Technical Mathematics Grade 12 Paper 1 NSC November 2018 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE 12/GRAAD 12 TECHNICAL MATHEMATICS P1/TEGNIESE WISKUNDE V1 NOVEMBER 2018 MARKING GUIDELINES/NASIENRIGLYNE MARKS: 150 PUNTE: 150 Marking Codes / Nasienkodes A Accuracy / Akkuraatheid CA Consistent Accuracy / Volgehoue Akkuraatheid M Method / Metode R Rounding/ Afronding NPR No Penalty for Rounding/ Geen penaliseering vir Afronding NPU No Penalty for Units omitted /Geen penaliseering vir Eenhede weggelaat S Simplification / Vereenvoudiging SF Substitution in correct formula/ Vervanging in korrekte formule 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 Technical Mathematics/P1/Tegniese Wiskunde/V1 2 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne NOTE: • If a candidate answers a question TWICE, only mark the FIRST attempt. • Consistent accuracy applies in all aspects of the marking guidelines where appropriate. LET WEL: • Indien 'n kandidaat 'n vraag TWEE keer beantwoord, sien slegs die EERSTE poging na. • Volgehoue akkuraatheid is deurgaans op alle aspekte van die nasienriglyne van toepassing. QUESTION/VRAAG 1 1.1.1 − 2 x ( x + a) (3 − x) = 0 x =0 A x= 0 or/of x = − a or/of x =3  x=−a A  x =3 A (3) 1.1.2 2x = 6 − x2  standard form/ standaardvorm x 2 + 2x − 6 = 0 − b ± b 2 − 4ac x= 2a  SF CA − 2 ± 2 2 − 4( 1 )( −6 ) = 2( 1 ) S CA − 2 ± 28 =  both values of/ beide waardes van x 2 CA ∴ x ≈ 1,65 or/of x ≈ −3,65 OR/OF OR/OF 2 2x = 6 − x x2 + 2x = 6 x2 + 2x + 1 = 6 + 1  completing square/ kwadraatsvoltooiing ( x + 1) 2 = 7  square as subject/ vierkant as onderwerp x +1= ± 7 CA  square root/ vierkantswortel CA x = −1± 7 ∴ x ≈ 1,65 or/of x ≈ −3,65  both values of/beide waardes van x CA NPR AO, full marks (exact values)/ volpunte (eksakte waardes) (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 3 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 1.1.3 5 x( x − 3) ≤ 0 Critical values: 0 and 3  both critical values/ ∴0 ≤ x ≤ 3 albei kritiese waardes OR / OF x ∈ [ 0;3 ] OR/OF  notation/notasie x ≥ 0 and x ≤ 3  graphical representation/ grafiese voorstelling CA (3) 0 3 1.2 x 2 + xy + y 2 = 21 y − 2 x = −7 and  y subject of formula/ y = 2x − 7 onderwerp van formule x 2 + x(2 x − 7) + (2 x − 7) 2 = 21  SF CA x 2 + 2 x 2 − 7 x + 4 x 2 − 28 x + 49 − 21 = 0 S CA 2 7 x − 35 x + 28 = 0 x 2 − 5x + 4 = 0 OR/OF (7x – 28 ) ( x – 1 ) = 0  factors/faktore CA ( x − 4)( x − 1) = 0  x-values/-waardes CA ∴ x = 4 or x = 1 y = 2(4) − 7 or y = 2(1) − 7 y = 1 or y ≠ − 5  y-values/-waardes CA  y =1 and/en x = 4 CA ∴ y = 1 and x = 4 OR/OF OR/OF y − 2 x = −7 y+7 x subject of formula/ x= 2 onderwerp van formule x 2 + xy + y 2 = 21 2  y+7  y+7 2   + y  + y = 21  substitution/ vervanging CA  2   2  y 2 + 14 y + 49 y 2 7 y + + + y 2 = 21 4 2 2 y 2 + 14 y + 49 + 2 y 2 + 14 y + 4 y 2 = 84  correct standard form/ 7 y 2 + 28 y − 35 = 0 korrekte standaardvorm CA y2 + 4 y − 5 = 0  factors/faktore CA  y-value/-waarde CA ( y + 5)( y − 1) = 0 OR/OF (y +5) (7y – 7) = 0 ∴ y ≠ −5 or y = 1  x-values/-waardes CA x = 1 or/of x = 4  y =1 and/en x = 4 CA ∴ y = 1 and/en x = 4 If not squaring y or