Mathematics Grade 10 P2 National November 2017 Memo (Afr)

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 10 MATHEMATICS P2/WISKUNDE V2 NOVEMBER 2017 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 100 These marking guidelines consist of 10 pages. Hierdie nasienriglyne bestaan uit 10 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 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 Median/Mediaan = 54 answ./antw. (2) 1.2 Range/Variasiewydte = 90 − 34 = 56 answ./antw. (2) 1.3 IQR(IKV) = Q 3 − Q1  Q1 =46 = 73 − 46  Q 3 =73 = 27 answ./antw. (3) 1.4 min. & max./maks. median/mediaan (Q 2 ) Q 1 and/en Q 3 (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 3 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1 30 days/dae answ./antw. (1) 2.2 28 ≤ T < 32 answ./antw. (1) 2.3 44 + 104 + 270 + 170 + 266 + 126  addition/optel The mean/Gemiddeld (X ) = 30 30 980 = 30 answ./antw. = 32,666 (3) o = 32,67 C. 2.4 9 + 5 + 7 + 3 = 24 days/dae addition/optel 24 % of number of days/getal dae = × 100 answ./antw. 30 (2) = 80% [7] QUESTION/VRAAG 3 3.1 PQ = ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2 subst./verv. = (7 − 6) 2 + (4 − 6) 2 = (1) 2 + (−2) 2 answ./antw. = 5 (2) 3.2 M QS = T ( x; y ) 6+ x 7 6+ x 6+ y 7 7  =  ; = ;  2 2  2 2  2 2 6+ y 7 6+ x 7 6+ y 7  = = = 2 2 2 2 2 2 x =1 y =1 answ./antw. S (1;1) (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 4 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 3.3 PR = ( x p − x R ) 2 + ( y p − y R ) 2 = (7 − 0) 2 + (4 − 3) 2 = 50 answ./antw. =5 2 = 7,07 OR/OF QS = ( x S − xQ ) 2 + ( y S − y Q ) 2 = (1 − 6) 2 + (1 − 6) 2 answ./antw. = 50 =5 2 = 7,07 ∴ PR = QS (2) 3.4 6−3 1 1 mQR = =  mQR = 6−0 2 2 3 −1  m RS = −2 m RS = = −2 0 −1 mQR × m RS 1 1  × −2 = × −2 2 2  mQR × mRS = −1 = −1 mQR × m RS = −1 ∴ QR ⊥ RS (4) 3.5 Rectangle. /Reghoek. Rectangle/Reghoek The diagonals are equal and one of the interior reason/rede angles is equal to 90 0. Die hoeklyne is gelyk en een van die binnehoeke is gelyk aan 90°. (2) 3.6 5 5 cos RŜQ =  cos RŜQ = 5 2 5 2 RŜQ = 71,57°  answ./antw. (3) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 5 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1.1 4 cot θ + 3 = 0 (a) 3 3 cot θ = −  cot θ = − 4 4 diagram  r =5 3 3 cosθ = −  cosθ = − 5 5 (4) 4.1.1 3 sin θ sec θ 4 (b)  tan θ 5   4  5   5    −   − 5 3 3 = 3    4   −  simpl./vereenv.  3  answ./antw. =3 (4) 4.1.2 4 2 LHS =   − 1 subst./verv. 5 9 =− 25 answ./antw. 2  3 RHS = −  5 9 =− 25 answ./antw. ∴ sin 2 θ − 1 = −cos 2 θ. (3) 4.2 cos 30 o tan 60 o + cosec 2 45 o sin 2 60 o 3  and/en 3 2 2 2 3  2   3  = × 3 +  ×  2 3 2  2   2   and/en 2 2 3 4 3 = + × 2 2 4 3 3 = + 2 2 answ./antw. =3 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 6 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 4.3 4 sin θ = cos 37 o 3 multiplying by/ 3(0,79863551) sin θ = 3 4 vermenigvuldig met o 4 θ = 36,80 answ./antw. (2) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 7 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1 f shape/vorm  x-intercept/afsnit y-intercept/afsnit g shape/vorm x-intercepts/afsnitte y-intercept/afsnit (6) 5.2.1 Amplitude of/van g = 2 answ./antw. (1) 5.2.2 Range of/Waardeversameling van f : −2 ≤ y ≤ 0 critical values/kritieke OR/OF waardes y ε [−2;0] notation/notasie (2) 5.3.1 