Mathematics Grade 12 Paper 2 MP Mock 2023 Paper & Memo

education MPUMALANGA PROVINCE NATIONAL SENIOR CERTIFICATE MARKS: 150 TIME: 3 hours This question paper consists of 13 pages and 1 information sheet and an answer book is provided.

Mathelaaevanm@adiatr ‘om Stanmor ephysics.com Mpumalanga/Preparatory 2023 CAPS/KABV ~ Grade/Graad 12 INSTRUCTIONS AND INFORMATION Read the following-instructions carefully before answering the questions. 1. The question|paper consists of 10 questions. 2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining the answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical) unless stated otherwise. 6. Ifnecessary, round off answers to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Write neatly and legibly.

MathernaticR OMIAAGED from Stanmor ep hysics.com Mpumalanga/Preparatory 2023 CAPS/KABV ~ Grade/Graad 12 QUESTION 1 The table below shows the masses (in kg) of 15 randomly chosen weight lifters of a certain gymnasium. . ira > danny 11 | 83 | 88 oa! 92 | 92 | 95 | 97 | 104 | 108 | 109] 110 | 11 | 115] 129 TaTey ~ L.1 Calculate the mean mass of the weight lifters. (2) 1.2 Calculate the standard deviation of the masses of the weight lifters. (1) 1.3 What percentage of weight lifters fall in the feather weight division, if the criteria is that your mass must be below one standard deviation below the mean? (3) 1.4 If all the weight lifters loose 3kg, what will be the new 1.4.1 Mean mass of the weight lifters? (1) 1.4.2 Standard deviation of their masses? (1) [8]

maneheeMaleaded.from Stanmorephysics.com CAPS/KABV ~ Grade/Graad 12 QUESTION 2 Mpumalanga/Preparatory 2023 2.1 The box-and-whisker plots show the wages of workers (in Rand) at two companies for the same-type of work. Both companies have 20 workers. Company A Company B 200 300 400 (Wages in Rand) 500 600 2.1.1 State whether the following statement is TRUE or FALSE: All the workers at Company A earn more than 25% of the workers at 700 800 Company B. qa) 2.1.2 Comment on the skewness of the data for company B. () 2.1.3 Which company has the biggest range? Motivate your answer with the necessary (2) calculations. 2.1.4 How many workers at Company B earn more than R200? (2) 2.2 A table of data, showing the price of crude oil at the end of each year in US Dollars ($) (to the nearest dollar) per barrel, is given. Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2019 | 2020 | 2021 Price 90 92 98 54 37 54 60 61 49 75 2.2.1 Determine the equation of the least squares regression linesfor the price of crude oil per year (3) 2.2.2 Calculate the value of the correlation coefficient. () 2.2.3 Use calculations to predict the price of crude oil (in US $) per barrel at the end of 2018. Discuss the validity of the answer that you obtained by using your answer in 2.2.2. (2) [12]

ManemaidoeMnlegded from Stanmorephysics.com CAPS/KABV ~ Grade/Graad 12 Mpumalanga/Preparatory 2023 QUESTION 3 In the diagram A(2 ; 6), B(11; 1) and C(-1; —3) are the vertices of A ABC. Point D is shown in thediagram such that BD | BC. N is the x-intercept of BC. AON =86. D ty A(2; 6) B11; 1) 8 > N T «x C(-1; -3) 3.1 If the gradient of BC is ; and the gradient of AC is 3, calculate 3.1.1 the x-coordinate of N, (2) 3.12 the size of ACB. (5) 3.2 Determine the equation of AC. (2) If it is further given that point D lies on AC produced such that BC _L BDI calculate 3.3 (5) the coordinates of D. A000] [14]

M sine WORMED from Stanmorephysics.com Mpumalanga/Preparatory 2023 CAPS/KABV - Grade/Graad 12 QUESTION 4 In the diagram A(-3; 11) and C(1; 3) are points on the circumference of a circle with diameter AB and centre T. The equation of AB is given by y= 3x+20. ay A(-3; 11 Ne (1; 3) wa Oo * B 41 Determine the equation of the perpendicular bisector of AC. 4 42 Show that the coordinates of the centre of the circle are (—5 ; 5). (6) 43 Calculate the length of diameter AB. (3) 44 Write down the equation of the circle. (2) 45 The tangent to the circle at A cuts the y-axis at (0 ; p). Calculate the numerical value of p. (4) 4.6 If the circle through A, B and C is moved 3 units to the right and 2 units upwards, and the radius is halved, write down the equation of the new circle. (3) 4.7 A new circle with equation (x—2)?+ (y-3 =4 and centre P is given. Will this circle intersect the original circle or not? Motivate your answer_with the necessary (4) calculations. [23]

Mathemadgownieaded fr ‘om Stanmorephysics -com Mpumalanga/Preparatory 2023 CAPS/KABV — Grade/Graad 12 QUESTION 5 3 5.1 If @isa reflex: angle, and tan@ = — 4 , determine without the use of a calculator and with the aidjofa sketch, the value of: 5.1.1 (2) 5.1.2 cos26 (3) 5.1.3 cos (8 + 30°) (3) 5.2 If x=4 sino and y=4 cosa, calculate the value of x? + y2. (2) 5.3 Simplify the expression to a single trigonometric ratio: sin(900°~ x) . cos(—x) — sin(x—-180°).. sin (90° +x) (6) Given the following the identity: intl Sia sin4x 5.4 2cos3x 5.4.1 Prove the identity. (4) 5.4.2 For which values is the identity above, undefined. Determine the general solution of x for which the identity is undefined. QB) 5.5 Calculate the general solution of xif 2sin (3x+20°) = 2cosx (6) [29]

Mather eueHAade dh from Stanmorephysics.com Mpumalanga/Preparatory 2023 CAPS/KABV ~ Grade/Graad 12 QUESTION 6 In the diagram below, the graphs of f(x) = 2 cos x and g(x) = cos 2x are drawn for the interval x €[-45°;180°]. 6.1 Write down the period of g. qd) 6.2 Write down the values of x for which the graph of f is increasing in the given interval. (2) 63 Write down the range of y=3g(x)-1. (2) 6.4 Determine the values of x for which f (x) 2 ; in the given interval. (4) 6.5 Determine the minimum value of cos" te 7 in the interval x ¢[0°; 180°] (4) (13)

MathemaicdROWweHAn ded fr ‘om Stanmarephysics.com Mpumalanga/Preparatory 2023 CAPS/KABV ~ Grade/Graad 12 QUESTION 7 In the diagram AD is a3m vertical pole with support cables attached at T and A to a point R which is x meters fro uf foot of the pole, D. D and R are in the same horizontal plane. T is 1m above the foot of the ‘The angle of elevation of A from R is 6. TRA=a iim A, 2 T 1 6 D x R Show that TR = > — 7 cos(O- @) @) 72 Provethat x= 2008@cos(0 - a) “ sin @& 73 If it is further given that 9 = 68,33° and @ = 28° calculate the Area of AATR by using the formulas in 7.1 and 7.2. (4) [10]

Math aMrlwadederr ‘om Stanmorephysics .com Mpumalanga/Preparatory 2023 CAPS/KABV — Grade/Graad 12 Give reasons for your statements and calculations in QUESTIONS 8, 9 and 10. QUESTION 8 onny 8.1 In the diagram below, O is the centre of the circle ABC. AB and AC are chords. OB and OGare joined. Prove the theorem that states that BOC =2x BAC . (5)

Mathematicsowealeaded from Stanmor ephysics - COM Mpumalanga/Preparatory 2023 CAPS/KABV = Grade/Graad 12 8.2 O is the centre of circle CBE. DB is a tangent to the circle at B. EC produced meets BD in D and intersects OB at F. CD = CB. OE and BE are joined. B, = x. D 8.2.1 Name, with reasons, TWO other angles each equal to x. (4) 8.2.2 Express EOB in terms of x. 3) 8.2.3. Determine, with reasons, the size of Bo in terms of x. (2) 8.2.4 Show that DC =CF. QB) {17]

manereRaadecns rom Stanmor ephysics -com Mpumalanga/Preparatory 2023 CAPS/KABV — Grade/Graad 12 QUESTION 9 In quadrilateral ABDC, diagonals AD and BC intersect at E. AB =8cm Simm BD=I5cm fp 40nn DC=18cm fp AC=10cm aw BC=12cm J A 8 B 15 10 Cc 18 D 9.1 Prove that ABCA ||| ACDB. (4) 9.2 Hence prove that AB || CD. (2) 9.3 Calculate the length of CE. (4) [10]

Mathemaicdpowinloaded from Stanmorephysics.com Mpumalanga/Preparatory 2023 CAPS/KABV ~ Grade/Graad 12 QUESTION 10 In the diagram O is the centre of circle PSRT. TR produced intersects SV in V. ST bisects PTR and TS = SV. TOP, OSvand SR are joined. sonar pe 10.1 Determine with reasons the size of PST . (2) 10.2 Determine the size of Sa. (5) 10.3 Prove that ATSO||| ATVS. (3) 10.4. Show that 2VS? = PT.TV (4) [14] / TOTAL: 150

manirawmnaadedvfrom Stanmorephysics.com Mpumalanga/Preparatory 2023 CAPS/KABV ~ Grade/Graad 12 INFORMATION SHEET 1 —b+ Vb’ -4ac 2a Ina? 7 A= P(L+ni) Jappp A= P(1~ni) A=P(1-i) A= P(i+i) aay es T,=a+(n in n $,= Ska +(n-Dd] ia | T, =ar"'! S eae) sre S$, = 3-1e<r<l psi i] pail (1+i)" F , ny — tim LEENA FO F@)= fn, h d=y(x,-x%,) +0, -yy y=mxte (x-a) +(y-8 =? ab sinA sinB a’ =b? +c? —2be.cosA __¢ In AABC: —— sinC area AABC = 5 absin (e sin(a + #)=sin a.cos 8 + cosa.sin 8 cos(a + £)=cosa.cos 8 - sin a.sin B cos’ a—sin’? @ cos2a =41-2sin’? a 2cos? a-1 yx n n(A) n{S) ypoathx x P(A) = yy; = m(x- x) A tX. Vit y2 2 2 y27Y mat m=tan@ xy % sin(a — 8) =sin a.cos B —cosa.sin B cos(a — £)=cosa.cos + sin a.sin B sin 2a = 2sina.cosa n (x, - XY —> 1 n th On] P(A or B) = P(A) + Peay P(Aand B) p — t= FY W) Gx —

morephysics.com education MPUMALANGA PROVINCE REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS PAPER 2 SEPTEMBER 2023 MARKING GUIDELINES MARKS: 150 This marking guidelines consist of 18 pages: NOTE: Copyright reserved/Kopiereg voorbehou Please turn over/Blaai aseblief om

mattbawntoaded from Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 - Marking Guideline/Nasienriglyn e Ifacandidate answered a question TWICE, mark only the FIRST attempt. e Ifacandidate crossed out an answer and did not redo it, mark the crossed-out answer. « Consistent accuracy applies to ALL aspects of the marking guidelines. e Assuming values/answers in order to solve a problem is unacceptable. LET WEL: As ‘'n kandidaat’n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na. As 'n kandidaat 'n antwoord deurgehaal en nie oorgedoen het nie, sien die deurgehaalde antwoord na. ° = Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyn van toepassing. e — Dit is onaanvaarbaar om waardes/antwoorde te veronderstel om 'n probleem op te los. QUESTION/VRAAG 1 71 | 83 | 88 | 9L | 92 | 92 | 95 | 97 | 104 | 108 | 109 | 110) 111 } 115 | 129 1.1 1495 5) = 99,67 V¥ 99,67 (2) 1.2 o =14,06 ¥SD (1) 1.3 99,67 —14,06 = 85,61 ¥ boundary 2 = 4100 =13,33% v= 15 15 v answer (3) 1.4.1 | 96,67 v answer (1) 1.4.2 | 14,06 v answer (1) [8]

matbawntoaded from Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn QUESTION/VRAAG 2 2.1.1 | True Y answer () 2.1.2 | Positively-skewed / Skewed to the right Y answer ) 2.1.3 | Range for company A = 800-200 = 600 Range for company B = 600-100 = 500 Y both ranges Biggest range : Company A ¥ Company A (2) 2.1.4 | 20x 75% =15 workers V75% ¥ 15 workers (2) 2.2.1 | y=5965,51-—2,93x ¥ 5329,84 v -2,61 Y equation (3) 2.2.2 | r=-0,49 vy ) 2.2.3 | y = 5965,51—2,93(2018) v prediction =52,77 The correlation coefficient is moderate thus the value is fairly reliably | Y answer + reason predicted. (2) [12]

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn QUESTION/VRAAG 3 D y ar ae A(2; 6) B(11: 1) 0 . T x | — C(-1;-3) 3.1.1) N:(x;0) Y subst into gradient 0-(-3) 1 formula Mnc = ae x-(-l) 3 x+1=9 x=8 Y answer (2) OR y-(3)= Fo 1) ¥ subst into equation 1,8 “3 3 For y=0:x=8 v answer ria 5 l i

matbowntoaded from Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn 3.1.2 | tand =3 ¥ substitution 0=711,565... v0 tan BN ¥ substitution B 8,434...° v BNT C=71,565...°-18,434...° = 53,13° v answer Accept C= 53,14° (5) 3.2 | y-6=3(x-2) v substitution y=3x Y equation (2) 3.30 | m, =-3 Ym, =-3 y-1=-3(x-11) y : y=-3x434 equation 3x =-3x +34 . . Y setting equations 6x = 34 equal x= 7 5,67 “3° ¥ value of x 17 =3/—]=17 * (5 ¥ value of y (5) [14]

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn QUESTION/VRAAG 4 y A(-3:11) D C(1;3) + fe B 4.1 m= 11-3 -8__, ¥ gradient of AC. aC 3-1-4 ¥ Midpt AC mdpt yc =(-137) ep y-T= 3(*-(-0) ¥ Lgradient and subst ye l x+ IS Y equation 2 2? (4) 42 i. + 15 3x42 Y set equations equal 2 2 — 2,5x =12,5 x=—5 v solve x y=3(-5)+20=5 Vsolve y 6) a centre(—5;5) 43 radius = |(-5-(-3))" +(5-11) = 40 = 210 diameter = 4/10 units = 12,65 Y¥ substitution in formula ¥tadius ¥ diameter (3) 44 | (x45) +(v-5) =40 Y (x +5), (7-5) v 40 (2)

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn as |m -_lic5 _3 rad ~ (5) 1 Y gradient ¥ subst in form Y¥ equation Y value of p (4) 2 v 46 | (x+2) +(y-7S= (Jo) ae (x+2/ +(y-7) =10 Y10 (3) 47 Centres: (2; 3) and (—5; 5) Distance between centres = ./(2 —(-5)? + (3-5) v subst of centres ¥ distance = /53 =7,28 Sum of radii =2 + 2 J10 =8,32 ¥ Sum of radii Distance between centres < Sum of radii .. They will intesect. Y¥ conclusion (4) [23]

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn QUESTION 5 5.1 aN y, S11 | (3+ =r 2 = 25 v value of r r=5 . - v answer sin@ = = Q) 5.1.2 | cos20 =cos?6 — sin’0 ¥ expansion = (=) - (=) ¥ substitution 5 5 _lo 9 v answer 25 25 (3) ae 25 5.1.3 | cos(@+30°) = cos0cos30° — sinOsin30° ¥ expansion -(3) 3 -(2\3) ¥ substitution S5)\ 2 5 )\2 = 43 +3 v answer 10 (3) 5.2 (4sina)” +(4cosa) ae , ¥ simplification =l6sin’a+16cos’@ trararg =16(sin? a +cos’ @) Janay =16(1) =16 as (2)

matbewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn 53 sin(900° - x) : cos(-x) - sin(x - 180°) : sin(90° + x) =sin(180°— x) . cos(360° — x) — sin(180° + x) .sin(90°+ x) | ¥ sinx = sin xcosx —(-sinx)cosx Vcosx ¢ > —smnx ¥ cosx Y simplification v double angle identity ‘ (6) 5.4.1 | sin7x+sinx . ————_ = sin4x 2cos3x Y both brackets sin(4x+3x)+sin(4x—3x LHS= ( ) ( ) v sin(4x+3x) 2cos3x . _ sin4xcos3x + cos 4xsin 3x + sin 4x cos 3x — cos 4x sin 3x expansion 2cos3x ¥ sin(4x—3x) _ sin4xcos3x+sin 1x cos 3x expansion 2cos3x . : : _ 2sin4xcos3x ¥ simplification 2cos3x (4) =sin4x =RHS 54.2 | 9 c0s3x=0 ¥ 2cos3x=0 cos3x=0 90°+360% v3 -{% +300 oe kez = or kez _909° 0 90° + 360°k 90° + 360° re 30° +120°h _ [30°+120° 30° +120°% ~)_39°4.120°% OR oR (3) 2cos3x=0 ¥ 2cos3x=0 cos3x=0 90°+360°% ‘0 0 = or kez _ {90° #360% 270° +360°k 270° + 360°% 30° + 120°% 30° +120°% x= Vx= 90° + 120° 90+ 120°K

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn 5.5 sin (3x + 20°) =cosx sin (3x + 20°) = sin(90°— x) 3x+20°=90°-x+360° kez 4x = 7054360°K x =17,524/ 90° OR 3x + 20° = 180° —(90°- x) +360°%% kez 3x + 20° = 180° —90° + x + 360° 2x = 70° + 360°k x =35°+180°% OR sin(3x + 20°) =cosx cos[90° — (3x + 20°)] =cosx —3x+70°=x+360°h kez —4x =-70° + 360° x =17,5°+90°% OR —3x+ 70° =-x+ 360° kez —2x =—70° + 360° x =35°+180°K ¥ sin(90-x) ¥ 3x+ 20° =90°-x+360°% kez ¥ x =17,5°+90°K ¥ 3x+ 20° =180°—(90°- x) +360°K ¥ 2x = 70° + 360°K ¥ x=35°+180°% (6) ¥ cos[90° — (3x + 20°)] ¥ Ax =-70° + 360° ¥ x =17,5°+90°K ¥-3x + 70° =-x+300°% kez v¥—2x =—70° +360°%% vv x=35°+180°% [29]

matbowntoaded vfrom Stanmorephysics.com CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn MPU/September 2023 QUESTION 6 6.1 180° ¥ answer (1) 6.2 Y critical values ¥ notation (2) 6.3 Range of g: y e[-I; 1] Range of 3g: y €[-3; 3] V critical values Range of y=3g(x)-l: 4S y<2 or ye|-+4;2] ¥ notation Q) 6.4 2 1 ¥ equation cosx=— 2 1 cosx= 7 ¥ x= 75,5° x =75,5° ° ° ¥ critical values ~45° <x S75,5 ¥ notation (4) 65 1, 1 =cos* x — — 2 = * (2cos? x-1) 4 ut = dco 2x) lv double angle 4 KE ~ ri ) ¥ min of cos2x 1 “4 v answer (4)

matbowntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn | | [13] | QUESTION 7 1 TRD=0-a ; % ¥TRD cos(0-a) =— TR ¥ cos definition x TR = ————_ cos(8-@) (2) 72 A A=90°-0 TR _ AT sin(90°-6) sina Vx TR 2 cos@ sing ¥ TR TR = 20088 sm a@ x _ 2cos8 ¥ Subst in area-rule cos(0-a) sina _ 2cosAcos(0-a) ¥ answer * sing (4)

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 - Marking Guideline/Nasienriglyn 73 a 2.cos68,33cos(68,33 — 28°) 7 sin 28° vx Vv TR ATR = 130,33° Area AATR = 320145730) sin130,33° v subst in area formula =1,1992... ¥ answer (4) = 1, 20units? [10]

mattDewntoaded vfrom Stanmorephysics.com CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn QUESTION 8 MPU/September 2023 8.1 Draw line from A through O to T let Ai =x and A> =y Ai =B =x (2's opp = sides) Oo: =2x (ext Z of A) similarly O2 =2y BOC =2x+2y=2(x+y) “BOC =2xBAC ¥ construction vS/R v SIR vs ¥ deduction (6)

matbewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn 8.2 a fo / / / | \ \ \ \ \ NN A vS v 8.2.1 D=x (Z opp = sides) Ss vR A VS v Ez =x (tan-chord theorem) Ss vR (4) 2.2 A vSIR 8 C, =2x (extZ of A) A A . vS 2C, =EOB=4x (Zatcentre=2x Z atcircumf ) VR @) 823 | OBD=90° (tan L rad) Vs A VR Bz =90°-x (2) 824 | OBD=90° (tan 1 rad) Aa A Vv F2 =180°-x-OBD (sum Zs A) ve F, =90°- 2 =90°-x SiR ”. BC = FC (opp 2's =) (3) “. DC = BC = FC [ [17]

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn QUESTION 9 A 8 B E 10 12 Cc D 9.1 In ABCA and ACDB Be _ 2 2 VS cD 18 3 AB ft Sem2 vs BC 12 3 AC _10_2 vs DB 15 3 v ABCA ||| ACDB (sides in proportion) sR 4) A A v 9.2 ABC=BCD (ABCA ||| ACDB) s -AB||CD. (alt Zs=) VR (2) 9.3 In AABE and ADCE: ABC=BCD (proven) AEB=CED (vertically opp Z) AABE ||| ADCE (222) AB BE ((lia's) DC CE 8 x 18 12-x 8(12—x) = 18x 96 —8x =18x 96 = 26x x = 3,69 CE = 8,31 V AABE ||| ADCE vy AB _ BE DC CE wis __* 18 12-x ¥ CE=8,31 (4)

matbewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 — Marking Guideline/Nasienriglyn | | [10) | QUESTION 10 mM Vv i A ¥vS VR 10.1 PST =90° (Zinsemi-circle) Q) A x v 10.2 T, =T2 (STis abisector) s T> =V (Zopp=sides) vs T=V R =P (ext Z of cyclic quad) YS VR Ss =PST =90°(sum Z of A) VS+R (5) 10.3 ATSO ||| ATVS Tet (STisa bisector) S:=V= [om=F: O1 =TSV (3rd ZA) ATSO ||| ATVS (777) (3)

mattDewntoaded vfrom Stanmorephysics.com MPU/September 2023 CAPS/KABV — Grade/Graad 12 - Marking Guideline/Nasienriglyn 10.4 TS _OS — =— _ ATSO||ATVS (2422 TV VS ll ( ) vs TS.VS=OS.TV YS but VS given and SPT both radii ¥S+R 1 VSVS= SPIT Y substitution ©. 2VS? = PT.TV (4) [14] TOTAL: 150