Mathematics P2 Grade 10 Nov 2015 Afr & Eng Memo_hlayiso.com_.pdf

Downloaded from hlayiso.com basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 10 ‘ MATHEMATICS P2/WISKUNDE V2 " : NOVEMBER 2015 " " MEMORANDUM " *. ee ee o” MARKS: 150 PUNTE: 150 This memorandum consists of 13 pages./ Hierdie memorandum bestaan uit 13 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

NOTE: e Ifacandidate answers a question TWICE, mark only the FIRST attempt. Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 2 CAPS/KABV — Grade/Graad 10 (Memorandum) DBE/November 2015 e Ifa candidate crossed out an attempt of a question and did not redo the question, mark the crossed-out version. « Consistent accuracy applies in ALL aspects of the marking memorandum. Stop marking at the second calculation error. e Assuming answers/values in order to solve a problem is NOT acceptable. LET WEL: e Indien 'n kandidaat 'n vraag TWEE KEER beantwoord, sien slegs die EERSTE poging na. e Indien 'n kandidaat 'n antwoord doodgetrek het en nie oorgedoen het nie, sien die doodgetrekte poging na. e Volgehoue akkuraatheid word in ALLE aspekte van die memorandum toegepas. Hou op nasien by die tweede berekeningsfout. Om antwoorde/waardes om 'n probleem op te los, te veronderstel, word NIE toegelaat NIE. QUESTION/VRAAG 1 15 16 16 17 17 18 18 20 21 21 22 23 24 24 19 19 29 Median/Mediaan = 19 seconds/sekondes v answer/antw () 1.2 Lower quartile/Onderste kwartiel (Qi) = 17 YQ) Upper quartile/Boonste kwartiel (Q3) = 22 YQ; (2) 1.3 —— p___ ¥ box/mond T l14 T 17 T 19 T 722 T T T 29 T T v whiskers/snor 12 16 20 24 28 32 (2) 1.4.1 IQR/IKO = 26 - 19 ¥Q3-Q: =7 v answer/antw Q) 1.4.2 75% of the boys took at least 19 seconds to complete the puzzle./ v 75% 75% van die seuns het ten minste 19 sekondes geneem om die legkaart te voltooi. d) 1.5 About 50% but not more than 75% of the boys completed the Y relevant/relevante puzzle in less than 23 seconds./Ongeveer 50% maar nie meer as explanation/ver- 75% van die seuns het die legkaart in minder as 23 sekondes duideliking voltooi. More than 75% of the girls completed the puzzle in less than 23 seconds./Meer as 75% van die dogters het die legkaart in minder as 23 sekondes voltooi. Y girls/dogters Therefore more girls completed the puzzle in less than 23 seconds./Meer dogters het dus die legkaart in minder as 23 sekondes voltooi. (2) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 3 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) QUESTION/VRAAG 2 eNO ROF FREQUENCY GETAL UUR (h) FREKWENSIE 0<h <2 10 2<h <4 15 4<h <6 30 6<h <8 35 8<h <10 25 10<hA <12 5 2.1 The modal class is/Die modale klas is 6<h<8 V6<h<8 d) 2.2 vee ¥ midpts/midpt Average/Gemiddelde = 1x10+3x15+ +11x5 midpts/midpte 120 Estimated mean/Geskatte gemiddelde (X) = ~ v 730 = 6,08 hours/uur ¥ answer/antw (3) [4] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 4 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) QUESTION/VRAAG 3 y ‘A(0 ; 4) DC 4; 2y x 3.1 _ 2 2 Y correct formula/ DB = y(%1 —¥2)" +1 —¥2) korrekte formule = (4-4)? +(2-(-4))? 