# Mathematics Grade 12 Paper 2 North West Mock 2016 Memo > Grade 12 Mathematics Paper 2 memorandum from the North West Mock Exam 2016, 20 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/2016-grade-12-math-trial-exam-paper-2-nw-memo/27b1ef31-88b2-4ae5-989b-3803275ad4dc - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 12 - Document type: Memorandum - Year: 2016 - Exam period: North West Mock Exam - Paper: 2 - Curriculum: CAPS - Pages: 20 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 12](https://www.hlayiso.com/library/grade-12) › [Mathematics](https://www.hlayiso.com/library/grade-12/mathematics) › [Mathematics Grade 12 Paper 2 North West Mock 2016 Memo](https://www.hlayiso.com/library/2016-grade-12-math-trial-exam-paper-2-nw-memo/27b1ef31-88b2-4ae5-989b-3803275ad4dc) ## About this document Mathematics · Grade 12 · North West Mock Exam · 2016. Memorandum, 20 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com Education and Sport Development Department of Education and Sport Development Departement van Onderwys en Sportontwikkeling Lefapha la Thuto le Tlhabololo ya Metshameko NORTH WEST PROVINCE NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT MARKS: 150 PUNTE: 150 This memorandum consists of 17 pages. Hierdie memorandum bestaan uit 17 bladsye. ### Page 2 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 2 NW/September 2016 NSC/NSS — Memorandum QUESTION 1/ VRAAG 1 11 y= 12,01 + 0,88x Y value of a/waarde van a v value of b/waarde van b Y equation / vergelyking (3) 1.2 y= 12,01 +0,88(46) v sub. 46 into the = 52% equation / vervang 46 in die vergelyking v answer / antwoord (2) 13 No, the preparatory exam mark is the independent v answer / antwoord variable. Hence we cannot determine the prep. exam v reason /rede marks using the final exam./Nee,die voorbereidende (2) eksamenpunt is die onafhanklike veranderlike. Dus kan ons nie die voorbereidende eksamenpunt met behulp van die finale eksmenpunt bepaal nie. 14 x =60,58 Y x = 60,58 y = 65,33 Vv y =65,33 LHS/ ILK = y = 65,33 ¥ sub. into RHS / RHS/RK = 12,01 + 0,88(60,58) = 65,32 vervang in RK LHS/ILK = RHS / RK (x ; y) lies on the regression line v LHS = RHS and conclusion / LK = RK en gevolgtrekking (4) 1.5 r = 0,98 Y value of r/ waarde van r (1) 1.6 There is a very strong positive correlation between ¥ very strong / baie prep. marks and final marks./ Daar is’n sterk positiewe korrelasie tussen die voorbereidende punte en die finale punte. sterk Y positive / positief (2) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 3 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 3 NW/September 2016 NSC/NSS — Memorandum QUESTION 2 / VRAAG 2 21|/a=6 Y answer / antwoord () 22 Expenditure (in rand) Frequency Cumulative ' frequency 50 < x <100 24 24 100 < x <150 ae 76 150 < x <200 14 90 v 76; 90 200 < 25 x <250 6 96 ¥96:100 250 < x <300 4 100 2) 231] 120 3 sg 2 100 8 & g = 804 3 3 3 S69 SI Fs x 40 & £ 3 20 | =| 0 it 0 50 100 150 200 250 300 350 Expenditure/Uitgawes ¥ Correct points Y Shape V Grounding /¥ Korrekte punte ~Vorm “grondvlak @) 2.4 | 100 < x <150 ¥ answer / antwoord () (7] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 4 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 4 NSC/NSS — Memorandum QUESTION 3 / VRAAG 3 NW/September 2016 y 7 A(455) WA, —> x BC-3 ; -2 D C(6 ; -5) 31) Bc = Yl—x) +O.