NATIONALE SENIOR SERTIFIKAAT EKSAMEN WISKUNDE JUNIE EKSAMEN GRAAD 10 VRAESTEL
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1 NATIONALE SENIOR SERTIFIKAAT EKSAMEN WISKUNDE JUNIE EKSAMEN 05 GRAAD 0 VRAESTEL PUNTE : 00 TYD : UUR Hierdie vraestel bestaan uit 7 bladsye.
2 Wiskunde MDoE/Junie Eksamen 05 INSTRUKSIES: Lees die volgende instruksies aandagtig deur voordat die vrae beantwoord word.. Hierdie vraestel bestaan uit 8 vrae. Beantwoord AL die vrae.. Dui ALLE berekeninge, diagramme, grafieke ensovoorts wat jy in die bepaling van jou antwoorde gebruik het, duidelik aan. 3. Volpunte sal nie noodwendig aan antwoorde alleen toegeken word nie. 4. Jy mag n goedgekeurde, wetenskaplike sakrekenaar (nie-programmeerbaar en nie-grafies) gebruik, tensy anders vermeld. 5. Rond antwoorde af tot TWEE desimale plekke indien nodig, tensy anders vermeld. 6. Diagramme is NIE noodwendig volgens skaal geteken nie. 7. Nommer die antwoorde duidelik en korrek volgens die nommeringstelsel wat in hierdie vraestel gebruik is. 8. Dit is in jou eie belang om leesbaar te skryf en die vraestel so netjies moontlik te beantwoord. Kopiereg voorbehou
3 Wiskunde 3 MDoE/Junie Eksamen 05 VRAAG. Bewys dat n rasionale getal is. (3). Bepaal tussen watter twee opeenvolgende heelgetalle die getal, 5 7 sal lê. (3).3 Bepaal die produk ( 3y)( 3y + 7y ) en vereenvoudig dan jou antwoord. (3).4 Vereenvoudig:.4. (4) (3) n n n 6. (3).5 Bewys dat 3 ook geskryf kan word as 3 4 VRAAG. Los op vir :. (3) [].. ( + 5) 3( +) = 9 (4) = 5 (). Los vir op en illustreer die antwoord op n getallelyn: 5 3 < 9 (4).3 Die formule gee die buite-oppervlakte van n silinder: SA = rh + r Maak H die onderwerp van die formule: ().4 Drie liniale en vyf potlode kos R6. Een liniaal en twee potlode kos R0. Gestel die prys van een liniaal is rand en die prys van een potlood is y rand..4. Skryf n stelsel vergelykings neer, in terme van en y wat die gebruik kan word om die bogenoemde problem mee op te los. ().4. Los nou die stelsel vergelykings in VRAAG.4. gelyktydig op en bereken dan die prys van n liniaal en n potlood. (4) [8] Kopiereg voorbehou
4 Wiskunde 4 MDoE/Junie Eksamen 05 VRAAG 3 3. Vir n begin verdien Linda R400 per maand as verkoopsdame. Elke maand daarna ontvang sy n verhoging van R Bereken wat Linda elke maand vir die eerste drie maande verdien. (3) 3.. Skryf n formule neer vir die bedrag wat sy na n maande verdien. () 3..3 Hoeveel verdien Linda na een jaar? () 3. n Patroon bestaande uit driehoekige en reghoekige-vorms word deur pyle as volg gekontrueer: Figuur Figuur Figuur Bereken die totale aantal pyle wat gebruik word vir die eerste 4 figure. () 3.. Bepaal die aantal pyle in die de n figuur :... T n () 3..3 Watter figuur sal presies 43 pyle gebruik? (3) [4] VRAAG 4 4. Bepaal die waarde van cos en die grootte van die hoek in die volgende figuur. () As sin =, 3 ( 0 < < 90 o ), bepaal elk van die volgende sonder die gebruik van n sakrekenaar: 4.. tan (3) 4.. sin + cos () 4.3 Bepaal die waarde van cos 45 sin 30 sonder die gebruik van n sakrekenaar. (3) 4.4 As = 37 0 en y = 4 0, gebruik jou sakrekenaar en bepaal die waarde van sin ( + y) korrek tot een desimale plek. () [] Kopiereg voorbehou
