Technical Mathematics Grade 12 Paper 2 NSC June 2023 Memo

Downloaded from hlayiso.com SENIOR CERTIFICATE EXAMINATIONS/ NATIONAL SENIOR CERTIFICATE EXAMINATIONS SENIORSERTIFIKAAT-EKSAMEN/ NASIONALE SENIORSERTIFIKAAT-EKSAMEN GRADE/GRAAD 12 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 2023 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 150 CODE/ EXPLANATION/VERDUIDELIKING KODE A Accuracy/Akkuraatheid AO Answer only/Slegs antwoord CA Consistent accuracy/Volgehoue akkuraatheid I Identity/Identiteit M Method/Metode NPR No penalty for rounding/Geen penalisering vir afronding nie NPU No penalty for omitting units/Geen penalisering vir eenhede weggelaat nie R Rounding/Afronding RE Reason/Rede S Simplification/Vereenvoudiging SF Substitution in correct formula/Vervanging in korrekte formule ST/RE Statement with reason/Bewering met rede F Correct formula/Korrekte formule These marking guidelines consist of 26 pages. Hierdie nasienriglyne bestaan uit 26 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 2 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne NOTE:  If a candidate answers a question TWICE, only mark the FIRST attempt.  Consistent Accuracy marking must be applied where indicated.  Questions where Tolerance Range will be applied: Q4.3; Q7.3.3; Q10.4 and Q11.2.2 LET WEL:  Indien 'n kandidaat 'n vraag TWEE keer beantwoord, sien slegs die EERSTE poging na.  Volgehoue akkuraatheid-nasien moet toegepas word soos aangedui.  Vrae waar Tolaransie wydte toegepas word: V4.3; V7.3.3; V10.4 and V11.2.2 QUESTION/VRAAG 1 y x 1.1 m 1 gradient/gradiënt A (1) 1.2.1 tan   m  1  SF CA    45 value of angle/waarde van hoek AO: full marks/ volpunte CA (2) 1.2.2 y  x  6 OR/OF yx6  SF A 4  d  6 OR/OF 4d 6  d  2 value of/ waarde van d CA OR/OF OR/OF 4    4  SF 1 CA d   10  8  d  10 value of/ waarde van d CA d  2 AO: full marks/ volpunte (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 3 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne  x  xm y k  y m  1.2.3 P k ;   2 2   2   10 2   4  P ;   2 2   x-value/waarde A P  4 ;  1  y-value /waarde A AO: full marks/ volpunte (2) 1.3.1 m 1 gradient/gradiënt CA From/ vanuit 1.1 (1) 1.3.2 y  1x  c 2  12  c  substitution/ vervanging CA m from/van 1.3.1 and/en K(2; 2) c  0 equation/ vergelyking CA y  x OR/OF OR/OF y  y1  m x  x1   substitution/ vervanging CA y  2  1  x  2 m from/van 1.3.1 and/en K(2; 2) y2x2 equation/ vergelyking CA  y x AO: full marks/ volpunte (2) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 4 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1.1 x2  y 2  r 2  F A 62   82  r 2  subsitution/ vervanging A x  y  100 2 2 OR/OF y   100  x 2 equation/ vergelyking CA OR/OF x   100  y 2 AO: full marks/ volpunte (3) 8 4 SF A 2.1.2 mOG    6 3  mOG CA 3  mtan mtan  CA 4 y  mx  c OR/OF y  y1  mx  x1  8  3 6  c y   8  3 x  6 substitution/vervanging CA 4 4 25 c 2 3 25 y  x 4 2 equation/vergelyking CA OR/OF OR/OF y. y1  x.x1  r 2 F y  8  x 6  100 A  8 y  6 x  100 substitution/verv (6;  8) A 3 25 substitution/verv r 2 CA y  x  S CA 4 2 equation/vergelyking CA (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 5 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 2.2 E  10 ; 0 coordinates/ koördinate CA (1) 3 25 2.3 y x 4 2 y   10  3 25 4 2 substitution /Vervang CA   20 length/ lengte EF CA EF = 20 units EG   x2  x1    y2  y1  2 2  SF CA  10  6    0   8  2  2 length/ lengte EG CA  320 OR /OF 8 5  17,89 units / eenhede  conclusion/gevolgtr CA  EF  EG (5) 2.4 both x- intercepts/ beide x-afsnitte A both y- intercepts beide y-afsnitte A elliptical shape/eliptiese vorm CA (3) [17] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 6 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1 sin B  sin 59   0 , 86   0 , 86 A NPR (1) 3.1.2 sec A  cos B  sec 66   cos 59   substitution/ vervanging A 1   cos 59 cos 66  2 ,97 CA NPR  2 ,97 AO: full marks/volpunte (2) 3.2 r2  x2  y2 r 2   3 2  (2) 2  r value/ waarde van A r  13 y  diagram A 3 O diagram can be implied by the use x of /diagram kan deur die –2 gebruik van geïmpliseer word. 4 cot   sin 2  2  cot ratio/verhouding CA  3  2   sin ratio/ verhouding CA  4         2  13  74   simplification/ vereenv CA 13 (5) 3.3 cosec x   3, 054 1   3, 054 I A sin x 1 sinx the subject/ onderwerp A sin x   OR / OF sin x  0,327... 3, 054 Ref/verw..   19,11  reference angle/ verw.hk CA x  180   19,11 or/of x  360  19,11 x- values in 3rd quadr/  x  199,11 or/of x  340,89 waarde in die 3de kwadr. CA x- values in 4th quadr/ waarde in die 4de kwadr. CA NPR Accept negetive ref. angle/ aanvaar negatiewe verw.hk (5) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 7 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1 cos B  cos B A (1) 4.2.1 2 sin P  sin P2 A (1) sin  1  sec 2   1 I A 4.2.2 OR/OF OR/OF (1) cos  cot  1 2 4.3 2 sin(  B)  cos(2  B)  tan(180  B)  cos(180  B)  sec(180  B) 2  ( 2 sin B)  cos B  ( tan B)  ( cos B)   2sin B A ( sec B)   tan B A sin B  2 sin B  cos B   cos B  2cos B   cos B A cos B  sec B A  2sin 2 B  2cos 2 B  I cos B A  2(sin 2 B  cos 2 B)  2 (1) 2 CA 2 (6) cos θ  sin 2 θ  sec θ 4.4  tan  cosec θ cos θ  sin 2 θ  sec θ LHS/ LK  cosec θ 1 1 cos θ  sin 2 θ  I A cos θ cos θ  1 1 I A sin θ sin θ cos 2 θ  sin 2 θ 1    S cos 2 θ  sin 2 θ CA cos θ sin θ 1 sin θ   I 1 A cos θ 1 S CA  tan   RHS/RK (5) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 8 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1 f:  shape/vorm A  intercept/afsnit A  turning point/ draaipunt A g:  shape/vorm A  intercepts/ afsnitte A  asymptote/ asimptoot A (6) 5.2.1 y [1 ; 2]  end points/eindpunte CA OR/OF  notation/notasie CA 1 y  2 (2) OR/OF y  1 and /en y  2 5.2.2 180  period/ periode A (1) 5.2.3 h(x) = tan x  equation/vergelyking A (1) 5.3  sin 0  1  ( tan 0)  Substitution / vervang A 1 0 1 CA 1 AO: full marks/ volpunte (2) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 9 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1   QR 2  QS 2  SR 2  2 QS SR cos Q S R  2 QS SR cos Q S R A OR/OF (1)  in QRS: s 2  r 2  q 2  2 r  q cos S  QR 2  QS 2  SR 2  2QS  SR cos S 6.2 QR 2  (23) 2  (14) 2  2 (23) (14) cos 86  SF A  680 , 0768309  value of/ waarde van QR  26 , 08 m QR CA NPR (2) 1  6.3 Area of/Oppervlakte van  QRS  QS SR sin S  QS×SR OR/OF r  q 2 OR/OF 23 14 A 1  1  OR/OF rqsin S OR/OF  2314  sin S 2 2 (1) 6.4 Area of/oppervlakte van QRS  1 2314sin 86  SF A 2  area value/  160 , 61 m 2 oppervlakte waarde CA NPR (2) PQ r PQ r 6.5 tan 59   OR / OF OR/OF QR p  QR p A (1) PQ PQ 26, 08 6.6 tan 59    substitution/ 26 , 08 OR/OF sin 59 sin 31 vervanging CA PQ  26 , 08 tan 59   43 , 40 m PQ  43, 40  value of/ waarde van PQ CA NPR (2) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 10 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7.1 Bisects/ halveer ST A (1) 7.2 7.2.1 AO = 7 cm  ST A (1)  line from centre to midpt of chord  7.2.2 OC  BD    RE A  