Technical Mathematics Grade 12 P1 NSC November 2021 QP

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE 12/GRAAD 12 TECHNICAL MATHEMATICS P1/TEGNIESE WISKUNDE V1 NOVEMBER 2021 MARKING GUIDELINES/NASIENRIGLYNE MARKS/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 penalisering vir afronding nie NPU No penalty for units omitted Geen penalisering vir eenhede weggelaat nie S Simplification/Vereenvoudiging SF Substitution in correct formula/Vervanging in korrekte formule These marking guidelines consist of 21 pages. Hierdie nasienriglyne bestaan uit 21 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 2 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne NOTE:  If a candidate answers a question TWICE, only mark the FIRST attempt.  The method of consistent accuracy marking must be applied to all aspects of the marking guideline where applicable as indicated with the marking code CA.  If a candidate strikes off a response to a question and does not attempt the question again, then the struck off question should be marked.  # Shows questions where Tolerance Range will be applied: 3.3.2 ; 5.2 ; 5.3.2 ; 9.2 LET WEL:  Indien 'n kandidaat 'n vraag TWEE keer beantwoord, sien slegs die EERSTE poging na.  Die metode van volgehoue akkuraatheid-nasien moet waar moontlik op alle aspekte van die nasienriglyne toegepas word soos aangedui deur die nasienkode CA.  Indien ʼn kandidaat ʼn antwoord deurhaal en nie poog om die vraag weer te beantwoord dan moet die deurgehaalde antwoord gemerk word.  # Toon vrae waar Toleransie Wydte (Verdraagsaamheids omvang) toegepas word: 3.3.2 ; 5.2 ; 5.3.2 ; 9.2 QUESTION/VRAAG 1 1.1.1 2 x ( x  3)  0 x 0 or/of x 3  x 0 A  x3 A (2) 1.1.2 x ( x  9 )  12 x 2  9 x  12  0  standard form/standaardvorm A  b  b  4ac 2 x 2a  9  92  4(1)(12)  SF CA  2(1)  9  129  2   each x -value/elke waarde CA  x  1,18 or/of x  10,18 R (4) 1.1.3 x(6  x)  0 Critical values/kritiese waardes: 0 and 6  both critical values/ A albei kritiese waardes  0  x  6 OR/OF x  0 ; 6 OR/OF  notation/notasie A x  0 and/en x  6  number line representation/ getallelyn voorstelling CA 0 6 Note: Award full marks if ONLY the correct number line representation is shown. Nota: Ken vol punte toe SLEGS as korrekte getallelyn getoon word (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 3 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 1.2 x  1  2 y and/en 3x 2  3  x  y 31  2 y   3  (1  2 y)  y 2  substitution/vervanging A 3  12 y  12 y  4  y 2 S CA 12 y  11y  1  0 2 correct standard form/ korrekte standaard vorm CA (12 y  1)( y  1)  0 OR/OF 1  factors/formula / y    0,08 or/of y  1 faktore/formule. CA 12 1  both y-values/-waardes CA x  1  2( ) or/of x  1  2 (1) 12 7  x   1,17 or/of x   1  both x-values/-waardes CA 6 OR/OF OR/OF 1 x y and/ en 3x  3  x  y 2 2 1 x  substitution/ vervanging 3x 2  3  x  A 2 6x2  6  2x  1  x S CA  correct standard form/ 6x2  x  7  0 korrekte standaardvorm CA (6 x  7)( x  1)  0 OR/OF  factors/form./faktore/form. CA 