Mathematics Grade 11 Paper 1 KZN November 2016 Paper & Memo

MARKS: 150 f ) TIME: 3 hours Copyright reserved basic education Department: Basic Education -. NATIONAL ~ SENIOR CERTIFICATE GRADE I1 This question paper consists of 9 pages. NI. 0 REPUBLIC OF SOUTH AFRICA QAP RRP SSAA RS SRR RRR RRR RRR RY | u MATHEMATICS P1 t 1 i NOVEMBER 2016 " Please turn over eer eS SIa NNT Lo

Mathematics/P1 2 DBE/November 2016 CAPS ~ Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. Ll: 2. 3. This question paper consists of 10 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 et cetera 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. If necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. Write neatly and legibly. Conyright reserved UNA AA A Please tn over

Mathematics/P 1 3 DBE/November 2016 CAPS ~ Grade 11 QUESTION 1 Ld Solve for x in each of the following: | inn 3x? —-5x~-1=0 (leave your answer correct toT WO decimal places) (3) 1.1.2 x? -6x+8 =0 @) 1.1.3 4x-2x" <0 (4) Li4 244 26 = 12 (4) 1.1.5 Vx-1+3=x-4 ©) () 1.2 Solve for x and y simultaneously: 3x-y+2=0 and y=—-x? +2x+8 (6) 13 Show that the roots of 3x? +(k+2)x=1—k are real and rational for all values of &. (4) [30] QUESTION 2 21 Simplify fully, WITHOUT using a calculator: 5-2 . gute J 5 21.41 10°—-10°".2 ©) ) 27m? —V48m' a2 Ls (3) 12m® 2.2 WITHOUT using a calculator, show that 28 =-2 (4) , 1+v2 V8 [12] Comittee Please turn over

Mathematics/P1 4 DBE/November 2016 CAPS - Grade 11 QUESTION 3 Consider the quadratic pattern: -9;-65;1;12;%5... 3.1 Determine the value of x. (1) 3,2 Determine a formula for the 2” term of the pattern. (4) 33 A new pattern, P,, is formed by adding 3 to each term in the given quadratic pattern. Write down the general term of P, inthe form P, = an’ +bn+e. 65) 3.4 Which term of the sequence found in QUESTION 3.3 has.a value of 400? tio) QUESTION 4 C 41 Given the linear pattern: 18; 14;10;... 41.1 Write down the fourth term. qd) 4.1.2 Determine a formula for the general term of the pattern. (2) 4.13 Which term of the pattern will have a value of — 70? @) 4.14 If this linear pattern forms the first differences of a quadratic pattern, Qn determine the first difference between Qso9 and Qsio. (2) 42 A quadratic pattern has:a constant second difference of 2 and 7; =T, = 29, 4.2.1 Does this pattern have a minimum or maximum value? Justify the ( \ answer. 3). 4.2.2 Determine an expression for the n term in the form T, =an’ +bnte, (5) [5] Conyright reserved INU AE AL AA Please tm over

7) Mathematics/P1 5 DBE/November 2016 CAPS ~ Grade 11 QUESTION 5 Given: f(x) = 2x +x4+6 5.1 5.2 5.3 5.4 5.5 5.6 Calculate the coordinates of the turning point of f, Determine the y-intercept of f Determine the x-intercepts of f. Sketch the graph of f showing clearly all intercepts with the axes and turning point. Determine the values of k such that fx) =k has equal roots. If the graph of f is shifted two units to the right and one unit upwards to form h, determine the equation A inthe form y= a(x+ p)’ +q. Conyright reserved NOTA E A Please tam over i) (1) (4) (3) (2) G3) [17]

Mathematies/P 1 6 DBE/November 2016 CAPS ~ Grade tl QUESTION 6 The diagram below shows the graph of f(x) = 5 ~ 1 and g(x) oye x: The graph of f intersects the x-axis at A and the y-axis at B. The graph of f and g intersect at points C and D. P A fe) x Cc B f an ( Dd & 6.1 Write down the equations of the asymptotes of /- (2) 6.2 Determine the domain of f (2) ( , 6.3 Calculate the length of: 6.3.1 OB 2) 6.3.2 OA (3) 6.4 Determine the coordinates of C and D. (6) ____ 6.5 Use the graphs to obtain the solution to: 5 > a (4) x3 , ee as [19] Copyright resrved NEAT AAT Please rum over

Mathematics/P1 7 DBE/November 2016 CAPS ~ Grade 11 QUESTION 7 The sketch below is the graph of f(x) =2.b°"' + q. The graph of f passes through the points A(1 ;20) and B (-1;y). The line y=2 is an asymptote of f- y ACL; 20) B(-1;y) asin nce 2 x 4 a > 7A Show that the equation of f is f(x)=2(@)"" +2 7.2 Calculate the y-coordinate of the point B. 73 Determine the average gradient of the curve between the points A and B. 74 A new function / is obtained when / is reflected about its asymptote. Determine the equation of A, 75 Write down the range of , Copyniget reserved UNCAATAR A Please turn over B) (1) (2) @ (t) 19}

Mathematics/P! 8 DBE/November 2016 CAPS ~ Grade 11 QUESTION 8 8.1 A machine costs R25 000 in 2016. Calculate the book value of the machine after 4 years if it depreciates at 9% p.a, according to the reducing balance method. 3) 8.2 The nominal interest rate of an investment is 12,35% p.a., compounded monthly. Calculate the effective interest rate. (4) 8.3 ‘The value of a property increased from R145 000 to R221 292,32 over 6 years. Calculate the average annual rate of increase of the property over 6 years. 4) 8.4 Tebogo made an initial deposit of R15 000 into an account that paid interest at 9,6% p.a., compounded quarterly. Six months later she withdrew R5 000 from the account. Two yeats after the initial deposit she deposited another R3 500 into this account. How much does she have in the account 3 years after her initial deposit? (5) QUESTION 9 91 Given: 9A 9.1.2 [16} P(A) = 0,2 ¢ ‘ P(B) = 0,5 P(AorB)=0,6 where A and B ate two different events Calculate P(A and B). (2) Are the events A and B independent ? Show your calculations. (3) 9.2. A survey was conducted amongst 100 learners at a school to establish their involvement in three codes of sport, soccer, netball and volleyball. The results are shown below. eensneee 55 learners play soccer (S) 21 learners play netball (N) "7 learners play volleyball (V) 3 learners play netball only 2 learners play soccer and volleyball 1 learner plays all 3 sports The Venn diagram below shows the information above. ( 9.21 9.2.2 Copyright reserved Determine the values of a, b, c, d and e. (6) What is the probability that one of the learners chosen at random from this group plays netball or volleyball? (2) AM OETTINAN|Pseve

C) Mathematics/P 1 9 DBE/November 2016 CAPS ~ Grade 11 9.3 The probability that the first answer in a maths quiz competition will be correct is 0,4. If the first answer is correct, the probability of getting the next answer correct rises to 0,5. However, if the first answer is wrong, the probability of getting the next answer correct is only 0,3. 9.3.1 Represent the information on a tree diagram. Show the probabilities associated with each branch as well as the possible outcomes. @) 9.3.2 Calculate the probability of getting the second answer correct. (3) [18] QUESTION 10 Bongani wants to start a small vegetable garden at his house. He wants to use an existing wall and 14 m of fencing to enclose a rectangular area for the garden. Calculate the dimensions of : the largest rectangular area that he can enclose. [4] | TOTAL: 150 Conese | NILH

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Mathematios/PL/Wiskunde VE 3 DBENovenber 2016 *__ CAPS/KABY — Grade/Graad 11 ~Memorandura 113 Option/Opsie 1 OR/OF ‘Option/Opsie 2 4x-2x* <0 4n—-2x? <0 —2x? +42<0 v 2x(2—x)<0 2x? -4x>0 ice ile method/mett x<Oorx>2 xQQx-4)>0 Wu <Oorx 22 x<9orx>2 2 Mosimum 2 for ® a incorect notation OR 3. Maksim 3 vi . verkeerde notasie Pe] 20 “et B-r9 ‘Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief Mathematics/P1/Piskunde Vi 4 DBE/November 2016 ‘CAPS/KABY — Grade/Graad 11 — ‘Memorandum H oe & ‘+ q = | ¥common/gemene factor : 2* 3512 H ¥ simplification/vereenv. | ¥ equating/gelpkst exponents ' | Y answerlantie, ® : Visolate/isoleer V signiteken i Fak -1F || Veguaring/owade both sides gala x? 140449 | x? 15 +50=0 , td vormistandvorm (e-5)(z-10) = 9 i es x#Sor x #10 i eate tO 12 By-y42=0 and sx? 42048 ! . i * H ov y= 3x42 ops 3xt2 OR i Bxt2=—x? 42x48 3x (a? t2e+8)+2=0 | | veubstitution/vervanging x’ +x-6=0 7 i (+3¥e—2)=0 | | std forméstand vorm 4 é=-T ote 2 \ ¥ factors{faktoré pH3-3}o2 or y=3(2)42 ! v‘x-values/x-waardes i = | 7 or ys | Vy -waun | © LS Sx" 4(k+2x=1-k 3x? HE EDE IEE =: ' VA Age AaB age | =(£+27-43) C144) | vs ‘substitution /vervanging =P 4 Ake 4412-12k | |" 8k H6 =k Bk +16 lve at eo | @ <b? —4ae is aperfect square. | Rootsare zealand sational. | 01 [ OSrARIMaNT SF Saas | EER PRON . Dey Copyright reserved/Kopieregvoorbehou BUBLIC EXGRUPLATEOR Btease turn ever!Blaai om asseblief

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DBE/November 2016 Mathematics/P L/Wiskunde VI 7 DBE/November 2016 ‘CAPS/KABV — Grade/Graad 11 ~Memorandum a i r 12 x NAN AON LON 4 3 7 IL 12 NZ N ZA NZ 4 #2 Vanswer/antw. — (1) a a a sae Ya=2 %be3 : Yea$ &; _ ~S3HRR VT, =2n? 32-8 . oa & Te: BR SH—S49 GA fen 3:2 Vanswerlantw. =2n*—3n-5 a5 34 T, = 400 — E 2n? —3n—5 =400 CA fim 33 ~ equating/verg. 2n* —3n-405=0 © std form/stand vorm (2-15K2n+27)=0 ¥ factorisation/falt. n=15 or at wn=15 OR @ ~ equating/verg. 2n® -3n-8+3=400 2 std form/stand vorm 2n? —3n-8=397 “factorisation/fakz. 20? ~3n—405=0 (n—-5)@n+27)=0 Yonly/ slegs n= 15 nelson neh i) 2 19} Copyright reserved/Kapieregvoorbehou Please turn over/Blaai om asseblief “Mathematics/P 1/Wiskunde VI CAPS/KABV —' GradeKGraad li- Menor QUESTION/IVRAAG 4 ail 18 14 10 | N ZAN 4 +4 1 1,=6 ' ~answer/antw. | Oy I 412 | F=a+(e-1 5 p= at (nla Answer only, full ¥ substitution/verv. =184(2-1(-4) marks/slegs | Y answerlantw. =—4n+22 antwoord volpunte I Q) qs] EoBada ¥ substitution/very, -10=22-4n Vanswer/ “poeta fantw. 223 | ® BLA! Osi — Qapy = Toy OF te linear sequence | ¥ making = 22-4x509 association/ass. =-2014 | answer/antw. | @) 421 saat T,= am*+bn +e Yo “valuefwrde of a 2aal Ya>0 .a>0 Y minimum = this patteon has a mininauza value/hierdic petrooa het ininimum wearde value/wrde The shape of the graph will be concave up / die vorm van die grofiekis Konkaafna bo | | & 422 | B=29 | 1.16) +5b+0=29 ; © je 5b+e=4... | and T, = 29 ¥~ equations/verg. & 2. 1G7P +17b+e 29 | £0) ie 17b+e=-260...2) solve the equations simultaneously | ¥ value offwaarde —12b = 264 van 5 “ 2 b=-22 substitute in (1) | fe 5(-22)-+e=4 | -1l0+e=4 | Y value offwaarde ne=ll4 van Pent 2 FE, =? -22n+14 ! ¥ answer/antwoord. I ORIOF DEPARTMENT OF BASIC! Copyright reserved/Kopieregvoorbehou PRIVATE BAG Koos, SopETGAA CoOT | [PANRIE SASSOON GearcaRGeeT | Please tum over/Blaai om asseblief

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i \ | j DBE/November 2016 vihen / warmer rel ys-} when/wanneer x =—4; y=—2 ae ed and D (-4;~2) ¥ x-values/waardes Mathematics/P1/Wiskande V7 2 CAPS/KABY ~ Grade/Graad 1] ~Memorandom 7 {631 AtB,x =0 1 | ¥ substituton/vervanging. yon3 -1 | ¥ answer/aniwoord. +r | aad | x 3 | op =? units | "—™ | ® I 6.3.2 AtA, y=0 i o=. i 1 i ¥ substitution/vervanging. x43 | — | x43 ' ¥ simplification/vereenv, x4351 | wan? |_| answer/antwoorde. -- OA = 2units/eenhede i @) . \ 64 1 1 |_| ¥ equating the two equations/ ga3 39% |__| verg: van 2 vergelykings 2-2 (x43) =x (x +3) | x? 43x-242x4+6=0 | ¥ standard form/std vorm | x? 45244=0 ' | ¥ factors/fakzore. (+4)@+1)=0 : x=-4 or/of x=—1 | | | ¥ co-ordinates/kodrdinate C ¥ co-ordinates! kodrdinate D © Mathematics UWiskunde V2 il DBE/November 2016 CAPS/KABY — Grade/Graad 11 ~Memorandum 53 x intercepts 0=~2x +246 vyn0 0=2x? -x-6 O= (x +3)(x-2) v & faciorisation/faktorisering. ox= Bex S- 5 2 v ¥ x-values/waardes 3 2:0) and |—=50 ct) ana (-3:0) @ 54 ¥ shape/vorm We imeteepisleysmille! z a omning pointdranipot é @) 5.5 49 vv answer/antwoorde. ko 8 @ 5.6 «, . 9 57 ¥ 7 tming ‘New/Niave tuning point/drpn.t (@ 3 2) pointdraput © ‘i equation/verg. = € Equation/verg. of hk OR/OF --f, 2) 57 vv¥¥ ensweronly (3) ya-Bx-t}] + 4) 8 . [£7] QUESTION/VRAAG 6 61 x=—3 and y=—i Yu=3 v y=-1 2) 6.2 xeR ,x¥—-3 ¥ ¥ answev/aniwoord, 2) Din | MB ite Ga Copyright reserved/Kopiaregvoorbehou | APPRGUEO Me Ryils Guns me | Please turn over/Blaai om asseblief i Dane nae Bare, Pale 20% -t- 44 Copyright reserved/Xopieregvoorbehow Dm

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DBE/November 2016 Mathematics/P1/Wiskunde ¥I 15, DBE/November 2016 CAPS/KABV — Grade/Graad 11 —- Memorandum oR ttt, 3 a y nas A=15006{1+ a , = RIS728,64 A at T,=R15728,64 -R5000 : ¥ RIO728,64 =R10728,64 T, to Ty 2 bes A= riers -2ey ¥ R12369,28 = R12369,28 Aat F, =R12369,28 + R3500 =R15869.28 ¥ R15869.28 en TrtoTs= 15869241 +o) =R 1744846 YR 1748,46 @ {16] = I PASE th 206 -i- 47 Dm Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief “Mathematics/P1/Wiskunde YI 16 ‘CAPS/KABV— Grade/Graad 11 ~-Memorandum QUESTION/VRAAG 9 9.1 | Givew/Gegee: P(A)=02 | P@)=05 | P(A or B)=0,6 9.1.1 | P(A or B) = P(A) +P) —P(A and B) 70,6 =0,2+0,5 —P(A and B) 0,6 =02+0,5 -P(A and B) | | | vA and B) =0,1 P(A and B) =0,1 @) 9.12 | P(A and B) = 0,1 P(A) x PB)=0,2 x 0,5 | =0,1 | ¥ P(A) x PB)=0,1 <.P(Aand B) = P(A)xP@) | | @ P(A and B) = P(A)xPCB) ~. AandB ate independent/ A en B is onafhanklik | | ~ conclusion/gevolgirelking | 6) 921 [aqis — 7 | %a=5 CA must be applied if the values of || | yp-1 bal aandb are caloulated incomectly/ || | 2238 e=38 CA moet toegepas word as die i | vd]=3 d=3 waardes van a en b verkeerd | | %e+37 6) bereken is i es e=37 9.22 25 1 v25 P(one learner playsnetball or volleytall} = Too = a Yanswer/entwoord Q 931 | if | 05, fol C30 i | | ™ branch at first level with c | | probebilities/ eerste 04 0,5 Ww (36) vertakking met | | wacrskynlikiede | 0,6 0,3 c wc) | | ¥ branches at second level Ww |_| with probabilities’ | | tweede vertakkings met 0,7 Ww (w;W) | | waarskyntitinede | ¥ outcomes/uitkomste | rn DEPARTEN 6) PRIVATE BAS XO, ji i eT | De | Plgase tum over/Blaai om asseblief Copyright reserved/Kopieregvoorbehou

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