lyn vanuit midpt na midpt van koord  BC  5,5 cm  ST A OC2  BO2  BC2 (Pythagoras)  7 2  5,5 2  ST CA OC  18,75  ST length of/lengte van  4,33 cm OC CA OR/OF OR/OF 4h 2  4dh  x 2  0 F A 4h 2  4 14  h  11  0 2  SF A 4h  56h  121  0 2  Standard form/ Standaard vorm CA   56    56   4  4 121 2 h 2  4 h  11,33 or / of h  2, 67  ST length of/lengte van  OC  7  2, 67  4,33cm OC CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 11 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne  line from centre to midpt of chord  OC  BD    lyn vanuit midpt na m idpt koord   RE A BC  5,5 cm  5,5  ST A In OBC, cos OBC  7  cos definition/ def CA  O BC  38,21 OC OC tan 38, 21  OR/OF sin 38, 21  5,5 7 OC  4,33 cm OC  4,33 cm  ST length of/lengte van OC (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 12 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 7.3  7.3.1 O1  4  27  108  ST A (1)    at centre =2   at circm  7.3.2 D1  54    ST CA  midpts   2  omtreks   RE A (2)  7.3.3 C2  54  27  27  ext  of  / buite  van    ST CA  DC  DF sides opp =s / sye teenoor  e   RE A  RE A OR/OF OR/OF  D2  180  54  126  on str line / op reguitlyn   C2  180  126  27  27  sum  of  / som  van    ST CA  RE A  DC  DF sides opp =s / sye teenoor  e   RE A (3) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 13 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1 Perpendicular / loodreg ST A (1) 8.2   ST A 8.2.1 D1  55  tan - chord / raaklyn -koord )  RE A (2)  8.2.2 F3  55  alt/verw s; CD || FH  ST CA  RE A (2)  8.2.3 C 3  35  tan/raaklyn  rad   ST A  RE A   F1  35  s opp  sides / e teenoor  sye  ST/RE CA OR/OF OR/OF  O1  110  at centre  2  circmf  / mdpts   2  omtrks   ST A  RE A    70  s opp  sides / e teenoor  sye 1 F1  C 3   ST/RE CA 2  35  (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 14 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne  8.2.4 D F C  180   38   35   55  int s of  / binne e van Δ  ST CA  52  int s of  / binne e van Δ  RE A OR/OF OR/OF  C1  52  on straight line / op reguitlyn   ST CA  D FC  52  tan  chord th./ raaklyn  koord   RE A OR/OF OR/OF  C1  52  tan  rad th./ raaklyn  rad    ST CA D FC  52  tan  chord th./ raaklyn  koord   RE A (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 15 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 8.3  8.3.1 A  90   in semi-circle/sirkel   ST A   RE A  D1  31  Int s of  / Binne e van    ST CA (3)   equal chords, equal s /  8.3.2 D2  31    ST CA  gelyke krde, gelyke e   RE A (2)  8.3.3 B3  62  ext  of cyclic quad / buite  van kdvk   ST CA  RE A OR/OF OR/OF    B3  180  B2  B1  sum  on str line / som  op reguitlyn   ST CA  RE A  180  59  59  62 (2) [17] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 16 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 9.1 Corresponding angles must be equal/ angles equal/ gelyke hoeke ooreenstemmende hoeke moet gelyk wees A Corresponding sides must be proportional/ Ooreenstemmende sye moet eweredig wees sides proportional / sye eweredig A (2) 2 2 9.2 Piece/stuk 1 =  3 m  1,2 m OR/OF  120 cm  ST  3 A 5 5 Piece/stuk 2 = 3  1,2  1,8 m OR/OF  180 cm  ST length of piece 1/ 3 lengte van stuk 1 CA OR/OF Piece/stuk 2   300 cm  180 cm  ST length of piece 2 5 /lengte van stuk2 CA OR/OF OR/ OF  ST x = 0,6 m A 2 x  3x  3m x  0,6 m  ST length of piece 1/ Piece /stuk 1  2 x  1, 2m OR/OF  120cm lengte van stuk 1 CA Piece/stuk 2  3x  1,8m OR/OF  180cm  ST length of piece 2 /lengte van stuk 2 CA (3) 