NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 JUNE/JUNIE 2018 MATHEMATICS P2/WISKUNDE V2 MARKING GUIDELINE/NASIENRIGLYN

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1 NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD JUNE/JUNIE 8 MATHEMATICS P/WISKUNDE V MARKING GUIDELINE/NASIENRIGLYN MARKS /PUNTE: 5 This marking guideline consists of pages./ Hierdie nasienriglyn bestaan uit bladsye.

2 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) NOTE: If a candidate answers a question TWICE, only mark the FIRST attempt. If a candidate has crossed out an attempt of a question and not redone the question, mark the crossed out version. Consistent accuracy applies in ALL aspects of the marking guideline. Assuming answers/ values in order to solve a problem is NOT acceptable. NEEM KENNIS: As ŉ kandidaat ŉ vraag TWEEKEER beantwoord, merk slegs die EERSTE poging As ŉ kandidaat ŉ poging om ŉ vraag te beantwoord deurgehaal het en nie weer probeer het nie, merk die deurgehaalde poging. Volgehoue akkuraatheid is van toepassing op ALLE aspekte van die nasienriglyn. Aanvaarding van antwoorde/waardes om sodoende probleme op te los is NIE aanvaarbaar NIE. S GEOMETRY/MEETKUNDE A mark for a correct statement. (A statement mark is independent of a reason.) ŉ Punt vir korrekte stelling/bewering. (ŉ Stelling/bewering punt is onafhanklik van die rede.) R A mark for a correct reason. (A reason mark may only be awarded if the statement is correct.) ŉ Punt vir korrekte rede. (ŉ Rede punt mag slegs toegeken word indien die stelling/bewering korrek is.) S/R Award a mark if statement and reason are both correct. Ken ŉ punt toe indien die stelling/bewering sowel as die rede korrek is.

3 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 3 QUESTION/VRAAG. x x n Answer only full marks/ Slegs antwoord volpunte 5 4,7 4,7., 63 Answer / antwoord.3 4, 7, 63 x 4, 7, 63 3, 64 x 5,9 8 learners/leerders.4 Q 9 Q Semi IQR/IKW both c.v s / beide k.w s notation / notasie 8 learners/leerders Q Q3 answer/antwoord () () (3) (3) [] QUESTION/VRAAG. 56 y 64 y 8 y 4 Answer only mark Slegs antwoord punt. Time (in minutes) Tyd (in minute) Frequency / Frekwensie Cumulative frequency/ Kumulatiewe frekwensie 5 t 3 3 t t 4 t t t t correct equation korrekte vergelyking y-value/waarde 8, and/en 8 43, 6 and/en 64 () ()

4 4 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8).3 Cummulative frequency/ Kumulatiewe frekwensie Ogive/Ogief grounding/anker plotting against the upper limit/ afsteek teen die boonste limiet shape / vorm.4 Number of learners / Accept / Aanvaar 9 Time in minutes/ Tyd in minute Aantal leerders method/metode 54 answer/antwoord (3) (3) []

5 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 5 QUESTION/VRAAG 3 A y B O F C x E ; x py p y x p y-subject of formula y-onderwerp van formule A ; coordinates of A koördinate van A () OA OC 4 4 OC C 4; p 4 mac p 4 simplification/vereenvoudiging p 4 p-value/waarde (4) meb 4 EB AC m EB 4 equation/vergelyking y 4x 7 ()

6 6 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) x 4x 7 4 x 4 6x 3 7x 34 x y 4x 7 5 4x 5 x 8 5 F ; 8 5 BF Area FOAB AreaΔAOC AreaΔBFC ,47 OR/OF BF AreaFOAB AreaΔAOF Area ΔABF 7 r 6 47 x y 6 5 8, equating / gelykstel simplification / vereenvoudiging x-value/waarde y-value/waarde y = x-value/waarde substitution / vervanging BF BC substitution / vervanging answer / antwoord substitution / vervanging BF OF substitution / vervanging answer / antwoord (4) () (5) answer / antwoord () r equation / vergelyking () []

