Mathematics Grade 12 P1 Free State Mock 2023 Paper & Memo

Downloaded from Stanmorephysics.com | education Department of Education FREE STATE PROVINCE Gr 12 MATHEMATICS P1 IAN 12611B MARKS: 1530 This question paper consists of 9 pages and 1 information sheet. X10 P2 Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 10. tion paper consists of 10 questions. sie] ALL the questions. sr your 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. Answer only will NOT necessarily be awarded full marks. An approved scientific calculator (non-programmable, non-graphic) may be used, unless stated otherwise. If necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. An information sheet with formulae is included at the end of the question paper. Write neatly and legibly. Copyright reserved Please turn over

Rawnlaaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. QUESTION 1 1.1 Solve for x: Al 1(2x+1)=0. (2) 1.12 1(2x+1)=4 (correct to two decimal places) (4) 11.3 x+v¥x-2=4 ) 11.4 3x74+x<0 GB) 1.2 Solve for x and _y in the following simultaneous equations: xy=8and 2x+y=17 (6) 1.3. Simplify the following WITHOUT USING A CALCULATOR : atx? — V5x? xVV2ix? + V5x2 (3) [23] QUESTION 2 2.1 Consider the series: a+(a+d)+(a+2d)+... 2.1.1 Prove that the sum of the first n terms of this arithmetic series will be S, = Fhe +(n-1)d]. (3) 2.1.2 Given: 2* +2,.2* +3.2* +... The sum of the first 20 terms of the series is 1680. Calculate the value of x. (4) nin 2.2 Given: S, = , calculate 7, . (3) 2.3. Consider the series: 32 + (—16)+8+(—4)+... Calculate the sum of the first 10 terms of the series. (3) [13] Copyright reserved Please turn over

Dawaleaded from Stanmorephysics.com F8/September 2023 Grade 12 Prep. Exam QUESTION 3 3.1 Given the quadratic number pattern —4; —6; —10; —16; ... 3.1 etermine 7’. (4) 3. tween which consecutive terms of the pattern is the difference -100? (4) 3.2. Given that x - 3) = -3 . Calculate the value of k. (4) n=l [12] QUESTION 4 Given the function: A(x) = 5 42. x- 4.1 Write down the equations of the asymptotes of h . (2) 4.2 Calculate the x-intercept of h. (2) 43. Draw the graph of /. Clearly show all asymptotes and intercepts with the axes. (4) 4.4 Determine the equation of the axis of symmetry of #, in the form y= mx+c, where m<0. (3) 4.5 Determine the range of — A(x) +1 (2) 4.6 Determine the values of x where h(x) < 0. (2) [13] Copyright reserved Please turn over

wRawnlaaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. QUESTION 5 In the diagram, the graphs of f(x) = -30 +2x+6 and g(x)=—x—-2 are drawn, C and E are the y-inter of fand g, respectively. The parabola has a turning point at D and cuts the x-axis at A an} is also the x-intercept of g. DF is a line parallel to the y-axis with F a point on g. D | PNE 5.1 Calculate the: 5.1.1 Coordinates of D. (3) 5.1.2 Distance DF. (3) 5.2 For which values of k will f(x) =k have two positive roots? (2) 5.3. Given that f(x) =A'(x). Determine the x-coordinates of the turning points of h. (3) 5.4. Determine the value(s) of x where {'(x)x g(x) <0. (2) [13] Copyright reserved Please turn over

Dewnleaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep, Exam. QUESTION 6 The diagram shows the graphs of f(x) = a" and g, the reflection of fin the y-axis. af ;) li f The two graphs intersect at T. Y 6.1 Write down the coordinates of T. (1) 6.2 Calculate the value of a. (2) 6.3. Determine the equation of g. (2) 6.4. Write down the equation of 7 (x); the inverse of f, in the form y= ... (2) 6.5 For which values of x will f'(x) <1? (3) [10] Copyright reserved Please turn over

Rawnloaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. QUESTION 7 7A How many years will it take to triple an investment if the interest is compounded annuallyat a rate of 9,8% p.a.? (3) 7.2 Andi ds R64 000 for a holiday. He started to invest a fixed amount of his si Let a rate of 8,5% p.a. compounded monthly, at the end of each month, for tepryeers. 7.2.1 Calculate the monthly payment he will have to make to achieve this. (3) 7.2.2. Tf Andile has stopped his payment at the end of eight years, what will the total of his investment be at the end of ten years? 3) 7.3. Madri took out a loan of R400 000 at an interest rate of 10,4% p.a. compounded monthly. She repaid the loan at the end of the first month and every month for 15 years. Her monthly instalment is R4 396,83. 7.3.1 Calculate the outstanding balance after nine years. (3) 7.3.2 How much interest did she pay over the nine years? (3) [15] QUESTION 8 8.1 Determine the derivalive of f(%) =3-.° using FIRST PRINCIPLES. (5) 8.2 Determine: 2 8.2.1 D, E = vi (4) x dy . 3 82.2 =,if p=|x -l 3 @ if y=(e 1 @) 83 Given: f(x) = x* -12x-16 8.3.1 Calculate the: (a) Coordinates of the turning points of f. : (5) (b) _—_-x-intercepts of ff (3) 8.3.2 y=15x+ pis a tangent to the graph of f Calculate the x: inates of the point(s) of contact. (4) 8.3.3. For which value(s) of x will the given function be concave up? i o Copyright reserved Please turn over

Dewnleaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. QUESTION 9 91 The diagram shows the straight-line 2, where h(x) = f'(x). The x-intercept of h is 1. The wing is true for function i f(1)=—3 and f(3)=0. Y Draw a sketch graph of the function f; clearly indicating all x-intercepts and turning point(s). (3) 9.2 During an experiment the temperature, T in °C varies with time 7 in seconds, to the equation T(t) = 60 + 27t — Pote [0:6]. Calculate: 9.2.1 The average change of temperature between 3 and 6 seconds. (3) 9.2.2 After how many seconds the temperature will be a maximum. (3) [9] Copyright reserved Please turn over

Rewnlogded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. QUESTION 10 10.1 Given: P(4) = 0,4 and P(B) =0,5 10.1.1 sulate P(A or B) if Aand B are mutually exclusive events. (2) 10.1. an ulate P(A or B) if Aand Bare independent events. (3) 10.2 A four-digit code must be set using the letters A, E, I, O, U and digits 0 to 9. The letters may be repeated, but the digits may not be repeated. The code must consist of two letters and two digits in that order, for example, UO19. 10.2.1 How many different codes are possible with the information given? (4) 10.2.2 What is the probability that a code that is picked randomly will start with an A and be an even number? (4) [13] TOTAL: 150 Copyright reserved

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mRawnloaded from Stanmorephysics.com FS/September 2023 Grade 12 Prep. Exam. INFORMATION SHEET _ =btvb? —4ac 2a A=P(1+ni) A=P(l-ni) A=P(l-i)" A=P(1+i)" T, =a+(n~ 8, =F Pa+(n—d] alr" -1 T, =ar"" _al" =) gril Sse -teret fn " r-l 1— pai -1 pasi-b+)"] i i ™ i fth)-F() "(x)= lim fe) h>0 h xX, +x, yy ty d= ()-—m)+O,-V) Mj 1,-1.2 2 2 y=mxt+e y-y, =m(x-x,) m=22 71 m=tan@ %2—%y (x-af +(y-bf =r? inaspe. —* => = © sn A sinB sinC a =b’ +c? —2be.cos A area. AABC=-ab.sin C sin(a + £) = sina.cos B + cosa.sin 8 sin(a - £)=sin @.cos 8 -cosa.sin B cos(a + B)=cosa@.cos B -sina.sin B cos(a — f)= cos a@.cos f +sin a.sin 8 cos’ a-sin* @ cos2a@ =41-2sin’ @ sin 2@ = 2sina.cosa 2cos? a -1 _ vf >, - x) x= o ==! n n n(A) MA)="5) P(A or B) = P(A) + P(B) — P(A and B) pratbhx p= =F) DG@e-zy Copyright reserved