7  both x-values/-waarde CA x   1,17 or/of x  1 6 7 1 y 6 or/of y  1  (1) 2 2 1  both y-values/-waardes CA  y     0,08 or/of y  1 12 OR/OF OR/OF x  1  2 y 1 and / en 3x 2  3  x  y  2  Sub/verv  2  into/in 1  x  1 2 3x 2  3  x   substitution/ vervanging A x  1 6 x2  6  2 x S CA 6 x2  x  7  0  correct standard form/ korrekte standaardvorm CA  6 x  7  x 1   0  factors/form./faktore/form. CA 7 OR/OF x   1,17 or/of x  1  both x-values/-waarde CA 6 1  y     0,08 or/of y  1  both y-values/-waardes CA 12 NPR (6) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 4 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne L 1.3.1 T  2 g T L  2 g 2 2  T  L  M squaring both sides/       2  g kwadreer beide kante A 2  T   L subject/ onderwerp A L  g     2  OR/OF OR/OF L T  2 g 2   T    2  L  2  g  M squaring both sides/ L kwadreer beide kante A T 2  4 2 g gT 2  L subject/ onderwerp A L 4 2 (2) 2  T  1.3.2 L  g     2  2  1,74  L  9 , 8     SF CA  2  L  0 , 75 m  value of/waarde van L CA OR/OF OR/OF gT2 L 4 2 L 9,81,74 2  SF CA 4 2 L  0 , 75 m  value of/waarde van L CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 5 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne L T  2 g L 1,74  2  9,8  SF A 2  1,74  L  9 , 8     2  L  0, 75 m  value of/waarde van L CA NPR NPU (2) 1.4.1 1101100 2 11100 2  1010000 2  10100002 A Note: No penalty if base 2 is omitted. Nota: geen penaliseering indien basis 2 uitgelaat is (1) 1.4.2 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 0 1 0 0 0 0 M CA  64  16  80  decimal value/desimale waarde CA OR/OF OR/OF 6 5 4 3 2 1 0 2 2 2 2 2 2 2 1 1 0 1 1 0 0 =108 1 1 1 0 0 =28 M A  108  28  80  decimal value/desimale waarde CA AO: full marks/ vol punte (2) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 6 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1.1 Non-real/ nie-reël  non-real/ nie-reël (1) 2.1.2 Real, rational, equal  Real, rational, equal/ Reëel, rasionaal, gelyk Reëel, rasionaal, gelyk A (1) 2.2  x  2qx  4  0 2 OR/OF x  2qx  4  0 2   <0 A b  4ac  0 2 2q2  4 1 4  0 OR/OF  2q2  4 14  0  SF A 4q  16  0 2 q2  4  0 q  2q  2  0  2  q  2 OR/OF q  (2 ; 2) OR/OF q   2 and q  2 end points and correct notation/ eindpunte en korrekte notasie CA (3) [5] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 7 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1 81a  3 8  4 = 3 a  3  4 8 4  Prime base or exponential 1 6 a6 property/ priembasis of 3 6 = 3 a OR/OF a OR / OF eksponensiële eienskap A 27 27 3 3 CA  a 6 A AO: 2 marks/punte (3) 3.1.2 log 2 16  log 3 4 0 4  log 2 2 A  log 2 24  log 3 1  4 log 2 2  log 3 1  log 3 1 A  41  0  log 2 2  1 CA 4  4 CA OR/OF OR/OF log 2 16  log 3 40  log 2 2 4 A  log 2 2  0 log 3 4 4  4 log 2 2  0 log 3 4 A  4 log 2 2  0 log 3 4  log 2 2  1 CA  4(1)  0 4 CA 4 OR/OF OR/OF log 2 16  log 3 4 0 log 16 log 4 0 log 2 4    A log 2 log 3 log 2 log 2 4 log 1 log 1    A log 2 log 3 log 3 4 log 2 0 4 log 2    CA log 2 log 3 log 2 40  4 CA 4 AO: 3 marks/punte (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 8 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 3.1.3 50 x10  18x 4  900 x 6  Product of the surds/ produk van wortelvorm A  30 x 3  30 CA  x3 CA OR/OF OR/OF 50 x10  18x 4  Product of perfect squares and  25  2 x10  9  2 x 4 prime number/  5 2 x5  3 2 x 2 produk van volkome vierkante en  30x3 priem getalle A  30 CA  x 3 CA (3) 3.2 log 3 ( x  2)  2  log 3 x log 3 ( x  2)  log 3 x  2 x2 log 3 2  log property/log-eienskap A x x2 x2 exponential/log form/  32 OR/OF log 3  2log 3 3 x x eksponensiële /log vorm CA x  2  9x S CA 1 x OR/OF x  0,25  x – value/waarde CA 4 OR/OF OR/OF log 3 ( x  2)  2  log 3 x log 3 ( x  2)  2log 3 3  log 3 x  log property/log-eienskap A log 3 ( x  2)  log 3 9  log 3 x  log property/log-eienskap A log 3 ( x  2)  log 3 9 x S CA x  2  9x 1  x – value/waarde CA x OR/OF x  0,25 4 (4) 3.3.1 z  r  x2  y 2 2 5 = p + 4 2 2  SF A 20 = p 2 + 16 p 2 = 4 OR / OF ( p + 2) ( p  2) = 0 OR / OF p = ± 4 S CA p = ±2 S CA  p = 2 , θ  (90 o ;180 o ) –2 CA (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 9 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 3.3.2 y x tan   OR/OF cos   x r # 4 2 tan   OR/OF cos   2 2 5 ref .angle / verw. hoek  63,43o  ref. angle/verw. hoek CA  180o  63,43o 116,57 o OR/OF 2,03 rad  value of/ waarde van  CA  z  2 5 cis 116,57 o OR/OF  z in polar form/polêre vorm CA  z  2 5 cis 2,03 rad OR/OF OR/OF y sin   r 4 sin   2 5 ref .angle / verw. hoek  63,43o  ref. angle / verw. hoek A  180o  63,43o 116,57 o OR/OF 2,03 rad  value of/ waarde van  CA  z  2 5 cis 116,57 o OR/OF  z in polar form/polêre vorm CA  z  2 5 cis 2,03 rad (3) 3.4 2m  ni  6i   3i (4i  5) 2m  ni   12 i 2  15i  6i  Product/ produk A 2m  ni   12(1)  9i 2  substituting i with – 1/ 2m  ni  12  9i 2 vervang i met – 1 A  2m  12 m6  value of/ waarde van m CA   ni   9i n9  value of/ waarde van n CA OR/OF OR/OF 2m  ni  6i   3i(4i  5) 2m  (n  6) i   12 i 2  15 i  Product/ produk A 2m  (n  6) i   12 (1)  15i 2  substituting i with – 1/ 2m  (n  6) i  12  15i 2 vervang i met – 1 A  2m  12 m6  value of/ waarde van m CA   (n  6) i   15i  value of/ waarde van n CA n9 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 10 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne OR/OF OR/OF 2m  ni  6i   3i(4i  5) 2m  (n  6) i   12 i 2  15 i  Product/ produk A 2m  ni  6i   12 (1)  15i 2  substituting i with – 1/ 2 2m  ni  6i  12  15i vervang i met – 1 A  2m  12  ni  6i  15i 2m 12  0 and / en ni  9i  0  2m  12 m6  value of/ waarde van m CA  ni  9i n 9  value of/ waarde van n CA (4) [25] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 11 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1.1(a) y  6 OR/OF (0 ; 6 ) 6 A (1) 4.1.1(b) y5  y5 A (1) 4.1.1(c) k ( x )   2x 2  4x  6  y-int./ afsn. y  int / afsn.: y  6 A x  ints/afsn..:  2x 2  4x  6  0 x 2  2x  3  0 factors/form./faktore/form. A ( x  1) ( x  3)  0 OR/OF x    2   2  41 3 2 21 x   1 or / of x  3  both values of/ beide waardes van x CA (3) 4.1.1(d) TP/DP,  