7 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 7 QUESTION/VRAAG 4 y S R M Q O C x A P B 4. x 6x 9 y 8y x 3 y 4 6 M 3;4 completing the square kwadraatsvoltooiing x-value/waarde y-value/waarde (3) 4. r 6 answer/antwoord () 4.3 m 5 [SA QB] m 5 AS y 4 5 x 3 y 5x 9 AS subst. /verv. m & 3;4 AS equation/vergelyking (3)

8 8 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) 4.4 x 6x 9 5x substitution/vervanging simplification / x 6x 9 5x 5x 5 6 vereenvoudiging 6x 56x 8 standard form / x 6x 8 standaardvorm x 4x factors / faktore x 4 or x choosing correct x-value y 5( 4) 9 korrekte keuse van x- waarde Q 4; y-value/waarde (6) substitute/vervang 4 k 5 4; 9 k 5 answer / antwoord () tan tan size of θ / grootte van θ ˆ size ofo Qˆ P / OQP s on a str line / [ eop ' n reguitlyn] grootte van O Qˆ P OQP ˆ ORC ˆ RCPQis a cyclic quad conversessameseg R RCPQ is ' n koordevierhoek [ omgekeerdeein dieselfde seg] (4) [9]

9 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 9 QUESTION/VRAAG sin 7 sin 7 t t sin 7 t t 7 4 t 5.. x 4 t x 4 t sin 54 sin 7 cos 7 sin 7 cos 7 t 4 t substitution/vervanging t 4 t tan53.cos 7 ( tan7 )cos 7 tan7 sin 7 cos 7 t 5..3 cos87 cos6 7 cos 6.cos 7. 4 t 4 t t t..cos 7 sin6.sin 7 sin 7 cos 7 t 6 7 expansion / uitbreiding 4 t t subst./verv. & 3 subst. / verv. & (4) (3) (4)

10 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) 5. sin cos9 sin 36.cos 8 sin sin sin sin sin sin cos cos sin cos cos sin 5.3 9sin x4cos x x x x x 3sin cos 3sin cos 3sin xcosx tan x 3 x 33, k or/of x 46,3 8. k k Z sin cos sin (6) factors/faktore both equations beide vergelykings tan x 3 both / beide 33,69 &46,3 / 33,69 8. k & k Z (5) []

11 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V QUESTION/VRAAG 6 6. Amplitude answer/antwoord () y min & max/maks notation/notasie () y both x- intercepts beide x-afsnitte 3 &5 x max TP & y- intercept shape / vorm (3) x both c.v. s / beide k.w s notation/notasie () 6.5 h( x) sin( x 9 ) cos x sin( x 9 ) cos x (3) []

12 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) QUESTION/VRAAG 7 A D B C 7. A ˆ 9 answer / antwoord () 7. DB answer / antwoord sin DC () 7.3 DB DC sin θ and/en AD DB DB AD = DB sine rule/sinusreël in DC AD in ADC ADC sin9 θ sin θ subst. in sine rule / verv. DB in sinusreël sin θ DB cos θ sin θ cosθ DB DB sin θ. cos θ sin θ DB. sin θ DB. sin θ. cos θ equation / vergelyking cos θ cos θ (5) [7]

13 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 3 QUESTION/VRAAG 8 8. Perpendicular to the chord / Loodreg op die koord answer/antwoord () 8. D O P 3 M E Q x 3 OM 3 OR x 3 OM OQ OM 4x x 3 x 3 x 9 4x 4 4x 44 x 6 QM 6 x answer/antwoord OR/OF answer/antwoord susbt. in Pyth / verv. in Pyth. simplification / vereenvoudiging () standard form linear equation Standaardvorm van lineêre vergelyking x-value/waarde (4)

14 4 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) 8..3 DM DQ DM subst. in Pyth / verv. in Pyth answer / antwoord (3) [9]

15 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 5 QUESTION/VRAAG 9 A E F 3 x C T 3 B K 9. Â x [ at centre at circumf./ Middelpunts Omtreks ] S R Ĉ x [ sopp. sides / e teenoor gelykesye] S R ˆB x [ tan chord theorem / raaklyn-koord-stelling] S R Tˆ x [corresp. s, / ooreenk. e : TF BC] S R 9. ˆTAˆ x S ATBE is a cyclic quad [ converse s same segment] ATBE is ' n koordevierhoek [ omgekeerdeein dieselfde seg] R (8) () []

16 6 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8) QUESTION/VRAAG. A h k N M C B Contruction:Join BN and height hfrom N AM and CM and height k from M AN Konstruksie : Verbind BN en hoogte, hvanaf N AM CM en hoogte, k vanaf M AN AM h Area Δ AMN same height/dieselfde hoogte Area Δ BMN BM h AM BM AN k Area Δ AMN same height / dieselfde hoogte Area Δ CMN NC k AN NC same height,same dieselfde hoogte, dieselfde Area ΔBMN Area Δ CMN / base MN BC basis MN BC AM AN BM NC constr / konstr. S S R R (5)

17 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 7. M y E K x D N.. ND x ND x and/en 3x 3y verhouding stelling DE KM of / lyn getrek aaneensyvan' n KM KN MN Pyth theorem/stelling given/gegee NE prop theorem DE KM or y line drawn to oneside of a Δ NE y 9x 9y S R subst in Pyth theo verv. in Pyth stel simplification/ vereenvoudiging (4)

18 8 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8).. DM DN MN Pyth x 3y KE KN NE Pyth 3x y DM KE DM KE KM 4x 3 x 3 x y 9 x y 3 9 9y y 9x 4y subst in Pyth / verv. in Pyth subst in Pyth / verv. in Pyth value of / waarde van DM KE 3 x y 9 x y (4) [3]

19 (EC/JUNE/JUNIE 8) MATHEMATICS P/WISKUNDE V 9 QUESTION/VRAAG A 3 x P D 3 T 4 C B. Aˆ ˆ B alts,ac DB /[ verw. e, AC DB] Aˆ Bˆ tan chord / [ Raaklyn koord] Aˆ 3 Aˆ 3 ˆT ACB ˆ ext of a cyclic quad / [ buitevan koordev] Dˆ Bˆ 3rds /[3 dee] OR/OF S/R S S S OR/OF R R Aˆ ˆ B alts,ac DB /[ verw. e, AC DB] Aˆ Bˆ tan chord / [ Raaklyn koord] Aˆ 3 Aˆ 3 ˆT ACB ˆ ext of a cyclic quad / [ buitevan koordev ] ΔABC ΔADT S/R S R S R R (6)

20 MATHEMATICS P/WISKUNDE V (EC/JUNE/JUNIE 8). ˆ ˆ 4 ˆ ˆ 4 ˆ T T vertopps /[ regoorst. e] A T sinsameseg /[ ein dieselfde segment] A A3 proven / [ Bewys] ˆT ˆ A3 PTisa tangent tocircle ADT converse tan chord PT is ' n raaklyn aan sirkel ADT [ omgekeerde raaklyn koord] Aˆ 3 Tˆ proven / [ bewys] Pˆ Pˆ common / [ gemeen] PTA ˆ Dˆ 3rd s / [3 dee] Δ APT Δ TPD.3.4 OR/OF Aˆ 3 Tˆ proven / [ Bewys] Pˆ Pˆ common / [ gemeen] PTA ˆ Dˆ 3rd s /[3 dee] AP AP AD PT AP AP AP PT 3 AP AP. PT 3 AP 3PT AP PT TP PD AP.PD PT Δs S/R S R S S R S S S S/R R simplification vereenvoudiging PD i.t.o AP and AD PD i.t.v AP en AD (4) (3) subst in AD verv. in AD (4) [7] TOTAL/TOTAAL: 5

NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 SEPTEMBER 2018 MATHEMATICS P1/WISKUNDE V1 MARKING GUIDELINE/NASIENRIGLYN

NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 1 SEPTEMBER 018 MATHEMATICS P1/WISKUNDE V1 MARKING GUIDELINE/NASIENRIGLYN MARKS/PUNTE: 150 This marking guideline consists of 1 pages./