-9) J(6+3)? + (-5+2) 90 or/of 3V10 or /of 9,49 I ¥ sub. into the distance formula / Vervang in die afstandformule ¥ answer / antwoord (2) 32 _ Msc peTerae —5+2 64+3 1 3 +5 = eG) or/ of yr2= Le 43) 2 3 3 y= -$x-3 or 3y=-x-9 Y sub. into gradient formula / vervang in die gradiént formule gos 3 v equation / vergelyking @) ee ¥ Map = 3 ¥ sub. of the point / vervanging van die punt ¥ equation / vergelyking GB) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 5 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 5 NSC/NSS —- Memorandum NW/September 2016 3.4 1 a . Y equating the two equations / stel die _ twee vergelykings gelyk ee aan mekaar -10x = -12 6 x= 5 6 v x- value / x-waarde y = 3(2)-7 5 ul a : 6 17 y-value / y-waarde DG : -=) @) 3.5 _ 5+2 AB = ——— 4 +3 V map = 1 =1 ¥ tana = 1 tana = 1 Ya = 45° a = 45° tanB = 3 B =71,57° ¥B =71,57° BAD =71,57°—45° = 26,57° ¥ answer / antwoord GS) 3.6 | Equation of a line AE || BC/ vergelyking van AE || BC 1 —~5=-—(x-4 y 3% ) 3y-15 = -x+4 AE: 3y +x =19 x-intercept/x-afsnit is 3(0) +x =19 x =19 E (19: 0) 1 Y sub. of 2 and point into the equation / 7 1 vervanging van — 3 en die punt in die vergelyking Y equation of AE/ vergelyking van AE v x-intercepts / x-afsnit Yanswer / antwoord (4) [20] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 6 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 6 NSC/NSS — Memorandum NW/September 2016 QUESTION 4 / VRAAG 4 ys NQ; R »M(4 ; 2) oO 41 («-4" +(y-2" =P ¥ sub. of M into equation of a circle / vervang M (0-47 +(0-2P =r in die vergelyking van die sirkel 0~=r vsub. of O(0; 0) / vervang (0;0) 2 2 Y value of r’/ waarde (x-4)°+(y-2)° = 20 ae 3) 4.2 (x-4) + (y—-2)" = 20 Subst/Verv(2 ; y) ¥ sub of N(2; y)/ 2 _4y +(y- 2 = 20 vervang N(2 ; y) 4+y-4y+4=20 vy —4y-12 =0 y- 4y-12 =0 Y(- 6) +2) = 0 (y-6)(y +2) = 0 vy =6 4) y =6 or/of y =-2 N/A OR / OF OR/OF (x-4) +(y-2)° = 20 ¥ sub of N(2; y)/ Subst/Verv(2 ; y) vervang N(2 ; y) (2-4) +(y-2) = 20 2 Vv (y-2) =16 (y-2) =16 Voy, 2 = 4 y-2 =+4 y = 6 ot/of y =—2 N/A/INVT vy =6 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 7 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 u NSC/NSS — Memorandum NW/September 2016 43 2 tl 1 Moy “42 ¥ Mou a5 Mog =—2 Y Mop = —2 Equation of OR is /Vergelyking van OR ya-2 Vy =-2x @) 44 -2 Ym, = —-2 m, —— =_ 2) ‘MN MN 2-4 Myr =; Y Myx => 7 =+(-2) ee 2 Vv y-6= 1-2) 2y-12 = x-2 2 2(-2x) - x- 10 =0 -5x = 10 x=-2 y=2(2)=4 RC 2; 4) OR RO? = NR? vty = (x-2P + (W-6" ty =x -4x4+44 y? —12y +36 4x +12y =40 x+3y= 10 and y =-2x x +3(-2x)= 10 x-6x= 10 -5x= 10 x=-2 y=-2(-2) =4 RC 2;4) v 2(-2x) - x- 10 =0 (6) Ve +y = (x29 + (0-67 v4x +12y =40 Y x+3y= 10 ¥ x +3(-2x)= 10 v x=-2 vy=4 © Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 8 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 8 NW/September 2016 NSC/NSS — Memorandum 4.5 MNRO is a kite because/vlieér omdat OR =RN and /en ¥ Kite/Vlieér MN = OM ¥ adjacent sides equal /aangr.sye gelyk 2) [18] QUESTION 5 / VRAAG 5 5.1 ‘o Oy) ein 2(Q(0 _ cos(180°+ x) TELL x).sin“ (90° — x) Aghbe: sin(180° —x) (—cos x).(—tan x).cos? x Aer Y¥—cos x sin x v— tanx ¥cos*x sinx 4 vsin x cos x. COS” X = snk +sin’ x sinx = cos’ x + sin? x ¥ cos’ x + sin? x =1 Yanswer/antwoord (6) 5.2.1 | cos(A — B) — cos(A + B) ¥ expansion of cos(A-B) / = cos A cos B+ sin A sin B — [cos A cos B — sin A sin B] | uitbreiding van cos(A-B) = cos A cos B + sin A sin B—cos A cos B + sin A sin B | Yexpansion of cos(A+B) / = 2sin A sinB uitbreiding van cos(A+B) ¥ simplification / vereenvoudig (3) 22 cos15° — cos 75° = cos(45° — 30°) — cos(45° + 30°) v 45° — 30° and /en : 45° + 30° = 2sin 45°.sin 30° v 2sin 45°.sin 30 _ axr2yt or/of 2x-Lyb yy Lyd 272 v2 2 yO ap Db V2 1 ¥ answer / antwoord =— oof —~= 2 v2 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 9 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 9 NSC/NSS — Memorandum NW/September 2016 OR cos15° — cos 75° = cos(45° — 30°) — cos(45° + 30°) = cos 45°cos30°+sin45°sin 30°— [cos 45°cos 30° sin45°sin30°] = 2sin45° sin 30° = axd2 yh or/of 2x-Lxt D V2 2 v2 1 =— orof — 2 oT v 45° — 30° and /en 45° + 30° v 2sin 45°.sin 30 ya2 1b 1d Me yx 22 2 ¥ answer / antwoord 4) 5.3 AB? = (cos 0-6)" (sin0-7) 86 = cos’0 — 12cos 0+ 36 +sin’0 — 14sin 6 +49 86 = 1+ 36+ 49 - 12cos 0 -14sin 6 0 = - 12cos0 -14sin 0 14sin8 = — 12cos 0 sin® _ -12 cosO 14 tan® =-©/.0,86 7 Y sub. into the distance formula / vervang in die afstandformule ¥ simplification / vereenvoudig v14sin0 = —12cos 0 ¥ tand =-$/0,86 (4) a7) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 10 Downloaded from hlayiso.com NW/September 2016 10 NSC/NSS — Memorandum Mathematics/P2/Wiskunde/V2 QUESTION 6 / VRAAG 6 = Tae ae Cat Q eS @ ial » o g ’ AR fh ~7 ToincccpessqeceneeesPooe —————— . leis § \ 4 H ' A H a] S|] s8 ~ 1 1 ' ' 1 =o ° lo 1 4 t q d ' ' ww S I~ |~].- ¢ ' 7 t 1 ' ' 7 ' S isa wala fala” WO & H 0 ' 0 5 0 4 ' of SCT O/DlOonm gs 1 1 1 1 ' 1 ' " 4 B/Blo- H 4 H H i H ' " i ~..8 Suge - eee ba------- La------ de------ phe ee eee ee Fee — " Qala se SD H H H fe) t H ! t a RR x X88] 1 oO 8 ' H H : i H H ! H . 8 oS > op hs fh > : D ' p ' ' : 1 2 a ' ; : ‘ 1 ' ! ' 5s 5 ! H ‘ i t H 3 1 a ¢ ee ee ee Sey ae ee een ee ee Deere eres || on ek r iH g : ' ' sag H ' ' ' ' i Bo H 4 H H t H ' H Sox ' : \ ' ' ' ! ' 32s 4 ' ' a) eS wn-deneee--- b--------f------- N.----- ha------ Je------- L------- Ae fee Ege ' H H 1 ao ' 1 1 1 mn > 2° 1 ' 1 ete ha} H ! ’ : Ea | ' i t H sas 5 7 a a eos Kay = 4 : S wa — R 4 : 2 ot ah v7 ' j sas ° 1 1 3 oO 2. eas : > 2 a a DD» COUR, CS eee as S al 1 ' a on a a= a iS} ay 1 q £8 e r {| j= 3S ' ; 2 7. f oS isa} no {Ml Ss 8 ee Aco = R bal 1 H £8 " i] ° ' H go R > Isl Io & ' i iS) iS} + ' ‘ Sw — = > wm | ' ' So fs} ke 6 + ce i q ans) 5 iS) | Vv 2 ° 5° prc te cence en penne ne | ie hel ~ Yay onl roy R ! ! ee t Shel ie ' 4 ion I par 7 can) Vv i H r ° ' ' 8 " jes 2 US le x |uj_|y as SoooosS beee-f os a R O77 gl NN jes a ee N N |Qais Ne} Neo} So jololo Please turn over/Blaai om asseblief Copyright reserved/Kopiereg voorbehou ### Page 11 Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 ll NW/September 2016 NSC/NSS — Memorandum QUESTION 7 / VRAAG 7 A AC’ = 10? + 6? — 2(10)(6) cos100° ¥ sub. into cosine rule / vervang in die kosinus- = 156,8377813 reél AC = 12,5 units/eenhede Y 156,8377813 B = 80°( opp angles of a cyclic ¥ 12,5 units / eenhede quad/teenoorst