Mathematics Grade 12 Paper 2 North West Mock 2022 Memo

. Ff; ‘ (stag cur education Lefapha la Thuto la Bokone Bophirima Noordwes Departement van Onderwys North West Department of Education NORTH WEST PROVINCE NATIONAL i SENIOR CERTIFICATE i i GRADE 12 MATHEMATICS P2 | SEPTEMBER 2022 | MARKS: 150 | H TIME: 3 hours i This question paper consists of 14 pages, 1 information sheet and an answer book of 20 pages. Copyright reserved {SRE SPA ET

Downloaded from hlayiso.com Manewploaded from Stanmorephysics.com NW/September 2022 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1 2. This question paper consists of 10 questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. You may use an approved scientific calculator (non-programmable anc hon-graphical), unless stated otherwise. S . If necessary, round off answers to TWO decimal places, aia otherwise. Diagrams are NOT necessarily drawn to scale. es An information sheet with formulae is included at;théend of the question paper. Write neatly and legibly. “ (on PAS & «> s \\ ww ny Copyright reserved Please turn over

Downloaded from hlayiso.com Man NW/September 2022 ownloaded from Stanmoggphysics.com QUESTION 1 A study was conducted among eight (8) employees in a company to understand the relationship between the additional number of rest days given in a year and the productivity of each employee. The results are shown in the table below. Additional number of rest days 5 2 9 1 3 10 4 6 Productivity of the a employee (in %) 85 63 90 56 70 88 @ 62 a Ll Calculate the correlation coefficient of the data. \? qd) 1.2 Consider the correlation coefficient calculated in Q AN 1.1 and the four phrases below. Only write down the letter of the at best describes the relationship between the variables in the given A, Fairly strong, negative correlation Ss Very weak, positive correlation B. Cc. Fairly strong, positive cgebition D. Perfect, positive a ion (¢3) 1.3 Determine the cao the least squares regression line of the data. QB) 14 Use the cai tained in QUESTION 1.3 to predict an employee’s productivity if he/she was, iven eight (8) additional rest days. (2) 2) 15 Should the regression line in QUESTION 1.3 be used to predict the productivity of an employee if he/she was given thirty (30) additional rest days in the year? Explain your answer. (2) 19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mandgawwoaded from Stanmorephysics.com NW/September 2022 NSC QUESTION 2 A survey was conducted among a number of learners who were using the same cellphone company to establish the number of WhatsApp messages that they sent during a day. The results were summarised in the partially completed cumulative frequency graph (ogive) below. Cumulative Frequency Graph (Ogive) 560 450 at 400 i we a oe w& iJ —) usd nN wa eo 200 Cumulative frequency i 150 j 100 ra 7 50 pat 0 oF i A B Cc D E F G H Number of WhatsApp messages sent during a day Copyright reserved Please turn over

Downloaded from hlayiso.com “ptiioaded from Stanmorephysics.com NW/September 2022 The data shown in the cumulative frequency graph is also summarised in the partially completed frequency table below. WhatsApp messages sent | Frequency 40 <x <80 20 80 < x <120 30 120 < x < 160 Q 160 < x < 200 R 200 < x < 240 100 240 < x < 280 90 280 < x < 320 60 24 Write down the value of A, a tick mark on the horizontal axis of the cumulative frequency curve. (1) 2.2 How many learners participated in this survey? () 2.3 Calculate the values of Q and R, the frequencies in the frequency table above. (3) 2.4 Estimate the mean number of WhatsApp messages sent per day. (2) 2.5 Calculate the interquartile range. GB) 2.6 The cellphone company wants to introduce a new rule where you are not allowed to send more than 200 WhatsApp messages perdaym[f this rule is applied to this group of learners on the existing data, how would the standard deviation for the data be affected? Motivate your answer. (2) [12] Copyright reserved Please turn over

Downloaded from hlayiso.com mane Qugloaded from Stanmorephysics.com NW/September 2022 NSC QUESTION 3 In the diagram below, AC-1 ; 7), BG ; 1) and C are the vertices of AABC. The angle of inclination of AC is @. BC || x-axis and BC = 4 units. D and E are the x-intercepts of the lines AB and AC respectively. B and E are joined. py AC1;7) D \ > g e BG ; -1) 40 c 3.1 Write down the equation of the line BC. a) 3.2 Write down the x-coordinate of C. qd) 3.3 Determine the equation of the line AC. (4) 34 Calculate the size of ACB. (4) 3.5 If point K is the reflection of E in the line BC: 3.5.1 Write down the coordinates of K. G3) 3.5.2 Calculate the area of quadrilateral BECK. (3) 3.6 F is a point in the first quadrant, such that it forms an equilateral ABFC. Calculate the coordinates of F. 6) (21) Copyright reserved Please turn over

Downloaded from hlayiso.com Mat®Giiiloaded from Stanmogephysics.com — NW/September 2022 QUESTION 4 In the diagram below, a circle with centre M and a tangent PD to the circle at P(O ; 6) are drawn. The equation of the circle is given as x’ + 6x+y? —4y -12=0. PR is a diameter, T is a y-intercept and chord RT is produced to D. RTD |! x-axis. Ay PO; 6) M, x oO R T D 4.1 Determine the coordinates of M. (3) 42 Determine the length of PR. Q) 43 Determine the equation of the tangent PD. GB) 44 Determine the coordinates of D. (4 4.5 The circle, having centre M, is translated to the right such that the point D lies on the translated circle. Determine the coordinates of the possible centres of the translated circle. 4 [16] Copyright reserved Please turn over

Downloaded from hlayiso.com whloaded from Stanmogephysics.com Mathematics, NSC QUESTION 5 NW/September 2022 In the diagram below, f(x) = sinax and an incompleted g(x) = tan(x + 5) are drawn for the interval x <¢ [0° ; 135°]. 5.1 5.2 5.3 5.4 5.5 5.6 we ‘45° 90 135° Write down the values of a and b. Write down the range of f Write down the period of g. Write down the equation of the asymptote of g for the given interval. Write down TWO values of x, in the given interval, where f(x) = 1 — g(x) For which value(s) of x, in the given interval, is f’(x).g'(x) > 0? Copyright reserved (2) (2) (1) (i) (2) (2) [10] Please turn over

Downloaded from hlayiso.com Malpygifiioaded from Stanmokgphysics.com NW September 2022 QUESTION 6 6.1 In the diagram, K( P3 3 ) is a point in the 2"! quadrant. T is a point on the positive x-axis and obtuse KOT = 0. K(p 3 ty 6 ob X (e) T 6.1.1 Write down the value of tan @ in terms of p. qd) 6.1.2 If 6 =120°, WITHOUT using a calculator, calculate the value ofp. (3) 6.2 If cos 42° = ¢, WITHOUT using a calculator, write the following expressions in terms of t: 6.2.1 sin 48° 2) 6.2.2 cos 84° (3) 6.2.3 cos 72° (5) 6.3 Simplify the following expression to ONE trigonometric ratio: sinx ‘ sin (180° ~ x) | sin” x + cos’ x © sin 2x cos x 2sin(90° + x) 6.4 Consider f(x) = sin(2@ - 15°).cos(@ — 30°) +cos(2@ — 15°).sin(@ — 30°) Determine the general solution of f(x) = 0,8 (7) 6.5 Itis given that 48°* = 6, 6°°* =8 and 8 = 32!~2sin’s WITHOUT solving for x, determine the value of tan 2x. (5) [32] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathedaeyeploaded from Stanmogephysics.com Nw/September 2022 NSC QUESTION 7 In the diagram below, AD is a vertical pole having height # metres. B, D and C are three points in the same horizontal plane. AB and AC are cables and the angle of depression from Ato Cis 30°, AB=3h and BAC = 2x. 7A Write down the size of ACD . (i) 7.2 Determine the distance AC in terms of h. (2) 7.3 Calculate the size of ABD. (2) 74 Caloulate the size of x if BC = V7h. (5) {10} Copyright reserved Please turn over

. Downloaded from hlayiso.com Mattesatiiifoaded from Stanmoggphysics.com NW/Septemiber 2022 Give reasons for your statements in QUESTIONS 8, 9 and 16. QUESTION 8 In the diagram, ABCD is a cyclic quadrilateral. G is a point on AD such that BG || CD: ECF is a tangent to the circle at C. BD is a chord of the circle. GBD = 30° and DCE = 60°. A 8.1 Calculate, with reasons, the size of: 8.1.1 3B, _ 7 (1) 8.12 B, ; . (2) 813 é, Me a 8.1.4 DAB . a . 2) 8.2 Is BDa diameter of the circle? Motivate your answer. i a Q) [8] Copyright reserved “ Please turn over

Downloaded from hlayiso.com wloaded from Stanmogephysics.com NW/September 2022 NSC MathelD rH QUESTION 9 9.1 In the diagram below, AMVT and AAKF are drawn such that M=A, W=K and T=F. Use the diagram in the ANSWER BOOK to prove the theorem which states that if two triangles are equiangular, then the corresponding sides are in proportion, that is ——-= —— i) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 NW/September 2022 Downloaded from Stanmorephysics.com 9.2 In the diagram below, cyclic quadrilateral PORS is drawn. Chord SR produced and chord PQ produced meet at T. KPL is a tangent to the circle at P. U and V are points on PS and PQ respectively such that UV || SQ || KL. Let KPS = x L 9.2.1 Write down, with reasons, FIVE other angles EACH equal to x. (5) 9.2.2 Prove that: (a) PQ=PS qd) (b) KP is a tangent to the circle that passes through the points P, U and V, at P. @) 9.2.3. Give a reason why = = 5 @ 9.2.4 Prove that: (a) APTS ||| ARTQ 4) (b) PT.RQ=PS.RT @) (c) PQ=/PSPT-TSROQ (4) [25] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathehagailoaded from Stanmorephysics.com NW/September 2022 NSC QUESTION 10 In the diagram below, the circle with centre O, passes through the points C, D, and E, OT bisects chotd CD. DOE.= 4x . . oO Prove, with reasons, that sin x.cosx = = [7] TOTAL: 150 Copyright reserved

Mathematics/P2 Downloaded from hlayiso.com NW/September 2022 Downloaded from Stanmorephysics.com INFORMATION SHEET: MATHEMATICS ~b Vb? —4ac 2a x= A= P(tni) A= P(\-ni) T, =a+(n~-Vd T,=ar S, a i i d= (x, =x)? +0, =») ml yr MX+e y-y, = m(x-x,) (e-a)' +(y-b) =”? a 5b c sind sinB sinC In SABC: a? =b* +02 —2be.cos A area AABC = + ab,sin Cc sina + Ay= sin a.cos B + cosa@,sin B cosa + 8) =cosa.cos f ~ sin a.sin 2 cos’ @~sin’ @ cos 2a =41-2sin’ a 2c0s? a -1 x Le Pay =A n(S) poathx pa ee 20-7) Se-37 Copyright reserved mt alr” - roi ; pats)" -1] poxc a+") A=P0-i" A=P0+i)" S,= 502 +(n-Nd] Ss =); -1ere<l sre 0 , l-r He) = tim LTD LO) Fo A +%y Vit 2 ; pee) y27¥ ma 2k x2 7% m=tand sin(a — 8) = sin a.cos 8 —cosa.sin 8 cos(a ~ 8) = cosa@.cos f +sin a.sin 8 sin 2a = 2sin a.cosa ” 2 ; XG -3) P(A or B) = P(A) + P(B) — P(A and B)

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education Lefapha la Thuto la Bokone Bophirima Noordwes Departement van Onderwys North West Department of Education NORTH WEST PROVINCE NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADEI/GRAAD 12 MATHEMATICS P2/WISKUNDE V2 SEPTEMBER 2022 MARKING GUIDELINES/NASIENRIGLYNE MARKSI/PUNTE: 150 These marking guidelines consist of 18 pages with 3 pages containing the cognitive grid/ Hierdie nasienriglyne bestaan uit 18 bladsye met 3 bladsye wat die kognitiewe tabel bevat. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com Nw/September 2022 NSC/NSS — Marking Guidelines/Nasienriglyne NOTE: e If acandidate answers a question TWICE, only mark the FIRST attempt. e If acandidate has crossed out an attempt of a question and has not redone the question, mark the crossed out version. e Consistent accuracy applies in ALL aspects of the marking memorandum. Stop marking at the second calculation error. e Assuming answers/values in order to solve a problem is NOT acceptable. NOTA: e As ‘n kandidaat ‘n vraag TWEE KEER beantwoord, sien slegs die EERSTE poging na. e As ‘n kandidaat ‘n antwoord van ‘n vraag doodtrek en nie oordoen nie, merk die doodgetrekte poging. e Volgehoue akkuraatheid word in ALLE aspekte van die nasienriglyne toegepas. Hou op nasien by die tweede berekeningsfout. e Om antwoorde/waardes te aanvaar om ‘n probleem op te los, word NIE toegelaat nie. QUESTIONIVRAAG 1 Additional rest days given/ Addisionele rusdae gegee Productivity of the employee(in %)/ Produktiwiteit van werknemer (in %) 85 63 90 56 70 88 72 62 11 |r=0,81 ¥r=081 (1) 1.2 |[C ¥C (1) 13 | j=a+bx ¥ a=56,79 a = 56,79 and/en b = 3,29 v b=3,29 a ¥ — equation/ “. Y = 56,79+3,29x vergelyking (3) 14 | y =56,79+3,29(8) ¥ substitute 8 into eq. ¥ = 83,11% productivity / produktiwiteit /vervang 8 in vgl. y 4 productivity / produktiwitei ¥83,11 OR/OF y ~ 83,13% (calculator / sakrekenaar) vv answer/antwoord (2) 1.5 | No/Nee v¥ No/Nee The line of regression is only valid for /Die regressielyn is slegs | Y explanation/ geldig vir 1<x<10 verduideliking (2) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Cumulative frequency/ Kumulatiewe frekwensie Matenauy rama from Stanmoreph sics.com i NSC/NSS — Mar! Downloaded from hlayiso.com QUESTIONIVRAAG 2 Cumulative Frequency Graph (Ogive)/ ng Guidelines/Nasienriglyne Kumulatiewefrekwensie-grafiek (Ogief) NW/September 2022 500 WhatsApp messages sent / | Frequency! WhatsApp-boodskappe Frekwensie 450 a4 gestuur 40 < x < 80 20 400 Fo 80 < x <120 30 350 120 < x <160 Q ae 160 < x < 200 R 300 $+: 200 < x < 240 100 AH 240 < x < 280 90 250 280 < x < 320 60 200 #$: 150 a 100 an’ tH t 50 t 0 eed A B Cc D E F G H Number of WhatsApp messages sent/ Aantal WhatsApp-boodskappe gestuur 2.1 40 yv_ 40 (1) 2.2 | 450 Y¥ 450 (1) 2.3 Q = 100 — 50 = 50 (calculating from/bereken vanaf interval) ¥VQ=50 R= 100 vy R=100 (3) 2.4 209 vv 209 (2) 25 Q, = 168 Also accept/Aanvaar ook vy Q, = 168 Q3 = 255 Q, € [167;169] YQ, = 255 “ IQR / IKO = 255 - 168 Q, € [254; 256] = 87 ¥ — answer/antwoord (3) 2.6 The standard deviation will be smaller/Die standaardafwyking sal v¥smaller/kleiner kleiner wees. Because three intervals are taken away, the data becomes more ¥ explanation/ closely grouped together/Omdat drie intervalle verwyder word, sal verduideliking die data nader aan mekaar gegroepeer wees. (2) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com Nw/September 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONIVRAAG 3 Ay A(-1; 7) x 31 |y=-1 (1) 3.2 Xo =3+45=7 (1) 3.3 C(7;-1) ¥ method = 7-(-) gradient/metode ac -1-7 gradiént =-1 ¥Me =-1 Through / Deur(-1;7) OR/OF (7;-1) y-7 = -1(x-(-1)) y- (-1) = -1(x-7) v Subst./Vervang y-7=-1(x +) y+l=-x+7 (-1;7) OR/OF (7;-1) “ny=-xX+6 Vy=-X+6 (4) 3.4 tan = Myo v¥ tang =-1 tand=-1 tan“ (-1) =@ 0 = — 45° + 180° “8 = 135° ¥ 135° AED = 45° [4s on straight line / Ze op reguit lyn] v AED = 45° . ACB = 45° [corresp./s / oreenk.Ze; DE || BC] Y ACB= 45° (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com Nw/September 2022 NSC/NSS — Marking Guidelines/Nasienriglyne 3.5.1 |E(6;0) vx, =6 K(6 ; -2 ( ) VX =6 YY = 72 (3) 3.5.2 | EK =2 units/eenhede v¥ EK=2 BC x EK Area BECK = v¥ method/metode _4x2 2 = 4units’ / eenhede? Y answer/antwoord ORIOF (3) 1 Area ABEC = =(4)(1) , v Area ABEC = 2 1 Area ABKC = 3 (4) -2 v Area ABKC = 2 Area BECK = 2 + 2 = 4 units’ / eenhede” ¥ answer/antwoord (3) 3.6 % = Xp + Xo 2 _—3+7 -5 2 ¥ method/metode “FG: y) vx, =5 BF = (5-3) +(y +1) OR/JOF FC = (5-7) +(y +1) BF = FC = BC =4 16=4+(y +1) v distance form./ afstandsformule (y +1)? =12 Y(y+2) =12 y=t N12 -1 ays V12 -1 (first quadr. / eerste kwadr.) ¥ antwoord/answer (5) [21] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com Nw/September 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONIVRAAG 4 Ay P(O; 6) M oO R T 4.1 | x? + 6x + (3)? + y? —4y + (-2)? =124+94+4 ¥ method/metode (x +3) +(y-2) = 25 . M(-3; 2) v¥x=-3 Answer only: Full Marks vy=2 (3) 4.2 | r? =12 + (3)? + (-2)? = 25 vr? = 25 (can also be shown in “r=5 4.1/ kan ook in 4.1 gewys word) “PR =10 ¥ PR=10 (2) 43) _ 6-2 MP 0-(-3) 4 4 “3 “Tae 3 3 3 Meo =F [rad L tangent/rad 1 raaklyn] Ym, =- 4 y=-—x+c y= _ 3, +6 ¥ equation / vergelyking 4 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathai raced virom Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne Yo + Y, 44 ae You ¥ method/metode 6+ Ye _ 2 2 Ye =-2 YVR = 2 D(x ; — 2) 3 . 2 = - 7x46 ¥ subst. y = —2 into 32 equation/vervang y = —2 in X= 3 vergelyking 32 32 “ D(—;-2 ¥ D(—=;- ( 3 ) D(Fi-2) (4) 45 |T, >D,= = units / eenhede v = new centre / nuwe middelpunt (F ; 2) v & ; 2| R, 2D, = ° units / eenhede v0 3 new centre / nuwe middelpunt (F ; 2] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathai raced virom Stanmorephysics.com Nw/September 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONIVRAAG 5 4y x 5° 90) 135° . 5.1 | a=2 and/en b =— 45° Ya=2 vb=- 45° (2) 5.2) -1<y<1 ORIOF ye [-1 : 1 ¥ critical values/kritiese waardes ¥ notation/notasie (2) 5.3 | 180° vy 180° (1) 5.4 | x= 135° v 135° (1) 5.5 | x=0° orlof x = 45° or/of x = 90° v vany 2 correct solutions/ enige 2 korrekte oplossings (one mark per solution/ een punt per oplossing) (2) 5.6 | O° < x <45° ORIOF- x e[0%;A45°) ¥ 0° and/en 45° ¥ notation/notasie (2) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com Nw/September 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONI/VRAAG 6 K(p 33 y o> X 0 T 6.1.1 tang - 8 v x3 p p (1) 6.1.2 | tan120° = ¥3 p tan (180° = 60°) = aft = Pp —tan 60° = RE v —tan 60° 3 —J3 = 3 ¥—\3 = 3 p p p=-1 vp=-l (3) 6.2.1 cos 42° ¥ sin 48° = cos 42° = sin 48° vt =t Answer only: Full Marks (2) 6.2.2 | cos2(42°) ¥c0s2(42°) = 2cos’ 42° -1 v 2cos’ 42° -1 = 2t?-1 ¥ 2? -1 ORIOF cos 2(42°) ¥cos2(42°) =1- 2sin? 42° ¥1- 2sin’ 42° 2 =1- 2( 1-1") = 2t? -1 2? 1 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne 622 ORIOF ¥c0s2(42") cos 2(42°) Y cos? 42° — sin? 42° = cos’ 42° — sin? 42° 2 =? -(i-") v2? -1 = 2t?-1 (3) 6.2.3 cos (42° + 30°) ¥ manipulation / manipulasie = COS 42°.cos30° — sin 42°.sin 30° ¥ expansion of identity/ uitbreiding van identiteit -.8_ foe vB gh ato yin ts 2 2 vt&/jl-t? _ Bt fl -0? 2 2 2 _ vat~ yi-0 ¥ answer/antwoord 2 (5) 6.3 sinx | sin(180° - x) _ sin’ x + cos’ x sin 2x COS X ~ 2sin (90° + x) sin x . sin x 1 2sinx.cosx cOosSx 2CcOSXx 1 sin x 1 = +—- 2cosx cosx 2cosx sin x cos X = tanx ¥ sin 2x = 2sin x.cos X ¥ sin (180° — x) = sinx v sin? x + cos? x =1 ¥ 2sin(90° + x) = 2cosx y Sinx COS X v tan x (6) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmoreph sics.com i} ng Guidelines/Nasienriglyne NSC/NSS — Mar! NW/September 2022 6.4 | f(x) = sin[(20 - 15°) + (@ - 30°) ] f (x) = sin[3@ — 45°] .. sin[30 — 45°] = 0,8 30 — 45° = 53,1301...° + k.360°, ke Z 30 = 98,1301...° + k.360° 6 = 32,71° + k.120° or / of 30 — 45° = 180° — 53,1301...° + k.360°, keZ 30 = 171,8699...° + k.360° 6 = 57,29° + k.120° Y £(x) = sin[30 — 45°] Y sin[30 — 45°] = 0,8 ¥ 30 — 45° = 53,1301...° ¥6@= 32,71° + k.120° v 30 — 45° = 180° — 53,1301...° ¥ 0 = 57,29° + k.120° ¥+k.120°,keZ 0) 6.5 4sinx < 92sinx _ Y 2esinx _ geex = (22x ye = 2esinxcosx _ g ¥ 2esinx.cosx _ g Q = 22sinxc0sx _ gol - 2sin? x sin 2x = 5cos2x ¥ sin2x = 5cos2x tan2x =5 ¥tan2x=5 (5) [32] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne A QUESTIONIVRAAG 7 7.1 | ACD = 30° ¥30° (1) . h . h 7.2 30° = —~ v sin30° = — sn AC AC “. AC = 2h ¥ AC = 2h (2) 73 | sinaBp - t= Y sinABD = + 3h 3 3 ABD = sin 3 ABD = 19,47° ¥ ABD =19,47° (2) 7.4 | BC? = AB? + AC? - 2AB.AC.cos 2x ¥ correct use of cosine- rule/korrekte gebruik van cos-reél 2 2 2 . (¥7h) = (3h) + (2h) — 2(3h)(2h)cos2x ¥ subst/vervanging Th? = Qh? + 4h? — 12h? cos2x —6h? = —12h’ cos 2x 1 cos 2x = — Y cos2x = + 2 2 2x = 60° v 2x = 60° x = 30° vx = 30° (5) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne GEOMETRY/MEETKUNDE Please read carefully through the following table before marking QUESTION 8-10 / Lees asseblief sorgvuldig deur die volgende tabel alvorens VRAAG 8-10 nagesien word. The order in which the candidate answers a geometry question must follow logically/ Die volgorde waarin ‘n kandidaat ‘n meetkundevraag beantwoord moet logies volg. Example/Voorbeeld Given/Gegee AB || CD and/en EFD = 115° A D 65 B c The candidate first need to calculate x BEFORE he/she can calculate y/Die kandidaat moet eerste vir x bereken VOORDAT hy/sy vir y kan bereken. A mark for a correct statement (A statement mark is independent of a reason) ‘n Punt vir ‘n korrekte bewering (‘n Punt vir ‘n bewering is onafhanklik van die rede) A mark for the correct reason (A reason mark may only be awarded if the statement is correct) ‘n Punt vir ‘n korrekte rede (‘n Punt word slegs vir die rede toegeken as die bewering korrek is) Award a mark if the statement AND reason are both correct (Both MUST be correct to get one mark) Ken ‘n punt toe as die bewering EN rede beide korrek is (Beide MOET korrek wees om een punt te kry) S/R Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONIVRAAG 8 A 8.1.1] D, = 30° [alt 4s/ verwiss Ze; BG || DC] vSIR (4) 8.1.2 | B, = 60° [tan-chord th/raaklyn - koordst. ] vSYR (2) 8.1.3 | C, = 90° [Zs of A/binne.Ze van A] vSIR (1) 8.1.4 | DAB = 90° [opp.4 of cq / teenoorst.Ze van kvh] v¥SYR (2) 8.2 | Yes/Ja v yes/ja BD is adiameter/BD is 'n middellyn [converse omgekeerde Zin su | vSIR (2) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONIVRAAG 9 M 9.1 Construction: Mark P and Q such that MP = AK and MQ = AF. Y constr/ Draw PQ konstr Konstruksie: Merk P en Q sodat MP = AK en MQ = AF. Trek PQ In AMPQ and/en AAKF M = A [given / gegee] MP = AK [construction / konstruksie] MQ = AF [construction / konstruksie] “. AMPQ = AAKF[S, Z,S] Yv SIR P, = K [from / vanuit = ] YS but /maar V = K [given / gege] P= V vs .. PQ|IVT [corresp.2s = /ooreenk.Ze =] v¥ SIR MV MT we —= rop.th / eweredigheidst.; PQ|| VT MP” MO [prop 9 QIIVT] Vv SYR MP = AK and/en MQ = AF _MV _MT “AK AF (7) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne 9.2 L 9.2.1 KPS = PQS =x _ [tan-chord th./raaklyn - koordst. | VSIR KPS = PSQ=x [alt.Zs/verwissel.Ze;KL||SQ | VSIR KPS = PUV=x [alt. Zs/verwissel. Ze; KL||UV ] YSIR PVU = PQS = x [corresp. Zs/ooreenk. Ze; UV||SQ] VSIR LPQ = PSQ = x [tan-chord th./raaklyn - koordst.] YSIR (5) 9.2.2 (a) | PSQ =PQS= x -. PQ = PS [sides opp. = /s/ sye teenoor ="Ze } YR (4) 9.2.2(b) | KPU=PWU =x -. KP is a tangent /'n raaklyn [converse tan-chord th. / omgekeerde raaklyn — koordst. | YR (4) 9.2.3 Prop.th / eweredigheidst. ; UV || SQ YR (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Matenauy rama from Stanmorephysics. com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne 9.2.4 (a) In APTS and/en ARTQ T =T [common / gemeenskaplik ] YSIR TPS=TRQ [ext.Z of cq/buitez van kvh] YSYR PST = TOR [sum of “s of A/som van Ze van A] VSIR J ATPS ||| ATRQ [2 2 4] (4) 9.2.4 (b (0) | TP _ PS [from / vanuit ||| A] vSvYR TR RO . PT.RQ = PS.TR (2) 9.2.4 (Cc vs () PS _ 1S [from / vanuit ||| A] RQ TQ PS.TQ =TS.RQ vs but /maar TQ = PT — PQ PS(PT — PQ) =TS.RQ vs but/maar PQ = PS PS.PT — PQ’ = TS.RQ PQ? = PS.PT — TS.RQ vs PQ = JPS.PT —TS.RQ (4) [25] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com vata raaded vfrom Stanmorephysics.com NwiSeptember 2022 NSC/NSS — Marking Guidelines/Nasienriglyne QUESTIONIVRAAG 10 D 4x Cc [e) E 7 Z at centre = 2x /at circumference/ DCE = 2x . vSVR midpts.7 = 2xomtreks.Z A line from centre to midpt of chord/ OTC =90°| . P Y¥SYR midpt.0 ; midpt.koord In A OTC sin2x = oT vs oc 2sin XCOs X = oc ¥ 2sinxcosx sin Xcos x = OT 2x OC v axOG OT * sin Xcos x = — CE (7) [7] TOTALITOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief