Mathematical Literacy Grade 11 P1 KZN November 2018 Memo

MARKS: 150 TIME: 3 hours Copyright reserved basic education > y Department: x () Basic Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P1 NOVEMBER 2018 This question paper consists of 8 pages. A 014000 Please turn over

Mathematics/P1 Downloaded from hlayiso.com 2 DBE/November 2018 CAPS ~ Grade II INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. I. Bs 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. lial CCNA TA A Please aun over

Mathematics/P | Downloaded from hlayiso.co 3 CAPS — Grade 11 QUESTION 1 Ll 1.4 Solve for x in each of the following: Ltd x(2x+1)=0 1.1.2 5x? +2x-6=0 (correct to TWO decimal places) 1.1.3 2x? -2 = 3x 3 14 f2x+5- =-2 2x+5 Solve for x and y simultaneously: y+x=2 and x +3xy+8=0 4+ /16-4m(-m+ 5) The roots of the equation f(x) =0 are x= 5 mM Determine the values of m for which the roots will be non-real. Show that the maximum value of V—x? +4x412 is 4. QUESTION 2 2.) 2.2 Simplify fully, WITHOUT using a calculator: Solve for x: 291 2-16x? =0 22.2 4° +8 =9,2" 2.2.3 9 =243 Simplify fully: Jp? -¢ x(p+q) if peq (p-a)s Cony I m DBE/November 2018 Please turn over (6) (4) (4) [29] (4) (4) (3) (3) 17]

Downloaded from hlayiso.com Mathematics/P 1 DBE/November 2018 CAPS — Grade 11 QUESTION 3 3.1 Given the linear pattern: 7;2;-3;... 31,1 Determine the general term, 7, , of the linear pattern. (2) 3.1.2 Calculate the value of 7,, . Q) 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) 19] 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) 4.3 Determine the value of # if 7, =232. (4) 4.4 If the sum of two consecutive terms in the pattern is | 227, calculate the difference between these two terms. (5) [16] Cappnightxesnana HOTTA EAR Ps term over

Downloaded from hlayiso.com Mathematics/P 1 5 DBE/November 2018 CAPS = Grade 11 QUESTION 5 Given: f (x)= 4 +2 and g(x)=x+2 x-3 5.1 Write down the equations of the asymptotes of f. (2) oa Determine the x-intercept of (3) 53 Determine the y-intercept of (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) 55 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 $ s+2<x+2. (2) x- 2) 5.7 The line y=x—1 cuts f at P(1;0) and Q, Write down the coordinates of Q. (3) [21] Copyrighted NUT UAT A AA ANE Pease ermover

Downloaded from hlayiso.com Mathematics/P | 6 DBE/November 2018 CAPS — Grade 11 QUESTION 6 xt] The diagram below shows the graphs of f(x) = -(x - 3y +25 and g(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 \ 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 f. (1) 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 f. (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] Conon esr AN) eM

Downloaded from hlayiso.com Mathematies/? 1 7 DBE/November 2018 CAPS — Grade 11 QUESTION 7 Bl 7.2 13 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. Nhlanhla 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. 731 Calculate how much Nhlanhla had in this investment account 2 years after the initial deposit was made. 7.3.2 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 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. Peasihebosere=t INIA A AA HY Piste over (3) (4) [13] () (4) (4) 19]

Downloaded from hlayiso.com Mathematics/P 1] QUESTION 9 8 CAPS —Grade 11 DBE/November 2018 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] Comat NTA 0 0 TOTAL: 150

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Downloaded from hlayiso.com Mathematios/P1/MFiskunde FE CAPSIKABY 3 DBE/Noveniber 2018 Grade/Graad 11 ~ Marking Guidelines/Nasienrigh ne [LLay pee 8 j aet fx +5 Let j2x+5 =k —— Y2x45 = no solution OR/OF =-2 -3a-2 k -3=-2k k*+2k-3=0 (k+3)(k-1)=0 | k=-3 owof k=l i \y2rt5 = ; 2x45 =1 nosolution orloft 2x+5=1 ax= | xy=-2 1 OR/IOF | \2xe3 -2=-2 fxe5 - +5 F-s=-2Jax45 ( (2x +5 3 ((2e +5 +3) (2e 45 ~t- 0 y2x45 =-3 or f2r45 =i orfof V2 +5 =I 2x+5=1 2x=-4 =-2 BEPARRIING OF SRS (roe BOUC ATION SS f [one PRUATE was aba PETS GOST 208 -11- 18 APPROVED MARKING GUIDELINE PUBLIC EXAMINATION “changing to quadratic! A verander na kwadraties ¥ factors or using formula! CA faktore of gebruik formule Yk=3 orlofk= cA Yno solution’ geen oplossing ¥ square both sides/ On kwadreer beide kanve — (f\ vo y=-2 10) V changing to quadratic/ verander na lnvadraties 6 akt. 2x +5 =—-Jorlof (2x +5 =1 ¥ no solution/ geen oplossing square both sides/ howadreer beide kante v x=-2 ©) Mathematios/P 1/Wiskunde Ft 4 DBE/November 2018 CAPS/KABY ~ Grade/Graad 11 - Marking Guidelines/Nasienrighne Qe 5 - a = -2 V2x+5 2x+5-3=-2V2x+5 2x42=-2y2x+5 4x7 +8r4+4=4(2r45) 4x? +8r4+4=8x420 (2x42) =(-2V2e+5) V2x45/ “square both sides/ kwadreer beide kante ¥ Multiplying by/ Vermenigy. met x? 43x(2-x) +8=0 x? +6x-3x" +8=0 2x7 +6x+8=0 x’ —3x-4=0 (x-4)(x+1) <0 v y=2- Y¥ substitution/ver A CA On Y std form/stand. vorm Yfactors or using formula’ Cf\ faktore of gebruik formule Y both x-values/urdes OA Y both y-valueshvrdes (f\ fx rie=t ¥ sid form! vorm vo4s “ead fo (x+2)-2)=0 V factor rs/faake. xa-2 orlof x#2 x#2 — ¥ x=-2 (6) {2 yrx=2 anden x° +3xy+8=0 o ys2~a PRIVATE AAG X285, PETORIA 6607 2018 -11- 18 APPROVED MARKING GUIDELINE PUBLIC EXAMINATION OR/OF (6) yrxra2 and x? +3xy+8=0 i oxe2-y Vxs2-y f | Q — yf +3(2—y) yp +8=0 ¥ substitution/very, 4-Ay+y' +6y-3y? +8=0 -2y?+2y412=0 “std form/stand, vorm y-y-6=0 (y-3)(y+2)=0 ¥ factors or using formula/ y=3or y=-2 faktore of gebruik formule ~2-3 or x=2-(2) Y both y-values/wrdes gt or aed “both x-values/wrdes (6) (DEPART OE YS AF BASES | ' EDUCATION H

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Downloaded from hlayiso.com ES eave il MATHEMATICS Mathematics/P L/Iistunde V1 DBE/November 2013 CAPS/KABI’— Grade/Graad 11 — Rigi GuidelinestNastenrighne NOVEMBER 2018: PAPER 1 ADDENDUM TO THE MARKING GUIDELINES These notes have been created to provide options that learners may use and the appropriate mark QUESTION/VRAAG 9 allocation for their answers. j 91 P( V) x P(M} A | | 32 «67 yo) BO 1.12] CA onxifincorrect formula. Only accept the following as incorrect formula: ] i | 22x24 = 0,095 jut? al ee vee = al ne | 150 150 2 an (bre A parte , Le. negative sign omitted before 6 or wa GEM » Le, incorrect hawt | P(Wand/en M)= 750028 A | sign che root. | | P(Vand/en M) # PC V) x P(M) ¥ PCV) xP(M)=0,095 -b+ Jo? + 400 | © SL mark for correct value of answer at | Hoeven Aa a8 + Penalty -1 for incorrect rounding | The events are not independent/Die gebeurtenisse is nie onafhanklik 7 taster ole 1.1.3] IFNO factors shown, the factors marks can be awarded for the absolutely correct critical i i HEN EV18 (s) | | values in the answer. If NO factors shown, no marks for incorrect answer. | OR/OF __ cA * Final answer marks cannot be spilt into critical values and notation. It is a combinati | - | PEO 2 mark for reading the correct interval —~——4 aoc ascrcr ee vo . lo Is wi PCV) x P(E) PRIVATE BAG E85, PRETORIA dOOT 150 «xs - j x22. Accept as correct ; in the place of or: 4 marks | g ls | 33 83 orig 2018 -11- 18 83 1 a8 Bet KAY] | 150% 150 7° —_— . 150 © xS-= and x22 + maximum 2 marks Inzi2 eo 3/8 { 0 APPROVED MARKING GUIDE! YPC V)x P(E) =0,118 2 ooe — ais NE =01 pate § | - YPC and F)=0,133 | A tals ali i | P(Vand F)# P( V) x P(F) (V and F) = 0, 1.1.4 ¢ Ifno factors are shown, then award 2 marks for the correct values of &. ie is an v ionreeiolal | ¢ B/D ifeach term is squared independent! z Bld The events are not independent/Die gebeurtenisse is nie onafhanklik | “ Conctuston/gey oe i | eee aid WS |G oR se | s 5 ae “| ebead | ‘= le om<4 or m>1 orm<4 m>1:award3 marks Bue 9.2.1 | P(Aand/enB)=0,12#0 vP(Aand B)eo A 3.1.2 | CA from 3.1.1 provided that Ty is linear. Y conclusion/gevolgir, |/\ | 3:13 [+ CA from 3.1.1 provided that Ty is linear. Events are not mutually exclusive’ Gebeurtenisse nie onderling (2) * IfCA from 3.1.1 results inn not being an integral value and candidate goes on to reject uitsluitend nie this value of n, then award 2 marks. — ' — 3.1.4 | If first differences are incorrect, then CA applies. 9.2.2 | P(AorB)= P(A)+P(B)— P(A and B) ain | | 4.2 1 3 | ~ | eleesns2: 0,83 = P(A) + 4(A)—0,12 BAe = 4 pyar or / ¥ formula! formule A Answer only 7, gt tyat 2: 1 mark for final answer only | 0,95 = 5P(A) , fee Y substitution/very, A 43 |* CA fom42 P(A) = 0,19 tm © Answer only n= 20: 1 mark for final answer only ae P(A) ca 44 [e° CA from 42 P(B) = 4(0,19) = 0,76 —_—— v (8) e : 7a © If Trial and error used and arrive at T,, -Tiy = 35 : award $ marks (4) [+ Answer onl y 35: | mark for final answer only 9.23 tA)=1— =a P(not A) =1-P(A) v P(nat A) =1-P(a) 5.2. ] + Simplification mark is awarded for any of the 2, 3" or 4 line in the memo. =1-0,19 A ( yn tee @ ‘No penalty if answer not given iw‘cbordinate form =0,81 Yanswer/andw. Or e Answer only (1 ; 0): award 3 marks tis! ¢ Answer only x = 1: award 2 marks 13] 33 [FT sie only (0 : 3) z award 2 marks | ai TOTAL/TOTAAL: 150 5.4 |-Shape mark is awarded if 2 parts to hyperbola, a decreasing function and not touching asymptotes 5.6°_| CA from 5.1 and 5.5 for critical values / I Phe oO

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