Mathematics Grade 11 P1 National Exemplar November 2020 Memo

NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 2020 MATHEMATICS P1 EXEMPLAR MARKS: 150 TIME: 3 hours *Imat1* This question paper consists of 8 pages.

2 MATHEMATICS P1 (EC/NOVEMBER 2020) INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of TEN questions. Answer ALL the questions. 2. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answer. 3. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 4. Answers only will not necessarily be awarded full marks. 5. If necessary, round off answers to TWO decimal places, unless stated otherwise. 6. Diagrams are NOT necessarily drawn to scale. 7. Number the answers correctly according to the numbering system used in this question paper. 8. Write neatly and legibly. Copyright reserved Please turn over

(EC/NOVEMBER 2020) MATHEMATICS P1 3 QUESTION 1 1.1 Solve for x: 1.1.1 (3x  2)( x  5) 0 (2) 1.1.2 3x2  5x  1 0 (correct to 2 decimal places) (3) 1.1.3 x 4 x2 (5) 1.1.4 2 x 2  5x d 3 (4) 1.2 Simplify the following, without using a calculator: 2 1.2.1 § 8 ·3 (2) ¨ ¸ © 27 ¹ 1.2.2 12  2 3 1 (3) 1.3 Solve for x and y simultaneously: 5 y  x 2 and x  3xy  4 y 2 4 (6) 1.4 The diagram below shows an oval piece of land that Eli acquired for his poultry project. He decides to use the biggest possible rectangular piece of land out of the entire piece. The rectangular piece will have a length of 2x metres and a breadth of y metres, as shown: A B y D 2x C 1.4.1 Show that the area A, of the rectangle can be written as: A 280 x  4 x 2 , given that the perimeter of the rectangle is 280 m. (3) 1.4.2 Determine the maximum possible area that the rectangle can occupy. (3) [31] Copyright reserved Please turn over

4 MATHEMATICS P1 (EC/NOVEMBER 2020) QUESTION 2 2.1 Simplify: 3.2 x 1  2.4 x 3.2 x  2 2 x (4) 2.2 Solve for x: 2 2.2.1 5x 5 20 (3) 2.2.2 12x.3x1 648 (4) 3x  2 2.3 Given: f ( x) , x  10 x  25 2 Determine the values of x for which f (x) is defined. (4) [15] QUESTION 3 3.1 Given the linear pattern: 9 ; 5 ; 1; … ; െ143. 3.1.1 Determine the formula for the n th term of the pattern. (2) 3.1.2 Calculate the value of T7 . (2) 3.1.3 Determine the number of terms in the pattern. (2) 3.2 Given that, in a linear number pattern, the 16th term is 38 and the 41st term is 113. Which term is െ1? (4) [10] QUESTION 4 Given the quadratic pattern: 12;  8;0;12;... 4.1 Determine the next two terms of the pattern. (2) 4.2 Determine Tn , the general term of the pattern, in the form Tn an 2  bn  c . (4) 4.3 Between which two consecutive terms does the first difference of 192 lie? (3) 4.4 A new pattern, Pn , is formed. It is given that Pn Tn  168 , determine the number of negative terms in the new pattern. (5) 4.5 Show that Tn is always an even number. (2) [16] Copyright reserved Please turn over

(EC/NOVEMBER 2020) MATHEMATICS P1 5 QUESTION 5 Given: f ( x)  x2  6x  7 5.1 Determine the coordinates of the turning point of f. (3) 5.2 Determine the x-intercepts of f. (2) 5.3 Draw a neat sketch of f, clearly indicating all intercepts with the axes and the turning point. (4) 5.4 Write down the equation of the axis of symmetry of f. (1) 5.5 Determine the average gradient of f between x 3 and x 1 . (4) 5.6 The graph of f is shifted 4 units to the left and reflected in the x-axis to form h. Write down the equation of h in the form h ( x) a( x  p) 2  q. (2) [16] QUESTION 6 a The diagram below shows the graphs of f ( x)  q and g ( x) bx  c . The x p asymptotes of f are at x 3 and at y 1. f and g intersect at A, the x-intercept of f, and B, while C(െ2;6) is a point that lies on f. g passes through the point D (3;1) , the point of intersection of the asymptotes of f. y C (-2;6) x g B f D 1 A െ3 0 x Copyright reserved Please turn over

6 MATHEMATICS P1 (EC/NOVEMBER 2020) 6.1 Write down the equation of f in terms of a. (2) 6.2 Determine the value of a. (2) 6.3 Determine the coordinates of the x-intercept of f. (2) 6.4 Determine the values of b and c and write down the equation of g. (4) 6.5 Write down the domain of f. (2) 6.6 Determine the coordinates of B. (4) 6.7 Determine the values of x for which x. f ( x) t 0. (3) [19] QUESTION 7 x §1· 7.1 Given: g ( x) ¨ ¸  4 ©2¹ 7.1.1 Write down the equation of asymptote of g. (1) 7.1.2 Write down the range of g. (1) 7.1.3 Determine the coordinates of the x and y-intercepts of g. (3) 7.1.4 Hence, write down the values of x for which g ( x)  0. (1) 7.2 Draw a neat sketch of the graph of h ( x) a.b x  q where x a 1 x 0  b 1 x q !1 (3) [9] Copyright reserved Please turn over

(EC/NOVEMBER 2020) MATHEMATICS P1 7 QUESTION8 8.1 Calculate the effective interest rate per annum if an investment earns 9,5% interest per annum, compounded monthly. (3) 8.2 The value of a house increased to R764 050,60 over a period of 5 years due to inflation. The price of the house increased at a rate of 5% p.a. compounded annually. Calculate the original price of the house. (3) 8.3 Kamvelihle invested R28 000 into a savings account that pays interest at 7,5% p.a. compounded monthly for the first 4 years and 11% p.a. compounded quarterly thereafter. At the end of the 4th year, he withdrew R7 300. 8.3.1 Calculate his balance at the end of the 7th year of his investment. (5) 8.3.2 Assuming that at the end of 7 years, his balance is R42 181, 59, Kamvelihle wants his investment to grow to R80 000 in another 5 years’ time. How much must he deposit into the account immediately to achieve this goal if the bank offers 8% p.a. interest compounded monthly? Write your answer correct to the nearest rand. (5) [16] Copyright reserved Please turn over

8 MATHEMATICS P1 (EC/NOVEMBER 2020) QUESTION 9 9.1 Two events A and B are such that: x P(not A) = 0,45 x P(B) = 0,3 x P(A or B) = 0,685 Are events A and B independent? Justify your answer. (5) 9.2 A survey was done among a group of 75 learners to determine which sports they watch on television. They chose from athletics (A), netball (N) and rugby (R). Some of the information that was collected is as follows: x 12 learners watch netball, rugby and athletics x 25 learners watch rugby and athletics x 22 learners watch netball and athletics x 38 learners watch rugby x 5 learners watch only netball and rugby x 9 learners watch netball only x 4 learners watch athletics only The Venn diagram below shows the information: S N R 9 5 c 12 a b 4 d A 9.2.1 Determine the values of a, b, c and d. (4) 9.2.2 Calculate the probability that a learner selected at random watches athletics or both netball and rugby. (3) [12] QUESTION 10 A bag contains a certain number tennis balls that are the same in all respects except colour. There are 5 green balls and the rest are blue. Ncomi picks a ball, observes the colour and does not put it back in the bag. He picks a second ball and observes the colour. The probability that both balls that Ncomi 5 picks are green, is . Determine the total number of balls in the bag. 18 [6] TOTAL: 150 Copyright reserved Please turn over

NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 11 NOVEMBER 2020 MATHEMATICS P1/WISKUNDE V1 MARKING GUIDELINE/NASIENRIGLYN EXEMPLAR/EKSEMPLAAR MARKS/PUNTE: 150 This marking guideline consists of 15 pages./ Hierdie nasienriglyn bestaan uit 15 bladsye.

