Mathematical Literacy Grade 11 P1 KZN November 2016 Memo

MARKS: 150 f ) TIME: 3 hours Copyright reserved C3 RRR Re “a if it | " | im i | "0 basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA SANA S RR SRR RRR RRR RRR RRR MATHEMATICS P1 t a al NOVEMBER 2016 ‘ -. NATIONAL ~ SENIOR CERTIFICATE GRADE I1 This question paper consists of 9 pages. loaded from hlayiso.com eer eS SIa NNT Lo

Mathematics/P1 Downloaded from hlayiso.com 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

Downloaded from hlayiso.com 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 24 26 12 (4) 1.1.5 Ve-143=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 21.41 10°—-10°".2 ©) 27m? —V48m' 22 Zoe @) 12m® : 2 8 2.2 WITHOUT using a calculator, show that -~==-2 4 " 14/2 V8 ® [12] Comittee Please turn over

Downloaded from hlayiso.com 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) Downloaded from hlayiso.com Mathematics/P1 5 DBE/November 2016 CAPS ~ Grade 11 QUESTION 5 Given: f(x) = 2x +x4+6 5.1 Calculate the coordinates of the turning point of f, 5,2 Determine the y-intercept of f 5.3 Determine the x-intercepts of f. 5.4 Sketch the graph of f showing clearly all intercepts with the axes and turning point. 5.5 Determine the values of k such that fx) =k has equal roots. 5.6 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]

~ Downloaded from hlayiso.com Mathematies/P 1 DBE/November 2016 6 CAPS ~ Grade tl QUESTION 6 The diagram below shows the graph of f(x) = 5 ~1 and g(x) “5 x. 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 ie] x Cc B f an ( D & 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) 65 _Use the graphs to obtain the solution to: 5 > a (4) x3 , ee as Copyright resrved NEAT AAT Please rum over

Downloaded from hlayiso.com 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}

Downloaded from hlayiso.com 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) Downloaded from hlayiso.com 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/P&/Wishunde VI 3 DBE/Novertber 2016 7 __ CAPS/KABY — Grade/Graad 11 ~Memiorandum 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 fret x<Oorx>2 xQQx-4)>0 Veco ot 32 £ x<Oorx>2 ro} 2 Mosimum 2 for ® a (©) incorrect notation ° OR ; ° ati ve ” . verkeerde notasie —_ & KS [tag 2 See | 208 “at B-r9 ‘Copyright reserved/Kopieregvoorbehou Please tum over/Blaai om asseblief Mathematics/P1/Wiskunde VI 4 DBE/November 2016 CAPS/KABY - Grade/Graad 11 Memorandum I ae ge yaks " r : i | ¥comm ctor 2 b 4 = | jon/gemene fas : 2* 3512 H ¥ simplification/vereenv. Bad | 2 a 2 | 3x e2 i ¥ equating/gelykst exponents \ axed | Y answerlanti, ® fa H ve — || Hisolatelisoleer + signiteken Fak -1F || Veguaring/owade both sides gala x? 140449 | x? 15x +58=0 Y sté-vorma/stand vorm ¥ factors{fakt (e-5)(z-10) = 9 i “res Sor x «10 i Halo isd 12 3x-y+2=0.. and ys—x? +2x48 | y J ya3et2 OR i yoni Bxt2=—x? 42x48 3x (a? t2e+8)+2=0 | | veubstitution/vervanging x’ +x-6=0 7 i G+3fx—2)=0 || M std Sorm/stand vorm 4 &=-T at's a2 | Vfactors/faktoré pH3-3}o2 or y=3(2)42 ! vx-values/x-waardes =7 =8 | oF | pC praluesty waardes ®) LS Sx" 4(k+2x=1-k Bx ake De | vans? dae Aso dae | =(£+27-43) C144) | vs ‘substitution /vervanging =P 4 Ake 4412-12k | |" 8k H6 =k -8h+16 4k HP ={k-4F | rm <b? —4ae is aperfect square. | @ Rootsare zealand sational. | 01 Epvaermin "| - PRAATS ahd Xiva, PeUTORINCay ie) 208 -ff- 41 | Copyright reserved/Kopieregvoorbehou BUBLIC BXARMALATEON Please tum ever/Blaai on asseblicf

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Downloaded from hlayiso.com DBE/November 2016 Mathematics/P L/Wiskunde VI 7 DBE/November 2016 ‘CAPS/KABV — Grade/Graad 11 ~Memorandum ES . 2 as i r 3 NAN AON LON 4 3 7 IL #12 NZ N ZA NZ ne 4 4 ¥B ¥ answer/antw. re) adie M=27 sa rs a 3a+b=3 64033 YESS b=-3 athpen od indtea-9 ¥ge$ cand! Eystut -38 VT, =2n? 32-8 ~ es & Fy aul SHS Atenas Vansweelante, = 2n?—3n-5 a5 34 T, = 400 — r 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 n¥ = vn=15 OR @ ~ equating/verg. 2n® -3n-8+3=400 ae W std form/stand vorm 2n? —3n-8=397 V factorisation/fakt. 2n? ~3n—405=0 (n—-5)@n+27)=0 Yonly/ slegs n= 15 nelson neh i) 2 f19} Copyright reserved/Kapieregvoorbehou Please turn over/Blaai om asseblief ‘“Mathematics/P 1/Wiskunde VI 8 CAPS/KABV — Grade/Graad 11—Memoraudum QUESTION/IVRAAG 4 | Ait 18 14 10 | N ZAN 4 4 | T,=6 | ~answer/antw. | w i} 2 = — T 412) 7, =a+(e—-1a only, fall ¥ subst j =18+ 1-4) marks) slegs | Y answerlantw. =—4n+22 antwoord volpunte | Q) 413| 7, =22—4n | ¥ substitution/very, -10322-4n | v, lant -92=-4n i ° n=23 | ® FIAT Oro — Qayy = Fog OF the linear sequence | ¥ making = 22-4509 | association/ass. =-2014 | | Yanswer/antw. | @) i bn Eo if Vvaluehurde of a aah Ya>0 ard Y minim <. this patter has a minimum value/hierdie patron het'niminiowum waarde | value/wrde ‘The shape of the graph will be concave up / die vorm van die grafiekis kenkaafna bo | 6 42.2 | T,=29 | . 1G) + 5b +0 =29 ® je Sb+e=4.. ' and T, = 29 ¥~ equations/verg. | & 2. 1A7P +17b+e =29 \ Mee) ie 17b+e=-260...2) solve the equations simultaneously value offwaandle —12b = 264 van b 2 b=-22 | substitute in (1) | je (22) +e=4 | -1l0+e=4 ! Y value offwaarde ne=ll4 | vaa¢ oT, =a -22n+114 | ¥ answer/antwoord. I OR/OF. Copyright reserved/Kopieregvoorbehow Please tum over/Blaai om asseblief

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Downloaded from hlayiso.com DBE/November 2016 Mathematics UWiskunde V2 il DBE/November 2016 CAPS/IKABY — Grade/Graad 11 Memorandum, 53 x intercepts 0=~2x +246 vyn0 0=2x? -x-6 O= (Ox 43)(0-2) v % factorisation/faktorisering. ox= Bex S- 5 2 v ¥ x-values/waardes 3 (2;0) and |-=30 ct) ana (-3:0) &) 3.4 Y shapefvorm We imeteepisleysmille! z a omning pointdranipot é @) 5.5 49 vv answer/antwoorde. kos 8 @ 5.6 «, . 9 57 ¥ 7 tming New/Ninve tuming point/drpn.t (@ 5 2) poindaapat © ‘i equation/verg. = € Equation/verg. of hk OR/OF _ f 2) 57 vv¥¥ ensweronly (3) yo-2x-=] + 4 8 . [£7] QUESTIGN/VRAAG 6 61 x=—3 and y=—i Yu=3 v y=-1 2) 6.2 xeR ,x¥—-3 ¥ ¥ answev/aniwoord, 2) Din i ‘Copyright reserved/Koplaregvoorbehou | APP ROUSE Manele eetipss pst ——- om asseblief Copyright reserved/Xopieregvoorbehow Mathematics/P1/Wiskande V7 2 CAPS/KABY ~ Grade/Graad 1] ~Memorandom 7 | 631 AtB,x=0 | 1 | ¥ substituton/vervanging. yon3 -1 | ¥ answer/aniwoord. +r | -2 | x 3 | op =? units | "—™ | ® I 6.3.2 AtA, y=0 i i 1 i ¥ substitution/vervanging. x43 | — | 543 || ¥ simplification/vereenv. x4351 | ean? | | Manswerlantwoorde. < OA = 2units/ eenihede | @ 1 64 1 L i ¥ equating the two equations/ es3 1 =3* j verg. van 2 vergelykings 2-2 (x43) =x (x +3) | x? 43x-242x4+6=0 | ¥ standard form/std vorm | x? 45244=0 ' i ¥ factors/fakzore. (+4)@+1)=0 : x=-4 ot/ofx=-1 | i | ¥ x-values/waardes when/wanneer 2=-13 =~ 4 when/wanneer x =-4; y=—2 i ¥co-ordinates/kedrdinate C . . . 20 C4-d) ond D(-45-2) | co-ordinates! kodrdinate D 2 | © i | i i i i \ i Dm | Please turn over/Blaai om asseblief

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