SENIOR GRAAD 11 MARKS: PUNTE:

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1 Province of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE GRAAD NOVEMBER 2022 MATHEMATICS P2/WISKUNDE V2 MEMORANDUM MARKS: PUNTE: 50 This memorandum consists of 8 pages. p Hierdie memorandum bestaan uit 8 bladsye.

2 2 MATHEMATICS P2/WISKUNDE V2 (Memo) (NOVEMBER 202) QUESTION/VRAAG. Quadratic / Kwadraties answer/antwoord ().2 Yes. The shape of the graph shows it./ Ja. Die vorm van die grafiek toon dit Yes/Ja reason/rede.3 Drivers should drive at a speed between 80 km/h and 20 km/h. Bestuurders behoort teen n spoed tussen 80 km/h en 20 km/h te bestuur. answer/antwoord QUESTION/VRAAG ;8;22;25;3;35;36;42;44;49 Median/Mediaan = = Q = 22 Q 3 = 42 Semi IQR= = Min=, Q =22, Q 2 =33, Q 3 = 42, Max/Maks = x [5] Method/Metode Answer/Antwoord Answer only: 2/2 Slegs antwoord :2/2 Q Q 3 answer/antwoord min Q and/en Q 3 Q 2 max/maks Data is skewed to the left./data is skeef na links Data is more widely distributed below the median./ Data is wyer verspreid onder die mediaan answer/ antwoord (4) () [0]

3 (NOVEMBER 202) MATHEMATICS P2/WISKUNDE V2 (Memo) 3 QUESTION/VRAAG x = 27 3 x = X x x (x x) = = = = = = = = = = = = = 2 4 Sum/Som 698 SD = SD = 7, One standard deviation from the mean/een standaardafwyking vanaf die gemiddelde: 9,67 to/tot 34,33 9 spectators/toeskouers QUESTION/VRAAG 4 4. Interval Frequency Frekwensie 4.2 Cumulative frequency Kumulatiewe frekwensie method/metode answer/antwoord sum/som Answer/antwoord Answer only: 3/3 Slegs antwoord: 3/3 interval answer/antwoord [7] First 4 correct/eerste 4 korrek Last 3 correct/laaste 3 korrek (5 ; 0) All points correct/alle punte korrek Shape/vorm % of/van 40 = 32 Approximately 5 learners/ongeveer 5 leerders (Accept 4, 5 or 6/Aanvaar 4, 5 of 6) method/metode answer/antwoord [8]

4 4 MATHEMATICS P2/WISKUNDE V2 (Memo) (NOVEMBER 202) QUESTION/VRAAG 5 5. S( 6 ; 4), T( ; 3), R( 7 ; ) ST 6 34 ST 26 SR SR 26 ST = SR. ΔSTR is isosceles/gelykbenig. 5.2 B( ; B( 4 ; ) 5.3 S( 6 ; 4), B( 4 ; ) SB SB and/en A(p ; 7) T( ; 3), R( 7; ) and/en AS TR TR Substitution/instelling ST 26 SR 26 Conclusion/gevolgtrekking Substitution/instelling 4 Substitution/instelling Gradient/gradiënt Substitution/instelling (4) Answer/antwoord (4) Substitution of/instelling van 7 Substitution of/instelling van p Answer/antwoord TR Hence AS is perpendicular to TR AS is loodreg op TR 5.6 STAR is a kite/vlieër Diagonal AS bisects TR at right angles Skuinslyn AS halveer TR en is loodreg op TR ΔSTR and ΔRAT are both isosceles. ΔSTR en ΔRAT is albei gelykbenig. TR AS AS perpendicular to TR/ AS is loodreg op TR Kite/vlieër Reason/rede [20] QUESTION/VRAAG 6 6. x + y + 2 = 0 and/en Q(7;6) y = x 2 m = y 6 = (x 7) y = x + 3 m = substitution/instelling answer/antwoord

5 (NOVEMBER 202) MATHEMATICS P2/WISKUNDE V2 (Memo) Q(7 ; 6), R(4; 6) 6 6 substitution/instelling QR 47 QR 4 answer/antwoord 6.3 P( 2; 0) QR 2 Method/metode 3 T( ; 2) tan = 4 = 75,96 tan = 4 75,96 QR = 33,69 tan = PQ = 33,69 PQR = 75,96 33,69 = 42,27 Answer/antwoord (5) [5] QUESTION/VRAAG R / ( ; 6) R/(6 ; ) (x ; y) (x ; y) (x 3 ; y) x y (x ; y) (x 3 ; y) x 3 y (4) y D // ( ; 3) 5 E // ( 3 ; ) 4 F // (2 ; 2) 3 Diagram 2 F // E // x D // -4-5 (4) Rigid. The size and shape do not change Rigid/rigied Rigied. Die grootte en vorm verander nie reason/rede 7.3. N / ( ;6) Perimeter of/omtrek van KLMN = 0 units/eenhede Method/metode Perimeter of/omtrek van K / L / M / N / = 3 0 = 30 units/eenhede Answer/antwoord Answer only/slegs 7.4 Rotation about the origin through 90 anticlockwise Rotasie rondom die oorsprong deur 90 anti-kloksgewys antwoord: 2/2 90 anticlockwise/ anti-kloksgewys [20]

6 6 MATHEMATICS P2/WISKUNDE V2 (Memo) (NOVEMBER 202) QUESTION/VRAAG 8 8. V = π r 2 h and/en V = cm 3 π r 2 (5) = r = 9,2 cm 8.2 V cone = area of base/opp van basis H H = 0 9,2 = 3,89 cm V cone/kegel = π (9,2)2 (3,89) = 345,54 cm 3 V container/houer = cm ,54 cm 3 = 4 345,54 cm 3 [accept/aanvaar 4 346,4] 8.3 SA = π r 2 + 2π r h + π r s = π (9,2) 2 + 2π (9,2)(5) + π (9,2)(0) = 423,85 cm 2 Substitution of/instelling van 5 Substitution of/instelling van answer/antwoord H = 3,89 [or/of 3,9] Substitution/Vervanging V = 345,54 [or/of 346,4] answer/antwoord (4) substitution/instelling : in π r 2 in 2π r h in π r s answer/antwoord (4) [] QUESTION/VRAAG sin p diagram answer/antwoord cos 29 = sin cos 2 29 = p 2 + cos 2 29 = cos 29 = 9..2 tan ( 569 ) = tan 29 = identity/identiteit substitution/instelling answer/antwoord tan 29 answer/antwoord tan ( 569 ) = tan 29 = = 9..3 cos 2 6 = p 2 cos 2 6 = sin 2 6 = cos 2 29 = ( ) 2 = p 2 tan 29 answer/antwoord answer/antwoord sin 2 6 answer/antwoord

7 (NOVEMBER 202) MATHEMATICS P2/WISKUNDE V2 (Memo) LHS = = = = = = = = = RHS factors/faktore division/deel (5) [2] QUESTION/VRAAG 0 0. sin.tan 360. sin450 cos 80 cos 80 sin. tan. cos cos sin sin. cos.cos cos sin cos 0.2 sin x 3cos x = 0 sin x = 3cos x tan x = 3 x = 7, k (k ) sin α = tan x cos x answer/antwoord (8) sin x = 3cos x tan x = 3 7, k k (4) sin α = sin = = 80 4,48 = 65,52 sin = 4,48 65,52 [5]

8 8 MATHEMATICS P2/WISKUNDE V2 (Memo) (NOVEMBER 202) QUESTION/VRAAG. 3 3 () y f(x)=-sin x.2 f(x)=cos(x - 30) f : x intercepts/ x-afsnitte turning points/ draaipunte shape/vorm g(x) f(x) 0 g(x) f(x) x [ 80 ; 30 ] or/of x [50 ; 80 ] 80 x 30 or/of 50 x g(x) = cos (x 30 ) h(x) = cos (x ) + - x g : y-intercept/ y-afsnit x-intercepts/ x-afsnitte shape/vorm (6) Values/waardes Notation/notasie Values/waardes Notation/notasie per interval (4) 90 + = cos (x 90 ) Maximum value of/maksimum waarde van h(x) f(x) = sin x = sin ( x) sin x sin ( x) [7] QUESTION/VRAAG 2 2. sin QS QS = 80 m 2.2 PSQ 65 / QPS 85 PQ 80 sin 65 sin 85 PQ = 72,78 m ,78 sin 30 2 = 455,60 m sin 60 2 = 385,64 m , ,64 m 2 = 4 296,84 m 2 sin 30 QS answer/antwoord PSQ / QPS sine formula/sinus formule answer/antwoord substitution into area formula/instelling in area formule Substitution/instelling answer/antwoord (5) [0] TOTAL/TOTAAL: 50