7 subst = 7644+ 36 = +100 Y answer/antw =10 fe) 3.2 XtX) | V+, Y correct formula/ M > korrekte formule 2 2 w{="*4 : 2-4) 2 a) v x-value/waarde M(0;-1) v ywatuchvaard 33 _-y2 MaD = xX Y¥ correct formula/ korrekte formule - 4-2 ¥ subst into/in 0-(-4) gradient form/ _2 01 gradiéntvorm 4 2 ¥ answer/antw GB) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 5 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) MAB = 1 2 x1 — 2 = 4-C4) v subst 0-4 _ 8 2 Y gradient of AB/ “140 gradiént van AB m,.xm,. =—x—2=-1 ‘AD *""AB Y My* Mp “AD | AB =-1 G) 3.5 parallelogram with one internal angle = 90° VR parallelogram met een binnehoek = 90° d) 3.6 1 me = Map => [KL || AD] ¥ gradient of KL 1 1 gradiént van KL ya aen ar Y equation/vgl (2) 3.7 AC=DB= 10 units [diag of rectangle =/hkle v regh =] VR 4- yo =10 ¥ equation/vgl yo = 6 “. C(O; -6) Y answer/antw (3) OR/OF mpc =™Map => [sides of rectangle | |/sye v regh | |] vR -4-yeo _1 4-0. 2 Y equation/vgl —8-2yc =4 yo =-6 C(O ; -6) Y answer/antw G3) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 6 CAPS/KABV — Grade/Graad 10 (Memorandum) DBE/November 2015 QUESTION/VRAAG 4 6 24 8 6 0 Q 10 R 411 10.5 impli tan P= ba _ > Accept answers as unsimplified Y answer/antw : ) 412 [| o. 63 sin SQR= 1 “3 v answer/antw @) 4.1.3 cos 0 105 Aanvaar antwoorde as nie- Y answer/ant 26 13 vereenvoudigde breuke. answenangy (1) 4.1.4 ~. 10 5 sec SRQ 7 = 3 Y answer/antw e) 42 [cot cosec QRS 1010 evades _10 10 24 8 24 8 1 1 ve =— 3 3 (3) [7] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 7 CAPS/KABV — Grade/Graad 10 (Memorandum) DBE/November 2015 QUESTION/VRAAG 5 y an 0 R r PO; y) v 5.1.1 x=-15 v x-value/waarde r=17 v r-value/waarde v4ytar? 2.2 442 . . (-15)* + y* =17 ¥ using/gebruik Pyth y? =64 y=-8 v y-value/waarde (4) 5.1.2(a) sin B = 8 Y answer/antw 17 (1) 5.1.2(b) | cos? 30°. tan B 2 v3 : (2) =8 “ 2) -15 vy 8 3. 8 -15 ary? 4 15 2 v answer/antw 5 @) 5.13 | ROP= 180° + 28,07° Y ref verwZ = 208,07° Y answer/antw (2) 5.2.1 tan x = 2,22 x= 65,75° vv answer/antw 2) 5.2.2 | sec(x+10°) = 5,759 1 Vv oOo °) = °) = ——_ cos(x +10 ) =——— cos(x+10°) = 0,173... OR/OF cos(x+10°) 5755 ( ) 5,759 x +10°= 80,0° Vv ref/verw Z x =70,0° Y answer/antw (3) $.2.3 sinX 5 494 a = 3,24 ¥ addition/optelling sin x = 0,648 ¥ multipl/vermenigv x = 40,39° Y answer/antw 3) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 8 CAPS/KABV — Grade/Graad 10 (Memorandum) DBE/November 2015 QUESTION/VRAAG 6 6.1 amplitude = 2 v answer/antw @) 6.2 min value/waarde = -2 + 3 =1 v answer/antw (e) 63 y ¥ y-intercept/afsnit 2 a g f Y (90° ; 2) | a ¥ (270° ; 0) x 0° 0° 180° 278 360° —l —2 (3) 64.1 | f(80°)—g(180°) =2-1 Y correct values/ =] korrekte waardes Y answer/antw (2) 6.4.2 | x € (90°; 270°) OR/OF 90° <x <270° Y correct values/ korrekte waardes Y notation/notasie (2) 6.5.1 f(x) =2 cosx-3 vv answer/antw (2) 6.5.2 |ye[-5;-l] OR/JOF -5<y<-l vv answer/antw (2) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 9 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) QUESTION/VRAAG 7 8cm [ 150 cm 30cm 30cm TA Vol of post = vol of rectangle + vol of pyramid Y sum of formulae/ = area of base x h+ + area of base x h Vol van pilaar = vol v reghoek + vol v piramide = oppervl v basis x h + + oppervl v basis x h som v formules ¥ subst into/in Volume = (30x 30x150)+ [$00 30x 8) both/beide 3 formulae = 137400 cm? ¥ answer/antw G) 7.2 Slant height of pyramid/Skuinshoogte van piramide =8? +15? =17 V17 Total surface area of pyramid = area of base + + (perimeter of base x slant height) Surface area of pyramid section = 4x & 30x1 7] = 1020 cm? Totale buite-oppervlakte van 'n piramide = oppervl v basis + 5 (omtrek v die basis x skuinshoogte) Surface area of pyramid section/Buite-opp van piramide gedeelte Y subst into/in 1 correct/korrekte = 4x{$<30x17] form Y answer/antw =1020 cm? (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 10 CAPS/KABV — Grade/Graad 10 (Memorandum) DBE/November 2015 73 Volume (new) -“( 37400) = 34350 cm? 137400 34350 Number of smaller posts that can be made = =4 Volume (nuwe) = <(137 400) = 34350 cm? 137400 34350 Getal kleiner pilare wat gemaak kan word = =4 OR/OF Volume (nuwe) = (15 x15 x150)+ [as x15x8)] = 34 350m’ 137400 34350 Getal kleiner pilare wat gemaak kan word = =4 1 Volume (new) = (15 x15 «150)+(S(tsx15x8)| = 34350 cm’* 137400 34350 Getal kleiner pilare wat gemaak kan word = =4 v 34 350 v4 (2) v 34 350 v4 (2) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 11 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) QUESTION/VRAAG 8 A B oO 56,878 8 cm D Cc 8.1.1 CDO = 36,87° ¥ answer/antw d 8.1.2 AOD = 90° ¥ answer/antw Q) 8.2 tan 36,87° -“° ¥ tan3687° =92 AO = 8x tan 36,87° =6em v answer/antw (2) 8.3 AD? =87 +67 [Theorem of Pythagoras/se = stelling] 100 v¥ AD= 10 with AD =10 reason/met rede AE =EB [converse midpoint theorem/omgekeerde midptst] YS VR OE = 5aD =S5cem [midpoint theorem/midptst] v Scm (4) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 12 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) QUESTION/VRAAG 9 9.1 9.1.1 Two sides and an included angle/Twee sye en 'n ingeslote hoek YR e) 9.1.2 one pr of sides = and | | VR een pr sye = en | | () wl. v 9.13 DE= 5 DF [DE = EF] s DF=BC [opp sides of parm/tos sye v parm =] vs “. DE= 5BC (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 13 DBE/November 2015 CAPS/KABV — Grade/Graad 10 (Memorandum) 9.2 S ae R M P B AA Q A 9.2.1 In ASAR, SB=BA [given/gegee] QR = QA [converse midpoint th/omgekeerde midptst] VSVYR But/maar QR= SP __ [opp sides of parm =/tos sye v parm=] YSYR . SP=QA (4) 9.2.2 SP=QA [proven/bewys/ ¥ both statements/ SP || QA [opp sides of parm | |/tos sye v parm | |] beide bewerings “. SPAQ isa parm [one pr of sides = and | |/een pr sye = en | |] YR (2) 9.2.3 M midpoint of/midpt van PR and/en B midpoint of/midpt van PQ [diag bisect of parm/hkle halveer parm] | VS 1 oye : VSVR MB = FOr [midpoint theorem/midptst] 1 mB =1(1ar VOR =) AR 2\2 .. 4MB = AR (4) [14] TOTAL/TOTAL: 100 Copyright reserved/Kopiereg voorbehou