5 Wiskunde 5 MDoE/Junie Eksamen 05 VRAAG 5 5. In die onderstaande diagram is AD BC en AB AC. A B D C Skryf TWEE formules neer vir elke verhouding : 5.. sin B () 5.. cos B () [4] VRAAG 6 6. Bereken met redes die waarde in die volgende diagram wat uit reguitlyne bestaan. AB // CD E H A T + 30 B C K D F G (3) Kopiereg voorbehou
6 Wiskunde 6 MDoE/Junie Eksamen ABCD is n parallelogram met hoeklyne AC en BD wat in O sny. A B O D C VRAAG 7 Bewys met nodige redes dat : 6.. AOB DOC (4) 6.. Die hoeklyne mekaar halveer. () Gegee die funksies g ( ) 9 en f ( ) 6 7. Teken die grafiek van f en g op dieselfde assestelsel. (4) 7. Bereken die waardes van waarvoor f() g(). (4) 7.3 Vervolgens of andersins, gebruik jou grafiek om die waardes van te bepaal waarvoor: 7.3. g( ) f ( ) () 7.3. g ( ) 0 () 7.4 Gee die vergelyking van die refleksie van g in die ais. () [3] [9] Kopiereg voorbehou
7 Wiskunde 7 MDoE/Junie Eksamen 05 VRAAG 8 8. Die skets toon grafieke van f () = en y k g( ). Die Die grafieke sny in die punt A(;). f A(;) ) g 0 Gebruik die grafiek en beantwoord die volgende vrae: 8.. Skryf die definisieversameling van die grafiek van f neer? () 8.. Skryf die vergelyking van die asimptote van die grafiek van y = neer. () 8..3 Bepaal die waarde van k? () 8. Geskets g ( ) cos en f ( ) sin vir [ 0 ; 360] y g f - Gee die amplitude van die volgende: 8.. g () 8... f () 8.3 Vir watter waarde(s) van is f dalend, waar [ 0 ; 360]? () TOTAAL: 00 punte [8] Kopiereg voorbehou
8 NATIONAL SENIOR CERTIFICATE MATHEMATICS/WISKUNDE JUNE EXAMINATION JUNIE EKSAMEN 05 GRADE/ GRAAD 0 MEMORANDUM MARKS/ PUNTE : 00 TIME/ TYD : H
9 Mathematics/ Wiskunde MDoE/June/Junie Eamination/Eksamen 05 QUESTION/VRAAG. Let / stel 3, ( ) , : answer/ antw. 75 (3) method/ metode answer/ antw. 5 7 lies between/ lê tussen 3 and/en 4.3 ( 3y)( 3y 7y ).4. ( 3y 7y ) 3y( 3y 7y ) ( 3y + 7y ) 3y( 3y + 7y ) y 4y 6y 9y y y 3y y 3 ( )( ) ( ) ( ) (3) 4 3 and/en y 3 6 y 4y 6y 9y answer/ antw. ( )( ) simplification/ vereenvoudiging (3) answer/antw. (4)
10 Mathematics/ Wiskunde 3 MDoE/June/Junie Eamination/Eksamen 05 ( ) ( ) = 4 = = 4 ( ( ). 4 n n n 6. n 4n )( ) n.. n n 4n ( ) factors/faktore answer/antw. (3) (n+) and/en 4n method/ metode answer/antw. (3).5 ( ) ( 3) ( -) ( 3) [( ) ( 3)][( ) ( 3)] ( 3)( 3) ( )(3 4) QUESTION/ VRAAG.. ( 5) 3( ) ( 3)( 5) or 5 0 [ ( ) ( 3)] [( ) ( 3)] simplification/ vereenvoudiging (3) simplification/ vereenvoudiging [] standard form/ stdvorm factors/ faktore answer (both -values)/ Antw. (beide -waardes)
11 Mathematics/ Wiskunde 4 MDoE/June/Junie Eamination/Eksamen 05 3 or / of 5 (4) answer/ antw. () method/ metode change of inequality sign when divided by -/ verander die ongelykheids teken sodra deling deur - plaasvind.3 SA = rh + r SA r = rh SAr H r -3 - value of / waarde van correct representation on number line/ korrekte voorstelling op getallelyn (4) SA r = rh answer/ antw. () y 6 3 5y 6 y 0 y 0 () y 6...(i) y 0...(ii) equation (iii)/
12 Mathematics/ Wiskunde 5 MDoE/June/Junie Eamination/Eksamen 05 From/ van (ii) 0 y...(iii) Substitute/ vervang (iii) into/ in (i) 3(0 y ) 5y y 5y 6 y 4 vergelyking(iii) substitution/ vervanging y 4y = 4 From/ uit (iii) 0 (4) A ruler cost R and a pencil cost R4 n Liniaal kos R en n potlood kos R4 y = 4 = QUESTION/ VRAAG ; 440 ; () 3.. T n = 40n n 360 () 3..3 T n = 40n substitute/vervang n = T () = 40() answer/antw. () = R ; ; 4;.... The number of arrows increases by 3/ Die aantal pyle vermeerder met 3 i.e the sequence is/ die ry is 8; ; 4; 7 forming the sequence/ vorming van ry (4) [8] Sum of arrows in st 4 figures/ som van pyle in die eerste 4 figure is: = = 50 adding the sequence/ optel van ry answer/ antw. (3) 3.. The common difference is 3. Die algemene verskil is 3. method/ metode answer/ antw. () [Give full marks for answer only i.e. T n 3n5] [ Gee volpunte indien slegs
13 Mathematics/ Wiskunde 6 MDoE/June/Junie Eamination/Eksamen 05 T 3 T 3 T 3 3 T n n 5 die antwoord neergeskryf het] 3..3 T n 3n5 3n5 43 3n 38 n 46 Figure 46 will have 43 arrows. formula/ formule 3n 5 43 answer/ antw. (3) Dus sal figuur 46, 43 pyle gebruik. [4] QUESTION/ VRAAG 4 4. cos 9 cos 9 = 68, 0 answer/antw. () tan 5 sketch/ skets = answer/antw. (3) 4.. sin cos substitution/ vervanging answer/ antw. () 4.3 cos 45 sin 30 =
14 Mathematics/ Wiskunde 7 MDoE/June/Junie Eamination/Eksamen sin37 4 answer/antw. (3) sin 6 substitution/ vervanging,75 answer/ antw. () [] QUESTION/ VRAAG AD sin B AB sin B AC BC sin B AD AB AC sin B () BC 5.. BD cos B AB BD cos B AB cos B AB BC AB cos B () BC [4] QUESTION/ VRAAG 6 6. ATE = 3.(Alts, vert.opp. s AB// CD,) (Ooreenk e, AB //CD) ATE + ETH + HTB = 80 o (sum of s on a str. Line/ ( + 30 o ) = 80 o o = 80 o 5 = 50 o ( op rtlyn) ATE = 3 ( statement & reason)/ (stelling en rede) ( + 30 o ) = 80 o (statement & reason)/ (stelling en rede) answer/ antw. (3) = 30 o
15 Mathematics/ Wiskunde 8 MDoE/June/Junie Eamination/Eksamen AOB and/ en DOC A = C.(Alts/ verw. s AB// DC) B = D.(Alts/ verw. s AB// DC) AB = DC (Opposite sides of a parallelogram/ teenoorst sye parm) AOB DOC (,, S) statement & reason /stelling en rede statement & reason Stelling en rede statement & reason/ Stelling en rede answer / antw. (4) AOB DOC (Proved/ bewys in 6..) In AOB AO = OC from congruency/ uit kongruensie statement & reason/ Stelling en rede answer/ antw. () DO = OB from congruency/ uit kongruensie the diagonals bisect each other/ hoeklyne halveer mekaar. [9] QUESTION/ VRAAG y 6 g and y-intercepts of g/ en y-as afsnit van g f and y-intercept of f/ X en y-as afsnit van f shape of g/ vorm van g shape of f/ vorm van f (4)
16 Mathematics/ Wiskunde 9 MDoE/June/Junie Eamination/Eksamen f ( ) g( ) ( 3)( ) factors/ faktore 3 or both -values Beide -waardes (4) critical values - & 3 Kritiesepunte - en 3 correct inequalities Korrekte ongelykhede () critical values -3 & After reflection in the -ais g will become/ na refleksie in -as g ( ) ( 9) or g ( ) 9 Kritiesepunte -3 en 3 correct inequalities Korrekte ongelykhede () answer/antw. QUESTION R answer/antw. () 8.. y = - answer/antw () 8..3 k substitution/ vervanging () [3] k answer / antw. () 8.. Amplitude = answer/antw. () 8.. Amplitude = answer / antw. () critical values/ kritiese punte correct inequalities Korrekte ongelykheids
17 Mathematics/ Wiskunde 0 MDoE/June/Junie Eamination/Eksamen 05 tekens () [8] TOTAL/ TOTAAL: 00 Marks/ Punte
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