NATIONAL SENIOR CERTIFICATE EXAMINATION MATHEMATICS JUNE EXAMINATION GRADE 11 PAPER 1

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1 NATIONAL SENIOR CERTIFICATE EXAMINATION MATHEMATICS JUNE EXAMINATION 05 GRADE PAPER MARKS : 00 This questio paper cosists of 5 pages TIME : hours

2 Mathematics P MDoE/Jue Eam 05 INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios.. This questio paper cosists of questios.. Aswer ALL the questios.. Clearly show ALL calculatios, diagrams, graphs, etcetera which you have used i determiig your aswers.. Aswer oly will NOT ecessarily be awarded full marks. 5. You may use a approved scietific calculator (o programmable ad o-graphical), uless stated otherwise.. If ecessary, roud off aswers to TWO decimal places, uless stated otherwise. 7. Diagrams are NOT ecessarily draw to scale. 8. Number the aswers correctly accordig to the umberig system used i this questio paper. 9. Write eatly ad legibly.

3 Mathematics P MDoE/Jue Eam 05 QUESTION. Solve for.. ( 5)( ) 0 ().. (correct to decimal places) ().. ( ) 0 ().. 7 ()..5 (). Give: ab b.. Show that: b a ().. Hece, solve for a ad b simultaeously if it is further give that a ab (5). If 5, without solvig for, determie the value of:.. ().. () [] QUESTION. Calculate.8. without the use of calculator. (). Simplify : (7) () []

4 Mathematics P MDoE/Jue Eam 05 QUESTION. Cosider the epressio which the epressio is: 5 5 ad determie the value(s) of for.. equal to 0 ().. udefied (). Determie the value(s) of p for which the equatio, p where p 0 has o real roots. (). The roots of a quadratic equatio are give by r QUESTION 0 8r, where 7 ; ; ;0;;;. Write dow two values of r for which the roots will be ratioal. (). Cosider the followig umber patter: ; - ; -9 ; -7 ;..... Determie the geeral term for the above umber patter: ().. Determie the value of the 0 th term. ().. Which term i the patter will equal to -57? (). The secod differece of the quadratic umber patter QUESTION 5 8 ; y ; 0 ; is. Determie the value of y. () Give: h ( ) 5. State the equatios of the asymptotes of h. () 5. Write dow the equatio of the lie of symmetry of h which has a egative gradiet. () 5. State the domai of h. () 5. Determie the - ad y -itercept of h (). () [5] []

5 Mathematics P 5 MDoE/Jue Eam Sketch h, o the set of aes, idicatig the itercept with the aes ad the asymptotes. () 5. Determie the average gradiet of h betwee ad () QUESTION [5]. The graphs of f ( ) b ad g ( ) a are draw below. K(;) is a commo poit of the two graphs. K(;) f g.. Determie the equatios of f ad g ().. For which values of is f decreasig? ().. For which value of is g ( ) f ( )? ().. Write dow the equatio of the ais of symmetry of f. ()..5 Write dow the equatio of g, if g is the graph formed by traslatig the graph of f uits to the right ad uits up. (). Draw the sketch graphs of f ( ) a b c i the followig case: a 0, b 0, c 0, 0 () [] TOTAL: 00

6 NATIONAL SENIOR CERTIFICATE MATHEMATICS/ WISKUNDE JUNE EXAMINATION JUNIE EKSAMEN 05 GRADE/ GRAAD PAPER / VRAESTEL MEMORANDUM MARKS/ PUNTE: 00 TIME/ TYD : H This memoradum cosists of 8 pages/ Hierdie memoradum bestaa uit 8 bladsye.

7 Mathematics/Wiskude/Grade P Memo MDoE/Jue/ Juie Eam 05 Mark accordig to the method used by cadidate. / Merk volges leerder se metode. Cosistece accuracy to be used./ Volg atwoorde op met kosekwete akkuraatheid. QUESTION/ VRAAG.. ( 5)( ) 0 5 or/ of.. 0 ( ) ( ) () ()(),58 or/ of 0, 5 () stadard form/stadaardvorm substitutio/ substitusie, 58 0, Pealise mark for wrog roudig off Pealiseer met put vir afrodig wat verkeerd is. ().. ( ) 0 ( )( ) 0 critical value/ kritiese waarde: Critical value/ kritiese waarde R, () R,.. 7 () 7 () 9 ()..5 ( ) ( ) or / of N/A / vt 7 squarig both sides/ kwadreer beide kate stadard form/stadaardvorm both factors/ albei faktore 7 or / of choosig/ kies 7 ()

8 Mathematics/Wiskude/Grade P Memo MDoE/Jue/ Juie Eam 05.. ab b ( ) a b b a b b b a ( ab) a b b ().. b a.() a ab. () Subst./ vervag () ito/i () : a a( a) a a a 8a a 0 a a 0 a a 0 a or a b b substitutio/ vervag stadard form / stadaardvorm factors/ faktore values of a/ waardes va a values of b / waardes va b (5) squarig both sides/ kwadreer beide simplificatio/ vereevoudig aswer/ atw... (5)(7 ) 0 factors/ faktore substitutio/ vervag aswer/ atw. () () QUESTION / VRAAG additio of epoets/ tel ekspoete op aswer/ atw. [] ()

9 Mathematics/Wiskude/Grade P Memo MDoE/Jue/ Juie Eam rewritig the powers with prime bases Herskryf met priembasisse multiplyig the epoets Vermeigvuldig ekspoete addig epoets of like terms optel va ekspoete met selfde basisse takig out a commo factor Haal gemeeskaplike factor uit (7) aswer/ atw. () []

10 Mathematics/Wiskude/Grade P Memo 5 MDoE/Jue/ Juie Eam 05 QUESTION / VRAAG or / of p p b or / of p p p p p p ac p p (0) 5 p p 0 p ( p ) for o-real roots/ ie-reële wortels 0 p p 0 p p 0 p(p ) 0 critical values : p 0 or p 5 0 stadard form/ stadaardvorm factors/ faktore values/ -waardes 5 0 factors/ faktore values / -waardes stadard form/ stadaardvorm substitutio/ vervag 0 factorisatio/ faktore () () 0 p 0 or /of p p 0 ; p or / of (). - ad /e - () [5]

11 Mathematics/Wiskude/Grade P Memo MDoE/Jue/ Juie Eam 05 QUESTION/ VRAAG.. ; - ; -9 ; -7 st diff eerste verskil d diff - - tweede verskil a a a b ( ) b b a b c c.... T T or 5 (N/A) ; y ; 0 value of a/ waarde va a value of b/ waarde va b value of c/ waarde va c T () substitutio/vervag aswer/ atw () T -57 factors/ faktore values of / waardes va choosig correct value/ kies die korrekte waarde vir () y 8 0 y ( 0 y ) ( y 8) 8 y y st differeces/ ste verskille ( 0 y ) ( y 8) aswer/ atw. () []

12 Mathematics/Wiskude/Grade P Memo 7 MDoE/Jue/ Juie Eam 05 QUESTION / VRAAG 5 y y 5. () 5. y c Substitutio/ vervag c Equatio/ vergelykig c () y 5. domai/ defversamelig: R, domai/ defversamelig: R, () 5. -it/ afsit; let/ laat y 0 y 0 0 simplificatio/ vereevoudig ;0 5.5 y-it/afsit; let/laat 0 y 0 y 0; y () shape/ vorm itercecpts with the aes/ afsitte met asse asymptotes/ asimptote ()

13 Mathematics/Wiskude/Grade P Memo 8 MDoE/Jue/ Juie Eam h 5 h h Average / gem h 5 h() 5 h() - average/ gemiddelde gradiët () [5] QUESTION / VRAAG.. f ( ) b b b f ( ) substitutio/ vervag equatio/ vergelykig g( ) a a a substitutio/ vervag a equatio / vergelykig () g( ).. 0 R OR/OF ;0 aswer / atw. ().. 0 aswer / atw. ().. 0 aswer / atw. () y aswer / atw. ()..5. y shape/ vorm 0 c turig poit i the th quadrat & graph ot cuttig ais dp i die de kwadrat e grafiek sy ie die -as ie y itercept below - ais y-as afsit oder die -as () [] TOTAL/ TOTAAL 00

GRADE 12 NATIONAL SENIOR CERTIFICATE MATHEMATICS P1 PREPARATORY EXAMINATION 2008

GRADE 12 NATIONAL SENIOR CERTIFICATE MATHEMATICS P1 PREPARATORY EXAMINATION 2008 GRADE NATIONAL SENIOR CERTIFICATE MATHEMATICS P PREPARATORY EXAMINATION 008 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, a formula sheet ad diagram sheet. Mathematics/P DoE/Preparatory