Mathematics Grade 11 Paper 1 North West June 2018 Memo

Downloaded from hlayiso.com GRADE/GRAAD 11 MATHEMATICS P1/WISKUNDE V1 MEMORANDUM MID –YEAR EXAMINATION 2018/ HALF-JAAR EKSAMEN 2018 MARKS: 100 PUNTE: 100 Demo NW/JUNE/MATH/ EMIS/6******* This memorandum consists of 8 pages. Hierdie memorandum bestaan uit 8 blabsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 2 June/Junie2018 NSC/NSS QUESTION/VRAAG 1 1.1.1 ( 3x –1 )( x + 3 ) = 0  Equating to 0 / Gelykstelling aan 0 1 x = or/of x = –3 3  Both Answers / Beide antwoorde (2) 1.1.2. ( 3x –1 )( x + 3 ) = – 5 3x2 + 8x + 2 = 0 3x2 + 8x + 2 = 0  b  b 2  4ac  formula/formule x 2a sub. into correct formula/ invervanging in korrekte  (8)  (8) 2  4(3)(2) x formule 2(3)  8  40  8  40 x  x 6 6 answers/antwoorde (5) x = – 0,28 or/of x = – 2,39 1.2.1 x 2  x  4 x 2  4  x  1 x  4  x x + 2 = 16 – 8x + x 2 x2 – 9x + 14 = 0  squaring/kwadrering (x – 7 )( x – 2 ) = 0 standard form/standaard x = 7 N/A/ N.V.T or/of x = 2 vorm factors/faktore answer/antwoord (5) 1.2.2 2 4( x 2  x)  7 x x 2 Let/Laat x2 – x = k  x2 -x = k 2 std form in k /stdvorm in k 4k  7 k factors/faktore 4k – 7k – 2 2 = 0 ( 4k + 1 )(k – 2 ) = 0 vales of k/waardes van k Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 3 June/Junie2018 NSC/NSS 1 k = or / of k =2 4 1 x2  x =  or / of x 2  x = 2  2 eqs. in x/2 vgl’s in x 4 4x2 – 4x + 1 = 0 or/of x2 – x – 2 = 0  3 values of x/ (2x – 1) (2x – 1) = 0 or/of (x – 2)(x + 1) = 0 3 waardes van x (7) 1 x= or / of x = 2 or / of x =  1 2 1.2.3 3x  2  3x 1  28   3x 3 2  31  28  taking CF outside/  28  faktorisering van GF 3x    28  9   simplification/ 3 9 x vereenvoudiging 3x  32 3x = 9 x  2  answer/antwoord (4) 1.2.4 x 2  4x  x 2  4x  0 x 2  4x  0  factors/faktore - end values/kritieke waardes x ( x  4)  0 0 4 0  x 4 notation/notasie (4) 1.3 x – 3 – y = 0 and/en x y = – 2 x = y+3  x = y+3 (y + 3) y = – 2 sub. of/inverv van x y2 +3y + 2 = 0 std form/std vorm (y + 2)( y +1) = 0 factors/faktore y = – 2 or/of y = – 1  y values/y-waardes x = – 2 + 3 = 1 or/of x = – 1 + 3 = 2 x values/x-waardes (7) Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 4 June/Junie2018 NSC/NSS QUESTION/VRAAG 2 2.1 x  3  18  2a 2   0 For equal roots/Vir gelyke wortels,   0  18  2a 2  0 18  2a 2  0 a2  9 a  3 a   3 (3) 2.2.1 ( a + 3 )2 + 12  0 ( a + 3 )2 is always positive /is altyd positief  Roots are real/ Wortels is reëel (2) ( a + 3 )2 + 12 will also positive/sal altyd positief wees Roots are real / Wortels is reëel 2.2.3 – 4( a – b )2< 0  – 4( a – b )2< 0 Roots are non-real / Wortels in nie-reëel  Roots are non-real / Wortels is nie-reëel (2) NB: Accept Irrational/ Aanvaar Irrasionaal QUESTION/VRAAG 3 3.1.1 3 a .9 a 1 3a .32( a 1) 4 =4 3a .32( a 1) 27 a  2 33( a  2)  4 33( a  2) = 4 33a 2 3a 6  4 33a 2 3a 6 = 4 3 4 answer / antwoord (3) 1 = 3 3.1.2 2 x 3  3.2 x 1 2 x (8  3.2 1 ) taking common factor = 2x2 2 x . 