Gr 12 Technical Mathematics P1 (English) June 2024 Question Paper hlayiso.com

Downloaded from hlayiso.com Confidential . <n basic education aa D (@) S225. Zs REPUBLIC OF SOUTH AFRICA SENIOR CERTIFICATE EXAMINATIONS/ NATIONAL SENIOR CERTIFICATE EXAMINATIONS TECHNICAL MATHEMATICS P1 MAY/JUNE 2024 TECHNICAL MATHEMATICS: Paper 1 MARKS: 150 AY TIME: 3 hours 11091E This question paper consists of 13 pages, a 2-page information sheet and 2 answer sheets. X05 na Copyright reserved B Please turn over

Downloaded from hlayiso.com Technical Mathematics/P} 2 DBE/May/fune 2024 SC/NSC Confidential INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of NINE questions. 2. Answer ALL the questions. 3. Answer QUESTION 4.1.3, QUESTION 4.1.5 and QUESTION 4.3 on the ANSWER SHEETS provided. Write your centre number and examination number in the spaces provided on the ANSWER SHEETS and hand in the ANSWER SHEETS with your ANSWER BOOK. 4. Number the answers correctly according to the numbering system used in this question paper. 5. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining your answers. 6. Answers only will NOT necessarily be awarded full marks. 7. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 8. If necessary, round off answers to TWO decimal places, unless stated otherwise. 9. Diagrams are NOT necessarily drawn to scale. 10. An information sheet with formulae is included at the end of the question paper. 11. Write neatly and legibly. Copyright reserved gem Piease turn over

Downloaded from hlayiso.com Technical Mathematics/P ! 3 DBE/Maay/June 2024 SC/NSC Confidential QUESTION 1 1.1 Given: x?-x-12=p Solve for x ift 11. p=0 (2) 1.1.2 pso (ql) 1.1.3 p = —5 (correct to TWO decimal places) (4) 12 Given: = 2y-x=7 and x? +xy=21-y? 1.2.1 Make x the subject of the equation 2y - x =7 (1) 1.2.2 Hence, or otherwise solve for x and y. (5) 13 The picture below shows a milling cutter. The formula used to determine the relationship between the number of teeth (7'), the diameter (D) of the cutter and the depth (d) of the cutter is given by: 12,5 D ie = D+4d T = Number of teeth D = Diameter of the cutter in cm d = Depth of the cutter in cm 13.1 Make d the subject of the formula. (3) 1.3.2 Hence, or otherwise, calculate the depth of the cutter (d) if T = 10 and D = 32 cm (2) 14 Evaluate 2 (111110, + 38). Leave your answer in decimal form. (2) (20) Copyright reserved OF AO] Please turn over Pose

Downloaded from hlayiso.com Technical Mathematics/P 1 4 DBE/May/June 2024 SC/NSC Confidential QUESTION 2 2 —5b 2.1 Given: T= ——— 3b Determine the numerical value of 6, for which T is: 2.1.1 Undefined 2.1.2 Equal to zero 2.2 Determine the value(s) of & for which the equation ko? = 35 — 2x has real roots. QUESTION 3 3.1 Simplify the following without the use of a calculator: 31d vax a 3.1.2 gt! x At x 6I 2 313 Ve(2-Ve)-Vak 3.2 Given: 1og72 ~ log? log6 3.2.1 Write the following as a single logarithm: log 72 — log 2 3.2.2 Hence, simplify without using a calculator: ere ee 08 3.3 Solve for x: 5**?- 5* = 600 Copyright reserved 5 Please turn over [OF] Q) (1) 6) {7} () (3) 3) (1) (2) (3) -

Downloaded from hlayiso.com Technical Mathematics/P | 5 SC/NSC Confidential 3.4 Given the complex numbers: r,=2+3i and r, =i 3.4.1 Write down the conjugate of 7, . 3.4.2 Hence, simplify 4. Show ALL steps. y a5 Write down the numerical values of @ and b if a+bi=-—i-14 Copyright reserved igh ieee DBE/MaytJune 2024 Please turn over (1) (4) (2) (22)