b  4 x  2a 2 2 SF A 1  x-value/waarde CA y   2 (1)  4 (1)  6  8 2  y-value/ waarde CA  1; 8 OR/OF OR/OF 1  3 M TP/DP, x  1 CA 2  x-value/waarde CA y   2 (1) 2  4 (1)  6  8  y-value/ waarde CA  1; 8 OR/OF OR/OF k ( x )   2x  4x  6 2 k / (x )   4x  4  0 M A x 1  x-value/waarde CA y   2 (1) 2  4 (1)  6  8  y-value/ waarde CA  1; 8 OR/OF OR/OF   b 4ac  b  2  ;   2 a 4 a    4 4 26  42  SF A    x-value/waarde CA  2 2 ;      4 2   y-value/ waarde CA  1; 8 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 12 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 4.1.2 h:  shape/vorm A  y- int./afsn CA  asymptote/ asimptote CA k:  shape/vorm A  x & y int../afsn CA Turning point/ draaipt CA (6) 4.1.3 a p( x)   q and/en  1; 8 x q5  value of/ waarde van q A a 8 5  SF A 1 a   3  value of/ waarde van a CA (3) 4.2.1 C 5 ; 0   x-value at/waarde by C A  y-value at/ waarde by C A (2) 4.2.2 D 0 ; 10  and/en B 0 ;  5  coordinates of/ koördinate van B & D CA BD   5  (10)  5 units / eenhede  length of/ lengte van BD CA AO: Full marks/Volpunte (2) 4.2.3 f ( x)   25  x 2 OR/OF f ( x)   52  x 2  equation/vergelyking CA (1) 4.2.4 3  x  5 OR/OF x( 3; 5 ) OR/OF x  3 and x  5  critical values/ kritiese waardes CA  correct notation/ korrekte notasie A (2) [24] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 13 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 4 5.1.1 17 , 39 %  17 , 39 % A 23 NPR (1) 5.1.2 A  P1  i n  4  A  R63 150 1   7  OR/ OF R63 150 1  17, 39 %  7   SF A  23   R140028, 26 CA  R140028, 26  R140022,50 OR/OF OR/OF SI / ER = P× i × n 4  SF A  R63 150  7 OR/OF 23  R63150 17,39%  7  R76 878, 26  R76 872,50  R140028, 26 CA A  R63 150  R76 878, 26 OR/OF NPR R 63150  R76 872,50 (2) »R140 028, 26  R140 022,50 A  P 1  i  n 5.2 # R274 000  R726 900 1  15,8%  n  SF A 2 740  1  15,8%  n S CA 7 269  2 740  log   log form/vorm 7 269  CA n  log( 0,842) n  5,67  n  5, 67 years/jare  value of/ waarde van n CA (4) 5.3.1 A  P1  i  n  R25 000 1  2,8%  4  SF A  R 27 919,81 CA  R 27 919,81 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 14 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 5.3.2 Value of investment after 27 months/ Waarde van belegging na 27 maande A  P1  i  n # 27  5,98%   5,98%  27  R15 000 1    1   A  12   12   R17154,59482 value of/ waarde van A CA Value of investment after 21 months/ Waarde van belegging na 21 maande P  R17154,59482  R 6823,54  R 23 978, 13482 M adding/ byvoeging R6 823,54 Value of investment after 7 quarters/ A Waarde van belegging na 7 kwartale 7  7,78%  7  7,78%   R23 978, 13482 1    1   A  4   4   R 27 439, 55  R 27 439, 55  R 27 919,81  value of/ waarde van A CA He will not have enough money/ hy sal nie genoeg conclusion/ gevolgtrekking CA geld hȇ nie OR/OF OR/OF 27  5,98%   5,98%  27  7,78%  7  1   A A  R15 000 1   1    12   12   4  7  7,78%   1   A  7,78%  7  4  + R6 823,54 1    4  M A 7  7,78%   R 27 439, 55  1   A  4   R 27 439, 55  R 27 919,81   R 27 439, 55 CA conclusion/gvlgtr CA He will not