9.3 9.3.1 In ∆ABE and/en ∆DCE: Any two/enige twee    ST A AD alt./verw. s; AB || CD    ST A B C  alt./verw.s; AB || CD    E1  E 2  vertically opposite/regoorstaande  ∴ ∆ABE ||| ∆DCE ()  RE A (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 17 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 9.3.2 AE BE  ST A  prop./ eweredig AB / / CD  RE A AD CB 4 BE   ST AD = 9 A 9 80 320 ∴ BE = mm OR/OF  35,56 mm  ST CA 9 OR/OF OR/OF BE AE  ST  ||| s  A CE DE BE AE 4  RE A   80  BE DE 5 ∴5 BE = 320 – 4 BE ∴9 BE = 320  ST CE = 80 – BE A 320 ∴ BE = mm OR/OF  35,56 mm  ST CA 9 (4) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 18 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 10  conversion factor/ 10.1 OR / OF  0,17 180 herleidingsfaktor A (1) 10.2 False/ Onwaar answer/ antwoord A (1) 1000 10.3.1 v  45   12,5 m/s both conversions / beide A 3600 herleidings r  650  1000  0, 65 m D  1,3m v  Dn F A 12,5   1,3 n  SF CA n  3, 06 rev / omw / s  value of/ waarde van n CA OR/OF OR/OF 1 000 A v  45   12,5 m/s both conversions/ beide 3 600 herleidings r  650  1000  0,65 m v  2 r n F A 12,5  2 0,65 n  SF CA  value of/ waarde van n n  3,06 rev / omw / s CA OR/OF OR/OF v  45  3600  0, 0125 km/s both conversions / beide r  650  1 000 000  0, 00065 km herleidings v  2 r n F A A 0, 0125  2  0, 00065  n  SF n  3, 06 rev / omw / s  value of/ waarde van n CA CA (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 19 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 10.3.2   2  n F A  2   3, 06   SF CA 153  angular velocity/   OR / OF  19, 23 rad / s CA 25 hoeksnelheid OR/OF OR/OF v r F A 12,5    0, 65   SF CA 12,5 250  angular velocity/   OR / OF  19, 23 rad / s CA 0, 65 13 hoeksnelheid OR/OF OR/OF   360 n F A  360 3, 06  SF CA   angular velocity/  1101, 06  CA 180 hoeksnelheid   19, 23 rad / s (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 20 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 10.4 r 2 10.4 A F A 2 2  (50) 2    A1   9   2 500  m 2  872, 66m 2 SF 50 A 2 9 2  (85) 2    A2   9   7 225  m 2  2522, 00m 2  SF 85 A 2 9 7 225 2 500 Shaded area/Gearseerde oppervlakte   m2   m2 9 9  525  1 649,34 m 2  Area/Oppervlakte  the area CANNOT be fully covered/ CA oppervlakte KAN NIE volledig bedek word NIE  Conclusion/ gevolgtrekking CA OR/OF OR/OF r 2  A OR/OF  r 2 where   40 F A 2 360 2  2     85  50   SF 85 A 2   9 1  SF 50 A OR/OF  (852  502 ) 2 9  525  1 649,34 m 2  Area/Oppervlakte  the area CANNOT be fully covered CA  Conclusion/ oppervlakte KAN NIE volledig bedek word NIE gevolgtrekking CA OR/OF OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 21 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne s1  r 2 100  50     m  34,91m 9 9 rs F A1  A 2 100 50   2 500  9   m 2  872, 66m 2 2 9 SF 50 A s 2  r 2 170  85     m  59,34m 9 9 rs A2  2 170 85   7 225  9   m 2  2522, 00m 2  SF 85 A 2 9 7 225 2 500  Shaded/Gearseerde oppervlakte   m2   m2 9 9  525 m 2  1 649,34 m 2  Area/Oppervlakte  the area CANNOT be fully covered CA oppervlakte KAN NIE volledig bedek word NIE  Conclusion / Gevolgtrekking CA (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 22 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 10.5 4h 2  4dh  x 2  0 F A  SF A 4h 2  4  30  h  18   0 2 Standard form/Standaard 4h 2  120h  324  0 vorm CA   120   120   4  4  324  2 h OR / OF  h  27  h  3  0  formula/factors/ formule 2  4 faktore CA h  27 or / of h  3  BR  3cm length of/lengte van BR CA OR/OF OR/OF Half chord method/ halfkoord metode:  line from centre  chord/   length of/lengte van AB AB  BC  9 cm   A  lyn vanuit mdpt  koord  AB2  OB2  OA 2 (Pythagoras Thm. / St.)  