Downloaded from Stanmorephysics.com education Department of Education FREE STATE PROVINCE PREPARATORY EXAMINATION VOORBEREIDENDE EKSAMEN GRADE/GRAAD 12 MATHEMATICS P1 WISKUNDE V1 SEPTEMBER 2023 MARKS/PUNTE: 150 MARKING GUIDELINES NASTENRIGLYNE These marking guidelines consist of 17 pages. Hierdie nasienriglyne bestaan uit 17 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne NOTE: e Constant accuracy applies in the whole marking guideline. e Ifa learner answers a question twice, mark only the first attempt. e Ifa leame cancels a question, but does not redo it, mark that attempt. al iy 4000 NOTA: onay e = Volgeh kuraatheid word in ALLE aspekte van die nasienriglyne toegepas. e = As 'n kandidaat 'n vraag TWEE KEER beantwoord, sien slegs die EERSTE poging na. e As 'n kandidaat 'n antwoord van 'n vraag doodtrek en nie oordoen nie, sien die doodgetrekte poging na. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTION/VRAAG 1 al 1.1.1 (x —1)(2x+1) =0 x=1 or/of x = —+ ¥x=1 2 Vxa-i (2) 1.1.2 (x-I(2x+1)=4 2x? ~y-5-0 Y standard form -C1)+¥C1) - 42-5) Y correct substitution in 2(2) correct formula _1+V41 Y 1,85 4 Y -1,35 Penalise/mark -1 for x=185 — or/of x=—1,35 incorrect rounding (4) 1.1.3 x+vx-2=4 Vi Vx-2=4- isolate the surd * 2 * v squaring both sides (vx=2) =(4-x)? x—2=16—8x +x? Y standard form 0=x?-9x +18 0 = (x - 6)(x - 3) Y factors Y answer with choice x=6 or/of x=3 Not applicable/Nie van toepassing nie (5) 11.4 3x7 +x<0 x(3x+1)<0 V factors Critical values: 0 and/en -: xe [-+;0| Or -F<x<0 Y critical values Y answer (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne 1.2 2x+y=17 oy =17-2x VY y=17-2x Substitute in/verv. in xy =8 y . iy x(I 7- 2x) =8 substitution m4 0 =2x? -17x+8 Y standard form foamy 0 = (2x-1)(x-8) i 1 ¥ factors Ox= 5 or x=8 \ Y both answers for x »=17-2) — -17- Y both answers for y y=l7 (+) ovof » 17-2(8) y=16 7 OR/OF OR xe 17-y 2 a in/erv. in xy =8 17-y -y x= ——~ ly=8 2 ( 2 p ITp—y? =16 ¥ substitution O=y? -17y +16 Y standard form 0=(y-16Xy-1) y “y=l6 oof y=l factors ,-lc6 17-1 ¥ both answers for x 2 x= or/of 2 xe 1 x=8 ¥ both answers for y 2 (6) v 1.3 Vv2ix _ 5x2 x vax asx? one square root = Wai — 5x? |V2tx? + V5x?) V ; difference between = 21x" —5x° squares =V16x" = =4x v nse @) Lay Et [23] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 =a+(a+d)+(a4+2d)+...4a+(n—1)d Ss 8, =a+(n-lId+a+(n-2)d+...+4 Y T, =a+(n-1)d v reverse =n(2a+(n-1 , = n2a+ (=I) vr (3) 2.1.2 2° 4+2.2* +3.2* +... “a=2* value a] v dad! value d 20 (4/5 x x Y substitution in correct 1 =—(2|2 19)\2 680 = = (2(2")+ (19)2")) foeke 168 = 21.2* g-2* ¥ Simplification (8 = 2”) x=3 v answer (4) 22 S, = mn v T, =5,-S, correct method 3 , ¥ substitution _8 +8 7 +7 4 4 v answer =18-14 a (3) a(l-r") 23 " To? 7 ba : ; 1 values of a and r 32(1-(-3) Sio Y substitution into correct S, _341 21,31 10 = 46 or/of 21, formula (3) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTIONVRAAG 3 3.1 -4;-6;-10;-16;... given/gegee 3.1.1 First difference/eerste verskil : -2 5-4; -6 Second differences/tweede verskil -2 ; -2 ¥ value of a 2a=-2 3(-1)+b=-2 Y¥ value of b a=-l b=1 v value of c -l+l+c=—+4 cu--44 Y T,=-n’ +n-4 (4) ANSWER ONLY FULL MARKS 3.1.2 T, =-2+(n-1X-2) ¥d=2 T, =-2n VT, =-2n -100 =-2n v 50 v answer “n=S0 Between/tussen Ts) and/en T:, OR OR/OF YT, ~T, =~100 Ta —T, =—100 Y substitution =(n+1) +(n+1)-4-[n? +n-4]=-100 | “50 5 v =n? —2n-ltn4l—44n?-n+4=-100 |” WT —2n = -100 n=50 Between/tussen Ts, and/en T;, (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne 3.2 a=k-> 2 3 v value of a and r r=k-— 2 § = l-r Ls k- 3 Y substitution in correct -2=—__2_ formula 2 5 5, 5 3 Y — simplification shown -St+ik- =k-= 3 3 2 2 -10+10k-15=6k-9 Y answer 4k =16 k=4 (4) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 . 2 Given/gegee h(x)=—- +2 fo - 41 2 Vv x=2 2 v y=2 (2) 4.2 0=- +2 x-2 Vv y=0 —2(x-2)=-2 Vx= x-2=1 x=3 x=3 (2) 43 v BOTH asymptotes stbcotiet tea Ean cPade ——! _ v x- intercept ¥ y- intercept v shape (4) 4.4 Y gradient -1 y-2=-l(x-2) ¥ substitute (2; 2) ys-x+4 ¥ equation Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednénom Stanmoreph Grade/Graad 12 Prep. Exam./Voorb. Eksam. sics.com Marking Guidelines/Nasienriglyne FS/VS/September 2023 4.5 —hA(x)+1 2 = 722 Y new equation -] v answer 2 eR;sy#-1 (2) ANSWER ONLY FULL MARKS 46 h(x) <0 Y critical values “x € (2;3] Y notation OR/OF 2<x<3 (2) [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne FS/VS/September 2023 QUESTION/VRAAG 5 Given/gegee f(x) = -ix +2x+6 g(x) =-x-2 f'(x) =0 5.1.1 y= 2 Q=-x+2 ¥ method for turning point _ 1 {- } x=2 Vx 2 OR/OF ¥ x -value | y- value y= 5h -4x)+6 =2 * y= 1 (e248 (3) . D(2:8) 2 D(2;8) 5.1.2 D(2;8) Vv coordinates F v F(2;-4) v answer DF = 12 units/eenhede GB) 5.2 6<k<8 vv answer (2) 53 h'(x) = f(x) 1 0 =-—x° +2x+6 VY f(x)=h'(x) =0 O=x* —4x-12 0 =(x—6)(x +2) v Factors A(-2:0) Y both x values B(6;0) “x =-2 . . - for turning points of/vir v= (3) draaipunte van h 3.4 S'(x)* g(a) $0 Y criticalvalues 2.x €[-2;2] Y notation (2) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmorephysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTIONVRAAG 6 6.1 | T(O; 1) v answer fair Q) had »y -@ Y substitute B 6.2 pe 8 | 3 v answer ast 2 (2) 2 3)" v base 6.3 &(x) = (5) OR/OF g(x) = (3) Y exponent (2) 3y Y swop x and y a. _(3 6.4 Joix= (5) Y answer “y=log,x : (2) 6.5 log, x=1 2 3 vv x= > yu} _ . 5 ; lx) <1 critical values £® 3 Y notation xe(0;—] GB) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadedénom Stanmoreph sics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7A A= P(l+i)" Bx = x(1+ 0,098)" Y correct substitution in 3 = 1,098" correct formula =| 3 no OB 108 Y use of logs (independent n=11,751 It will take 12 years to triple the money/Dit sal 12 jaar neem om die geld te mark) ¥ 12 also accept 11,75 verdriedubbel. (3) 72 i)’ j= 22085 42.1 rp -Ml+)) -1 via i n=120 bothiandn 0,085 \'° y( + D | - Y substitution in correct 64000 = formula 0,085 Y answer 12 x = 34018 3) 96 ¥9%=n 8: sous (1- 0,0 *) ] o4 | ¥ compound interest 24 722 F= 12 + 0,085 months . 0,085 12 v answer 12 = 55135,69 GB) 73 0,104\~7 4 1-(1+-——- P= 396,83] ( +? ) ¥2=nandi == 73.1 , 0,104 = R234770,75 12 ¥ substittition into correct formula v answer; Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednénom Stanmoreph Grade/Graad 12 Prep. Exam./Voorb. Eksam. sics.com Marking FS/VS/September 2023 uidelines/Nasienriglyne Jan} Jonni — ALTERNATIVE methodALTERNATIEWE metode 74 108 4000001 + al 108 i 19693 (16) -| 2 7 0,104 12 = R234770,77 ¥ loan with n = 108 Y F, with n= 108 v answer (G3) Copyright reserved/Kopiereg voorbehou 7.3.2 During 9 years, she paid R474 857,64. Y R474 857,64 Her payment on the loan however is only Y R165 229,25 or R165 229,25. R165 229,23 She paid interest of R309 628,39 over the 9 | Vv R309 628,39 or years./Gedurende 9 jaar het sy R474 857,64 R306 628,41 betaal. Haar betaling op die lening is egter slegs R165 229,25. Sy het rente van R309 (3) 628,39 oor die 9 jaar betaal [15] NO] Please turn over/Blaai om asseblief

DPewnleadednénom Stanmoreph sics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTIONWVRAAG 8 Penalise 1 mark for incorrect notation in question 8 only/Penaliseer slegs 1 punt vir verkeerde notasie in vraag 8. 8.1 f(x) =3-x° ; Y =3-x°-2xh-h f(x+h)=3-(x+A) wes =3-—x*? —2xh-h? He) = Tey LEFF) F(x) = fim ) v substitution in correct . 3-x° -2xh-? -(3-x7 formula = fim, 7 . 2 = lim 224 Y simplify =) h = Tim A(- 2x- h) ¥ factors =) h = lim (-2x-h) Y answer =-2x (5) 8.2 Vv -1 8.2.1 oJ? -vs| x Ve i = Ty? = o,|2s x | V 2x2 - 1G 2x -=x yi x2 2 (4) 8.2.2 =(x3-1 * (° y Y x6 2x +1 yp=x’-2x' +1 Y 6x5 oD 6x5 — 6x? ¥ — 6x? dx (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dawnloadednérom Stanmorephysics.com F9/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne 8.3 f(x) =x° -12x-16 8.3.1 (a) f(x) = 3x? -12 Y 3x7 -12 v=0 0 =3(v-2\x+2 (x—2\v+2) Y¥ factors x=2 x=-2 ¥ (2; -32) 2. (2-32) ¥(-2; 0) (-2;0) (5) 8.3.1(b) x -12x-16=0 v y=0 Y factors 2 2\x-4)= (« * Ke * Ke ) ° Y BOTH answers x=-2 x=4 (3) 8.3.2 15=3x? -12 Y derivative = 15 > Y standard form 0=3x° -27 V x=3 x =9 Y x=-3 x=33 (4) 8.3.3 S'"(x) = 6x 0=6x ¥ 6x=0 Con 0 ‘honk ; , Y values oncave up/konkaaf op: x €(0;0) V notation or writlen/ofgeskryfas x > 0 (3) [27] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Dewnleadednfnom Stanmoreplysics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTION/WVRAAG 9 9.1 lag A v turning point loi , im v shape Y x- intercepts 0 1 (i 5) (1:3) (3) 9.2 T(t) =60+27t-t* _ T(6)-T@) Y correct formula 9.2.1 Average change/ | Y substitution 6-114 v answer Gemid. verandering = 3 =-36 (3) 9.2.2 0=27-30° Y 27-307 By? v=0 Stank Y answer es (3) 19] = Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Hewnleadednférom Stanmore physics.com FS/VS/September 2023 Grade/Graad 12 Prep. Exam./Voorb. Eksam. | Marking Guidelines/Nasienriglyne QUESTIONVRAAG 10 10.1 P(A) = 0,4 P(B) = 0,5 10.1.1 P(A or/of B) = P(A) + P(B) Vv P(AandB)=0 — P(A and/en B) Y answer = 0,4+0,5-0 =0,9 (2) 10.1.2 P(A or/of B) = P(A) + P(B) Y tule — P(A and/en B) V P(A)x P(B) = P(AandB) =0,4+ 0,5 -(0,4 x 0,5) v answer =0.7 (3) 10.2 10.2.1 5x5x10x9 v5 = 2250 v5 v 10 v9 (4) 10.2.2 1x5x9x5 Y denominator 2250 2250 v 1x5 l ¥ 9x5 “10 v answer =0,1 (4) [13] Copyright reserved/Kopiereg voorbehou TOTAL/TOTAAL: 150 Please turn over/Blaai om asseblief