have enough money/ hy sal nie genoeg geld hȇ nie OR/OF OR/OF 27  5,98%   27   7, 78% 7  1   A  5,98%   12  A   R15 000 1    R6 823,54  1     12    4   M A  R 27 439,55  M A 7  7,78%   R 27 439, 55  R 27 919,81  1   A  4  He will not have enough money/ hy sal nie genoeg geld hȇ nie   R 27 439, 55 CA conclusion/gvlgtr CA (6) Conclusion without calculation: 0 marks/ Gevolgtrekking sonder berekeninge gee: 0 punte [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 15 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1 f ( x )   3x f ( x  h) f ( x) f / ( x )  lim definition/definisie A h0 h  3 ( x  h )  (  3x)  lim  SF CA h0 h  3 x  3h  3 x  lim S CA h0 h  3h  lim S CA h0 h  lim (  3) h0  f ( x)   3 / –3 CA AO: 1 mark/ punt Penalty of one mark for incorrect notation Penaliseer een punt indien notasie foutief is. (5) 6.2.1  D x p 3 x 2  7 x  10   2 p3 x  7  2p x 3 A  7 A (2) 6.2.2 x  3x 2 y x7 y  x  6  3x  5 S A dy   6 x  7  15 x  6 7 dx   6x CA  15 x  6 CA (3) 6.2.3 f ( x )  x  5x 3 2 4 2 2 f ( x )  x 3  5x 4  x3 A 1 2  1  f / (x )  x 3  20 x 3 2 3  x CA 3 3  20x 3 A (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 16 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 6.3.1 m9  value of/ waarde van m A (1) 6.3.2 y  x 2  3x  2 dy  2x  3  derivative of / afgeleide van y dx A 2x  3   9  equat.deriv/ verg. afgeleide 2 x  12 =–9 CA  x  6  value of/ waarde van x CA y  (  6 ) 2  3 ( 6 )  2  y  16  value of/ waarde van y (  6 ; 16 ) CA (4) 6.3.3 g ( x)  x  3x  2 2 g ( x)  ( 2) 2  3( 2)  2   4 g ( x)  (3) 2  3(3)  2  16  both values of/ beide waardes y  y1 van y A Ave. grad./Gem grad  2 x2  x1 16  ( 4)  M subst. into Ave. gradient  3  ( 2) Formula/verv in gem grad 20 vorm CA  5 4  mave value/ waarde CA OR/OF OR/OF g ( x)  x 2  3x  2 g( x2 )  g( x1 ) Ave. grad./Gem grad  x2  x1  M subst. into Ave. gradient  (3)  3(3)  2  (2)  3( 2)  2 2 2 Formula/verv. in gem grad 3  ( 2) vorm A 16  ( 4)  both values of/ beide waardes  3  ( 2) van y CA 20  5 4  mave value/ waarde CA (3) [21] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 17 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7.1 f ( x)  x 3  2 x 2  7 x  4 y   4 OR/OF 0 ;  4  y-intercept/ afsnit A (1) 7.2 f (4)  (4) 3  2(4) 2  7(4)  4  substitution/ vervanging A 0 0 A  ( x  4) is a factor of/ is ʼn faktor van f (x) (2) 7.3 x-intercepts/afsnitte; y  0 ( x  4)( x 2  2 x  1)  0  quadratic factor/ kwdr. faktor A ( x  4 ) ( x 1) ( x  1)  0  factors/ faktore CA  x  1 or x  4  x-intercepts/ afsnitte CA OR/OF OR/OF ( x  1)( x  3x  4)  0 2  quadratic factor/ kwdr faktor A ( x  1) ( x  4 ) ( x  1)  0  factors/ faktore CA  x  1 or x  4  x-intercepts/ afsnitte CA AO: Full marks/Volpunte (3) 7.4 f ( x)  3 x  4 x  7  0 / 2 derivative/afgeleide A equating derivative to 0/ (3x  7) ( x  1)  0 OR/OF x    4   4  43 7 2 stel afgeleide gelyk aan 0 A 23 factors/formula/faktore CA 7 both values of /beide waardes x  or/of x  1 3 van x CA 3 2 7  7 7 7 500 f       2   7   4     18, 52  both values of /beide