SF A 92  15  h   152 2 Standard form/ 81  15  30h  h  15  0 2 2 2 Standaard vorm CA h 2  30h  81  0  formula/factors/ formule faktore CA   30    30   4 181 2 h OR / OF  h  27  h  3  0 2 1 h  27 or / of h  3 length of/lengte van BR CA  BR  3cm OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 23 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne  length of/lengte van AB A OR/OF  line from centre  chord/   value of/waarde van AB  BC  9 cm     lyn vanuit mdpt  koord  AOC A  In AOC, sin AOC  9  ratio/verhouding CA 15   AOC  36,87  9  OB tan AOB  OR/OF cos AOB  length of/lengte van OB OB 15 CA 9 length of/lengte van BR OB  tan 36,87 OB  15cos 36,87 CA  12 cm  12 cm BR  15  OB BR  15  OB OR/OF  3 cm  3 cm  length of/lengte van AB A OR/OF  line from centre  chord/  AB  BC  9 cm    lyn vanuit mdpt  koord   SF A AB2  OB2  OA 2 (Pythagoras )  length of/lengte van OB 9  OB  15 2 2 2 CA M CA OB2  152  9 2 length of/lengte van BR OB2  144 CA OB  12 cm (5) BR  15  12  BR  3 cm [19] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 24 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 11 11.1.1 0,2 m 0,2 m A (1)  o o  F A 11.1.2 A T  a  1 n  o2  o3  ...  on1   2   2  1,42  SF CA  0,2   1,7  1,59  1,52  1,48  m 2  2   0,2 8 m 2 value of/ waarde 1,6 m 2 van AT CA OR/OF OR/OF A T  a m1  m2  m3  ...  mn  F A  2  1,7 1,7  1,59 1,59  1,52 1,52  1,48 1,48  1,42  2  0,2      m SF CA  2 2 2 2 2   0,2 8 m 2 value of/ waarde 1,6 m 2 van AT CA (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 25 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 11.1.3 4  0, 2  8  5 x  m 2 substitution of 5x/vervang 5x CA 4  1, 6  x simplification/ vereenv CA 4  1, 6  x 2, 4m  x value of / waarde van x CA OR / OF OR / OF  x  0, 2  5  1, 6  4 m 2 setting up equation/opstel van vergelyking CA x  4  1, 6 simplification/ vereenv CA x  2, 4m value of / waarde van x CA (3) 11.2 F A 11.2.1 Surface area of hemisphere/  1  4 r 2 Buite opp. van hemisfeer 2 SF A  2  30  2 surface.area/buite  1 800 OR / OF oppervlakte CA  5 654,87 cm 2 NPR OR/OF OR /OF Surface area of sphere/  4 r 2 F A Buite opp. van sfeer SF  4  30  2 A  3 600 cm 2 OR / OF  11309, 73 cm 2 Surface area of hemisphere/  3 600  1 800 surface area/buite Buite opp. van hemisfeer 2 oppervlakte CA NPR OR/OF  5 654,89 cm 2 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Technical Mathematics/P2/Tegniese Wiskunde/V2 26 DBE/2023 SC/NSC/SS/NSS – Marking Guidelines/Nasienriglyne 11.2.2 Volume of 75% hemisphere/ = 1  4  r 3  75% Volume van hemisfeer F A 2 3 1 4 SF     30   0, 75 A 3 2 3  13 500 cm3 OR / OF  value of/ waarde van V CA  42 411,50 cm3 Time taken to fill/ 13500  M (dividing /deel deer by 90) tyd geneem om te vul 90 A  150 sec OR/OF  471, 24 s  time taken/tyd geneem CA  2,5 min OR/OF  7,85 minutes NPR OR/OF OR/OF 4 Volume of sphere/van sfeer =  r 3 F A 3   30  4 3 SF A 3  36 000 cm 3 OR / OF  113 079 ,34 cm 3 Volume of 75% hemisphere/ = 36 000  75% Volume van hemisfeer 2  13500 cm3  value of/ waarde van V CA OR/OF  42 411,50 cm 3 time taken to fill/ 13500 M (dividing deel deer by 90)  tyd geneem om te vul 90 A  150 s OR/OF  471, 24 s  time taken/tyd geneem CA NPR  2,5 min OR/OF  7,85 minutes (5) [15] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou