Mathematics Grade 11 P1 Eastern Cape November 2018 QP (Eng)

Downloaded from hlayiso.com basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 11 ee a Ce ee a ee i MATHEMATICS P1 i" " Hw : NOVEMBER 2018 7 PTT TTTITTTCTTPTITrrrrererrer ees MARKS: 150 TIME: 3 hours This question paper consists of 8 pages. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 2 DBE/November 2018 CAPS — Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of NINE questions. Answer ALL the questions. Number the answers correctly according to the numbering system used in this question paper. 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 and non-graphical), unless stated otherwise. Round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 3 CAPS — Grade 11 QUESTION 1 Ll 1.2 Solve for x and y simultaneously: ytx=2 and x?+3xy+8=0 1.3 The roots of the equation f(x)=0 are x= 44 Vl6=4m(=m +5) ae) m Determine the values of m for which the roots will be non-real. 14 Show that the maximum value of V—x?+4x+12 is 4. QUESTION 2 oy . 233,29 2.1 Simplify fully, WITHOUT using a calculator: “———-— 2.2 Solve for x: 2.2.1 2-16x? =0 2.2.2 4 4+8=9.2* 2.2.3 9 =243 2.3 Simplify fully: 5 2_ 2 2 \P-4 *(p+4) if peq (pq) Solve for x in each of the following: 11d x(2x+1)=0 1.1.2 5x? +2x—6=0 (correct to TWO decimal places) 1.1.3 2x? -2 >3x 3 f2x+5- =-2 Copyright reserved DBE/November 2018 Please turn over 2) G3) (4) (6) (6) (4) (4) [29] ) (3) (4) (3) (3) [17]

Downloaded from hlayiso.com Mathematics/P1 4 DBE/November 2018 CAPS — Grade 11 QUESTION 3 3.1 Given the linear pattern: 7; 2;-3;... 3.1.1 Determine the general term, 7,,, of the linear pattern. (2) 3.1.2 Calculate the value of T7,, . (2) 3.1.3 Which term in the pattern has a value of —138? (2) 3.2 6; 2x+1 and 3x—3 are the first three terms of a linear pattern. Calculate the value of x. (3) [9] QUESTION 4 The quadratic number pattern: 4; p;11;q; 22; ... has a constant second difference of 1. 4.1 Show that p=7 and q=16. (3) 42 Determine the general term, 7,,, of the quadratic pattern. (4) 43 Determine the value of n if 7, =232. (4) 44 If the sum of two consecutive terms in the pattern is 1 227, calculate the difference between these two terms. : (5) [16] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 5 DBE/November 2018 CAPS — Grade 11 QUESTION 5 Given: fx)=— 42 and g(x)=x+2 x- 5.1 Write down the equations of the asymptotes of f. (2) 5.2 Determine the x-intercept of f (3) 5.3 Determine the y-intercept of f (2) 5.4 Sketch the graphs of f and g on the same system of axes. Show clearly ALL the intercepts with the axes and any asymptotes. (5) 5.5 Calculate the x-coordinates of the points of intersection of f and g. (4) 5.6 If x <3, determine the values of x for which 4 +2<x42, (2) x- 5.7 The line y=x—1 cuts f at P(1;0) and Q. Write down the coordinates of Q. (3) [21] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 6 DBE/November 2018 CAPS — Grade 11 QUESTION 6 xtl The diagram below shows the graphs of S(x)= (x _ 3 425 and e(x) _ 5) 4. Graph f cuts the x-axis at A and C, the y-axis at E and has a turning point at D. Graph g cuts the x-axis at A and the y-axis at B. y D 6.1 Write down the equation of the asymptote of g. (1) 6.2 Write down the coordinates of D. (2) 6.3 Write down the range of /. a) 6.4 Calculate the length of EB. (4) 6.5 Determine the values of x for which / is decreasing. (2) 6.6 Calculate the average gradient between points A and B. (5) 6.7 Graph ¢ is obtained by reflecting g about the x-axis. Write down the range of ¢. (2) 6.8 If p(x) = f(x) +2, write down the coordinates of the turning point of p. (2) 6.9 Determine the value of & for which the straight line y=2x+k will be a tangent tof (4) [23] Copyright reserved Please tun over

Downloaded from hlayiso.com Mathematics/P1 7 DBE/November 2018 CAPS — Grade 11 QUESTION 7 71 7.2 73 Calculate the effective interest rate per annum if an investment earns interest at a rate of 11,5% p.a., compounded monthly. Karabo bought a computer for R4 700. The value of the computer depreciated at a rate of 18% p.a. Using the reducing-balance method, calculate the book value of the computer 4 years after it was bought. Nhianhla made an initial deposit of R20 000 into an investment account that paid interest at the rate of 7,2% p.a., compounded quarterly. After 2 years the interest rate changed to 7,8% p.a., compounded monthly. Four years after his initial deposit, Nhlanhla withdrew R2 500 from his investment. 7.3.1 Calculate how much Nhlanhla had in this investment account 2 years after the initial deposit was made. 73.2 How much will the investment be worth 7 years after the initial deposit was made? QUESTION 8 A bag contains 6 red balls, 8 green balls and an unknown number of yellow balls. The probability of randomly choosing a green ball from the bag is 25%. 8.1 8.2 8.3 Show that there are 32 balls in the bag. A ball is drawn from the bag, the colour is recorded and it is not returned to the bag. Thereafter another ball is drawn from the bag, the colour is recorded and it is also not returned to the bag. Draw a tree diagram to represent ALL the possible ways in which the two balls could have been drawn from the bag. Show the probabilities associated with EACH branch, as well as the outcomes. Calculate the probability that the two balls drawn from the bag will have the same colour. Copyright reserved Please turn over GB) (3) 3) (4) [13] qd) 4) (A) [9]

Downloaded from hlayiso.com Mathematics/P1 8 DBE/November 2018 CAPS — Grade 11 QUESTION 9 9.1 On a flight, passengers could choose between a vegetarian snack and a chicken snack. The snacks selected by the passengers were recorded. The results are shown in the table below. SNACK MALE | FEMALE | TOTAL Vegetarian 12 20 32 Chicken 55 63 118 TOTAL 67 83 150 Was the choice of snack on this flight independent of gender? Motivate your answer with the necessary calculations. (5) 9.2 For any two events, A and B, it is given that P(A and B) = 0,12, P(A or B) = 0,83 and P(B) = 4 P(A). 9.2.1 Are events A and B mutually exclusive? Justify your answer. (2) 9.2.2 Calculate P(B). (4) 9.2.3 Calculate P(not A). (2) [13] TOTAL: 150 Copyright reserved

— Downloaded from hlayiso.com____ ~~ basic education UE. ilaca\s Department: (G) Basic Education IW REPUBLIC OF SOUTH AFRICA NASIONALE SENIOR SERTIFIKAAT GRAAD 11 a WISKUNDE V1 iF i NOVEMBER 2018 7 PUNTE: 150 TYD: 3 uur Hierdie vraestel bestaan uit 8 bladsye. Kopiereg voorbehou Blaai om asseblief

Downloaded from hlayiso.com Wiskunde/V1 2 DBE/November 2018 KABV — Graad i1 INSTRUKSIES EN INLIGTING Lees die volgende instruksies aandagtig deur voordat jy die vrae beantwoord. 1. 2. Hierdie vraestel bestaan uit NEGE vrae. Beantwoord AL die vrae. Nommer die antwoorde korrek volgens die nommeringstelsel wat in hierdie vraestel gebruik is. Dui ALLE berekeninge, diagramme, grafieke, ens. wat jy gebruik het om die antwoorde te bepaal, duidelik aan. Volpunte sal nie noodwendig aan slegs antwoorde toegeken word nie. Jy mag 'n goedgekeurde wetenskaplike sakrekenaar (nieprogrammeerbaar en niegrafies) gebruik, tensy anders aangedui. Rond antwoorde tot TWEE desimale plekke af, tensy anders aangedui. Diagramme is NIE noodwendig volgens skaal geteken NIE. Skryf netjies en leesbaar. Kopiereg voorbehou Blaai om asseblief

Downloaded from hlayiso.com Wiskunde/V1 3 DBE/November 2018 KABV - Graad 11 VRAAG 1 11 Los op vir x in elk van die volgende: Ll x(2x+1)=0 1.1.2 5x? +2x—6=0 (korrek tot TWEE desimale plekke) 1.13 2x? 2 > 3x 3 f2xt+5— =-2 114 a 2x45 1.2 Los gelyktydig op vir x en y: ytx=2 en x°4+3xy+8=0 44 /16—4m(—m +5) 1.3 Die wortels van die vergelyking /(x)=0 is x= Om Bepaal die waardes van m waarvoor die wortels nie-reéel sal wees, 1.4 Toon dat die maksimum waarde van Vox 44x412 » 4 is. VRAAG 2 21 Vereenvoudig volledig, SONDER om 'n sakrekenaar te gebruik: a 22 Los op vir x: 2.24 2-16x? =0 2.2.2 4° +8=9.2* 2.2.3 9 =243 2.3 Vereenvoudig volledig: 2 2 3 VP eee as p¥q Kopiereg voorbehou Blaai om asseblief (2) (3) (4) 6) (6) (4) (4) [29] (4) (3) (4) (3) (3) [17]

Downloaded from hlayiso.com Wiskunde/V 1 4 DBE/November 2018 KABV — Graad 11 VRAAG 3 3.1 Gegee die liniére patroon: 7 ;2;-3;... 3.1.1 Bepaal die algemene term, 7,,, van die liniére patroon. (2) 3.1.2 Bereken die waarde van T,, . (2) 3.1.3 Watter term in die patroon het 'n waarde van —138? (2) 3.2 6; 2x+1 en 3x~3 is die eerste drie terme van 'n liniére patroon. Bereken die waarde van x. @) 19] VRAAG 4 Die kwadratiese syferpatroon: 4; ; 11;q;22;... het 'n konstante tweede verskil van 1. 4.1 Toon dat p=7 en g=16. (3) 42 Bepaal die algemene term, 7, , van die kwadratiese patroon. (4) 43 Bepaal die waarde van n as T, =232. (4) 4.4 Indien die som van twee opeenvolgende terme in die patroon 1 227 is, bereken die verskil tussen hierdie twee terme. (5) [16] Kopiereg voorbehou Blaai om asseblief

Downloaded from hlayiso.com Wiskunde/V1 5 DBE/November 2018 KABV -Graad 11 VRAAG 5 Gegee: Fls)-—4 42 en g(x)=x+2 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Skryf die vergelykings van die asimptote van f neer. Bepaal die x-afsnit van f. Bepaal die y-afsnit van f Skets die grafieke van f en g op dieselfde assestelsel. Toon duidelik AL die afsnitte met die asse en enige asimptote. Bereken die x-koérdinate van die snypunte van f en g. +2<x+2. Indien x <3, bepaal die waardes van x waarvoor x- Die lyn y=x—1sny f by P(1;0) en Q. Skryf die kodrdinate van Q neer. Kopiereg voorbehou Blaai om asseblief (2) @) (2) 6) (4) (2) )) [21]

Downloaded from hlayiso.com Wiskunde/V1 6 DBE/November 2018 KABV -Graad 11 VRAAG 6 x41 Die diagram hieronder toon die grafieke van f(x)=-(x-3) +25 en g(x)= 5) -4. Grafiek f sny die x-as by A en C, die y-as by E en het'n draaipunt by D. Grafiek g sny die x-asby A endie y-as by B. y i \ 6.1 Skryf die vergelyking van die asimptoot van g neer. qd) 6.2 Skryf die kodrdinate van D neer. (2) 6.3 Skryf die waardeversameling van f neer. dd) 6.4 Bereken die lengte van EB. (4) 6.5 Bepaal die waardes van x waarvoor f afneem. (2) 6.6 Bereken die gemiddelde gradiént tussen punt A en B. (5) 6.7 Grafiek + word verkry deur g om die x-as te reflekteer. Skryf die waardeversameling van f neer. @) 6.8 Indien p(x) = f(x)+2, skryf die kodrdinate van die draaipunt van p heer. (2) 6.9 Bepaal die waarde van & waarvoor die reguitlyn y=2x+k 'n raaklyn aan f sal wees. (4) [23] Kopiereg voorbehou Blaai om asseblief

Downloaded from hlayiso.com Wiskunde/V1 7 DBE/November 2018 KABV ~ Graad 11 VRAAG 7 7A Bereken die effektiewe rentekoers per jaar indien 'n belegging rente verdien teen 7.2 73 'n koers van 11,5% p.j., maandeliks saamgestel. Karabo het 'n rekenaar vir R4 700 gekoop. Die waarde van die rekenaar het teen 'n koers van 18% p,j. verminder. Gebruik die verminderdesaldo-metode en bereken die boekwaarde van die rekenaar 4 jaar nadat dit gekoop is. Nblanhla het 'n aanvanklike deposito van R20 000 in 'n beleggingsrekening gemaak wat rente betaal het teen 'n koers van 7,2% p,j., kwartaalliks saamgestel. Die rentekoers het na 2 jaar verander na 7,8% p,j., maandeliks saamgestel. Nhlanhla het 4 jaar na sy aanvanklike deposito R2 500 uit sy belegging onttrelk. 7.3.1 Bercken hoeveel Nhlanhla in hierdie beleggingsrekening gehad het 2 jaar nadat die aanvanklike deposito gemaak is. 7.3.2 Hoeveel sal die belegging werd wees 7 jaar nadat die aanvanklike deposito gemaak is? VRAAG 8 'n Sak bevat 6 rooi balle, 8 groen balle en 'n onbekende aantal geel balle. Die waarskynlikheid dat 'n groen bal willekeurig uit die sak gekies sal word, is 25%. 8.1 8.2 8.3 Toon dat daar 32 balle in die sak is. ‘n Bal word uit die sak gehaal, die kleur word aangeteken en dit word nie in die sak teruggesit nic. Daarna word nog 'n bal uit die sak gehaal, die kleur word aangeteken en dit word ook nie in die sak teruggesit nie. Teken 'n boomdiagram om AL die moontlike maniere waarop die twee balle uit dic sak gehaal kon word, voor te stel. Toon die waarskynlikhede wat met ELKE tak, asook die uitkomste, geassosieer word. Bercken die waarskynlikheid dat die twee balle wat uit die sak gehaal is, dieselfde kleur sal hé. Kopiereg voorbehou Blaai om asseblief @) (3) (3) (4) {13] (1) @) @) [9]

Downloaded from hlayiso.com Wiskunde/V1 8 DBE/November 2018 KABV — Graad 11 VRAAG 9 9.1 Passasiers kon op 'n vlug tussen 'n vegetariese peuselhappie en ‘'n hoenderpeuselhappie kies. Die peuselhappies wat die passasiers gekies het, is aangeteken. Die resultate word in die tabel hieronder getoon. PEUSELHAPPIE | MANLIK | VROULIK | TOTAAL Vegetaries 12 20 32 Hoender 55 63 118 TOTAAL 67 83 150 Was die keuse van peuselhappie op hierdie vlug onafhanklik van geslag? Motiveer jou antwoord met die nodige berekeninge. (5) 9.2 Vir enige twee gebeurtenisse, A en B, word gegee dat P(A en B) = 0,12, P(A of B) = 0,83 en P(B)= 4 P(A). 9.2.1 Is gebeurtenisse A en B onderling uitsluitend? Regverdig jou antwoord. (2) 9.2.2 Bereken P(B). (4) 9.2.3 Bereken P(nie A). (2) [13] TOTAAL: 150 Kopiereg voorbehou