Downloaded from hlayiso.com Technical Mathematics/P! 6 DBE/May/June 2024 SC/NSC Confidential QUESTION 4 41 Given: Functions f and defined by f(x) =~2(x—3)?+18 and A(x) =2x+0 4.1.1 Write down the coordinates of the turning point of / 4.1.2 Determine the x-intercepts of f 4.13 Hence, sketch the graph of f on the ANSWER SHEET provided. Clearly show the intercepts with the axes and coordinates of the turning point of f 4.1.4 A (5; ¢) isa point of intersection of f and A. (a) Calculate the numerical value of ¢. (b) Hence, determine the numerical value of c. 4.1.5 Sketch the graph of A on the same set of axes as graph f on the ANSWER SHEET provided. Clearly show the intercepts with the axes and the coordinates of A. Copyright reserved al Please turn over (2) (4) G) (2) (2) (2)

Downloaded from hlayiso.com Technical Mathematics/P } SC/NSC Confidential 7 DBE/Meay/June 2024 42 The graph below represents functions p and g defined by p(x) = -— g 4 and x g(x)=a%+ q ¢ Functions p and g have a common horizontal asymptote. ¢ Dis the y-intercept of g and C the x-intercept of both p and g. 4.2.1 Write down: (a) The domain of p (b) The range of g (c) The numerical value of ¢ (d) The coordinates of D 4.2.2 Determine the coordinates of C. 4.2.3 Determine the numerical value of a. 4.3 Theline y=c isa tangent to semi-circle A defined by h(x) = Jr? — x? The distance between the x-intercepts of A is 10 units. Sketch the graph of # and the line y=c on the ANSWER SHEET provided. Clearly show all intercepts with the axes. Copyright reserved OO} a AO] % Please turn over (1) (1) (1) (2) @) (2) (3) [28]

Downloaded from hlayiso.com Technical Mathematics/Pt 8 DBE/May/June 2024 SC/NSC Confidential QUESTION 5 5.1 The exponential graph below shows the number of views of a popular online video, that grows at a compound rate of 50% per month. The number of months since the video was posted online is shown on the x-axis and the number of views on the y-axis. Online Video Views ¥ 18007- 16004 14004 wn 12004 z a] > 10004 ee ° 8 800 4 E 7, 6004 4007 200+ Oo 1 2 3 4 5 6% Time (months) 5.1.1 Write down the number of views the online video received immediately after it was posted. Q) 5.1.2 Hence, calculate the total number of views the online video received at the end of the first year (rounded to nearest whole number). (G) 5.1.3 Online videos with 100 000 views are considered to go viral. Determine, to the nearest month, how long it will take (counting from the start) for this online video to go viral if the growth rate remains 50% per month. (4) Copyright reserved ‘a Please turn over Oro

Downloaded from hlayiso.com Technical Mathematics/P I 9 DBE/Meay June 2024 SC/NSC Confidential 5:2 Timo wants to buy a welding machine in 5 years’ time that will cost R23 O00. He decides to invest R15 000 in an investment account. Interest rate for the first three years is 8,5% per annum, compounded quarterly. * Interest rate for the next two years is 6% per annum, compounded semi-aranually. 5.2.1 Determine whether the value of the investment at the end of five years will be enough to buy the welding machine. (5) $.2.2 Hence, calculate the total interest earned by the investment over five years. (2) [15] Copyright reserved & a Please turn over

Downloaded from hlayiso.com Technical Mathematics/P | 10 DBE/May/June 2024 SC/NSC Confidential QUESTION 6 6.1 Given: f(x) =11+4 7x Determine f ‘(x) using FIRST PRINCIPLES. (5) 6.2 Determine: yy. 8 = if x 6.2.1 ae y a) 6.22 fo if f (xye Vx" (2) ? 16 623 o,f * 4-x (4) 6.3 Determine the average gradient of the function defined by g(x)= 2 between x x=-3 andx=-l (3) 64 Given: f(x)= mx? + mx—4 6.4.1 Determine f’(x) in terms of m (2) 6.4.2 Hence, calculate /'(2) in terms of m (1) 6.4.3 Determine the numerical value of m if the gradient of the tangent to f at x=2 isequalto 39. (2) [20] Copyright reserved ao Please turn over

Downloaded from hlayiso.com— Technical Mathematics/P I I DBE/May/ June 2024 SC/NSC Confidential QUESTION 7 The graph below shows a cubic function defined by h(x) =x?+ px?+9x—2 which cuts the x-axis at A, B(2;0) and C. The graph of A cuts the y-axis at F and has turning points at D and E. +” D h A B(2 ; 0) c x E 71 Write down the coordinates of F, the y-intercept of A. (2) 72 Show that p=-6 (2) 73 Determine the length of BC. Leave the answer in surd form. (5) 74 Hence, determine the coordinates of D and E. (5) 75 Hence, write down the values of x for which A(x) x A/(x) > 0 for x > 2 3) (17) Copyright reserved ee Please turn over 4 r @

Downloaded from hlayiso.com Technical Mathematics/P ! 12 DBE/May/June 2024 SC/NSC Confidential QUESTION 8 The movement of a ball thrown from a ball-throwing machine forms a parabolic path given by the equation A(t) = 1? + 641,62 where / is the height (in metres) of the ball above the ground and ¢ is the time in seconds. 8.1 Determine the initial height of the ball above the ground. qa) 8.2 Determine A‘(t). qd) 8.3 Hence, calculate the maximum height the ball reaches. (4) 8.4 Determine the height of the ball above the ground when it reaches a velocity (rate of change) of 3 m/s. (3) [9] Copyright reserved Please turn over

Downloaded from hlayiso.com Technical Mathematics/P 1 13 DBE/Mayr‘June 2024 SC/NSC Confidential QUESTION 9 91 Determine the following integrals: 9.1.1 it x" dx (2) 4 9.1.2 2a +—~| dk J (2x +4) @) 91.3 f @x?) a& (2) 9.2 The sketch below shows function g defined by g(x) = 2* +2 and the shaded area bounded by the curve of g and the x-axis between x = —1 and x =3 hy Determine the area of the shaded region. Show ALL working details. (6) {12} TOTAL; 150 Copyright reserved Of gel

Downloaded from hlayiso.com Technical Mathematics/P! DBE/May/June 2024 SC/NSC Confidential INFORMATION SHEET: TECHNICAL MATHEMATICS -b+ yb? - 4ac 2a x= b _ 4ac-b? x2-— 2a uf 4a at =bex=log,b, a>0,a¢land b>0 A=P(i+ni) ieg =(14 EY" 1 f'@)= sim, Leh) f() n+l x Nod = x n+l +C, n#-1 jraesinx +C, x>0 x x a* fa* de =—+C, a>0 Ina d= (4 - 4)" +0.-ny y-yame—x) a_ 6 _¢ sinA sinB_ sinC In AABC- area of A ABC = > ab- sin C sin? 6 + cos’@=1 Copyright reserved A=P(1-ni) 1+ tan*@ =sec*@ LOR IO} A=P(1+i)" A=P(i-i)" yet kx" de =k- +C ,n#-l k #0 n+l k f<a&ak Inx+C, x>0, k#0 x a® fka™ dk =k- +C ,a>d, k2#0 nina mi Xp +X, Vo tW 2° 2 m = 2TH tan 0= m X_— % a =b? +c? ~2be-cosA 1+ cot? @ = cosec’@

Downloaded from hlayiso.com Technical Mathematics/P? DBE/Sune 2024 SC/NSC Confidential arad = 180° Angular velocity =@ = 2an where n = rotation frequency Angular velocity = @ = 360° n where n = rotation frequency Circurnferential velocity = v = a Dn where D = diameter and » = rotation frequency Circumferential velocity = v = w r where a= angular velocity and r = radius Arclength =s =r where r = radius and @ = central angle in radians rs . Area ofa sector = i where r = radius, s = arc length 2 Area ofa sector = > where 7 = radius and @ = central angle in radians 4h’ -4dh+x? =0 where / = height of segment, d= diameter of circle and x = length of chord . 0, +0, A, =a(m, +m, +m, +...4 m,) where a = width of the equal parts, m, = a O, = n" ordinate and» = number of ordinates OR a, +0, . : Arma 1 5 +O. + Ost ct ons] where a = width of the equal parts, 0, = 7" ordinate and » = number of ordinates Copyright reserved Oxe

Downloaded from hlayiso.com Technical Mathematics/P J DBE/May/ Sune 2024 SC/NSC Confidential ANSWER SHEET CENTRE NUMBER EXAMINATION NUMBER QUESTION 4.1.3 AND QUESTION 4.1.5 ay xy Copyright reserved SOFA

Downloaded from hlayiso.com Technical Mathematics/P] DBE/MayfJune 2024 SC/NSC Confidential ANSWER SHEET CENTRE N UMBER EXAMINATION NUMBER QUESTION 4.3 Copyright reserved fi: Ay i i

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Downloaded from hlayiso.com Vertroulik basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA SENIORSERTIFIKAAT-EKSAMEN/ NASIONALE SENIORSERTIFIKAAT-EKSAMEN TEGNIESE WISKUNDE V1 MEI/JUNIE 2024 TEGNIESE WISKUNDE : Vraestel 1 PUNTE: 150 MN meee 11091A Hierdie vraestel bestaan uit 13 bladsye, 'n 2 bladsy-inligtingsblad en 2 antwoordblaaie. X05 ani eRe FC igue Kopiereg voorbehou Blaai om asseblief

Downloaded from hlayiso.com Tegniese Wiskunde/V1 eg DBE/MeisJunie 2024 SS/NSS Vertroulik INSTRUKSIES EN INLIGTING Lees die volgende instruksies noukeurig deur voordat die vrae beantwoord word. 1. Hierdie vraestel bestaan uit NEGE vrae. 2. Beantwoord AL die vrae. 3. Beantwoord VRAAG 4.1.3, VRAAG 4.1.5 en VRAAG 4.33 op die ANTWOORDBLAAIE wat verskaf is. Skryf jou sentrumnommer en eksamennommer in die ruimtes wat op die ANTWOORDBLAAIE verskaf is en lewer die ANTWOORDBLAAIE saam met jou ANTWOORDEBOEK in. 4, Nommer die antwoorde korrek volgens die nommeringstelsel wat in hierdie vraestel gebruik is. 5. Toon duidelik ALLE berekeninge, diagramme, grafieke, ens. wat jy gebruik het om jou antwoorde te bepaal. 6. Volpunte sal NIE noodwendig aan slegs antwoorde toegeken word NIE. 7. Jy mag 'n goedgekeurde, wetenskaplike sakrekenaar (nieprogrammeerbaar en niegrafies) gebruik, tensy anders vermeld. 8. Indien nodig, rond antwoorde tot TWEE desimale plekke af, tensy anders vermeld. 9. Diagramme is NIE noodwendig volgens skaal geteken NIE. 10. ‘n Inligtingsblad met formules is aan die einde van die vraestel ingesluit. 11. Skryf netjies en leesbaar. Kopiereg voorbehou aa] Blaai om asseblief

Tegniese Wiskunde/V] 3 DBE/Mei/ Junie 2024 Downloaded from hlayiso.com SS/NSS Vertroulik VRAAG I Ll 1.2 1.3 1.4 Kopiereg voorbehou mous Blaai om asseblief C Gegee: x? -x-12 =p Los op vir x indien: Lil p=0 1.1.2 pso 1.1.3 p =—5S (korrek tot TWEE desimale plekke) Gegee: 2y-x=7enx’+xy=21-y? y y 1.2.1 Maak x die onderwerp van die vergelyking 2y - x =7 1.2.2 Vervolgens, of andersins, los op vir x en y. Die prent hieronder toon 'n freesmasjiensnyer. Die formule wat gebruik word om die verwantskap tussen die aantal tande (7), die middellyn (D) van die snyer en die diepte (d) van die snyer te bepaal, word gegee deur: 12,5 D D+4d T = Aantal tande D= Middellyn van die snyer in cm d = Diepte van die snyer in cm 13.1 Maak d die onderwerp van die formule. 1.3.2 Vervolgens, of andersins, bereken die diepte van die snyer (a) indien T=10en D=32 cm Evalueer 2 (111110 , + 38). Laat jou antwoord in desimale vorm. 22 (2) (1) (4) (1) 6) G) (2) (2) (20]

Downloaded from hlayiso.com Tegniese Wiskunde/V1I 4 DBE/Mei/Junie 2024 SS/NSS Vertroulik VRAAG 2 2-55 . Gegee: T= 2.1 egee 3B Bepaal die numeriese waarde van 5, waarvoor T: 2.1.1 Ongedefinieerd is ay 2.1.2 Gelyk is aan nul (1) 2.2 Bepaal die waarde(s) van k waarvoor die vergelyking ke? = 35 —2x reéle wortels het. (5) (7) VRAAG 3 3.1 Vereenvoudig die volgende sonder die gebruik van 'n sakrekenaar: 3.11 yax” (1) 3.1.2 g?t! yd 6-2 (3) 313 ve(2- ve)-Vak (3) 2 — log2 3.2 Gegee: 1og72 ~ log? log6 3.2.1 Skryf die volgende as 'n enkele logaritme: log 72 ~ log 2 (1) 3.2.2 Vereenvoudig vervolgens sonder die gebruik van 'n sakrekenaar: log72 — log2 log6 Q) 33 Los op vir x: 5°? - 5* = 600 (5). Kopiereg voorbehou Biaai om asseblief

Downloaded from hlayiso.com Tegniese Wiskunde/VI i DBE/Mei/Junie 2024 SS/NSS Vertroulik 3.4 Gegee die komplekse getalle: r,=2+3/ en 7, =i 3.4.1 Skryf neer die gekonjugeerde van rh. (1) 3.4.2 Vereenvoudig vervolgens 4. Toon ALLE stappe. % (4) 3.5 Skryf die numeriese waardes van a en b neerindien a+bi=-i-14 (2) (22] Kopiereg voorbehou ae Blaui om asseblief \

Tegniese Wiskunae/VT VRAAG 4 Downloaded from hlayiso.com 6 DBE/Mei/Junie 2024 SS/NSS Vertroulik 41 Gegee: Funksies f en h gedefinieer deur f (x) =-2(x-3)? 418 en A(x) = 2x4 411 4.1.2 4.1.3 Kopiereg voorbehou Skryf neer die kodrdinate van die draaipunt van f- Bepaal die x-afsnitte van f° Skets vervolgens die grafick van f op die ANTWOORDBLAD wat verskaf is. Toon duidelik die afsnitte met die asse en die kodrdinate van die draaipunt van f- A (5; ¢) is'nsnypunt van f en h. (a) Bereken die numeriese waarde van 1. (b) Bepaal vervolgens die numeriese waarde van c. Skets die grafiek van A op dieselfde assestelsel as grafiek f op die ANTWOORDBLAD wat verskaf is. Toon duidelik die afsnitte met die asse en die koérdinate van A. Af} Blaai om asseblief OFAC (2) (4) (3) (2) Q) (2)

Downloaded from hlayiso.com Tegniese Wiskunde/V] DBE/Mei/Junie 2024 SS/NSS Vertroulik 4.2 Die grafick hieronder verteenwoordig funksies p en g_ gedefinieer deur plzj=-5-4en gaa eg x ¢ Funksies p en g het 'n gemeenskaplike horisontale asimptoot. * D isdie y-afsnit van g en C isdie x-afsnit van beide p en g. Pp 4.2.1 Skryf neer: (a) Die definisieversameling van p ¢5) (b) Die waardeversameling (terrein) van g a (c) Die numeriese waarde van g a) (d) Die kodrdinate van D (2) 4.2.2 Bepaal die kodrdinate van C. @) 4.2.3 Bepaal die numeriese waarde van a. (2) 43 Die lyn y=c is'n raaklyn aan halfsirkel A gedefinieer deur h(x) = yr? - x? Die afstand tussen die x-afsnitte van A is 10 eenhede. Skets die grafiek van h en die lyn y=e op die ANTWOORDBLAD wat verskaf is. Toon duidelik alle afsnitte met die asse. (3) } [28] Kopiereg voorbehou Reo Blaai om asseblief if TH

Downloaded from hlayiso.com Tegniese Wiskunde/V1 8 DBE/Mei‘Junte 2024 SS/NSS Vertroulik VRAAG 5 5.1 Die eksponensiéle grafiek hieronder toon die aantal kere wat 'n gewilde aanlyn video gekyk is, wat teen 'n saamgestelde koers van 50% per maand groei. Die aantal maande sedert die video aanlyn geplaas is, word op die x-as getoon en die aantal kere wat die video gekyk is, word op die y-as getoon. Aanlyn video gekyk ys 18004 16004 14004 1200- 1000- 800+ 600- Aantal kere gekyk 4007 2007 Oo 1 2 3 4 5 6* Tyd (maande) 5.11 Skryf neer dic aantal kere wat die aanlyn video gckyk is onmiddellik nadat dit geplaas is. (1) 5.1.2 Bereken vervolgens die aantal kere wat die aanlyn video gekyk is aan die einde van die eerste jaar (rond jou antwoord tot die naaste heelgetal af). (3) 5.1.3 Aanlyn video's wat 100 000 keer gekyk is, word as gewild beskou. Bepaal, tot die naaste maand, hoe lank dit sal neem (deur van die begin af te tel) vir hierdie aanlyn video om as gewild beskou te word, indien die groeikoers 50% per maand bly. (4) Kopiereg voorbehou qo} Blaai om asseblief

Downloaded from hlayiso.com Tegniese Wiskunde/V] 9 DBE/Me i/Junie 2024 SS/NSS Vertroulik 5.2 Timo wil oor 5 jaar 'n sweismasjien koop wat R23 000 sal kos. Hy bes luit om R15 000 in 'n beleggingsrekening te belé. e Die rentekoers vir die eerste drie jaar is 8,5% per jaar, kwartaalliks saamgrestel. ¢ — Die rentekoers vir die volgende twee jaar is 6% per jaar, halfjaarliks saargestel. 5.2.1 Bepaal of die waarde van die belegging genoeg sal wees om aan die einde van vyf jaar die sweismasjien te koop. (5) 5.2.2 Bereken vervolgens die totale rente wat oor vyf jaar deur die be legging verdien is. (2) [15] Kopiereg voorbehou Ee Blaai om asseblief ere

Downloaded from hlayiso.com Tegniese Wiskunde/V1 10 DBE/Mei/Junie 2024 SS/NSS Vertroulik VRAAG 6 6.1 Gegee: f(x) =11+ 7x Bepaal f/(x) deur EERSTE BEGINSELS te gebruik. (5) 6.2 Bepaal: dy... 8 — indien y= x 6.2.1 ak ¥ () 622 f(x) indien f (x)= Vx" @ 216) 6.23 o,| x —16 ao% (4) 6.3 Bepaal die gemiddelde gradiént van die funksie gedefinieer deur g(x)=- tussen x x=-3enx=-l (3) 6.4 Gegee: (x)= mx? +mx-4 6.4.1 Bepaal f’ (x) in terme van mt (2) 6.4.2 Bereken vervolgens /’ (2) in terme van m (1) 6.4.3 Bepaal die numeriese waarde van m indien die gradiént van die raaklyn aan f by x=2 gelyk is aan 39. (2) [20} Kopiereg voorbehou ay Blaai om asseblief Ee

Downloaded from hlayiso.com Tegniese Wiskunde/V? il DBE/Mei/Aunie 2024 SS/NSS Vertroulik VRAAG 7 Die grafiek hieronder toon 'n kubiese funksie gedefinieer deur h(x) =x°+ px?+9x-2 wat die x-as by A, B (2; 0) en Csny. Die grafiek van A sny die y-as by F en het draaipumte by Den E. ¥ D h B(2 ; 0) c x 0 F; E Vl Skryf neer die kodrdinate van F, die y-afsnit van A. (2) 7.2 Toon dat p=-6 (2) 7.3 Bepaal die lengte van BC. Laat die antwoord in wortelvorm. (5) 74 Bepaal vervolgens die kodrdinate van D en E. (5) 75 Skryf vervolgens die waardes van x neer waarvoor A(x) x h "(x) > 0 waar x > 2 (3) [17] oe Kopiereg voorbehou fees Blaai om asseblief eat

Downloaded from hlayiso.com Tegniese Wiskunde/V1 12 DBE/Mei/Junie 2024 SS/NSS Vertroulik VRAAG 8 Die beweging van 'n bal wat deur 'n balgooimasjien gegooi word, vorm 'n paraboliese pad wat deur die vergelyking h(t) =-1° + 61+ 1,62 gegee word, waar h die hoogte (in meter) van die bal bo die grond is en ¢ die tyd in sekondes is. 8.1 8.2 8.3 8.4 Kopiereg voorbehou Bepaal die aanvanklike hoogte van die bal bo die grond. Bepaal h ‘(t). Bereken vervolgens die maksimum hoogte wat die bal bereik. Bepaal die hoogte van die bal bo die grond wanneer dit 'n snelheid (tempo van verandering) van 3 m/s bereik. qo) Blaai om asseblief tel (1) Q) (4) (3) 19]

Downloaded from hlayiso.com Tegniese Wiskunde/V1 13 DBE/Mei/ Junie 2024 SS/NSS Vertroulik VRAAG 9 9.1 Bepaal die volgende integrale: 9.2 Kopiereg voorbehou Rod 9.1.1 f x* dx (2) 9.1.2 { [z= +4) dx (2) 9.13 [ Qx) ae 2) Die skets hieronder toon funksie g gedefinieer deur g(x) =2*+2 endie gearseerde oppervlakte begrens deur die kromme van gen die x-as tussen x =~] en x =3 Ay Bepaal die opperviakte van die gearseerde gebied. Toon ALLE berekeninge. (6) 12] TOTAAL: 150 eh

Downloaded from hlayiso.com Tegniese Wiskunde/V! SS/NSS Vertroutik INLIGTINGSBLAD: TEGNIESE WISKUNDE -bt yo? — 4dac 2a a a* =boox= log,b, A=P(1+ni) A=P(1-ni) n+l [xtdx == +C, n#-1 nth pide eine +C, x>0 x x a* Ja dx=——+C, a>d0 Ina d= (4, -4) +O, -nY ysomxre y-y, =m(x- x,) 2 2 ey a b 5 In AABC: — = = = — sinA sinB_ sinC opperviakte van A ABC = ; ab - sin C sin? @+cos*@=1 Kopiereg voorbehou a>0,azlen b>0 DBE/Mei/Junie 2024 reek _4ac-b* 2a Aa A=P(1+i)" A=P(i-i)" xn fax” de =k--——-+C ,n#-l, k #0 n+l k J tdeak- Inx+C, x>0, k#0 x ai® fea™ de =k- +C ,a>0, k#0 nina M Xy +X, Path 2° 2 =22 71 tan O= m %2—% 1+ tan? @ =sec?6 &: & a=b' +e? —2be-cosA 1+ cot? @ = cosec’@

Downloaded from hlayiso.com Tegniese Wiskunde/V1 DBE/Mei/_Junie 2024 SS/NSS Vertroulik arad = 180° Hoeksnelheid = @ = 2277 waar n = rotasiefrekwensie Hoeksnelheid = w = 360° n waar n = rotasiefrekwensie Omtreksnelheid =v=2Dn waar D = middellyn en n = rotasiefrekwensie Omtreksnelheid = v = @ r waar w = hoeksnelheid en r = radius Booglengte = s =r waar r = radius en @ = sentrale hoek in radiale Oppervlakte van 'n sektor = > waar r = radius, s = booglengte re Oppervlakte van 'n sektor = ra waar r = radius en @ = sentrale hoek in radiale 4h? -4dh+x? =0 waar = hoogte van segment, d= middellyn van sirkel en x = lengte van koord 0, +0, A,=a(m,+m, +m, +...+m,) waar a = wydte van gelyke dele, m, = + O, = n® ordinaat en n= aantal ordinate OF 0, +9, dey: A,=a “3 t 0, +0; +..4+0,, | Waar a = wydte van gelyke dele, 0, =“ ordinaat en # = aantal ordinate Kopiereg voorbehou rad

Downloaded from hlayiso.com Tegniese Wiskunde/V} DBE/Mei/Junie 2024 SS/NSS Vertroulik ANTWOORDBLAD SENTRUMNOMMER EKSAMENNOMMER VRAAG 4.1.3 EN VRAAG 4.1.5 ! |_4y| | { | | | it r jo | | | |0 x Kopiereg voorbehou ate

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