PAST EXAM PAPER & MEMO N6 - Engineering N1-N6 Past
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T980(E)(A6)TAPRIL EXAMINATIONNATIONAL CERTIFICATEMATHEMATICS N6(16030186)6 April 2016 (X-Paper)09:00–12:00Calculators may be used.This question paper consists of 5 pages and 1 formula sheet of 7 pages.Copyright reservedPlease turn over
(16030186)-2-T980(E)(A6)TDEPARTMENT OF HIGHER EDUCATION AND TRAININGREPUBLIC OF SOUTH AFRICANATIONAL CERTIFICATEMATHEMATICS N6TIME: 3 HOURSMARKS: 100INSTRUCTIONS AND INFORMATION1.Answer ALL the questions.2.Read ALL the questions carefully.3.Number the answers according to the numbering system used in this question paper.4.Questions may be answered in any order, but subsections of questions must be kepttogether.5.Show ALL the intermediate steps.6.ALL the formulae used must be written down.7.Questions must be answered in BLUE or BLACK ink.8.Write neatly and legibly.Copyright reservedPlease turn over
(16030186)-3-T980(E)(A6)TQUESTION 11.11.2If z 5 x 3 y 2 y 4 3x 2 y , determineGiven: I 2z x y(2)VRCalculate the change in I if V decreases with 5 volts and R with 8 ohms. The originalvalue of V is 30 volts and of R is 10 ohms.(4)[6]QUESTION 2 y dx if:Determine2.1y sin4 5 x cos3 5 x2.2y 2.3y sin 4 mx2.4(5)116x x 2x2y e . cos 3x(3)(4)(6)[18]QUESTION 3Use partial fractions to calculate the following integrals:3.13.2 x 2 3x 4dxx (1 2 x ) 2 10x 2 7 x 1dx( 2 x 2 1)(4 x 1)Copyright reserved(6)(6)[12]Please turn over
(16030186)-4-T980(E)(A6)TQUESTION 44.1Calculate the particular solution of:dy2 sin x2 sin x y (sin 2 x ) at (0;1)dxsec x(5)4.2Calculate the particular solution of:dydyd2y 7 6 y 2 x 3 , if y 1 when x 0 and 2 when x 0 .2dxdxdx(7)[12]QUESTION 55.15.1.15.1.25.25.2.15.2.25.2.35.35.3.1Copyright reserved3andxy x 4 0 . Make a neat sketch of the curves and show the area, in thefirst quadrant, bounded by the curves.Show the representativestrip/element that you will use to calculate the volume (use the SHELLmethod only) generated if the area bounded by the curves rotates aboutthe y -axis.(3)Use the SHELL method to calculate the volume generated if the area,3described in QUESTION 5.1.1, bounded by the two curves y andxy x 4 0, rotates about the y-axis.(5)Make a neat sketch of the graph y tan x . Show the representativestrip/element that you will use to calculate the volume generated if the area bounded by the graph, the ordinates y 0 and x rotates about3the x-axis.(2)Calculate the volume generated if theQUESTION 5.1.1, rotates about the x -axis.(3)Calculate the points of intersection of the two curves y area,describedinCalculate the volume moment about the y -axis as well as the distance ofthe centre of gravity from the y -axis.(6)Calculate the points of intersection of the two curves y 2x 2 andyx . Make a neat sketch of the curves and show the area bounded by3the curves. Show the representative strip/element, PERPENDICULAR tothe x -axis, that you will use to calculate the area bounded by the curves.(3)Please turn over
(16030186)-5-5.3.2Calculate the area described in QUESTION 5.3.1, bounded by the twoycurves y 2x 2 and x .3(3)Calculate the second moment of area of the area described inQUESTION 5.3.1 about the y-axis.(4)5.3.4Express the answer in QUESTION 5.3.3 in terms of the area.(1)5.4.1A weir in the form of a trapezium is 2 m high, 10 m wide at the top and4 m wide at the bottom. The top of the weir is in the water surface.5.3.35.4T980(E)(A6)TSketch the weir and show the representative strip/element that you willuse to calculate the depth of the centre of pressure on the retaining wall.5.4.25.4.3Calculate the relation between the two variables x and y.(3)Calculate, by using integration, the area moment of the weir about thewater level.(3)Calculate, by using integration, the second moment of area of the weirabout the water level, as well as the depth of the centre of pressure on theweir.(4)[40]QUESTION 66.16.2Calculate the arc length of the curve described by the parametric equations,x 5(cost t sin t ) and y 5(sin t t cos t ) , between the points t 0 and t .Calculate the surface area generated when the curve of y 16x , over the interval1 x 4 , is rotated about the x-axis.TOTAL:Copyright reserved(6)(6)[12]100
(16030186)-1-T980(E)(A6)TMATHEMATICS N6FORMULA SHEETAny other applicable formula may also be used.Trigonometrysin2 x cos2 x 11 tan2 x sec2 x1 cot2 x cosec2 xsin 2A 2 sin A cos Acos 2A cos2A - sin2Atan 2A 2 tan A1 tan2 Asin2 A ½ - ½ cos 2Acos2 A ½ ½ cos 2Asin (A B) sin A cos B sin B cos Acos (A B) cos A cos B sin A sin Btan (A B) tan A tan B1 tan A tan Bsin A cos B ½ [sin (A B) sin (A - B)]cos A sin B ½ [sin (A B) - sin (A - B)]cos A cos B ½ [cos (A B) cos (A - B)]sin A sin B ½ [cos (A - B) - cos (A B)]tan x sin x11; sin x ; cos x cos xcosec xsec xCopyright reservedPlease turn over
(16030186)-2-T980(E)(A6)Tdf (x ) f(x)dxdxx n 1nn-1( n - 1)xnx Cn 1f(x)naxeax badx ed nxdxaeax bana x dxd.(ax b)dxdx ed. ln a.(dx e)dxln(ax)1 d.axax dxe f (x)e f ( x)a f (x)a f ( x ) . ln a.ln f(x)1d.f ( x)f ( x) dxe ax bd ax b dx Ca dx e Cdln a. dx e dxxln ax - x Cdf ( x)dx-df ( x)dx-cos ax Casin axa cos ax-cos ax-a sin axsin ax Catan axa sec2 ax1ln [sec (ax)] Cacot ax-a cosec2 ax1ln [sin (ax)] Casec axa sec ax tan ax1ln [sec ax tan ax] Cacosec ax-a cosec ax cot ax1 ax ln tan Ca 2 Copyright reservedPlease turn over
(16030186)-3-T980(E)(A6)Tdf (x) f (x) dxdxf (x)sin f (x)cos f (x) . f '(x)-cos f (x)-sin f (x) . f '(x)-tan f (x)sec2 f (x) . f '(x)-cot f (x)-cosec2f (x) . f '(x)-sec f (x)sec f (x) tan f (x) . f '(x)-cosec f (x)-cosec f (x) cot f (x) . f '(x)-f' ( x)-sin 1 f (x)1 [ f ( x )]- f' ( x)-cos 1 f (x)-tan 1 f (x)-cot 1 f (x)f ' ( x)-[ f ( x)]2 1- f' ( x)-[ f ( x )] 2 1f ' ( x)-f ( x) f ( x) 2 1- f' ( x)-2f ( x ) [ f ( x )] 1sin2(ax)-cos2(ax)-tan2(ax)-Copyright reserved-1 [ f ( x )] 2sec 1 f (x)cosec 1 f (x)-2--x sin( 2 ax ) C24ax sin(2ax) C24a1tan ( ax ) x CaPlease turn over
(16030186)-4-T980(E)(A6)Tdf (x) f (x) dxdxf (x)cot2 (ax)--1cot ( ax ) x Ca f(x) g' (x) dx f(x) g(x) - f ' (x) g(x) dx f ( x) n 1 C f ( x) n f ' ( x) dx f ' ( x)dx ln f ( x) Cf ( x)dxa 2 b2 x 21bxsin-1 Cba dx1 a2 b2 x2 ab tan (n - 1)n 1-1 bxa Ca2bx xa b x dx sin-1 2ba222 2dxa 2 b2 x2 C a bx 1 a 2 b2 x 2 2ab ln a bx C x 2 b 2 dx dxb x a2 22 x 2b2x b2 ln x 22 x2 b2 C 1ln bx b 2 x 2 a 2 CbApplications of integrationAREASbbaa y1 y2 dxbbaa x1 x2 dyAx ydx ; Ax Ay xdy ; Ay Copyright reservedPlease turn over
(16030186)-5-T980(E)(A6)TVOLUMESbbaabbaaVx y 2dx ; Vx V y x 2dy ; Vy y y22 dx ; Vx 2 xydy x x22 dy ; V y 2 xydx2121 ba baAREA MOMENTSAm x rdAAm y rdACENTROIDbx Am yAb rdA ; y Am x a rdA aAAASECOND MOMENT OF AREAbI x r 2 dAbI y r 2dA;aaVOLUME MOMENTSbVm x rdVbVm y rdV;aaCENTRE OF GRAVITYbx vm yV rdV aVb;y vm xV rdV aVMOMENTS OF INERTIAMass Density volumeM VDEFINITION: I m r2Copyright reservedPlease turn over
(16030186)-6-T980(E)(A6)TGENERALI b 2 a rbdm r 2 dVaCIRCULAR LAMINA1 2mr2Iz I 1 b 21r dm a22Ix 1 2b ab 2 a rdVIy y 4 dx1 2 b 4x dyaCENTRE OF FLUID PRESSUREb 2 r dAy ab a rdAf ( x)ABCZ .n23ax b (ax b)(ax b)(ax b)(ax b)nf ( x)3(ax b) (cx d )3 ABCDEF 232ax b (ax b)(cx d ) (cx d )(ax b)(cx d )3f ( x)Ax FBCZ 2 . n2(ax bx c)(dx e)ax bx c dx e (dx e)(dx e)n22b dy Ax 2 y 1 dxa dx 2c dx Ax 2 y 1 dyd dy Ay bAy cad2 dy 2 x 1 dx dx 2 dx 2 x 1 dy dy Copyright reservedPlease turn over
(16030186)Ax u2u1Ay u2u1S bS daS cu2u1-7-2222 dx dy 2 y du du du dx dy 2 x du du du 2 dy 1 dx dx 2 dx 1 dy dy 22 dx dy du du du dyPdx Py Q ye dx Qe Pdxdxy Aer 1x Ber2x r1 r2y erx ( A Bx) r1 r2y eax[ A cosbx B sin bx] r a ibd2yd dy d 2d dx dxdxCopyright reservedT980(E)(A6)T
MARKING GUIDELINENATIONAL CERTIFICATEAPRIL EXAMINATIONMATHEMATICS N66 APRIL 2016This marking guideline consists of 17 pages.Copyright reservedPlease turn over
MARKING GUIDELINETOTAL:-2MATHEMATICS N6T980(E)(A6)T200 1002NOTE: Do NOT subtract marks for incorrect units or units omitted.QUESTION 11.1z 5 x 3 y 2 y 4 3x 2 y z 33 ( 10x y 4 y 3x 2 ) x y x 30x 2 y 6 x1.2 (4)VRI VR 1I I I V R V R 1 2 R V VR R I 1V V 2 RRR 130 ( 5) ( 8)(10)(10) 2 1,9 A Copyright reserved(8)[12]Please turn over
MARKING GUIDELINE-3MATHEMATICS N6T980(E)(A6)TQUESTION 22.1y sin4 5x cos3 5xdx sin 5x cos2 5x. cos5xdx4 sin 5x(1 sin2 5x) cos5xdx4u sin 5 xdu 5 cos5xdx1sin4 5 x (1 sin2 5 x )5 cos5 xdx 5 1 u 4 (1 u 2 )du5 1 u 4 u 6 )du5 1 u5 u7 c5 57 51 sin 5 x sin7 5 x c 5 57 OR11 sin5 5 x sin7 5 x c2535ORy sin4 5x cos3 5xdx sin 5x cos2 5x. cos5xdx4 sin 5x(1 sin2 5x) cos5xdx4 sin4 5x. cos5xdx sin6 5x. cos5xdx 571 sin 5 x 1 sin 5 x . c .5557Copyright reservedu sin 5 xdu 5 cos5xdx(10)Please turn over
MARKING GUIDELINE2.2y -4MATHEMATICS N61 16x x 2 x 2 16xT980(E)(A6)Tdx ( x 2 16x ) 2 [( x 8) 64] 64 ( x 8) 2 164 ( x 8) 2 sin 12.3 dx( x 8) c8 (6)y sin4 mxdx (sin2 mx ) 2 dx 1 1 ( cos 2mx ) 2 dx 2 21 11 1 ( cos 2mx )( cos 2mx )dx2 22 21 11 ( cos 2mx cos2 2mx )dx 4 24 11 sin 2mx 1 x sin 4mx x . c42 2m4 28m 1sin 2mx x sin 4mx c x 44m832mCopyright reserved(8)Please turn over
MARKING GUIDELINE2.4y -5MATHEMATICS N6x2T980(E)(A6)Txe . cos3xdxf ( x) e 2 xsin 3x1sin 3x ydx e ( 3 ) 2 e 2 ( 3 )dxxf ' ( x) x2x 11 e sin 3x e . sin 3xdx36x21 2e2f ( x) e 2x2xf ' ( x) 1 2e2g ' ( x ) cos3xsin 3xg ( x) 3g ' ( x ) sin 3xcos 3xg ( x) 3 11 cos3x1cos 3x e sin 3x e . e . dx 36 323 x2x2x2x2x2 x2111 e sin 3x e . cos3x e . cos3xdx31836xx111I e 2 sin 3x e 2 . cos3x I 31836 xx371 21 2 I e sin 3x e . cos3x 36318 xx36 11I ( e 2 sin 3x e 2 . cos3x ) c37 318xx 0,973(0,333e 2 sin 3x 0,054e 2 . cos3x ) cx2x2 0,324e sin 3x 0,054e . cos 3x cORy x2e . cos3xdx x x2f ( x ) cos3xf ' ( x ) 3sin 3xx ydx 2e cos3x ( 3sin 3x)2e 2 dx x2x 2e cos3x 6 sin 3x.e 2 dx xx 22 2e cos3x 6 sin 3x.2e 3 cos3x.2e dx x2xxg ' ( x) e 2xxe2g ( x) 2e 212f ( x ) sin 3xf ' ( x ) 3cos3xg ' ( x) ex2g ( x ) 2ex2x 2e 2 cos3x 12 sin 3x.e 2 36 cos3x.e 2 dxCopyright reservedPlease turn over
MARKING GUIDELINE-6MATHEMATICS N6xT980(E)(A6)TxI 2e 2 cos3x 12e 2 . sin 3x 36I xx 37.I 2e 2 cos3x 12e 2 . sin 3x xx1I ( 2e 2 cos3x 12e 2 . sin 3x ) c37x2x2 0,054e cos3x 0,324e sin 3x c(12)[36]QUESTION 33.1 x 2 3x 4dxx (1 2 x ) 2 x 2 3x 4 ABC 22x (1 2 x )x (1 2 x )(1 2 x ) x 2 3x 4 A(1 2 x ) 2 Bx Cx (1 2 x ) Let x 0; A 4 121 Let x ; B (10,5)22 x 2 3x 4 A 4 Ax 4 Ax 2 Bx Cx 2Cx 217Equate coeff of x 2 : C (8,5) 22117422 dx dx dx x(1 2 x ) 2(1 2 x ) 121 (1 2 x )17 4 ln x . ln(1 2 x ) c4 142117 4 ln x ln(1 2 x ) c4(1 2 x ) 45,25 0,444 ln x 1,444 ln(1 2 x ) c(1 2 x )Copyright reserved(12)Please turn over
MARKING GUIDELINE3.2 -7MATHEMATICS N6T980(E)(A6)T10x 2 7 x 1dx( 2 x 2 1)(4 x 1)10x 2 7 x 1Ax BC 2 2( 2 x 1)(4 x 1) 2 x 1 4 x 1 10x 2 7 x 1 ( Ax B )(4 x 1) C ( 2 x 2 1) 10x 2 7 x 1 4 Ax 2 4 Bx Ax B 2Cx 2 C1 let x C 34Equate coeff of x 2 : A 1 Equate x : B 2 x 23 2 dx dx 2x 14x 1 x23dx 2 dx dx2x 12x 14x 12 13 1 2 ln(2 x 1) 2 arctan2x ln(4x 1) c 44 2 (12)[24]QUESTION 44.1dy2 sin x y (sin 2 x ) dxsec xdy y ( 2 sin 2 x )1 dx2 sin xsec x dy y ( 2 sin x cos x )1 dx2 sin xsec xdy y. cos x cos x dx cosx . dxe e sin x 2 sin xe sin x . y e sin x . cos xdx e sin x c e sin 0 .(1) e sin 0 c c 2 sin x sin xe. y e 2 Copyright reserved(10)Please turn over
MARKING GUIDELINE4.2-8MATHEMATICS N6T980(E)(A6)Tdyd2y 7 6 y 2x 32dxdx2 y c : m 7m 6 0( m 6)(m 1) 0m 6; m 1y c Ae 6 x Be xTo find y p y Cx D dy Cdxd2y 0 dx 20 7C 6Cx 6 D 2 x 3 1C (0,333) 38 7C 6 D 3 D (0,889)918 yp x 39 18y Ae 6 x Be x x 39811 A B A B 99dy1 6 Ae 6 x Be x dx312 6A B 3 14 A 0,311 45 1 9and B 0,2 or 5 4514118 y e6x e x x 45539y 0,311e 6 x 0,2e x 0,333x 0,889Copyright reserved(14)[24]Please turn over
MARKING GUIDELINE-9MATHEMATICS N6T980(E)(A6)TQUESTION 55.15.1.13 x 4xx2 4x 3 0 x 3 x 1 0x 3; x 1 y 1; y 3 3;1 and (1;3)( x ; y2 ) ( x ; y1 ) x x(6) 5.1.2 V y 2 x ( y 2 y1 ) x 3V y 2 x ( y 2 y1 )dxIncorrect limits: max 7 marks1 2 31 3x ( x 4 )dxx3 2 ( x 2 4 x 3)dx 13 x3 4x2 2 3x 2 3 1 (3) 3 (1) 3 2 2(3) 2 3(3) 2(1) 2 3(1) 3 38 2,667 units3 or 8,278 or units3 3Copyright reserved (10)Please turn over
MARKING GUIDELINE5.2-10MATHEMATICS N6T980(E)(A6)T5.2.1 ( x; y ) x x (4)5.2.2 V x y 2 x Incorrect limits: max 3 marksV x 3 y 2 dx0 3 (tan 2 x ) dx 0 (tan x x ) 03 (tan ) (tan 0 0) 3 3 0,685 units3 or 2,152 units3Copyright reserved (6)Please turn over
MARKING GUIDELINE-11MATHEMATICS N6T980(E)(A6)T 5.2.3 M y y x x2 Incorrect limits: max 8 marks 3 M y xy 2 dx0f ( x) xf ' ( x) 1 g ' ( x ) tan 2 xg ( x ) tan x x x (tan 2 x )dx 0 x (tan x x ) 03 3 (tan x x )dx 0 x2 3 3 x (tan x x ) 0 ln sec x 2 0 3 2 ( 3 ) (tan ) ln sec 3 3 32 3 33 0,572 units or 1,798 u 1,798 x 2,152 0,836 units 5.35.3.1 (12)2 x 2 3x2 x 2 3x 0x 2 x 3 0x 0; x y 0;Copyright reserved32y 4 1 23 9 (0;0) and ( ; )2 2(6)Please turn over
MARKING GUIDELINE5.3.2-12MATHEMATICS N6 A y 2 y1 xT980(E)(A6)T A 1 y 2 y1 dx121 Incorrect limits: max 3 marks 1 3 x 2 x 2 dx21 3x 2 2 x 3 3 1 2 21 1 23( )2( ) 3 3(1) 2 2(1) 3 2 2 2323 2 0,542 units 5.3.3 (6) I y y 2 y1 x x 2 1 3x 2 x x dx12 Incorrect limits: max 5 marks22 1 3x 3 2 x 4 dx1 21 3x 4 2 x 5 5 1 4 21 1 42( ) 5 3(1) 4 2(1) 5 3( 2 )2 4 5 45 4 0,316 units 5.3.4Copyright reserved (8)0,316 0,542 0,553 A I (2)Please turn over
MARKING GUIDELINE5.4-13MATHEMATICS N6T980(E)(A6)T5.4.1 y( x; y )xy y1 y2 y1 x x1 x2 x1y 0 2 0 x 2 5 22y ( x 2)33 x y 2 25.4.23 dA 2( y 2)dy2or dA (3 y 4)dy(6)2 rdA0 Incorrect limits: max 4 marks 2 ( 2 y )(3 y 4)dy02 (6 y 8 3 y 2 4 y )dy 02 6 y23y3 4 y2 8y 32 0 2 6( 2) 23( 2)3 4( 2) 2 8( 2) 32 2 12 units3 Copyright reserved(6)Please turn over
MARKING GUIDELINE5.4.3-14MATHEMATICS N6 20T980(E)(A6)Tr 2 dA Incorrect limits: max 5 marks2 ( 2 y ) 2 (3 y 4)dy02 (12 y 12 y 2 3 y 3 16 16 y 4 y 2 )dy 02 12 y 2 12 y 3 3 y 416 y 2 4 y 3 16 y 3423 0 2 3( 2) 44236(2) 4(2) 16( 2) 8( 2) 2 ( 2)3 43 4 14,667 units 14,667y 12 1,222 units (8)Or alternative method5.45.4.1 y( x; y ) y y1 y2 y1 x x1 x2 x1y 0 2 0 x 52 52y ( x 5) 33 x y 5 2Copyright reserved3 dA 2( y 5)dy or dA (3 y 10)dy2(6)Please turn over
MARKING GUIDELINE5.4.2-15MATHEMATICS N6 T980(E)(A6)T 0 y (3 y 10)dy 2Incorrect limits: max 4 marks0 (3 y 2 10 y )dy 20 3 y 3 10 y 2 32 23 3(0) 10(0) 2 3( 2)3 10( 2) 2 2 32 3 - 12 units3 5.4.30(6) y (3 y 10)dy2 20Incorrect limits: max 5 marks (3 y 3 10 y 2 )dy 20 3 y 4 10 y 3 3 2 4 3(0) 4 10(0)3 3( 2) 4 10( 2)3 3 43 4 14,667 units4 14,667y 12 1,222 units Copyright reserved(8)[80]Please turn over
MARKING GUIDELINE-16MATHEMATICS N6T980(E)(A6)TQUESTION 66.1x 5(cost t sin t )anddx 5( sin t t cos t sin t ) dtdx 5 sin t 5t cos t 5 sin tOrdt 5t cos t 22 dx 2 (5t cos t )dt 2y 5(sin t t cos t )dy 5(cos t t sin t cos t ) dtdy 5 cos t 5t sin t 5 cos tORdt 5t sin t dy 2 (5t sin t )dt 2 dx dy 2222 25t cos t 25t sin t dtdt 25t 2 (cos2 t sin2 t ) 25t 2 S 0 22 dx dy dt dt dt Incorrect limits: max 9 marks25t 2 dt 0 5 t.dt 0 t 2 5 2 0 5 2 2 2,5 2 units or 24,674 units (12)y 16x6.21y 4x 2 1 dy 2x 2 dx2 dy 1 4x dx 24 dy 1 1 x dx x 4 x 4x 4Ax 2 ydx 1xCopyright reservedIncorrect limits: max 9 marksPlease turn over
MARKING GUIDELINE-17MATHEMATICS N6T980(E)(A6)T 41 2 4 x 21 8 414x 4dxxx 4dx 1 8 ( x 4) 2 dx143 ( x 4) 2 8 3 2 116 343 2(x 4) 143 23 2 (8) (5) 12 61,051 unitsor 191,798 units2 16 3(12)[24]TOTAL:Copyright reserved100
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Past exam papers from June 2019 GRADE 8 1. Afrikaans P2 Exam and Memo 2. Afrikaans P3 Exam 3. Creative Arts - Drama Exam 4. Creative Arts - Visual Arts Exam 5. English P1 Exam 6. English P3 Exam 7. EMS P1 Exam and Memo 8. EMS P2 Exam and Memo 9. Life Orientation Exam 10. Math P1 Exam 11. Social Science P1 Exam and Memo 12.
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GRADE 9 1. Afrikaans P2 Exam and Memo 2. Afrikaans P3 Exam 3. Creative Arts: Practical 4. Creative Arts: Theory 5. English P1 Exam 6. English P2 Exam 7. English P3 Exam 8. Geography Exam 9. Life Orientation Exam 10. MathP1 Exam 11. Math P2 Exam 12. Physical Science: Natural Science Exam 13. Social Science: History 14. Technology Theory Exam
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9. Life Orientation – Exam 10. Math Exam 11. Social Science – P1 Exam and Memo 12. Social Science – P2 Exam and Memo 13. Technology Theory Exam A FULL SET OF ALL SUBJECTS R 50-00 (Pre-packed and available immediately) AVAILABLE IN THE LIBRARY/ CONTACT sandrina.pillay@sutherlandhs.co.za/ violet.netshiumoni@sutherlandhs.co.za Top-up 1.
Super Locrian is often used in jazz over an Altered Dominant chord (b9, #9, b5, #5, #11, b13) Melodic Minor w h w, w w w h 1 w 2 h b3 w 4 w 5 w 6