x after substitution, then a maximum of 6 marks, Indien geen kwadrering van y of x na vervanging , dan ‘n maksimim van 6 punte (7) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 4 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 1.3.1 1  L2 subject/onderwerp E= ML2 12 12 E  L subject/ onderwerp CA L2 = (2) M 12 E 3E E AO, full marks /volpunte ∴L = OR / OF 2 OR / OF M M 12 M 1 1.3.2 12 E CA from Question 1.3.1/ L= van Vraag 1.3.1 M = ( 12 8, 3 × 10 − 2 )  SF CA 1,6 × 10 3  value of/waarde van L CA ∴ L ≈ 0 , 02 m OR/OF OR/OF 3E L =2 M 3( 8, 3 × 10− 2 )  SF CA =2 1,6 × 103  value of/waarde van L CA ∴ L ≈ 0 , 02 m OR/OF OR/OF 1 E= ML2 12 1 8,3 × 10− 2 = 12 ( 1,6 × 103 L2 )  SF CA 12 ( 8, 3 × 10−2 ) L= 1,6 × 103 ∴ L ≈ 0 , 02 m  value of/waarde van L CA (2) NPU NPR (Accept scientific notation/Aanvaar wetenskaplike notasie) 1.4 36 = 32 + 4  32 + 4 A = 100100 2  100100 2 A AO: Full marks/ Volpunte (2) [23] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 5 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1 −8± q−3 x= 2 2.1.1 Irrational / Irrasionaal  irrational / irrasionaal (Accept: real and unequal/ Aanvaar:reeel en ongelyk) (1) 2.1.2 Equal / gelyk  equal (Accept: real OR rational/ Aanvaar: reel OF rasionaal ) (1) 2.1.3 Non-real  non-real/nie-reël Nie-reël (accept imaginary/ aanvaar imaginer) (1) 2.2 2 3x + 7 x = 2 x + p 3x 2 + 5 x − p = 0 standard form/ standaardvorm ∆= b 2 − 4ac < 0  SF in ∆ CA ( 5 ) 2 − 4 (3 ) ( − p) < 0  correct inequality/ 25 + 12 p < 0 korrekte ongelykheid (<0) A 25 p<− 12 values of/waardes van p CA (4) [7] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 6 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1  73  3  73  3  2 a = 2 3 × a   exponent property/ eksponenteienskap A     = 8a 7  S CA OR/OF OR/OF 3  73   73   73   73   2 a  =  2a   2a   2a   exponent property/eksponenteienskap A       = 8a 7 S CA AO: Full marks / Volpunte (2) 3.1.2 log p p + log m 1 1 A = 1+ 0 0 A =1 AO: only one mark/ slegs een punt (2) 3.1.3 48 − 12 2 75 3 × 16 − 3 × 4 = 2 3 × 25 4 3−2 3 3 ( 4 − 2 )) 4 3−2 3 = OR  M 2× 5 3 10 3 2.5 3 2 3 = S CA 10 3 1 = S CA 5 OR/OF OR/OF 48 − 12 2 75 48 12 = − 2 75 2 75  M 4 3 2 3  S CA = − 10 3 10 3 2 1 1 = − =  S CA 5 5 5 AO: Only one mark / Slegs een punt (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 7 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 3.2 log 2 ( x + 62) − log 2 x = 5  x + 62  log 2  =5 log property/log-eienskape M  x  x + 62 exponential form/ eksponensiële vorm M 25 = x x + 62 S CA 32 = ⇒ 32 x =+ x 62 x x=2 value of/waarde van x CA OR/OF OR/OF log 2 ( x + 62) − log 2 x 5 = log property/ log-eienskap e M log 2 ( x + 62)= log 2 x + log 2 32 apply log property log 2 ( x + 62) = log 2 (32 x) pas log-eienskap toe M x + 62 = 32 x S CA x=2 value of/waarde van x CA OR/OF OR/OF log 2 ( x + 62) − log 2 x 5 = x + 62 log 2 = log 2 x log property/ log-eienskap M 25 x + 62 =x log propertys log-eienskap M 32 32 x= x + 62 S CA x=2 value of/waarde van x CA OR/OF OR/OF log 2 ( x + 62) − log 2 x 5 = log ( x + 62 ) log x − 5 =  log property/ log-eienskap M log 2 log 2 log ( x + 62 ) − log x = 5log 2 x + 62 log = log 25  log property/log-eienskap M x x + 62 = 32 ⇒ x + 62 = 32 x S CA x x=2 value of/waarde van x CA OR/OF OR/OF log 2 ( x + 62) − log 2 x 5 =  log 2 32 M log 2 ( x + 62) − log 2 x − log 2 32 0 = x + 62 log property / log-eienskap M log 2 =0 x ( 32 ) x + 62 S CA =1 value of/waarde van x CA x ( 32 ) AO: only one mark / slegs een punt 31= x 62 ∴= x 2 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 8 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 3.3 z= − 2+ 2 i z = r = x2 + y2 = (− 2 ) + ( 2 ) = 4 2 2 calculating the modulus/ bereken die modulus M =2 S CA  2  2  θ = tan −1   M θ = tan −1     2  2 OR any other trig. ratio to find θ OF enige ander trig verh, of θ te bepaal ref. angle/verwysingshoek CA π = 45° OR/OF 4 correct quadrant/ 3π θ = 180° − 45° = 135° OR/OF korrekte kwadrant CA 4  3π  polar form/polêre vorm CA ∴ z = 2cis(135° ) OR/OF z = 2cis    4  Accept/Aanvaar: z = 2[cos135° + i sin135° ]  3π 3π  z = 2 cos + i sin  4 4  (6) 3.4 p + qi = (2 − 3i ) 2 = 4 − 12i + 9i 2 expansion/uitbreiding = 4 − 12i + 9 (−1)  i 2 = −1 A = − 5 − 12i  p = −5 ∴ p = − 5 and/en q = −12  q = −12 CA (4) [21] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 9 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 Q4.1.2: Penalty of ONE mark if intercepts are not given as coordinates (refer also to Question 7.1}\ V 4.1.2: Penaliseer EEN punt indien afsnitte nie as ko-ordinate gegee (verwys ook na Vraag 7.1) 4.1.1 x = 0 and/en y = − 1 vertical asymptote/ vertikale asimptoot A  horizontal asymptote/ horisontale asimptoot A (2) 4.1.2 6 h( x) =− −1 x 6 6 0=− −1 0=− −1 M x x ∴ x =− 6  –6 A ( − 6; 0 ) (2) 4.1.3 horizontal asymptote/ horisontale asimptoot CA from /van Q/V 4.1.1 g:  intercept/afsnit (0 ; 0) A  shape/vorm A h:  x-intercept/-afsnit CA  both curves/beide kromme A (5) 4.1.4 g( − 2 ) = 2 −(−2) − 1 = 3 SF A OR/OF OR/OF −x 3=2 −1 22 = 2 − x ∴x = − 2 SF A (1) 4.1.5 y > −1 OR/OF y ∈ (−1 ; ∞ )  y > −1 A (1) 4.1.6 x≠0 OR/OF x ∈ ( −∞ ; 0 ) ∪ (0 ; ∞ )  A OR/OF x ∈R ; x ≠ 0 OR/OF x < 0 or x > 0 OR/OF x ∈R − {0} (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 10 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 4.2.1 M (1; 0)  (1; 0) A (1) 4.2.2 MT = 8 length of/lengte van MT A MR = g (1) = 36 − (1) 2 = 35 length of/lengte van MK SF ∴ TR = MT − MR = 8 − 35 length of/lengte van TR CA (3) 4.2.3 g (0) = 36 − (0) 2 = 6 SF A ∴L ( 0 ; 6 ) OR/OF OR/OF r = 36 = 6  calculating radius/bereken radius A L ( 0; 6 ) (1) 4.2.4 f ( x) = y = a (x + p )2 + q y = a (x − 1)2 + 8 SF (1 ; 8) 6 = a (0 − 1) + 8 2 a=− 2 a = – 2 CA ∴ f ( x) = −2(x − 1 )2 + 8 ( ) = − 2 x 2 − 2x + 1 + 8 S CA = − 2x 2 + 4x + 6 ( = − 2 x 2 − 2x − 3 ) common factor/ gemenee faktor M (4) ∴ f ( x) = − 2 (x + 1 )( x − 3) 4.2.5 ∴ K (−1 ; 0 ) coordinates of/ koördinate van K A (1) 4.2.6 CA from /van Q4.2.5 x ∈ (− 1 ; 0 ) OR/OF critical values/ kritiese waardes CA OR/OF −1 < x < 0 notation/notasie CA (2) [24] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 11 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1  i  m ieff = 1 + nom  − 1  m  12  i  SF 0 , 067 = 1 + nom  −1  12  12  i  1, 067 = 1 + nom   i   12   12 1, 067 = 1 + nom  CA  i  12 1, 067 = 1 + nom   12   12   12 ( 12 1, 067 −1 ) = inom CA ( inom = 12 12 1, 067 −1 ≈ 0,065 ) ∴nominal interest rate is/no min ale rentekoers is 6,5 %  6,5 % CA (Accept/aanvaar 0 ,065) (4) 5.2.1 R120 000  R120 000 A (1) 5.2.2 Reducing balance method/vermnderde balans-metode : A = P (1 − i ) n 120 000 = 240 000 ( 1 −16 % )n  SF n 0 , 5 = ( 0 , 84 ) n  0 , 5 = ( 0 , 84 ) CA n = log 0 , 84 0 ,5  logs/ logs CA ∴n ≈ 3 , 98  n = 3 , 98 CA ∴ it will take 4 years/dit sal 4 jaar neem R OR/OF OR/OF Straight line - method/ Re guitlynmetode : A = P (1 − i × n) 120 000 = 240 000 ( 1 −16 % × n )  SF − 0 , 5 = ( − 16% n)  − 0 , 5 = ( − 16% n) CA − 0,5  making n the subject/ n= − 16 % maak n de onderwerp CA ∴n ≈ 3 ,125  n = 3 , 125 CA ∴ it will take 3 years/dit sal 3 jaar neem R (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 12 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 5.3 For the first 4 years/Vir eerste 4 jaar : 4×4  11, 2 %   value of/waarde A = P (1 + i ) = 40 000  1 + n   4  van i and/en n A  SF CA ∴ A ≈ R 62 222 , 83...  62 222 , 83... CA For the last 3 years/Vir laaste 3 jaar : A = 62 222 , 83... ( 1 + 13 % )  SF CA 3 ≈ R 89 781 , 15  89 781 , 15 CA OR/OF OR/OF n n A = P (1 + i ) n ⋅ (1 + i ) n  A = P (1 + i ) ⋅ (1 + i ) M 4×4  value of/waarde van  11, 2 %  i and/en n A ⋅ × ( 1 + 13 % ) 3 = 40 000  1 +   4   value of/waarde va i and/en n A ≈ R 89 781 , 15  SF CA  89 781 , 15 CA (5) [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 13 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1 f ( x ) = 7x − 2 f ( x + h)− f ( x) f / ( x ) = lim definition/definisie A h→0 h = lim [7( x + h) − 2 ]− ( 7 x − 2 )  SF h→0 h  S CA 7 x + 7h − 2 − 7 x + 2 = lim h→0 h S CA 7h = lim 7 CA h→0 h = lim(7) h→0 AO only one mark/slegs ∴ f / ( x) =7 een punt Penalty of one mark incorrect notation Penaliseer een punt indien notasie foutief is. (5) Penalty of only one mark only once for incorrect notation (last step) for sub-questions 6.2.1 , 6.2.2 & 6.2.3 Penaliseer slegs een punt vir foutiewe notasie (laaste stap) vir subvrae 6.2.1 , 6.2.2 & 6.2.3 6.2.1 d dx ( ) π2 = 0 0 A (1) 6.2.2 ( D x x4 − 3 x )  1  power form/magvorm = Dx  x − x3  4     3 2  4x A − 3 1 2 = 4x − x 3 1 −3 3  x CA 3 (3) 6.2.3 5 x +2 y=  x3 A x2 −2 = x3 + 2 x − 2  2x A dy  3x 2 CA = 3x 2 − 4 x − 3 −3 dx  − 4x CA (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 14 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 6.3.1 p ( x ) = x 3 +1 S p ( 2 ) = (2 )3 +1 = k ∴k = 9 9 A (2) 6.3.2 p ( x) = x + 1 3 derivative/afgeleide A p / ( x ) = 3x 2 (1) 6.3.3 p / ( x ) = 3x 2 m = 3( 2 ) 2 = 12 gradient/gradient CA = 12 ( x − 2 ) OR / OF 9 y −9 = 12 ( 2 ) + c SF CA y= 12 x − 24 + 9 c= −15 ∴ y= 12 x − 15 ∴ y= 12 x − 15 OR/OF y − 12 x + 15 = 0  y = 12 x − 15 CA (3) [19] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 15 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 Q7.1: Penalty of ONE mark if intercepts not given as coordinates (refer also to Question 4}\ V 7.1 : Penaliseer EEN punt indien afsnitte nie as koordinate gegee (verwys ook na Vraag 4) 7.1 f ( x ) = − x ( x − 3) (x − 3) x = 0 and/en x = 3  (0 ; 0) A  (3 ; 0) A ( 0 ; 0 ) and/en ( 3 ; 0 ) (2) 7.2 f ( x ) = − x ( x − 3) (x − 3) y = f ( 0 ) = − ( 0 ) ( 0 − 3 ) (0 − 3 ) = 0 0 A (1) Accept/Aanvaar: (0 ; 0) 7.3 f ( x ) = − x ( x − 3) (x − 3) 2 = − x ( x 2 − 6x + 9 )  − x ( x − 6 x + 9 ) M A OR/OF OR/OF 2 = ( − x + 3 x ) ( x − 3) 2  ( − x + 3x ) ( x − 3 ) M A OR/OF OR/OF = ( x 2 − 3x ) ( − x + 3 ) ∴ f ( x ) = − x3 + 6x 2 − 9x 2  ( x − 3 x ) ( − x + 3 ) M A (2) 7.4 3 f ( x ) = − x + 6x −9x 2 f / ( x ) = − 3 x 2 +12 x − 9 derivative/afgeleide M 2 − 3 x +12 x − 9 = 0 equating derivative to 0/ stel afgeleide gelyk aan 0 M x2 − 4x + 3= 0 ( x − 3 ) ( x −1 ) = 0 factors/formula/faktore CA ∴ x = 3 or/of x = 1 both values of /beide waardes van x CA f (1) = − (1) 3 + 6 (1) 2 − 9 (1) = − 4 ( 3 ; 0 ) and/en (1; − 4 ) both values of/beide waardes van y CA AO: Full marks/Volpunte Coordinates of one turning point only: two marks/ Koordinate van een draaipunt slegs:twee punte (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 16 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne 7.5 correct shape/korrekte vorm A y-intercept/-afsnit CA x-intercepts/- afsnitte CA turning points/draaipunte CA (4) 7.6 1< x < 3 OR/OF x ∈ (1; 3 ) critical values/ kritieke waardes : 1 and/en 3 CA notation/notasie (2) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 17 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1.1 V =l ×b×h formula/formule V 4,5 x − 4,5 x 2 OR/OF = SF = 3 x (1,5 )(1 − x ) (3) 8.1.2 V = 4 , 5x − 4 , 5x 2 CA from Question/ Vraag 8.1.1 dV = 4,5 − 9 x dx derivative/afgeleide M 4, 5 − 9 x = 0 equating to 0/ 9x = 4,5 stel gelyk aan 0 M ∴ x = 0,5 value of/waarde van x CA OR/OF OR/OF b x=− 2a  using a formula/gebruik ‘n 4,5 formule =− 2( − 4,5) = 0,5 S value of/waarde van x CA (3) 8.2.1 v ( 0 ) = 8 + 4 ( 0 ) − ( 0 ) 2 m/s = 8 m/s ∴the initial velocity of the car/  8 m/s A die aanvanklike snelheid van die motor 8 m/s NPU (1) 8.2.2 v ( t ) = 8 + 4t − t 2 v ( 0 , 2 ) = 8 + 4 ( 0 , 2 ) − ( 0 , 2 ) 2 m/s S = 8 , 76 m/s  8 , 76 m/s A ∴the velocity of the car when 0, 2 seconds will be 8 , 76 m/s die snelheid van die motor wanneer 0,2 sekondes sal 8,76 m/s wees NPU (2) 8.2.3 v ( t ) = 8 + 4t − t 2  4 A v / ( t ) = 4 − 2t  − 2t A v / (1, 2 ) = 4 − 2 (1, 2 ) m/s 2 SF into a derivative/ = 1, 6 m/s 2 in ‘n afgeleide CA 2  1, 6 m/s CA NPU (4) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 18 DBE/November 2018 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 Penalty of one mark once only if the constant in Questions 9.1.1 & 9.1.2 is omitted/ Penalisering met slegs een punt , indien konstante in Vrae 9.1.1 & 9.1.2 weggelaat is. 9.1.1 6 ∫ − x dx  − 6 ln x 1 OR/OF = − 6 ∫ dx x 1 ln 6 1 x = − 6 ln x + C OR ln + C OR − 6 log e x + C OR/OF x6 − 6 log e x  C (2) 9.1.2 ∫ ( x − 1 ) dx 2 = ∫ ( x − 2 x + 1 ) dx 2  product / product M x3  CA 3 x3 = − x2 + x + C 2  − x CA 3  x + C CA (4) 9.2 Area notation using intergrals/ Area-notasie met gebruik van integrale M x3  A 3  3x A  SF CA bounded area/ begrensde oppervaklte CA NPU AO: 3 marks/punte (6) [12] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou