Technical Mathematics Grade 12 Paper 2 North West Mock 2019 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 12 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 SEPTEMBER 2019 MARKING GUIDELINES/NASIENRIGLYNE MARKS: 150 PUNTE: 150 These marking guidelines consist of 18 page Hierdie nasienriglyne bestaan uit 18 bladsye.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 2 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne GENERAL GUIDELINES FOR MARKING/ALGEMENE RIGLYNE OM TE MERK · If a learner makes more than one attempt at answering a question and does not cancel any of them out, only the first attempt will be marked irrespective of which of the attempt(s) may be the correct answer. / As ‘n leerder meer as een poging aanwend om ‘n vraag te beantwoord en nie een van hulle word uitgeskakel nie, sal slegs die eerste poging gemerk word ongeag watter van die poging(s) die regte antwoord kan wees. · Consistent accurate marking regarding calculations will be followed in the following cases / Konsekwente akkurate nasien met betrekking tot berekeninge sal in die volgende gevalle gevolg word: o Sub question to sub question: When a certain variable is incorrectly calculated in one sub question and needs to be substituted into another sub question full marks can be awarded for the subsequent sub questions provided the methods used are correct and the calculations are correct. / Subvraag na subvraag: Wanneer ‘n sekere veranderlike verkeerd in een subvraag bereken word en in ‘n ander subvraag vervang moet word, kan volpunte toegeken word vir die daaropvolgende subvrae, mits die metodes wat gebruik is, korrek is en die berekeninge korrek is. o Assuming values/answers to solve a problem is unacceptable. / Aanvaar waardes / antwoorde om ‘n probleem op te los, is onaanvaarbaar. · If a learner did a question in pencil, and did not write it over in pen, the pencil must be marked. Draw a line through and make note of it. / As ‘n leerder ‘n vraag in potlood gedoen het en dit nie in pen oorgeskryf het nie, moet die potlood gemerk word. Trek ‘n lyn deur en maak ‘n nota daarvan. 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 NPU No Penalty for Units omitted / Geen penalisering vir eenhede weggelaat S Simplification / Vereenvoudiging SF Substitution in correct Formula / Vervanging in korrekte formule AO Answer only / Antwoord alleenlik Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 3 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 1 y B(3;7) D (-3;1)A O x E C(4;0) 1.1 yB - y A mAB = xB - x A 7 -1 = ✓ SF 3 - (-3) ✓ Answer/Antwoord =1 Equation / vergelyking AB y - y1 = m( x - x1 ) ✓ SF y - 1 = 1( x - (-3)) ✓ Answer in std form/ Antwoord in std y = x+4 vorm or / of or/of y - 7 = 1( x - 3) ✓ SF ✓ Answer in std form/ Antwoord in std y = x+4 vorm (4) 1.2 D is the y-axis intercept/ D is die y-as afsnit ✓ x=0 x=0 ✓ SF in equation/ in vgl AB y =0+4 D (0; 4) \ O D = 4 units (2) 1.3 yC - y D mDC = xC - xD ✓ Gradient of DC/Gradiënt van DC 0-4 = 4-0 = -1 mAB ´ mDC = 1´ -1 = -1 ✓ Gradient of AB/Gradiënt van AB \ A B ^ DC CA van 1.1 ✓ product is –1/ produk is -1 CA ✓ Conclusion/ gevolgtrekking CA (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 4 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 1.4 tan q = mDC ✓ SF q ref = tan -1 ( -1) ✓ Ref Ð CA q ref = 45° / -45° eksponent eienskap q = 135° ✓ Answer/Antwoord CA (3) 1.5 E is the x - intercept of AB CA equation from 1.1 CA vergelyking van 1.1 E is die x - afsnit van AB ✓ SF y = 0 y=0 0= x+4 ✓ Coordinates of E/ koördinaat van x = -4 E CA \ E ( -4; 0 ) (2) 1.6 DAC = ( xc - x A ) + ( yc - y A ) 2 2 ✓ SF DAC = (4 - ( -3)) + (0 - 1)2 2 ✓ Answer/Antwoord A ✓ Conclusion/ gevolgtrekking A DAC = 5 2 \ AC = DC \D ABC is anisosceles D \D ABC is ' n gelykbenige D (3) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 5 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 2 y M (3;4) R(t;1) O x P(3;-4) Q 2.1.1 r 2 = (3) 2 + (4) 2 r 2 = 25 ✓ Value of r/waarde van r A r =5 or / of r 2 = (3) 2 + ( -4) 2 r 2 = 25 r =5 \ x 2 + y 2 = 25 ✓ equation of circle/vgl van sirkel A (2) 2.1.2 y p - yo mOP = x p - xo -4 - 0 = 3- 0 4 =- 3 ✓ m of/van OP A 3 ✓ m of/van RQ A mRQ = 4 Equation / vergelyking RQ y - y1 = m( x - x1 ) ✓ Substitution/vervanging CA 3 y - (-4) = ( x - 3) 4 3 25 y= x- (4) 4 4 ✓ Answer/antwoord CA Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 6 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 2.2 7 ✓ y - intercepts / afsnitte A ✓ x - intercepts / afsnitte A -4 O 4 x ✓ Shape/vorm A -7 (3) [9] QUESTION/VRAAG 3 β O • B (3; -3√3 ) ✓ SF (pythagoras) A ( 3) + (-3 3)2 3.1.1 2 OB = OB = 6 ✓ Length of OB/ Lengte van OB A (2) 3.1.2 2 CA from 3.1.1 (value of r/waarde ærö sec 2 b = ç ÷ van r) è xø 2 ✓ Ratio of sec/ verhouding van sec A æ6ö =ç ÷ è 3ø ✓ SF CA ✓ Answer/antwoord CA =4 (3) 3.1.3 3cot 2 b - sin2 b CA from 3.1.1 (value of r/waarde van r) 2 æ 3 ö æ -3 3 ö 2 = 3ç ÷ -ç ÷ è -3 3 ø çè 6 ÷ø ✓ Ratio of cot/ verhouding van cot A æ1ö 3 ✓ Ratio of sin/ verhouding van sin CA = 3ç ÷ - è 3ø 4 ✓ Answer/antwoord CA 1 = 4 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 7 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 3.2 æ 2p 180° ö ✓ Conversion/ herleiding A cos ç ´ è 3 p ÷ø = cos 120° 1 ✓ Answer/antwoord A =- 2 (2) 3.3 15 cos x = -12 12 cos x = - 15 (15) - ( -12 ) 2 2 y= ✓ pythagoras ✓ value of y/waarde van y A y =9 ✓ SF A 15 5 ✓ Answer/antwoord CA cos ec x = / 9 3 (4) 3.4.1 Second quadrant / tweede kwadrant ✓ Answer/antwoord A (1) 3.4.2 2 ✓ Ratio of tan/ verhouding van tan A tan q = - 5 ✓ Ref Ð A æ 2ö q ref = tan -1 ç - ÷ è 5ø ✓ Quadrant/ kwadrant CA q ref = 21,8° ✓ Answer/antwoord CA q = 180° - 21,8° = 158, 2° (4) [19] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 8 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 4 4.1 tan 2 (180° - x ) . cos 2 (180° + x ) . cosec ( 360° - x ) sin (180° + x ) -tan 2 ( x ) . - cos 2 ( x ) . cosec ( x ) ✓ - tan x 2 = -sin ( x ) ✓ - cos x 2 ✓ cosec x ✓ - sin x sin 2 x -cos ( x ) 1 2 - . . sin 2 x = cos 2 x 1 sin x ✓ - -sin ( x ) cos 2 x ✓ - sin x sin x sin x ✓ = - sin x - sin x ✓ Answer/antwoord = -1 (8) 4.2 1 ✓ Answer/antwoord (1) 4.3 1 tanq sin 2q + + sec q cotq 2 æ sinq ö ✓ cos q 2 ç ÷ cosq ø sin q = sin 2q + cos 2q + è ✓ æ cosq ö cosq ç ÷ è sinq ø cosq ✓ sinq sinq sin q = 1+ ´ cosq cosq ✓1 sin 2 q sin 2q ✓ = 1+ cos 2 q cos 2q = 1 + tan 2q ✓ tan q 2 ✓ sec q 2 = sec 2q (7) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 9 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 5 5.1 f ✓ Shape/vorm ✓ x -intercepts/afsnitte ✓ Turning points/ Draaipunte g ✓ Shape/vorm ✓ x -intercepts/afsnitte ✓ Turning points/ Draaipunte (6) 5.2.1 1 ✓ Answer/antwoord A (1) 5.2.2 360° ✓ Answer/antwoord A (1) 5.2.3 120° and / en 300° ✓ Reading from graph/lesing van grafiek CA ✓ Reading from graph/lesing van grafiek CA (2) 5.2.4 [120°; 300°] ✓ Answer/antwoord CA (2) ✓ Notation/notasie A [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 10 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 6 B C A D 35° 35° E ( 115°) 6.1 AB ✓ Ratio/verhouding A tan 35° = AE ✓ SF A AB = 15 tan 35° AB = 10,5m ✓ Answer/antwoord CA Height of both buildings/Hoogte van beide geboue 10,5 m (3) 6.2 µ ü Correct formula/Korrekte formule e 2 = d 2 + a 2 - 2da cos E A e 2 = 152 + 152 - 2.15.15cos115° ✓ SF (3) e = 640 ✓ Value of/waarde van e e = 25,3m [6] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 11 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 7 7.1 R 2 O S 1 1T 2 3 3 2 2 1 1 P M 7.1 7.1.1 ¶ = 100° (angle at centre = 2 x angle at circf/midpunts hoek = 2 x O ✓ SA 2 omtrekshoek) ✓ R (2) 7.1.2 OP = OM ( radii ) ü S,R ü R µ = (180° - 100°) / 2 P1 (angles opp equal sides/hoeke teenoor gelyke ü A (3) µ 1 = 40° P 7.1.3 sye) ü S S$ = 50° (angles sub by same chord/hoeke onderspan deur dieselfde ü R (2) koord) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 12 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 7.2 A 2 1 P >˃ R 1 S 2 T 3 3 4 2 C >˃ 1 B 7.2 7.21 Radius ⊥ Tangent / Radius⊥Raaklyn ✓ R (1) 7.2.2 µ = 60° (tan chord /raaklyn koord) ü S/R RCB µ 2 = 60° (angles opp equal sides / hoeke teenoor B gelyke sye) ü S/R µ 2 = 60° (alt angles /verwis hoekePT║CB) R ü S/R µ 1 = 60° (corsp angles/ooreenk hoeke PT║CB) R ü S/R (4) 7.2.3 µ A1 = 90° - 60° (radius⊥tangent /radius ⊥raaklyn) ü S/R µ A = 30° 1 (2) ü A 7.2.4 RTµ A = 180° - (90° + 60°) RTµ A = 30° ü S (2) (int angles of /binne hoeke van ∆) ü A 7.2.5 Kite /Vlieer (adj sides = /aangr sye =) OR ü A (2) Cyclic quad /Koordevierhoek (opp andles suppl/ ü R teenoorst hoeke suppl) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 13 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 7.3 P Q 1 2 R M O T S 7.3.1 Perpendicular / Loodreg ü A (1) 7.3.2 µ = 90° - 57° S PO ü S,R (2) (radius⊥tangent/radius ⊥raaklyn) ü A a) µ = 33° S PO ü µ = 180° - (90° + 33°) O ü S 1 (int angles of∆/binne hoeke v ∆) ü A (2) b) µ O = 57° 1 [23] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 14 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 8 8.1 Equiangular / Gelykhoekig ü R (2) Corresponding sides in proportion / ü R Ooreenstemmende sye in verhouding 8.2 C D 2 F 5 B 3 4 5 E 4 A 8.2 8.2.1 ∆ BFC (Equiangular / Gelykhoekig) ü A (1) 8.2.2 a) DE EF FD ü A(Proportionality/eweredigheid) = = (∆BFC BC FC BF sim/gelykv∆DFE) ü SF (Correct values /korrekte 4 2 waardes) = BC 5 ü A BC = 10 (3) b) FE DF ü A(Proportionality/eweredigheid) = FC FB 3 2 = FC 5 15 FC = 2 FC = 7, 5 ü A (length of FC/lengte van FC) (2) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 15 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 9 A E 160 mm • C D B 9.1.1 r = 120 mm ü A (1) 9.1.2 240 - 160 = 80mm ü A (1) 9.1.3 4h 2 - 4 dh + x 2 = 0 ü F 4(80) 2 - 4(240)(80) + x 2 = 0 ü SF 25600 - 76800 + x 2 = 0 x 2 = 51200 ü A (length of chord / lengte van x = 226, 27 mm koord) (3) 9.2 9.2.1 3 ´ 20 = 60m ü X 20 (1) ü A (1) 9.2.2 V = p Dn ü F 3 = p ´ 0, 6 ´ n ü SF 3 n= p ´ 0, 6 n = 1, 59 rev/s ü A (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 16 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 9.2.3 rev t= from n rev n= t ü SF 12 ü A t= 1,59 t = 7,55 (2) 9.3 M 700 mm K 60 cm 70° S1 220° S2 A B L N 9.3.1 Kµ AB = 110° ü 110° Supl angles, Given /Supl hoeke, ü R Gegee(KA║MB) (2) 9.3.2 Arc length S 2 = r ´ q ü F ü r = 20 ü Conversion degrees to 220°´ p radians/Herleiding grade na radiale Arc length S 2 = 20 ´ 180° Arc length S 2 = 76,8 cm ü CA (length/lengte S 2 ) length of belt = S1 + LN + S 2 + KM ü M (adding/ optel) length of belt = 38, 4 + 70 + 76,8 + 70 ü C (Conversion / Herleiding) length of belt = 255, 2 cm ü CA (Penalty unit/Penalisasie eenh) ü R (8) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 17 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne QUESTION/VRAAG 10 10.1 10.1.1 a = 30 ¸ 5 ü A a = 6 cm (1) 10.1.2 A = a ( m1 + m2 + m3 +¼+ mn ) ü F ü SF 3,1 + 6, 2 6, 2 + 8, 3 8,3 + 7, 2 7, 2 + 6,5 6,5 + 6 ü S A = 6( + + + + ) ü CA 2 2 2 2 2 A = 196,5 cm 2 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.

Downloaded from hlayiso.com Technical Mathematics P2/Tegniese Wiskunde V2 18 NW/September 2019 NSC/NSS – Marking Guideline/Nasienriglyne 10.2 10.2.1 æ4 ö ü F V = ç p r3 ÷ ¸ 2 è3 ø æ4 3ö ü ¸2 V = ç p ( 3) ÷ ¸ 2 è 3 ø ü SF V = 113, 097 ¸ 2 ü A unit/eenheid V = 56, 55mm 3 V = p r 2h ü SF V = p ( 2 ) 6, 75 2 V = 84,82 mm 3 TotalV = 56, 55 + 84, 82 ü M(adding / optel) ü CA TotalV = 141,37 mm3 (8) 10.2.2 V = s3 V = 703 ü A(volume of cube / - van kubus) V = 343 000 mm3 ü M( ¸ ) No. rivets = 343 000mm3 ¸ 141,37 mm3 ü CA ü R (whole number / Telgetal) No. rivets = 2 426 (4) [17] TOTAL/TOTAAL 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asb.