2 solutions/oplossings answ./antw. (1) 5.3.2 x = 180 o  x = 180 o (3) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 8 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1 θ = 47 o answ./antw. (1) 6.2 RQ  trig. ratio/trig. verhoud sin P = RP RQ subst./verv. sin 47 o = 21 RQ = 21sin 47 o answ./antw. RQ = 15,36m (3) 6.3 RQ tan S = QS 15,36 tan S = subst./verv. 17 ∧  15,36  S = tan −1    17  answ./antw. ∧ (2) o S = 42,10 6.4 PQ trig. ratio/trig. verhoud cos 47 o = 21 PQ = 21 × cos 47 o PQ = 14,32 m PQ = 14,32m PS = 14,32 + 17 addition/optel = 31,32m answ./antw. (4) [10] QUESTION/VRAAG 7 7.1 1 V = π r 2h 3 subst./verv. 1 83,38 = × 6,5π r 2 3 3 × 83,38 answ./antw. r2 = 6,5π (2) r = 3,5cm 7.2 s2 = h2 + r 2 subst./verv. s 2 = 6,5 2 + 3,5 2 answ./antw. s = 7,38cm (2) 7.3 Surface area of the solid/Buite-oppervlakte (Oppervlakarea) van die vaste liggaam = 2π r 2 + π rs subst./verv. = 2π (3,5) 2 + π (3,5)(7,38) answ./antw. = 158,12cm 2 (2) [6] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 9 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 ˆ = 90 o O Diagonal bisect at/Hoeklyne sny by 90 o . S/R 8.1.1 1 (1) 8.1.2 o o o L̂1. = 180 − (34 + 90 ) Sum of angles of/Som van hoeke ∆. S/R answ./antw. = 56 o (2) 8.1.3 Lˆ =Lˆ = 56 o diagonals bisect the/hoeklyne sny die ∠s. S/R 1 2 ˆL + L ˆ =Nˆ +N ˆ opp. ∠s of rhombus/ 1 2 1 2 teenoorst ∠evan die ruit = ∴ KNˆ M = 112 o answ./antw. (2) 8.2 m Given/Gegee : // PQRS with diagonals/met hoeklyne PR and/en R.P.T : PM = MR Proof/Bewys : In ∆PMS and/en ∆RMQ ∧ ∧  1. S/R 1. P1 = R1 (alt./verw. ∠ S , PS // QR) 2. S/R ∧ ∧ 3. S/R 2. S1 = Q1 (alt./verw. ∠ S , PS // QR) 3. PS = QR (opp. sides parm are /teenoorst. sye van parm. =) congruency/kongruensie ∴ ∆PMS ≡ ∆RMQ (AAS) (AAS) ⇒ PM = MR and MS = MQ (4) OR/OF OR/OF m Given/Gegee : // PQRS with diagonals/met hoeklyne PR and/en R.P.T : QM = MS Proof/Bewys : In ∆PQM and/en ∆RSM ∧ ∧ 1. P2 = R2 (alt./verw. ∠ S , QP // SR)  1. S/R ∧ ∧ 2. S/R 2. S 2 = Q2 (alt./verw. ∠ S , SR // PQ) 3. S/R 3. PQ = SR (opp. sides parm are/teenoorst. sye van parm =) ∴ ∆PQM ≡ ∆RSM (AAS) congruency/kongruensie ⇒ QM = MS and PM = MR (AAS) (4) 8.3 DB = 2DE (DE = EB) S/R DE = FC (opp. side of/teenoorst. sy van //gram.) S/R but/maar FC = 2KC (FK = KC) S/R DE = 2KC (DE = FC) DB = 2(2KC) (DB = 2DE) S/R DB = 4KC (4) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 10 DBE/November 2017 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 9.1 In ∆ACG F and/en H are midpoints/is middelpunte (given/gegee) ∴ FH // CG (midpoint theorem/middelpuntstelling)  FH // CG FE // BC (same straight lines/dieselfde reguitlyne) midpoint theorem/ In ∆AGB , H is the midpoint/is die middelpunt middelpuntstelling HE // BG (proved/bewys) ∴ E is the midpoint/is die middelpunt (Line drawn from midpt of side/Lyn getrek vanaf midpt van sy,  reason/rede // to 2nd side/na 2de sy ) (3) 9.2 AÊH = AB̂C = 90 0 (Corresponding angle/Ooreenst hoek ) 1 Area/Oppervl. = EH × AE 2 subst./verv. 1 9,5 = × 3,5 × AE 2  AE 38 AE = = 5,43cm 7 AB = 2 AE  38  AB = 2   7   AB 76 = 7 = 10,86cm (3) 9.3 BG = 7 cm (midpoint theorem/middelpuntstelling) BG =7 (midpt thm)/ BC = 14 cm (middelpuntstelling) 1 Area/Oppervl. = BC × AB BC=2BG=14 2 1 76 = × 14 × 2 7 2 = 76cm answ./antw. (3) [9] TOTAL/TOTAAL: 100 Copyright reserved/Kopiereg voorbehou