥x=1 (3) 1.1.2 | 3x° =-2-6x 3x? +6x+2=0 ¥ standard form 7 /standard vorm ge =(6) + Y(6) —43)(2) ¥ subst into correct 2(3) formula/subst in korrekte “.x=-1,58 or/of x=-0,42 formule ¥ x=-1,58 (4) ¥x=-0,42 1.1.3 2x-l=Vl-x 2x-1) =(VI=x) ( ) ( ) ¥ squaring both sides/ 4x°-4x+1=1-x kwadreer albei kante 4x°-3x=0 ¥ standard form x(4x-3) =0 /standard vorm ; 3 ¥ x=Oor/of x=— x=0 or/of x=— 4 2 x= i 4 x== a (4) 1.1.4 | (x+3)(3-x)<0 (x+3)(x-3)>0 CV:x=-3 or/of x=3 x<-3 or/of x>3 ¥ critical values/kritieke waardes ¥¥ answer/antwoord (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 3 NSC - Marking Guidelines/Nasienriglyne Limpopo DoE/ September 2024 12, 2x=y+2 a y-2=x°-3x (2) y=2x-2 V y=2x-2 Subst in (2) 2x-2-2=x7-3x ¥ substitution / substitusie 2x-4=x° -3x ¥ simplification/vereenvoudig x -5x+4=0 ¥ standard form (x-1)(x-4) =0 /standard vorm x=1 or/of x=4 ¥x=1 or/of x=4 y=0 or/of y=6 ¥ y=0 or/of y=6 (6) OR/OF OR/OF Qx=y+2 (dy y-2=x-3x (2) _yt2 a) Pen subst xin (2) 2, 2 2 ¥ substitution / substitusie y-2= yt4y+4 _ 3y-6 ¥ simplification/vereenvoudig 4 2 4y-8=y?+4y+4-6y-12 2 ¥ standard form y -6y=0 /standard vorm y=0 or/of y=6 Y y=0 or/of y=6 x=1 or/of x=4 ¥ x=lor/of x=4 (6) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 4 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne 13 x=— equate (1) and (2) 72_ 72 x ReES +0,2 72x+360=72x+0,2x° +x 0,2x" + x-360=0 x° +5x-1800=0 (x-40)(x+ 45) =0 x=40 or/of x=-45 x=40km/h 72(x+5) = 72x+0,2x(x+5) Pasi. x 2 Cy x+5 ¥ substitution / substitusie ¥ standard form /standard vorm ¥ x=40 GS) [25] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 5 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne QUESTIONVRAAG 2 21 214 ie A180 =D vccssmrcccsseel (Ll) ¥ a+3d =5. Bei CASE vscsscsceivases (2) V¥ a+13d =15 10d =10 ¥ 10d =10 d=1 Y answer/antwoord (4) 212 a=2 vY a=2 T, =a+(n-Nd =2+(n-I)l =n+l v T,=n+1 (2) 2.1.3 | S,= 5 [a+ (n-1)d] 22 3 = —[2(2) +(22- d)] ¥ subst into correct formula/ 2 subst in korrekte formule =11(25) 275 Y answer/antwoord (2) 2.2. x VY wa 7x 7x-13 v Ist difference// ste verskil 7x-19 v 2nd difference/2de verskil 7x—-13-6=6-(7-x) ¥ equation/vergelyking 7x-19=-1+x 6x=18 _ ¥ answer/antwoord (4) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 31 | s = l-r 1 Vr=— = 3 = 1 ¥ subst into correct formula 3 /subst in korrekte formule =3 Y answer/antwoord (3) 32 S,= a(l-r’ l-r of (4) S =~ 4 ¥ subst into correct formula " 1- 1 /subst in korrekte formule 3 2) 1- i) 2) 1- i) 3 3 = v 2 2 3 3 =3 -(5] 43 1-(3] 3 3 = (2) 3) 3 Ly" LY" 3.3, | 3-3] =| >2,99 ¥ 3-3] —| >2,99 3 3 1" 0,01 z] 3 ¥ simplification/vereenvoudig 1 0.01 ¥ use of logs/gebruik logs nlog = < log —— 8 3 0,01 log —— n> 3 log i 3 n>5,19 ¥n>5,19 Smallest value of/Kleinste waarde van n is 5 ¥ reasoning/redenasie (5) {11] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 QUESTION/VRAAG 4 7 NSC - Marking Guidelines/Nasienriglyne Limpopo DoE/ September 2024 4.1 4.1.1 f(x =-x? +x412 y — intercept/afsnit (x=0) y=12 A(0;12) “AF eH2=0 Y equate to 0/gelykstel 0 x’-x-12=0 (x-4)(x+3)=0 x=4 or/of x=-3 V¥x=4 or/of x=-3 (2) B(4;0) 4.1.2 | y=mxt+k y=mx+12 V¥k=12 Passing through/Gaan deur B (4;0) 4mrl2=0 ¥ substitution / substitusie m=-3 v 3 4 y=-3x4+12 me~ ®) OR/OF OR/OF 12-0 m>=— 0-4 =-3 ¥m=-3 y=mx+k B(4;0) 0=-3(4) +k ¥ substitution / substitusie wk=12 Vk=12 y=-3x+12 (3) 4.1.3 (a) EF =EG-FG = (—x? +.x+12)—(-3x+12) = [-(2)° +(2)4+12]—[-3(2) +12] ¥ substitution / substitusie EF = 4 units / eenhede Y answer/antwoord (2) OR/OF OR/OF EF = (-x? +x+12)—(-3x+12) =-x +4x =-(2) +4(2) ¥ substitution / substitusie .. EF = 4 units / eenhede Y answer/antwoord (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 8 NSC - Marking Guidelines/Nasienriglyne Limpopo DoE/ September 2024 Vv -~<x<4 2 (b) | Area of / Opy van AOGF construct / konstrueer : PF//OG = Area AAPF + Area OPFG 1 Ling 5 4 %5@) == (2)(3)+ (6x2) 2 v (6x2) =18 Y answer/antwoord (3) bo Ss OR/OF OR/OF AOGFis a trapezium Area / Opv = 5 (FG +AO)h 1 ¥ (6+12) =—(6+12)2 2! , v2 =18 v answer/antwoord (3) OR/OF OR/OF Area of / opv van AOGF = Area (AAOB — AGBF) 1 1 1 = = (4)(12) — —(2)(6) ¥ —(4)(12 3 ) 3 * )(12) =18 1 v¥ ~(2)(6) 2 (3) ¥_answer/antwoord 414 C(-3:0) f'(x)=-2x41 v f'Q)=-2x41 f'(-3)=-2(-3)+1 =7 ¥m=7 y—0=7(x+3) y=7x+21 V y=7x+21 7x+21=-3x+12 Y¥ 7x+21=-3x+12 10x=-9 x=-0,9 v¥x=-0,9 y=14,7 v y=14,7 (6) T ge 4.1.5 x<-3 or hegea as 2 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 9 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne 4.2 4.2.1 ¥ shape/vorm ¥ aymptotes/asimptote ¥ x — intercept/afsnit vy — intercept/afsnit (4) 4.2.2 x $29) x+2 +220 “+2 VV x<-3or/of x>-1 x<-3 or/of x>-2 (2) 4.2.3 y-2=-x-2 v y-2=-x-2 y=-x Pegs 5 (2) y=-(x+ p)+q y=-(x+2)+2 VY y=-(x+2)4+2 y=-x VY y=-x (2) OR/OF OR/OF y=-x+e 2=-(2)+e ¥2=-(2)+e c=0 y=-x Vv y=-x (2) [27] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayi Mathematics P1/Wiskunde V1 10 NSC - Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 so.com Limpopo DoE/ September 2024 5.1 h(x) = log, x Passing though/gaan deur (16;4 ) ¥ substitution / substitusie 4=log,16 a’ =16 ¥ change to exponents/ vernader na eksponente a=2 v answer/antwoord @) 5.2 | y=log,x =x x=2° x=1 B(1;0) v B(1;0) 1e0) 5.3 | y=log, x xelog,y v interchanging/ruil x & y y=2" ’ Vi'(x)=2" oA(x) = 2? Q) 5.4 | Range / waardeversameling: y >0 vy>0 (1) OR/OF OR/OF ye(0; ») ye(0; ~) @ [7] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 11 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 0.115)" ¥ subst in correct formula 6.1 | l+ig = (: ah on) /subst in korrekte formule : v 0,115 L+i,g =1,120055 ri iy =0,1200 -. rate / koers =12% Y answer/antwoord @) 40 62 | A=200 000(1+145 400 ¥n=40 = R621 475,37 Y answer/antwoord (2) 6.3 | Loan amount/Lening bedrag =1 850 000-621 475,37] ¥ Loan/lening = Rl 228 524,63 Y answer/antwoord (2) 64 P= x{l- d+) ] I -300 Gee) | ¥n=-300 ¥ subst in correct formula 228 524,63 12 /subst in korrekte formule 1200 y 12 1 228 524,63 =94,94655125x 1200 x=12 939,12 Y answer/antwoord (4) 65 | Balance/ Balans = “1—G+#)"1 i -120 12 sanaa|t-(14 3) vn=e120 = 1200 ¥ subst in correct formula 3 /subst in korrekte formule = R901 863,28 Y answer/antwoord (3) OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Mathematics P1/Wiskunde V1 Downloaded from hlayi 12 NSC - Marking Guidelines/Nasienriglyne so.com Limpopo DoE/ September 2024 Balance / Balans = A-F 180 12 939,12 (5) =f 1200 Y subst in compound formula/vervang in saamgestelde formule 180 Sorcritucts =1 208 524,63 14 12 _ subst in Future value/ 1200 12 vervang in toekomstige 1200 formule v 3 = 901 863,28 answer/antwoord G3) 6.6 | Interest/Rente =12 939,12x300-—1 228 524,63 ¥ calculation/bewerking = R2 653 210,76 Y answer/antwoord (2) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 13 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 TL | f(x) =3x° f (x+h) =3(xth) =3x° +6xh+3h? f= Him f(xth)- f(x) ¥ 3x? +6xh + 3h" =lim 3x1 + 6xh+ 3h 3x" ¥ substitution / substitusie h>0 h 2 2 = fim Sat 3h vlim Gxh+ 3h” h>0 h =H h + = fim 16%43h) V tim 2662+ 3h) hoo h hoo h shige ¥ lim(6x+3h) hoo off 0 =6x ¥ answer/antwoord (5) OR/OF OR/OF f(x) =3x7 h)— f'@)=lim£ e+ )-f@) - 0 h ¥ substitution / substitusie . 3(x+hy -3x? — , 5 8G ¥ 3x? +6xh+3h" . 3x +6xh+3h —3x" ee h 6xh+3h" , Vimo . 6xh+3h h>0 h a h(6x+3h) V lim Ox) =lim h(6x+3h) h0 h a0, ik Y lim(6x+3h) = lim(6x + 3h) cd (5) = Y answer/antwoord =6x 721 1 f(x) =(x-DOS 4+ 42448427 4+x41) Hx t x8 ex txt tx exr tx ¥ products/produkte —x§-x° —x4-x°-x?-x-1 =x’-1 S xh-A fi) = 73° V 7x8 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 14 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne 7.2.2 | D, 42x 44x , x+1 =D [zee] ¥ simplification/vereenvoudig . x+l1 P Biovee =D, [x +x] v 2x =2x+l v1 (4) 7 1 7.2.3 | y=¥x-— 3x ; - s 1 vx 3 vy dy 121, 3 six +=x 9 da 3 3 Gigs 3 1, v=x” 4 3 (4) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 15 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1 | £(3)=2(3)[)? -9(3)+24] “substitution / substitusie = 6 Y answer/antwoord 2) 8.2 | f(x) =2x3-18x7 + 48x f (x) = 6x° —36x+48 ¥ derivative/afgeleide 6x° -36x+48=0 ¥ standard form 2 /standard vorm —6x+8=0 ti ORE vx — values/waardes (x-4)(x-2)=0 J _ _ y — values/waardes x=4 or/of x=2 (4) y=32 or/of y=40 8.3 y (2;40) ¥ shape/vorm ¥ turning points/ draaipunte Y origin/oorsprong x | G3) 8.4 32<k<40 v V answer/antwoord (2) 8.5 Maximum/Maksimum is 40 ¥ max/maks 40 (1) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 16 Limpopo DoE/ September 2024 NSC - Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 9.1 | A=a2R* +2’. ¥ Equation of A/ R+r=200 Vergelyking A F=200 =Riecsxcseeceet (2) Yr subject of formula/ r Subst (2) in (1) onderwerp formule A=2R? +2(200-R)Y* ¥ substitution / substitusie = R? + 2(40000—400R + R?) = 2R’ +. 400002 — 4002R + 2R° = 22R° — 40072 R + 400002 (3) 9.2. | At minimum aA 0 fA. 0 dR dR 4zR-400z =0 Y 4xR-4007 "te e, ¥ R=100 r= 200-R=100 oe (4) 9.3. | R=r=100, will not get the desired shape because a shape with two equal circles touch externally/ sal nie ¥¥ valid explanation/ die gewenste vorm kry nie, want 'n vorm met twee gelyke geldige verduideliking sirkels raak ekstern (2) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai asseblief om Powered by @ camscanner

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 17 NSC - Marking Guidelines/Nasienriglyne Limpopo DoE/ September 2024 QUESTION/VRAAG 10 10.1 | P(A or/of B)=P(A)+P(B) = 0,45+0,25 ¥ 0,45+0,25 =0,7 Y answer/antwoord , (2) 10.2 | 10.2.1 = 2@ 49 30 c 7 Sand /en = 50 20 N v2 a oniten 49 v BU end fent 30 ° 20 49 50 N IN y 49 (3) 30. 20 20 30 30 20 10.2.2 | PONC)=( 30x22) 4/ 29.28 (2.2) = & a) (3 | 5049 =0,41 y{ 20 30 50 49 Y answer/antwoord (3) 10.2.3 | P(CC) = 20. 29 FBig2? 50 49 50 49 =0,36 Y answer/antwoord (2) 10.3 $103.1 | 40°52 Y10xS = 25000 Y answer/antwoord (2) 10.3.2 | 9x9x8x4x1 V¥9x9x8 = 12960 v4xl v answer/antwoord (3) [15] Copyright reserved/Kopiereg voorbehou TOTAL/TOTAAL: 150 Powered by @ camscanner