waardes 3  3 3 3 27 van y CA 7 500    ;  and /en 1 ; 0 3 27  OR/OF 2,33 ;  18,52 and /en 1 ; 0 (5) 7.5  shape /vorm A  y-intercept/ afsnit CA  both x-intercepts/ beide x-afsnitte CA  both turning points/ beide draaipunte CA (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 18 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne 7.6 7  crit. values/ krit. waarde CA 1  x  OR/OF 1  x  2,33  correct notation / 3 korrek notasie A OR/OF OR/OF  7 x  1 ;  OR/OF x   1 ; 2,33  crit. values/ krit. waarde CA  3  correct notation / korrek notasie A OR/OF OR/OF 7  crit. values/ krit. waarde x   1 and/en x  OR/OF x   1 and/en x  2,33 CA 3  correct notation / korrek notasie A (2) [17] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 19 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1 V lb h 4 000  x 2h  SF A 4 000 h  (1) x2 8.2 Tot. Surface Area = length  breadth + 2  length  height +2  breadth  height Tot. Buite oppervlakte = lengte  breedte + 2  lengte   SF A height +2  breedte  height Tot. Surface Area/ Buite Oppervlakte  x 2  2 xh  2 xh S . CA  4 000   x 2  4x  2   x  16 000  x2  x OR/OF OR/OF Tot. Surface Area = Area of base + (perimeter of base  height) Tot. Buite Oppervlakte = oppervlakte van die basis + (omtrek van basis  hoogte) 2 Tot. Surface Area/ Buite Oppervlakte  x  4 xh  4 000   x 2  4x  2   SF A  x  16 000 S CA  x2  . x (2) 8.3 16 000 Tot Surface Area/ Buite Oppe rvlakte  x 2  x  x 2  16 000 x 1 d (Tot. Surface Area / Buit. Oppervlakte)  2 x 16000 x  2  derivative/ afgeleide A dx S A 16 000  2x  x2  equating derivative to/ stel afgeleide aan 0 A 2 x 3  16 000  0 x 3  8 000  value of/ waarde van x x  20 cm CA 4 000  value of/waarde van h h 10 (20) 2 CA NPU (5) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 20 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9  x x  6 x dx 2 9.1.1   x  6 x dx 3 2 S A x4 x4   2x 3  C  CA 4 4  2x 3 CA  C A (4)  x 1 9.1.2   3  x  dx x 3x 3  A   ln x  C ln 3 ln 3  ln x  C A (2) 4  M Area notation using 9.2 A   g ( x) dx k integrals/ Area-notasie met 4 gebruik van integrale A #   3x 2 dx k  x3 k  4 x3 A  ( 4) 3  (k ) 3  SF CA  ( 4) 3  (k ) 3  56  equating area to/ stel oppervl gelyk aan 56 CA k 3  8 S CA k  2 value of / waarde van k CA OR/OF OR/OF 4 A   g ( x) dx  M Area notation using 0 4 integrals/ Area-notasie met   3x 2 dx gebruik van integrale A 0  x3 0  4 x3 A  SF CA  ( 4)  (0)  64 3 3 2 A   g ( x) dx 0  x3 0  2  ( 2) 3  (0) 3  8 S CA  64  8  56 M CA k  2 value of / waarde van k CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P1/Tegniese Wiskunde/V1 21 DBE/November 2021 NSC/NSS – Marking Guidelines/Nasienriglyne Trial & Error Method/ Probeer en Trefmetode 4 Area notation using A   g ( x) dx integrals/ Area-notasie met k 4 gebruik van integrale M   3x 2 dx k x3 x 3 4 k A Let/Laat k = 1 M CA  x3 1  4  ( 4) 3  (1) 3  SF CA  63 Let/Laat k = 2  x3 2  4  ( 4) 3  (2) 3  56  S CA k  2 value of / waarde van k CA (7) [13] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou