Mathematics Grade 12 P1 Mpumalanga November 2021 Question Paper

Downloaded from hlayiso.com - = CSREES aes Se] wg 4 ducea education education MPUMALANGA PROVINCE MPUMALANGA PROVINCE REPUBLIC OF SOUTH AFRICA REPUBLIC OF SOUTH AFRICA [ NATIONAL NASIONALE SENIOR CERTIFICATE SENIOR SERTIFIKAAT [Sexo re ——— GRADE 12 | GRAAD 12 MATHEMATICS PAPER 1 WISKUNDE VRAESTEL 1 q SEPTEMBER 2021 | SEPTEMBER 2021 | MARKS: 150 q PUNTE: 150 q TIME: 3 hours / TYD: 3 ure | | This question paper consists of 7 pages anda one-page information sheet. | Die vraestel bestaan uit 7 bladsye en een inligtingsblad

Downloaded from hlayiso.com Wiskunde Vy ’ 4 snber 2021 VRAAG 1 — ape 11 Los op virx: LL xQ-x)=0 2) M2 (2r+3)3—2) =2 (Laatjou antwoord korek tot TWEE desimaleplekke) @ 1130 27" 9 8) 14 V5—2y = 34 6) LS x(r+4) 2-3 (a) 1.2 Losop vir x en y Q2x—yYxr2y~ x-yel ) (23) VRAAG2 2:1 Die eerste drie terme van ‘a kwadatiese is: 1; —S;—13 2.1 Bepaal die algemene term van die ry @ 2.1.2 Watter term in die ry is 6437 ®) 2 In ‘ngegewe rekenkundige ry is die eerste term 2, dic laste tem 29 en dic som van al die terme 155. Bereken die gemene verskil @ u 23° Bereken: — $'(15—4p) 8) 24 Die eerste term van ‘n meetkundige ry is 9 en die verhouding van die som van die eerste 8 terme tot die som van die eerste 4 terme is 97: 81 Bercken die eerste drie terme van die ry, as dit gegee word dat al die terme positetis. (5) 2.5 Beskou die meetkundige recks : 20-5) +(p-8)' +3(p-5)'+ 2.5.1 Vir watter waardes van p sal die reeks konvergeer? 2.5.2 Bereken dic som tot oneindigheid as p=4. pes GB) 8) [25] Kopiereg voorbehou Sopiereg, 0 Blasi om assebliet Mathematies PL 3 September 2021 QUESTION 1 LI Solve for x: Lid x(Q2-x)=0 1.1.2 (2r43(3-x) =2 (Leave your answer correct to TWO decimal places) 113 277. 9°? Lia $=2e LS x(x+4) 2-3 1.2 Solve for x and y. (2x-y\x QUESTION 2 2.1 The first three terms of a quadratic sequence are: 2.1.1 Determine the general term of the sequence, 2.1.2 Which term has a value of -643? 2.2 Imagiven arithmetic series, the first term is 2, the last term is 29 and the sum of all the terms is 155. Calculate the common difference. Yes-4p) 2.3 Calculate: 24 The first term of a geometric series is 9 and the ratio of the sum of the 4 cight terms to the sum of the first four terms is 97 : 81 Calculate the first three terms of the sequence if itis given that all the terms are py 25 Consider the geomettie series: 1 pes a . 2(p-8) +(p-5) +3(P-5) + 2.5.1 For which value of p will the series be convergent? 2.5.2. Calculate the sum to infinity if p=4. Copyright reserved Please tum over Q) (4) @) (3) 4) () 123) 4) GB) (4) G3) Q) QB) 125]

Downloaded from hlayiso.com September 2021 Mathematics PL 4 QUESTION 3 a Given: ga)=—% 41 3 3.1 Determine the: 3.1.1 equations of the asymptotes of |g. Q) 3.1.2 y-intereept of g. ay 3.1.3. x-interceptof g . Q) 3.1.4 Sketch the graph of g, showing all intercepts with the axis and asymptotes, 8) 3.2. For which values of x is g(x) > 0? 2) 3.3. If h(x)=x+c is the axis of symmetry of g, determine the value of Q 3.4 Describe in words the transformation of g to. A(x) rhe Q) 14) QUESTION 4 4.1 Inthe diagram, f(x) =2" -8 and g(x)=ax?+br+e aredrawn. A (0; 4,5) isthe y+ intercept of g . Cis the x— intercept of both f and g. Bis the y-intercept of f- Cis the tuming point of ¢ A (3 C. i} de B 4.1.1 Determine the coordinates of B and C. @) 4.1.2. Calculate the values of a and 6. (4) 4.1.3. Write down the range of y=—f(x). @) 4.14 If h(x)=f(2x)+8, determine the equation of (x) in the form y= 8) 4.1.5 Determine the values of x for which | (a) fx) ge) 50 Q | (b) x. g (x)>0 2) | Please turn over ee ee Copyright reserved Wiskunde VI 4 ‘September 202) NSS VRAAG3 Gegee: g(x) 3.1 Bepaal de: 3.1.1 _vergelykings van die asimtote van g - Q) 3.1.2. jrafsnit van g a) 3.1.3 x-afsnit van g. Q). 3.1.4 Skets die grafiek van g, toon alle afsnitte met die asse en asimtote. @ 3.2 Vir watter waardes van x is g(x) > 0? @ 33. As A(x)=x+c ‘nsimmetic-as van g is, bepaal die waarde van c, Q 34 Beskryf die transformasie van g na i= +1 in woorde. 2 [4] VRAAG 4 4.1 Indie onderstaande diagram is, f(x) =2" —8 en g(x)=av? +hr +c geskets, A (0; 4,5) is die y-afsnit van g..Cisdie x-afsnit van beide f en g. Bis die y-afsnit van Cis die draaipuat van g. y & C f BI 4.1.1 Bepaal die kodrdinate van B en C. GB) 4.1.2 Bereken die waardes van a en 6. (4) 41.3. Gee die waardeversameling van y =—f(x) 2 4.1.4 As h(x)=f(2x)+8, bepaal die vergelyking van A(x) in die vorm y QB) 4.1.5. Bepaal die waardes van x waar: @ — f@)- gs) <0 Q) &) x.g'()>0 @) Kopiereg voorbehou Blasi om asseblief

Downloaded from hlayiso.com Wishunde V1 s September 2021 NSS 42 Indic onderstaande diagram is f(x) =4x-x" en (xy =! Xx geskets, 2 ; orsprong gaan, is geskets. A is "n punt op die raaklyn. B is’nsnypunt van feng. D is'n xafsnit van f. aoe " y ‘n Raaklyn aan f, wat deur die f Bereken AOB 6) (21) VRAAG 5 Sa Die Murray familie het twee kinders. Vir sy seun, Peter, besluit die paom'n co nalige bedrag met geboorte te belé, maar vir sy dogter, Cally besluit hy om maandeliks R150 te belé van dic einde van die maand van haar geboorte en dan aan die einde van etke maand daarna. Sul. Die bedrag wat vir Peter bele is, is R18 000 teen 'n rentekoers van 12% pj. maandeliks saamgestel. Hoc oud sal Peter wees teen die tyd wat sy aanvanklike belegging aangegroci het tot R 150 000? Laat jou antwoord tot die naaste jaar. (4) 5.1.2 Cally is gebore op 12 Maart. Die bank bied dieselfile rentekoers aan as vir Peter se belegging. Wat sal Cally se belegging werd wees aan die einde van die ‘maand waarin sy 18? @) 5.2 Tom gaan ‘a lening aan met die volgende voorwaardes: Hy sal die lening in 15 halfjaarlikse paaimente van R2 500, beginnende 6 maande van nou rentekoers is 16% pj. kwartaalliks saamgestel. crug betaal f. Die 5.2.1 Toon aan dat die halfjaarlikse rentekoers 16,32% pj. is 8) 5.2.2 Bereken die waarde van die lening. @) 115) Kopiereg voorbehou Blasi om asseblief AEST SET ates PI s September 2021 Nsc Mathes 42 — Inthe diagram below, f(x) =4x—27 and ate ty are sketched. A tangent to f is drawn at the origin. A isa point on this tangent to f- B is a point of intersection of f and g. D is an x-intercept of f Calculate AOB (5) 24) QUESTION 5 5.1 ‘The Murray family has two children, For the son, Peter, the father invested a lump ‘sum at his birth but for the daughter, Cally, he decided to make monthly payments of R150 from the end of the month she was bor and at the end of each month thereafter. 5.1.1 For Peter an amount of R18 000 was invested at a bank which offered an interest rate of 12% p.a. compounded monthly. What was Peter's age when the initial amount grew to R 150 000? Leave your answer to the nearest year, (4) 5.1.2 Cally was born on the 12 March, The bank offered the same interest rate as for Peter's investment. What would Cally’s investment be worth at the end of the month in which she turned 18? (@) 52 ‘Tom takes out a loan on the following conditions: He will repay the loan by means of 15 semi-annual payments of R2 $00, starting 6 months from now. Interest is charged at 16% pa. compounded quarterly 5.2.1 Show that the semi-annual interest rate is 16,32% p.a, B) 5.2.2 Calculate the value of the loan. «@ 1s} Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics PL ‘September 2021 QUESTION 6 61 Given: f(x)=3x? -2 Determine f(x) from FIRST PRINCIPLES. Determine 621 f(x) if f(x) =3x7 -Sx In the diagram, the graphs of f(x tbr? +ex+d and g(x)=2x are drawn, The graph of f passes through the x-axis at x= Vand x=3. A and B are the turning points of £ Pisapoint on fand Q isa point on g such that PQ is perpendicular to the x-axis.x, < 0 Show that f(x)=.° -2x° ~Sx+6 Q) 8) Caleulate the x-coordinate of B. ‘A tangent to f has a gradient of 1, Explain why the point of contact of the tangent and the graph of f lies between A and B. a @ ©) 13} For which values of x will fe concave up? Determine the maximum length of the line PQ. lease tur over Copyright reserved Wiskunde VI September 25 VRAAG 6 6.1 Gegee: f(x) =3x°-2 Bepaal f(x) vanuit EERSTE BEGINSELS. Bepaal 6.21 fix) as f(x) =3x" 5x 622 D, =a | VRAAG7 In die diagram is die graficke van f(x)=x' +bx? +cr+d en g(x)=2x geskets, Die x-afinitte van f is x= -2,x=1en x=3. A en B isdie draaipunte van f- Pis ‘n punt op f en Qis'n punt op g sodat PQ loodreg op die.x-as is. x, <0. Toonaandat f(x)= x? -2x*~Sx46 2 Bercken die x-kodrdinaat van B. GB) “n Raaklyn aan f het ‘n gradiént van —1. Verduidelik waarom dic. ‘Taakpunt van die raaklyn en die grafick van f tussen die punte A en B sal lé. a) ‘Vir watter waardes van.x sal f konkaaf op wee Q Bepaal die maksimum lengte van die lyn PQ. (6) 113] Kopiereg veorbchow Blasi om assebliet

Downloaded from hlayiso.com Wiskunde V1 September 2021 at VRAAGS. oe Dic wins van ‘n taxi is athanklik van die spoed waarteen die voertuig gery word. D ig gery Die wins (P) in rande per uuris bereken met die formule P = ape Poe —180, waar x die gemiddelde spoed in kilometer per uuris en x230. Bepaal: 8.1 Die spoed as geen wins gemaak word nie. @ 8.2 Die mees ekonomiese spoed met die ooreenstemmende wins per uur. @ 83. Die spoed waarteen die eienaar 'n verlies sal toon. e) 110) VRAAG 9 11236 Studente word gevra watter selfoon verskaffer hulle gebruik. Die uitslag word in die tabel vertoon, Ifoon verskaffer | Manlik | Vroulik ‘Vodacom 48 2 N 40 34 CellC 32 30 Total 120 116 [236 _| 9.1.1 Indie g isse Manlike en Vodacom onderling ? Motiveer jou antwoord. 2) 9.1.2 Wat is die waarskynlikheid dat ’n student wat willekeurig gekies word, manlike is en Vodacom as verskaffer sal gebruik? a) 9.1.3 Bewys dat manlike studente en Vodacom nie onafhanklik van mekaar is nie. (3) 9.2 Beskou die woord STAPLED. AAs die letters lukraak gekies word en al die leters word gebruik, bepaal die ‘waarskynlikeid dat die nuwe word met ’n klinker sal begin en eindig, @) 93 Die getalle 0, 1,2,3, 4, 5 en.6 word gebruik om 'n drie syfer kode te maak. 9.3.1 Hoeveel unieke kodes kan gevorm word as die getalle herhaal mag word? @) 9.3.2 Hoveel unieke kodes kan gevorm word as die getalle nie herhaal mag word nie? (2) 9.3.3 As die getalle herhaal mag word, hoeveel unicke drie syfer kodes kan gevorm word ‘wat groter as 300 en deelbaar deur 5 is? Q U5) TOTAAL: 150 Kopiereg voorbehou STEEPED ERENT RTE CMEC Mathematies PL NSC QUESTION 8 The profit made on a tax is dependent on the average speed at which itis being driven The profit (P) in rands per hour is calculated from the formula P= +6x-180, where « is the average speed in kilometres per hour and x 230 Determine: 8.1 The speed at which no profit is yielded. @) 8.2, The most economical speed and the corresponding profit per hour. @) 8.3. The speed at which the owner will show a loss. ® [10] QUESTION 9 9.1 236 Students were asked which cellphone provider they use, The results are shown in the table Cellphone provider [Male Total Vodacom [48 100 [sow 40 34 74 CellC 32 30 2 Total 120 16 236_| 9.1.1 Are the events Male students and Vodacom mutually exclusive? Justify your answer, 2) 9.1.2 What is the probability that a student chosen at random will be Male and use ‘Vodacom as a service provider? o) 9.1.3 Prove that the Male students and Vodacom are not independent. i) 9.2 Consider the word STAPLED. Ifthe leters are randomly selected, and all letters are used, what is the probability that the new word would start and end with a vowel ) 93 The numbers 0, 1, 2,3,4, 5 and 6 are used to forma three digit code. 9.3.1 How many unique codes ean be formed if the numbers may be repeated? 2 9.3.2. How many unique codes can be formed ifthe numbers may not be repeated? (2) 9.3.3 In the case where the digits can be repeated, how many 3 digit codes formed are ‘numbers that are greater than 300 and exactly divisible by $? Q) 115) TOTAL: 150 Copyright reserved