2 2 outside / faktorisering gemeensk faktor 3 8 3 = 2 8 1  2 1 4 4 = 26 answer/antwoord (3) Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 5 June/Junie2018 NSC/NSS 3.2 10 x 3 = 10x . 103  10x .103 = 1,7 x 1000 = 1700 answer/antwoord (2) 3.3 2. 9a  3. 2b = 2.32a  3. 2b  32a = 2.(p)2+ 3.(q)-1  sub of p and q./ Invervanging van p en q 3 = 2 p2  3 q  2 p2  (3) q QUESTON/VRAAG 4 4.1 4 ; 9 ; x ; 37  correct first differences/ 5 x-9 37- x korrekte eerste verskille x - 14 46- 2x  second differences / tweede verskille x – 14 = 46 – 2x answer / antwoord (3) x = 20 4.2 3a  b  5 abc  4 2a  6  value of/waarde van a 33  b  5 3  (4)  c  4 a3 value of/waarde van b b  4 c5 value of/waarde van c Tn  an2  bn  c  answer/antwoord (4)  3n  4n  5 4.3 3n – 4n + 5 = 212 2  equating to 212 / gelykstelling aan 212 3n2 – 4n - 207 = 0  standard form/std vorm 4 ± 16  4(3)(207) n= 6  values of/waardes van n 23 = 9 or / of 3 n = 9  answer/antwoord (4) Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 6 June/Junie2018 NSC/NSS QUESTION/VRAAG 5 5.1.1 𝑖 𝑚 𝑖𝑒𝑓𝑓 = (1 + ) − 1  formula/formule 𝑚 12 correct sub. into formula/  0,075  = 1   1 korrekte inverv. in formule  12  = 0,07763259... Rate/Koers = 7,76% answer /antwoord (3) 5.1.2 A  P(1  i )n formula/formule  0,075  412  1200001   sub. into the formula/  12  inverv. in formule = R 161831,90 answer/antwoord (3) 5.2 A  P( 1 i )n formula/formule = 80000(1– 0,12)3 sub. into the formula/ = R54517,76 inverv. in formule answer/antwoord (3) 5.3 0,12 12 0,14 4  0,12  12 x(1  ) (1  )  95000  1   4 6  4  12 4  0,12   0,14   0,14  4 x1   1    95000  1   4   2    2  x1,868881682  95000  equating to/gelykstelling x  R50832,54 aan 95000  1,868881682 answer/antwoord (5) QUESTION/VRAAG 6 6.1 a g ( x)  6 x2  value of/waarde van p a  value of/waarde van q 0 6  value of/waarde van a 5 2  equation/vergelyking 2 (4) a  3 Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 7 June/Junie2018 NSC/NSS 3 g ( x)  6 x2 6.2 x R , x  2  answer/antwoord (1) 6.3 5  end points/kritieke waardes 2 x  2  correct notation/korrekte notasie (2) 6.4 3  x coordinate/koördinaat F  ; 12  y coordinate/koördinaat 2  (2) QUESTION/VRAAG 7 7.1.1 y =–4 y =–4 7.1.2 f ( x)  2 x 1  4 making/maak y=0 0  2x 1  4 2 x 1  22  22 x = 3 x=3 (3 ; 0) (3) 7.1.3 y- intercept /y-afsnit y-int/y-afsnit 7 y = y  20  1  4  2 x-int/x-afsnit  shape(increasing)/ vorm(stygend)  asymptote / asimptote (4) Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 8 June/Junie2018 NSC/NSS 7.1.4 Range/Waardeversameling is y   4 answer/antwoord (1) 7.1.5 m  21  1  4   3 answer/antwoord (1) 7.2 y shape(concave up)/ vorm(konkaaf op)  x-intercepts (one +ve and one –ve)/ x-afsnitte ( een +tiewe en een - x tiewe)  -ve y-intercept/ -tiewe y-afsnit -ve axis of symmetry / -tiewe simmetrie-as (4) Demo Copyright reserved/Kopiereg voorbehou NW/JUNE/MATH/ EMIS/6******* Please turn over/Blaai om asseblief