Gr10 Math P1 (English and Afrikaans) November 2017 Possible Answers_hlayiso.com_.pdf

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 10 MATHEMATICS P1/WISKUNDE V1 NOVEMBER 2017 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 100 These marking guidelines consist of 12 pages. Hierdie nasienriglyne bestaan uit 12 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 2 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne NOTE: • If a candidate answered a question TWICE, mark only the FIRST attempt. • If a candidate crossed out an answer and did not redo it, mark the crossed-out answer. • Consistent accuracy applies to ALL aspects of the marking guidelines. • Assuming values/answers in order to solve a problem is unacceptable. LET WEL: • As 'n kandidaat 'n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na. • As 'n kandidaat 'n antwoord deurgehaal en nie oorgedoen het nie, sien die deurgehaalde antwoord na. • Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing. • Dit is onaanvaarbaar dat waardes/antwoorde veronderstel word om 'n probleem op te los. QUESTION/VRAAG 1 1.1.1 q = b 2 − 4ac q = ( −1) 2 − 4( 2 × −4) subst./verv. q = 33 answ/antw (2) 1.1.2 Irrational/Irrasioneel answ/antw (1) 1.1.3 5 and/en 6 answ/antw (1) 1.2.1 2 t (r − s) − r + s grouping/ = t 2 (r − s) − (r − s) groepering = (r − s )(t 2 − 1) factors/faktore = (r − s )(t − 1)(t + 1) difference of two squares/ verskil van twee kwadrate (3) 1.2.2 x +13 2 x − x +1 factors/faktore ( x + 1)( x 2 − x + 1) = x2 − x + 1 answ/antw = x +1 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 3 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 1.3.1 (2 y + 3)(7 y 2 − 6 y − 8) = 14 y 3 − 12 y 2 − 16 y + 21 y 2 − 18 y − 24 simpl./vereenv = 14 y 3 + 9 y 2 − 34 y − 24 answ/antw (2) 1.3.2 3 2 + x − 9 ( x − 3) 2 2 3 2 = + ( x − 3)( x + 3) ( x − 3) 2 3( x − 3) + 2( x + 3) = LCD/KGN ( x − 3) 2 ( x + 3) 3x − 9 + 2 x + 6 simpl./vereenv = ( x − 3) 2 ( x + 3) 5x − 3 = answ/antw ( x − 3) 2 ( x + 3) (3) 1.3.3 t 3 −3 t −2 2.3t − 3t 3t (1 − 3 − 2 ) factors/faktore = t 3 (2 − 1) 1 1−  simpl./vereenv = 9 1 8 = answ/antw 9 (3) [17] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 4 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1.1 4 − 2 x < 16 − 2 x < 12  simpl./vereenv answ/antw x > −6 (2) 2.1.2  answ/antw -6 0 (1) 2.2 3x − 4 y = −4............(1) − 2 x − y = 10............(2) 3x − 4 y = −4.................(1) (2) × −4 : 8 x + 4 y = −40..............(3) multipl/maal (2) by/met 4 (1) + (3) : 11x = −44 adding/tel op (1) & (3) x-value/waarde x = −4 substitute x = −4 into (2) − 2(−4) − y = 10 y-value/waarde y = −2 (4) OR From(2) : y = −2 x − 10................(3) equation/verg (3) subst. (3) into (1) : 3x − 4(−2 x − 10) = −4  subst./verv. 3x + 8 x + 40 = −4 11x = −44 x-value/waarde x = −4 subst. x = −4 into (3) : y = −2(−4) − 10 y-value/waarde y = −2 (4) 2.3.1 x( x − 5) −1 = 0 6 stand. form/-vorm x 2 − 5x − 6 = 0 ( x − 6)( x + 1) = 0 factors/faktore x = 6 or x = −1  answ/antw (3) 2.3.2 c = a + 2x squaring/kwadrering c 2 = a + 2x 2x = c 2 − a c2 − a x=  answ/antw 2 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 5 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 2.4 Let Linda's age now be x/Laat Linda se ouderdom nou x wees Therefore Tabelo's age is 4x/Dus is Tabelo se ouderdom 4x 4x 6 years/jaar later: Linda’s age will be:/ Linda se ouderdom sal wees: x + 6 x + 6 Tabelo's age will be:/ Tabelo se ouderdom sal wees:4x + 6 4 x + 6 = 3( x + 6 ) 4 x − 3 x = 18 − 6 equating/verg. x = 12 Linda' s age/Linda se ouderdom is 12 years/jaar  answ/antw (4) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 6 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1 b = 14  answ/antw (2) 3.1.2 The sequence is linear/Hierdie ry is lineêr: Tn = pn + q. Tn = 3n + q 3n Tn = 3n + 2 2 (2) 3.1.3 Tn = 3n + 2 T15 = 3(15) + 2  subst./verv. T15 = 47  answ/antw (2) 3.1.4 Tn = 3n + 2 83 = 3n + 2  Tn = 83 3n = 81  answ/antw n = 27 (2) 3.2.1 Sum of the terms in rows/Som van terme in ry: 2 ; 16 ; 54 ; 128 ;……. Row/Ry 1: 2 x 1= 2 Row/Ry 2 : 2 x 8 = 16 Row/Ry 3 : 2 x 27 = 54 Row/Ry 4 : 2 x 64 = 128 . . gen./alg. term Row/Ry n : 2n 3  subst./verv.  answ/antw (3) Row/Ry 8 = 2(8) 3 = 1024 OR/OF OR/OF Pattern for the first terms in rows/Patroon van die eerste terme in rye: 2; 6; 14 ; 26 ; … 2 ; 4(1)+2 ; 4(1)+4(2)+2 ; 4(1)+4(2)+4(3)+2 ; ….  T8 = 114 T8 = 4(1 + 2 + 3 + 4 + 5 + 6 + 7) + 2 = 114 Sum of the terms in row 8/Som van terme in ry 8 sum of terms in row/som = 114 + 118 + 122 + 136 + 130 + 134 + 138 + 142 van terme in ry 8  answ/antw = 1024 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 7 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 3.2.2 2(20) 3  subst./verv. Mean in row/Gemiddeld in ry 20 = = 800  answ/antw 20 (2) OR/OF OR/OF First term of row/Eerste term in ry 20: T20 = 4(1 + 2 + 3 + 4 + .... + 19) + 2 = 762 Sum of terms in row/Som van terme in ry 20 = 762 + 766 + 770 + ... + 838. = 16000 16000 16 000 ∴ Mean/Gemiddeld = = 800 20  answ/antw (2) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 8 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1.1 Prt SI = 100  subst./verv. 18000 × 4,5 × 7 = 100 = R 5670,00  answ/antw (2) OR/OF A = P (1 + i.n) OR/OF = 18000(1 + 0,045 × 7) = R 23670 Interest/Rente = 23670 − 18000  R23 670 = R5670 R5 670 (2) 4.1.2 A = P(1 + i ) n  subst./verv. in correct R27660 = P(1 + 0,067) 5 formula/ korrekte formule 27660 P= (1 + 0,067) 5  simpl./vereenv P = R20000  answ/antw (3) 4.1.3 A = P(1 + i.n) 27660 = 18000(1 + i × 7)  subst./verv. 27660 7i = −1 18000 27660  simpl./vereenv −1 i = 18000 7 i = 0,07666.... Simple interest rate should have been/ Eenvoudige rente moes wees 7,67%  answ/antw (3) 4.2 Pound/Pond R16,52 proportion/verhouding = Dollar R12,91  £1 ≈ $1,28 ∴ £1 ≈ $1,28 (2) OR/OF OR/OF Dollar R12,91 proportion/verhouding = Pound/Pond R16,52 ∴ $1 ≈ £0,78  $1 ≈ £0,78 (2) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 9 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1 Range of/Waardeversameling van g : y ≤ 8  answ/antw (1) 5.2 x = −2  answ/antw (1) 5.3 2 g ( x) = ax + 8 ⇒ q = 8 q = 8  subst./verv. (2 ; 0) g (2) = a (2) 2 + 8 = 0 a = –2 ⇒ a = −2 (3) 5.4 f ( x) = mx + c ⇒ c = 8 c = 8 f (−2) = −2m + 8 = 0 subst./verv. (–2 ; 0) m = 4 ⇒m=4 f ( x) = 4 x + 8 (3) 5.5.1 x = −2 or x = 0  x = −2  x=0 (2) 5.5.2 x . g ( x) ≤ 0 –2 ≤ x ≤ 0 − 2 ≤ x ≤ 0 or x ≥ 2 or x ≥ 2 (3) 5.6 2 h ( x ) = −( −2 x + 8) 2 h( x ) = 2 x 2 − 8  2 x − 8 (2) [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 10 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1.1 The range/Waardeversameling van is y > −9  answ/antw (1) 6.1.2 x p( x) = k + q q = –9 p( x) = k x − 9 0 = k2 −9 subst/verv. (2 ; 0) k2 = 9 k = ±3 k = 3 since k > 0 k = 3 p( x) = 3 x − 9 (3) 6.1.3 asymptote/asimptoot intercepts/afsnitte shape/vorm (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 11 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 6.2.1 w = −1  answ/antw (1) 6.2.2 k f ( x) = −1 x k  subst./verv. 7= −1 (2 ; –7) −2  answ/antw k = −16 (2) 6.2.3 f ( x) = g ( x) − 16 −1 = −x −1 equating/verg. x x 2 − 16 = 0  simpl./vereenv ( x − 4)( x + 4) = 0 xQ = 4 or x P = −4 x = -4 at/by P x = 4 at Q (4) 6.2.4 − 4 < x < 0 or x > 4 − 4< x < 0 x>4 (2) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P1/Wiskunde V1 12 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7.1.1 P ( A) + P ( B ) = 1  answ/antw (1) 7.1.2 P( A and B) = 0  answ/antw (1) 7.1.3 P( B) = P( A′)  answ/antw = 0,35 (1) 7.2.1 S = 150 S B 20 28 x – 20 20 28  x − 20 8 8 (4) 7.2.2 x − 20 + 20 + 28 + 8 = 150 equation/verg. x = 114  value/waarde of/van x Smartphone only/Slegs slimfoon = 114 - 20  answ/antw = 94 (3) 7.2.3 94  answ/antw (a) P( S only/slegs) = = 0 ,63 (1) 150 7.2.3 94 28 8 (b) P( S or/of T or neither/of geeneen) = + + addition/optel 150 150 150 130 = 150 13 = 15 = 0 ,87  answ/antw (2) [13] TOTAL/TOTAAL: 100 Copyright reserved/Kopiereg voorbehou