2 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) NOTE/LET WEL: x If a candidate answers a question TWICE, mark the FIRST attempt ONLY. Indien ƌ kandidaat ƌ vraag TWEE keer beantwoord, merk SLEGS die EERSTE poging. x Consistent accuracy applies in ALL aspects of the marking guideline. Volgehoue akkuraatheid geld deurgaans in ALLE aspekte van die nasienriglyn. x If a candidate crossed out an attempt of a question and did not redo the question, mark the crossed-out attempt. Indien ƌ kandidaat ƌ poging vir ƌ vraag deurgetrek het en nie die vraag weer beantwoord het nie, merk die poging wat deurgetrek is. x The mark for substitution is awarded for substitution into the correct formula. Die punt vir substitusie word toegeken vir substitusie in die korrekte formule. QUESTION 1/VRAAG 1 1.1.1 (3x  2)( x  5) 0 2 3 3 answers / antwoorde ? x  or / of x 5 (2) 3 1.1.2 3x 2  5 x  1 0 b r b 2  4ac ?x 2a (5) r (5) 2  4(3)( 1) 3 substitution / vervanging 2(3) 5 r 37 6 3 3 answers / antwoorde (3)  0,18 or / of 1,85 1.1.3 x 4 x2 x2 4 x 3 squaring both sides/ ( x  2) (4  x) 2 kwadreer beide kante x  2 16  8 x  x 2 3 standard form / standaardvorm x 2  9 x  18 0 3 factors / faktore ( x  6)( x  3) 0 3 both x-values / beide x-waardes 3 selection / keuse ? x 3 or / of xz6 (5) 1.1.4 2x2  5x d 3 3 standard form / standaardvorm 2x2  5x  3 d 0 3 factors / faktore (2 x  1)( x  3) d 0 -3 1 1 ?3 d x d 3 3 3 d x d 2 2 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 3 1.2.1 2 2 § 8 · 2 § 8 ·3 § 8 · ¨ ¸ ¨¨ 3 ¸¸ 3 ¨¨ 3 ¸¸ © 27 ¹ © 27 ¹ © 27 ¹ 2 §2· ¨ ¸ ©3¹ 3 answer / antwoord 4 (2) 9 OR/OF 2 OR/OF ª§ 2 ·3 º 3 2 3 «¨ ¸ » ª§ 2 ·3 º 3 «¬© 3 ¹ »¼ «¨ ¸ » «¬© 3 ¹ »¼ 2 §2· ¨ ¸ ©3¹ 3 answer / antwoord 4 9 (2) 1.2.2 12  2 3 1 2 32 3 1 3 2 3 3 4.3  2 3  2 3  2 2.3  2 3  2 3  2 62 3 answer / antwoord 4 (3) OR/OF OR/OF 3 36 12  2 3 1 36  12  2 3  2 3 62 3 2 3 2 3 answer / antwoord 62 3 2 3 2 (3) 4 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

4 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) 1.3 5y  x 2 (1) x 2  3 xy  4 y 4 (2) 3 x 5x  2 x 5y  2 (3) Subst. / Vervang (3) into/in (2) : 3 substitution / vervanging ? (5 y  2)  3 y (5 y  2)  4 y  4 2 0 3 standard form / standaardvorm 25 y  20 y  4  15 y  6 y  4 y  4 2 2 0 3 method;factors / metode;faktore 10 y 2  10 y 0 3 both x-values / beide x-waardes 10 y ( y  1) 0 ?y 0 or / of y 1 x 5y  2 3 both y-values / beide y-waardes x 5 0 2 or / of x 5 1 2 (6) ?x 2 or / of x 3 OR / OF 3 y 1 5 x2 5y  x 2 1 x 2  3 xy  4 y 4 (2) 3 substitution / vervanging x2 1 y x2 3 5 5 Subst./Vervang 3 into/in 2 , 3 standard form / standaardvorm x  3x 2 1 5 ( x  2)  4 1 5 ( x  2) 4 3 factors / faktore x  53 x( x  2)  54 ( x  2) 2 4 3 both y-values / beide y-waardes 5 x 2  3 x 2  6 x  4 x  8  20 0 2 x  2 x  12 2 0 3 both x-values / beide x-waardes (6) x2  x  6 0 ( x  3)( x  2) 0 ? x 2 or / of x 3 y 1 5 2  2 or / of y 1 5 (3  2) ?y 0 or / of y 1 1.4.1 Perimeter/Omtrek 2l  2b 280 2(2 x)  2 y 3 substitution / vervanging 2 y 280  4 x 3 simplification / vereenvoudiging ? y 140  2 x Area/Oppervlakte lb 3 A 2x(140  2x) 2x u y 2 x(140  2 x) 280 x  4 x 2 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 5 1.4.2 A 280 x  4 x 2  4( x 2  70 x)  4( x 2  70 x  1225  1225) 3 completing the square / vierkantsvoltooiing  4[( x  35) 2  1225]  4( x  35) 2  4900 3 4900 ? The maximum area is 4900 m 2 3 correct conclusion / korrekte gevolgtrekking Die maksimum oppervlakte is 4900 m 2 (3) OR/OF OR/OF b x  2a 3 method/metode  280 2(4) 3 35 m 35 m 3 answer / antwoord ? A 280 (35)  4(35) (3) 4 900 m 2 [31] QUESTION 2/VRAAG 2 2.1 3.2 x 1  2.4 x 3.2 x.2  2.22 x 3 3.2x.2  2.22 x 3.2 x  22 x 3.2 x  22 x 3 factorisation of numerator / 2.2 x (3  2 x ) faktorisering van teller 2 x (3  2 x ) 3 factorisation of denominator / 2 faktorisering van noemer 3 answer / antwoord (4) 2 2.2.1 5x 5 20 2 2 x 5 4 3 x5 4 5 2 2 5 x 5 4 3 x5 2 2 5 42 5 ?x 22 2 25 32 3 answer / antwoord (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

6 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) 2.2.2 12 x.3x 1 648 x x 12 .3 .3 648 3 12x.3x 216 x x 12 .3 216 x 12.3 216 36 x 216 3 62 x 63 62 x 63 3 equating exponents / 2x 3 gelykstel van eksponente 3 3 answer / antwoord x 2 (4) 2.3 3x  2 f ( x) x  10 x  25 2 3 x2  10x  25 0 for undefined / f is undefined when : f is ongedefinieerd wanneer vir ongedefinieerd x  10 x  25 0 2 ( x  5) 2 0 x 5 3 x 5 ? f is defined for : x  , but x z 5 3 x  Ⴆ 3 x z 5 f is gedefinieerd vir : x  , maar x z 5 (4) [15] QUESTION 3/VRAAG 3 3.1.1 9 ; 5 ; 1; …;െ143 Tn 13  4n 3 13 3 െ4n (2) 3.1.2 Tn 13  4n T7 13  4(7) 3 substitution / vervanging 15 3 െ15 (2) 3.1.3 Tn 13  4n 143 13  4n 3 substitution / vervanging 156  4n ? n 39 3 answer / antwoord (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 7 3.2 Tn an  b 16a  b 38 1 3 16a  b 38 and/en 41a  b 113 41a  b 113 2 25a 75 3 method / metode ?a 3 16 3  b 38 3 Tn 3n  10 48  b 38 ? b 10 Tn 3n  10 3n=3  1 3n  10 9 3n ?n 3 (4) [10] QUESTION 4/VRAAG 4 4.1 െ12 ; െ8 ; 0 ; 12 4 8 12 4 4 3 28 3 48 28 ; 48 (2) 4.2 2a 4 3a  b 4 a  b  c 12 ?a 2 3(2)  b 4 2  2  c 12 3 a 2 3 b 2 b 2 c 12 3 c 12 3 Tn 2n 2  2n  12 ?Tn 2n 2  2n  12 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

8 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) 4.3 For first differences: / Vir eerste verskille 4;8;12; ... 3 Tn 4n Tn 4n 3 n 48 192 4n 3 answer / antwoord ? n 48 (3) ?192 lies between T48 and T49 192 lê tussen T48 en T49 OR/OF OR/OF Tn 1  Tn 192 3 2(n  1) 2  2(n  1)  12  (2n 2  2n  12) 192 2(n  1) 2  2(n  1)  12  (2n 2  2n  12) 192 3 4n = 192 2(n 2  2n  1)  2n  2  12  2n 2  2n  12 192 2n 2  4n  2  2n  2  12  2n 2  2n  12 192 ? 4n 192 3 answer / antwoord (3) n 48 ?192 lies between T48 and T49 192 lê tussen T48 en T49 4.4 Pn  0 Ÿ Tn  168  0 Tn  168 3 2n2  2n 12  168 3 standard form / standaardvorm 2n 2  2n  12  168 2n 2  2n  180  0 3 factorisation / faktorisering 3 9  n  10 n 2  n  90  0 -9 10 (n  10)(n  9)  0 3 answer / antwoord 9  n  10 (5) but / maar : n ! 0 ? Number of terms 9 Aantal terme 9 4.5 Tn 2n 2  2n  12 3 Tn 2(n 2  n  6) 2(n 2  n  6) 3 explanation / verduideliking ? 2 u any n ! 0 is always even, so Tn will always be even 2 u enige n ! 0 is altyd ewe, so Tn sal altyd ewe wees. (2) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 9 QUESTION 5/VRAAG 5 5.1 b At TP/By Draaipunt: x  3 method / metode 2a 6  2(1) 3 3 x-coordinate / x-koördinaat ?y (3) 2  6(3)  7 3 y-coordinate / y-koördinaat 16 (3) OR/OF f ( x)  x2  6 x  7 ( x 2  6 x  7) 3 completing the square / [( x 2  6 x  9)  9  7] vierkantsvoltooiing [( x  3) 2  16] ( x  3) 2  16 3 x-coordinate / x-koördinaat 3 y-coordinate / y-koördinaat ? Turning point / Draaipunt : 3;16 (3) 5.2  x2  6 x  7 0 3 f ( x) 0 x2  6 x  7 0 ( x  7)( x  1) 0 ? x 7 or / of x 1 3 answers / antwoorde (2) 5.3 3 y-intercept / y-afsnit 3 x-intercepts / x-afsnitte 3 turning point / draaipunt 3 shape / vorm (4) 5.4 x 3 3answer / antwoord (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

10 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) 5.5 f ( x)  x2  6x  7 f (3) (3) 2  6(3)  7 3 f (3) 20 20 (1)2  6(1)  7 f (1) 3 f (1) 12 12 12  ( 20) 3 substituting into gradient formula / Average/Gemiddelde m vervanging in gradiënt-formule 1  (3) 32 4 8 3 answer / antwoord (4) 5.6 f ( x)  x  6 x  7 2 ( x  3) 2  16 2 3 a 1 and/en q 16 ? h( x ) ( x  3)  4  16 3 p 1 ( x  1) 2  16 (2) [16] QUESTION 6/VRAAG 6 6.1 a f ( x) q x p a 1 3 p 33q 1 x3 (2) 6.2 a f ( x) 1 x3 a 6 1 3 substitution / vervanging 2  3 ?a 5 3 answer / antwoord (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 11 6.3 5 f ( x) 1 x3 5 3 y 0 0 1 x3 5 1 x3 3 x 8  x3 5 x 8 ? A(8;0) (2) 6.4 A(8;0) and/en D(3;1) y2  y1 mAD x2  x1 1 0 3 substitution / vervanging 3  (8) 1 3 mAD ?b 5 g ( x) bx  c 1 3 substitution / vervanging xc 5 1 1 0 8  c or / of 1 3  c 5 5 8 3 equation / vergelyking ?c 5 1 8 g ( x) x 5 5 (4) 6.5 x  (f ; f) but / maar x z 3 3 x  (f ; f) 3 x z 3 OR / OF (2) x  Ⴆ, x z 3 3 x  Ⴆ 3 x z 3 (2) 6.6 f ( x) g ( x) 5 1 8 5 1 8 1 x 3 1 x x3 5 5 x3 5 5 25  5( x  3) x( x  3)  8( x  3) 25  5 x  15 x 2  3 x  8 x  24 3 standard form / standaardvorm x  6 x  16 0 2 3 x-values / x-waardes ( x  8)( x  2) 0 x 8 or x 2 5 y 1 3 coordinates / koördinate 23 2 ? B (2; 2) (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

12 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) 6.7 8 d x  3 or x t 0 33 8 d x  3 3 x t 0 OR / OF OR / OF x >[8;  3) ‰ [0; f)@ ‫[[ א ݔ‬െ8; െ3) 33 ‰ [0; λ)] 3 (3) [19] QUESTION 7/VRAAG 7 7.1.1 y 4 3 answer / antwoord (1) 7.1.2 y  (4; f) 3 answer / antwoord (1) OR / OF OR / OF 3 answer / antwoord (1) y ! 4 7.1.3 §1· x g ( x) ¨ ¸  4 ©2¹ 0 §1· 3 y-value / y-waarde y ¨ ¸ 4 ©2¹ 3 substitution / vervanging 3 x §1· 0 ¨ ¸ 4 ©2¹ x 4 21 3 answer / antwoord 22 2 x (3) ?2 x x 2 Intercepts / Afsnitte :(0;  3) and / en ( 2;0) 7.1.4 x ! 2 3 answer / antwoord (1) 7.2 y 3 asymptote above x-axis q asimptoot bo x-as 3 y-intercept positive y-afsnit positief 3 shape / vorm x h (3) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 13 QUESTION 8/VRAAG 8 8.1 § inom · m ieff ¨1  ¸ 1 3 formula / formule © m ¹ 12 § 0.095 · 3 substitution / vervanging ¨1  ¸ 1 © 12 ¹ 0,099247 ... ? r 9,92 % 3 answer / antwoord (3) 8.2 A P (1  i ) n R 764 050 ,60 P 1  0,08 5 3 A R764050,60 764050 .60 3 substitution / vervanging P 5 1  0.08 R 520 000 3 answer / antwoord (3) 8.3.1 ª § 0,075 · 48 º§ 0,11 ·12 A «28 000 ¨1  ¸  R 7 300 » ¨1  ¸ 48 «¬ © 12 ¹ »¼© 4 ¹ § 0,075 · 3 28 000¨1  ¸ 12 © 12 ¹ § 0,11 · R 37 760 ,78  R 7 300 ¨1  ¸ 3 െR7 300 © 4 ¹ 12 12 § 0,11 · § 0,11 · 3 u ¨1  ¸ R 30 460 ,78¨1  ¸ © 4 ¹ © 4 ¹ 3 simplification / vereenvoudiging R 42 181,59 3 answer / antwoord (5) 8.3.2 A P(1  i ) n 60 § 0, 08 · A R42181,59 ¨1  ¸ 3 substitution into correct formula © 12 ¹ vervanging in korrekte formule R62844, 06 R80 000  R62844, 06 3 R62 844,06 R17155,94 ?A P(1  i ) n 3 R17 155,964 60 § 0, 08 · R17155,94 P ¨1  ¸ © 12 ¹ 3 method / metode 17155,94 P 60 § 0, 08 · ¨1  ¸ © 12 ¹ R11515, 25 ? He needs to deposit R11 515 / Hy moet R11 515 deponeer 3 answer / antwoord (5) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

14 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2020) QUESTION 9/VRAAG 9 9.1 If A and B are independent, then: As A en B onafhanklik is, dan: P(A and/en B) = P(A) u P(B) P(A) = 1 P(not/nie A) = 1 0,45 3 0,55 = 0,55 11 = 20 P(A or/of B) = P(A) + P(B) – P(A and/en B) 0,685 = 0,55 + 0,3 – P(A and/en B) 3 substitution / vervanging ‫׵‬P(A and/en B) = 0,165 33 = 3 answer / antwoord 200 P(A) u P(B) = 0,55 u 0,3 3 P(A) u P(B) = 0,165 33 = 200 ‫ ׵‬A and B are independent events. / 3 conclusion / gevolgtrekking A en B is onafhanklike gebeurtenisse. (5) 9.2.1 S N R 9 5 c (8) 3 a = 10 12 a (10) b (13) 3 b =13 3c=8 4 3 d =14 d (14) A a = 10 ; b = 13 ; c = 8 ; d = 14 (4) 9.2.2 39 5 39 5 P A or/of (N and/en R)  3 3 75 75 75 75 44 3 answer / antwoord 75 (3) | 0,59 [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/NOVEMBER 2020) MATHEMATICS P1/WISKUNDE V1 15 QUESTION 10/VRAAG 10 10 Let the total number of balls be t. Laat die totale aantal balle t wees. 5 4 3 3and/en t t 1 Green/Groen: 5 G 4 Blue/Blou: t – 5 t 1 5 G t B G B B P(GG) = P(G) u P(G) 3 equation / vergelyking 5 4 5 u t t  1 18 20 5 3 standard form / standaardvorm t (t  1) 18 5t 2  5t 360 5t  5t  360 0 2 3 factorisation / faktorisering t 2  t  72 0 3t=9 (t  9)(t  8) 0 ? t 9 or t z 8 ? There are 9 balls. Daar is 9 balle. (6) TOTAL / TOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief