# Mathematics Grade 12 Paper 2 Free State Prelim 2024 Memo > Grade 12 Mathematics Paper 2 memorandum from the Free State Prelim Exam 2024, 22 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/fs-maths-p2-prep-sept-2024-mg/051e13af-8935-475e-ab6f-6fb780e44ba9 - Updated: 2026-10-29 - Subject: Mathematics - Grade: Grade 12 - Document type: Memorandum - Year: 2024 - Exam period: Free State Prelim Exam - Paper: 2 - Curriculum: CAPS - Pages: 22 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 Free State Prelim 2024 Memo](https://www.hlayiso.com/library/fs-maths-p2-prep-sept-2024-mg/051e13af-8935-475e-ab6f-6fb780e44ba9) ## About this document Mathematics · Grade 12 · Free State Prelim Exam · 2024. Memorandum. 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 PREPARATORY EXAMINATION/ VOORBEREIDENDE EKSAMEN GRADE/GRAAD 12 MATHEMATICS P2/ WISKUNDE V2 SEPTEMBER 2024 MARKS/PUNTE: 150 MARKING GUIDELINES/ NASIENRIGLYNE These marking guidelines consist of 22 pages./ Hierdie nasienriglyne bestaan uit 22 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 2 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 2 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne NOTE: • If a candidate answers a question TWICE, only mark the FIRST attempt. • If a candidate has crossed out an attempt of a question and not redone the question, mark the crossed-out version. • Consistent accuracy applies in ALL aspects of the marking memorandum. Stop marking the second calculation error. • Assuming answers/values in order to solve a problem is NOT acceptable. NOTA: • As 'n kandidaat 'n vraag TWEE KEER beantwoord, merk slegs die EERSTE poging. • As 'n kandidaat 'n antwoord van 'n vraag doodtrek en nie oordoen nie, merk die doodgetrekte poging. • Volgehoue akkuraatheid word in ALLE aspekte van die nasienriglyne toegepas. Hou op nasien by die tweede berekeningsfout. • Aanvaar van antwoorde/waardes om 'n probleem op te los, word NIE toegelaat nie. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 3 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 3 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 1 1.1 Midpoint Number of litres Frequency Cumulative of interval f.(x) used (f) frequency (x) 50 ≤ 𝑥 < 100 20 75 20 1500 100 ≤ 𝑥 < 150 30 125 50 3750 150 ≤ 𝑥 < 200 50 175 100 8750 200 ≤ 𝑥 < 250 100 225 200 22500 250 ≤ 𝑥 < 300 80 275 280 22000 300 ≤ 𝑥 < 350 70 325 350 22750 350 ≤ 𝑥 < 400 50 375 400 18750 TOTAL 100 000 ✓ midpoint of interval column/middelpunt van intervalkolom ✓ cumulative frequency column/kummulatiewe frekwensiekolom ✓ f.(x) column/f.(x) kolom (3) 1.2 100000 ✓substitute/substitusie 𝑥= 400 = 250 ✓ answer/antwoord (2) 1.3 ✓ plotting points correctly/stip punte korrek ✓shape/vorm (2) 1.4 Median = 250 ✓accept/aanvaar (249–251) (1) 1.5 Symmetrical. Mean = Median/ ✓answer/antwoord Simmetries. Gemiddeldeld =Mediaan ✓reason/rede (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 4 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 4 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 1.6 Standard deviation will increase/Standaard afwyking sal ✓increase/vermeerder toeneem The values will be further from the new mean./Die waardes sal ✓ reason/rede verder wees vanaf die nuwe gemiddelde. (2) [12] QUESTION/VRAAG 2 Number of leg presses done 36 136 51 126 90 43 77 68 103 124 per day (x) Strength of upper leg (y) 0,2 0,85 0,35 0,91 0,73 0,34 0,61 0,59 0,78 0,90 2.1 𝑎 = 0,0478072. . . . . ✓ a Answer only: full marks, but if a 𝑏 = 0,0067704. . . . . . and b are swopped only 1/3 marks/ ✓ 𝑦̂ = 0,05 + 0,01𝑥 b Slegs antwoord : volpunte, maar ✓ equation/vergelyking as a en b omgeruil is, slegs 1/3 punte. (3) 2.2 𝑦̂ = 0,0478072 + 0,0067704(110) ✓ substitute 110 into = 0,79255196 eq./vervang 110 in = 0,79 Answer only: full marks/ vgl. OR Slegs antwoord : volpunte 𝑦̂ = 0,05 + 0,01(110) ✓ answer/antwoord volpunte (2) = 1,15 Accept 1,15/Aanvaar 1,15 No. This is extrapolation./Nee. Dit is ekstrapolasie. ✓ answer/antwoord 2.3 ✓ reason/rede (2) 2.4 r = 0,97 ✓ ✓r = 0,97 No penalty for rounding/ (2) Geen penalisasie vir afronding 2.5 There is a positive strong correlation between the number of ✓ positive/positief leg presses and leg strength of an eighteen-year-old boy./ ✓ strong/sterk Daar is 'n positief sterk korrelasie tussen beendrukke en (2) beenkrag van'n agtienjarige seun. [11] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 5 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 5 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1 AB = √(2 + 4)2 + (1 − 9)2 ✓subst./vervang = √100 = 10 ✓answer/antwoord (2) 3.2 AB = BC = 10 ✓ x=–4 y-value 9 +10 BC∥ to y – axis Answer only: full marks/ ✓ y = 19 C (– 4 ; 19) Slegs antwoord: volpunte (2) 3.3  2 + (−4) 1 + 19  ✓ subst./vervang K= ;   2 2  Answer only: full marks./ ✓answer/antwoord = ( −1 ; 10 ) Slegs antwoord: volpunte (2) 3.4 19 − 1 𝑚AC = −4 − 2 18 = −6 ✓𝑚AC = –3 = −3 through/𝑑𝑒𝑢𝑟(2; 1) ✓subst./vervang (2; 1) 𝑦 − 1 = −3(𝑥 − 2) ∴ 𝑦 = −3𝑥 + 7 ✓equation/vergelyking (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 6 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 6 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne OR/OF 19 − 1 𝑚AC = −4 − 2 18 = ✓𝑚AC = –3 −6 = −3 through/𝑑𝑒𝑢𝑟(– 4; 19) ✓subst./vervang (– 4; 19) 𝑦 − 19 = −3(𝑥 − (– 4)) −19 = −3𝑥 − 12 ✓equation/vergelyking ∴ 𝑦 = −3𝑥 + 7 (3) 3.5 𝑡𝑎𝑛 𝛽 = 𝑚𝐴𝐶 = – 3 ✓𝑡𝑎𝑛 𝛽 = 𝑚𝐴𝐶 = −3 𝑟𝑒𝑓𝑎𝑛𝑔𝑙𝑒 = 71,57° 𝛽 = 108,43° 𝜃 = 90° − 71,57° ✓method/metode = 18,43° ✓answer/antwoord (3) OR/OF In a right angled triangle 6 tan𝜃 = ✓value of 6 18 𝜃 = 18,43° ✓value of 18 ✓answer/antwoord (3) 3.6 AC = 6 10 ✓ AC = 6 10 ⊥ h = 10 ✓ ⊥ h = 10 1 Area ΔABC = .b. ⊥ h ✓ substitution into correct 2 1 formula/substitusie in = 6 10 . 10 korrek formule 2 = 30 units2 /𝑒𝑒𝑛ℎ𝑒𝑑𝑒 2 ✓answer/antwoord (4) OR/OF ✓ AC = 6 10 AC = 6 10 ✓ BC = 10 BC = 10 ✓ substitution into correct 1 formula/substitusie in Area ΔABC = BC. AC. sinC 2 korrek formule 1 = .10.6 10.sin18, 43 ✓answer/antwoord 2 (4) = 29,99 units 2 /eenhede2 3.7 D ( 2 ; 11 ) ✓x - value/waarde ✓y - value/waarde (2) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 7 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 7 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1 𝑥 2 + 𝑥 + 𝑦 2 − 3𝑦 = −2 2 1 2 2 −3 2 𝑥 + 𝑥 + ( ) + 𝑦 − 3𝑦 + ( ) ✓ LHS/LK 2 2 1 9 ✓ RHS/RK = −2 + + 4 4 2 2 1 3 1 (𝑥 + ) + (𝑦 − ) = 2 2 2 −1 3 1 ✓centre/middelpunt centre ( ; ) radius = √ ✓radius/radius 2 2 2 (4) 4.2 𝑦 = −𝑥 + 1. . . . (1) 𝑥 2 + 𝑥 + 𝑦 2 − 3𝑦 + 2 = 0. . . . . . (2) substitute(1) into (2) 𝑥 2 + 𝑥 + (−𝑥 + 1)2 − 3(−𝑥 + 1) + 2 = 0 ✓substitute substitusie 𝑥 2 + 𝑥 + 𝑥 2 − 2𝑥 + 1 + 3𝑥 − 3 + 2 = 0 2𝑥 2 + 2𝑥 = 0 ✓standard form/standard vorm 2𝑥(𝑥 + 1) = 0 ✓factors/faktore 𝑥 = 0 or 𝑥 = −1 ✓value(s) of x/waardes van x 𝐴(−1; 2) ✓coordinates of A/koördinate van A (5) OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 8 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 8 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 𝑥 = −𝑦 + 1. . . . (1) 𝑥 2 + 2𝑥 + 𝑦 2 − 2𝑦 + 1 = 0 … … . . (2) substitute(1) into (2) (−𝑦 + 1)2 + 2(−𝑦 + 1) + 𝑦 2 − 2𝑦 + 1 = 0 ✓substitute substitusie 𝑦 2 − 2𝑦 + 1 − 2𝑦 + 2 + 𝑦 2 − 2𝑦 + 1 = 0 2𝑦 2 − 6𝑦 + 4 = 0 ✓standard form/standaard vorm 2(𝑦 2 − 3𝑦 + 2) = 0 (𝑦 − 2)(𝑦 − 1) = 0 ✓factors/faktore 𝑦 = 2 or/𝑜𝑓 𝑦 = 1 ✓value(s) of y/waardes van y 𝐴(−1; 2) ✓coordinates of A/koördinate van A (5) 4.3 y – intercept x = 0 𝑦 − intercept x = 0 (0)2 + 𝑦 2 + (0) − 3𝑦 + 2 = 0 ✓substitute/substitusie x = 0 𝑦 2 − 3𝑦 + 2 = 0 (𝑦 − 1)(𝑦 − 2) = 0 ✓factors/faktore 𝑦 = 2 or 𝑦 = 1 ✓both y-values/beide y-waardes Centre M (−1; 1) 𝑝asses through (0 ; 1) (𝑥 + 1)2 + (𝑦 − 1)2 = 𝑟 2 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 (0 ; 1) ✓substitute centre M and (0 + 1)2 + (1 − 1)2 = 𝑟 2 point/substitusie in middelpunt M en 𝑟2 = 1 punt (𝑥 + 1)2 + (𝑦 − 1)2 = 1 𝑥 2 + 2𝑥 + 1 + 𝑦 2 − 2𝑦 + 1 − 1 = 0 ✓equation/vergelyking 𝑥 2 + 2𝑥 + 𝑦 2 − 2𝑦 + 1 = 0 (5) OR/OF y = −x + 1 ✓substitute/substitusie x = 0 y − intercept x = 0 ✓point /punt (0 ; 1) y- intercept (0 ;1) ✓substitute centre M and Centre M (−1; 1) 𝑝asses through (0 ; 1) point/substitusie van middelpunt M en (𝑥 + 1)2 + (𝑦 − 1)2 = 𝑟 2 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 (0 ; 1) punt (0 + 1)2 + (1 − 1)2 = 𝑟 2 𝑟2 = 1 ✓𝑟 2 = 1 (𝑥 + 1)2 + (𝑦 − 1)2 = 1 𝑥 2 + 2𝑥 + 1 + 𝑦 2 − 2𝑦 + 1 − 1 = 0 ✓equation/vergelyking 𝑥 2 + 2𝑥 + 𝑦 2 − 2𝑦 + 1 = 0 (5) 4.4.1 𝑦 = −𝑥 + 𝑘 … . (1) 𝑥 2 + 𝑦 2 + 2𝑥 − 2𝑦 + 1 = 0 … … (2) substitute(1) 𝑖𝑛to (2) 𝑥 2 + (−𝑥 + 𝑘)2 + 2𝑥 − 2(−𝑥 + 𝑘) + 1 = 0 ✓substitute/substitusie 𝑥 2 + 𝑥 2 − 2𝑘𝑥 + 𝑘 2 + 2𝑥 + 2𝑥 − 2𝑘 + 1 = 0 ✓simplify/vereenvoudig 2𝑥 2 − 2𝑘𝑥 + 4𝑥 + 𝑘 2 − 2𝑘 + 1 = 0 2𝑥 2 + (4 − 2𝑘)𝑥 + (𝑘 2 − 2𝑘 + 1) = 0 ✓standard form/standaard vorm (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 9 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 9 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 4.4.2 Equal roots Δ = 0 𝑏2 − 4𝑎𝑐 = 0 (4 − 2𝑘)2 − 4(2)(𝑘 2 − 2𝑘 + 1) = 0 ✓(4 − 2𝑘)2 − 4(2)(𝑘 2 − 2𝑘 + 1) = 0 16 − 16𝑘 + 4𝑘 2 − 8𝑘 2 + 16𝑘 − 8 = 0 ✓ simplify/vereenvoudig −4𝑘 2 + 8 = 0 ✓ standard form/standaard vorm −4𝑘 2 = −8 𝑘2 = 2 ✓k = 2 or/of 1,41 𝑘 = ±√2 ✓k = − 2 or/of –1,41 (5) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 10 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 10 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1.1 ✓ x = –1 −2 tan  = −1 ✓ answer/antwoord =2 (2) 5.1.2 cos 2 𝜃 ✓ double angle identity/dubbel = 2 cos 2 𝜃 − 1 hoek identitiet −1 2 ✓ substitution into correct = 2( ) − 1 formula/substitusie in korrekte √5 −3 formule = ✓ answer/antwoord 5 (3) OR/OF 1 − 2 𝑠𝑖𝑛 2 𝜃 ✓ double angle identity/dubbel hoek identitiet −2 2 = 1− 2( ) ✓ substitution into correct √5 formula/substitusie in korrekte −3 formule = 5 ✓ answer/antwoord (3) OR/OF ✓ double angle identity dubbel hoek identitiet cos 2𝜃 − 𝑠𝑖𝑛 2 𝜃 ✓ substitution into correct −1 2 −2 2 formula/substitusie in korrekte =( ) −( ) √5 √5 formule −3 ✓ answer/antwoord = (3) 5 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 11 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 11 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 2sin140°. 5.2 2 𝑐𝑜𝑠 2 1 5° − 1 + cos 310° ✓ cos 30 ° (2 sin 40 °) ✓ sin 40 ° = cos 30 ° + ✓ cos 50 ° (cos 50 °) √3 2 sin 4 0° = + ✓ sin 40 ° 2 sin 4 0° √3 + 4 = ✓ answer/antwoord 2 (5) 5.3 𝑠𝑖𝑛 𝑥 − 1 ✓ x =√1 − 𝑝2 𝑥 𝑥 = 2 𝑠𝑖𝑛 𝑐𝑜𝑠 − 1 ✓ double angle/dubbelhoek 2 2 𝑝 √1 − 𝑝2 ✓ substitution/substitusie = 2( )( )−1 1 1 = 2𝑝√1 − 𝑝2 − 1 ✓ answer/antwoord (4) 5.4 3 sin 𝑥 + 2(2 𝑠in 𝑥 cos 𝑥) ✓2 sin 𝑥 cos 𝑥 2 + 3 𝑐𝑜𝑠 𝑥 + 2(2 cos 2 𝑥 − 1) ✓2 cos 2 𝑥 − 1 sin 𝑥 . (3 + 4 cos x) = ✓sin 𝑥 (3 + 4 cos 𝑥) 4 cos 2 𝑥 + 3 cos 𝑥 sin 𝑥 . (3 + 4 cos 𝑥) = ✓cos 𝑥 (4 cos 𝑥 + 3) cos 𝑥 . (4 cos 𝑥 + 3) = tan x (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 12 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 12 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 5.5 𝑠𝑖𝑛 𝑥 + 𝑐𝑜𝑠 𝑥 𝑠𝑖𝑛 𝑥 − 𝑐𝑜𝑠 𝑥 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 + = 𝑐𝑜𝑠 𝑥 𝑐𝑜𝑠 𝑥 ✓divide numerator and denominator 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 by cos x/deel noemer en teller met 𝑐𝑜𝑠 𝑥 − 𝑐𝑜𝑠 𝑥 cos x tan x + 1 tan x+1 = ✓ tan x−1 tan x − 1 p 𝑝 +1 +1 ✓ 𝑝𝑡 = pt 𝑡 −1 −1 t 𝑝+𝑡 𝑝−𝑡 ✓ ÷ 𝑡 p+t p−t 𝑡 = ÷ t t 𝑝+𝑡 𝑡 p+t t ✓ 𝑡 × 𝑝−𝑡 = × t p−t p+t = p−t (5) [23] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 13 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 13 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1 g g g f ✓ turning points/draaipunte ✓ x-intercepts/x-afsnitte ✓ end points/eindpunte (3) 6.2.1 sin 2 𝑥 = cos( 𝑥 − 45°) sin 2 𝑥 = sin[ 90° − (𝑥 − 45°)] ✓ sin 2 𝑥 = sin[ 90° − (𝑥 − 45°)] sin 2 𝑥 = sin( 135° − 𝑥) 2𝑥 = 135° − 𝑥 + 𝑘. 360°; 𝑘 ∈ 𝑍 ✓ 2𝑥 = 135° − 𝑥 + 𝑘. 360°; 𝑘 ∈ 𝑍 3𝑥 = 135° + 𝑘. 360°; 𝑘 ∈ 𝑍 𝑥 = 45° + 𝑘. 120°; 𝑘 ∈ 𝑍 ✓ 𝑥 = 45° + 𝑘. 120°; 𝑘 ∈ 𝑍 OR/OF 2𝑥 = 180° − (135° − 𝑥) + 𝑘, 360; 𝑘 ∈ 𝑍 ✓2𝑥 = 180° − (135° − 𝑥) + 𝑘, 360; 2𝑥 = 45° + 𝑥 + 𝑘. 360; 𝑘 ∈ 𝑍 𝑘∈𝑍 𝑥 = 45° + 𝑘. 360; 𝑘 ∈ 𝑍 𝑥 = 45° + 𝑘. 360; ✓𝑘∈𝑍 𝑥 ∈ {45°; 165°} ✓ x = 45° ✓ x = 165 OR/OF (7) sin 2 𝑥 = cos( 𝑥 − 45°) ✓cos (90° − 2𝑥) = cos (𝑥 − 45°) cos (90° − 2𝑥) = cos (𝑥 − 45°) 90° − 2 𝑥 = 𝑥 − 45° + 𝑘. 360°; 𝑘 ∈ 𝑍 ✓ −3𝑥 = −135° + 𝑘. 360°; 𝑘 ∈ 𝑍 −3𝑥 = −135° + 𝑘. 360°; 𝑘 ∈ 𝑍 ✓ 𝑥 = 45° + 𝑘. 120°; 𝑘 ∈ 𝑍 x = 45 + k .120; 𝑘 ∈ 𝑍 ✓90° − 2 𝑥 = 360° − (𝑥 − 45°) + 𝑘. 360°; 𝑘 ∈ 𝑍 𝑥 = −315° + 𝑘. 360; ✓𝑘∈𝑍 ✓ x = 45° ✓ x = 165 (7) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 14 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 14 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne OR/OF 90° − 2 𝑥 = 360° − (𝑥 − 45°) + 𝑘. 360°; 𝑘 ∈ 𝑍 90° − 2 𝑥 = 360° − 𝑥 + 45° + 𝑘. 360°; 𝑘 ∈ 𝑍 −𝑥 = 315° + 𝑘. 360; 𝑘 ∈ 𝑍 𝑥 = −315° + 𝑘. 360; 𝑘 ∈ 𝑍 𝑥 ∈ {45°; 165°} (7) 6.2.2 𝑥 ∈ {15°; 135°} ✓ x = 15° ✓ x = 135° (2) 6.2.3 𝑥 ∈ (165°; 180°) (2) OR/OF ✓✓ critical values & notation/kritiese waardes en notasie 165° < 𝑥 < 180° (2) 6.3 360° ✓answer/antwoord (1) 6.4 √2 sin 2 𝑥 = cos 𝑥 + sin 𝑥 cos 𝑥+sin 𝑥 cos 𝑥 + sin 𝑥 ✓ sin 2 𝑥 = sin 2 𝑥 = √2 √2 1 1 1 1 sin 2 𝑥 = cos 𝑥 + sin 𝑥 ✓sin 2 𝑥 = 𝑐𝑜𝑠 𝑥 + 𝑠𝑖𝑛 𝑥 √2 √2 √2 √2 sin 2 𝑥 = cos 𝑥 cos 45° + sin 𝑥 sin 45° ✓sin 2 𝑥 = cos 𝑥 cos 45° + sin 𝑥 sin 45° sin 2 𝑥 = cos (𝑥 − 45°) 𝑓(𝑥) = 𝑔(𝑥) (3) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 15 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 15 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7.1 4 ✓ substitution into the correct Tan 43° = CB formula/substitusie in korrek 4 formule CB = ✓ CB subject of formula tan 43 ✓ answer/antwoord = 4,29 m (3) OR/OF CB 4 ✓ substitution into the correct = formula/substitusie in korrek 𝑠𝑖𝑛 4 7 𝑠𝑖𝑛 4 3° formule 4 sin 47° CB= sin 43° ✓ CB subject of formula = 4,29 𝑚 ✓ answer/antwoord (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 16 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 16 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 7.2 CD2 = CB2 + BD2 -2CB.BD.cos 115° ✓ substitution into correct = (4,29)2 + (5,6)2 -2(4,29)(5,6) cos 115° formula/substitusie in = 70,07006 korrekte formule CD = 8,37 m ✓ simplification/vereenvoudig ✓ answer/antwoord (3) 7.3 1 ✓ formula/ formule Area Δ BCD = CB.BD.sinB 2 1 = (4, 29)(5, 6)sin115 ✓ substitution into correct 2 formula/substitusie in korrekte = 10,89m2 formule ✓answer/antwoord (3) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 17 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 17 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne GEOMETRY/MEETKUNDE Please read carefully through the following table before marking QUESTION 8–10/ Lees asseblief sorgvuldig deur die volgende tabel alvorens VRAAG 8–10 nagesien word. The order in which the candidate answers a geometry question must follow logically/Die volgorde waarin 'n kandidaat 'n meetkundevraag beantwoord moet logies volg. Example/Voorbeeld Given/Gegee AB || CD and/en EF̂𝐷 = 115° A D 65° 115° F E y x B C The candidate first needs to calculate x BEFORE he/she can calculate y/Die kandidaat moet eerste vir x bereken VOORDAT hy/sy vir y kan bereken. A mark for a correct statement S (A statement mark is independent of a reason) 'n Punt vir 'n korrekte bewering ('n Punt vir 'n bewering is onafhanklik van die rede) A mark for the correct reason R (A reason mark may only be awarded if the statement is correct) 'n Punt vir 'n korrekte rede ('n Punt word slegs vir die rede toegeken as die bewering korrek is) Award a mark if the statement AND reason are both correct S/R (Both MUST be correct to get one mark) Ken 'n punt toe as die bewering EN rede beide korrek is (Beide MOET korrek wees om een punt te kry) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 18 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 18 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 8.1 Construction/Konstruksie: Draw AE through O and join BE/Trek AE  constr./ deur O en verbind BE. konstr. 𝐴̂1 + 𝐴̂2 = 90° radius ⊥ tangent/radius ⊥ 𝑟𝑎𝑎𝑘𝑙𝑦𝑛  S/R 𝐵̂1 + 𝐵̂2 = 90° angles in a semi circle/hoeke in halfsirkel  S/R Â1 = B̂2 subtended by the same arc/𝑜𝑛𝑑𝑒𝑟𝑠𝑝𝑎𝑛  S/R deur dieselfde boog ̂2 = ̂ A B1 S (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 19 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 19 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 8.2 8.2.1 P̂4 = 90° radius ⊥ tangent/𝑟𝑎𝑑𝑖𝑢𝑠 ⊥ 𝑟𝑎𝑎𝑘𝑙𝑦𝑛 ✓S✓R P̂3 = 130° − 90° = 40° ✓S (3) 8.2.2 ̂ B2 = 90° angles in semi-circle/ℎ𝑜𝑒𝑘𝑒 𝑖𝑛 ℎ𝑎𝑙𝑓𝑠𝑖𝑟𝑘𝑒𝑙 ✓S✓R ̂ ̂ Q1 + Q 2 = 50° sum of interior angles of Δ/𝑏𝑖𝑛𝑛𝑒ℎ𝑜𝑒𝑘𝑒 𝑣𝑎𝑛 𝛥 ✓S/R (3) 8.2.3 ̂B = 130° opp. angles of cyclic quad OR tan chord theorem/ PA ✓S✓R teenoorst. hoeke van koordevierhoek OF tan koordstelling (2) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 20 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 20 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 9.1.1 P1 + P2 + P3 = 90 given/gegee ✓S/R Q1 + ̂ ̂ Q2 + ̂ P3 = 90° sum int ∠’s of Δ/som van binne ∠'e van Δ ✓S/R ̂1 + Q Q ̂2 = ̂P1 + ̂ P2 ✓S Q1 = ̂ ̂ Q 2 and ̂ P1 = ̂ P2 given/gegee ✓S 2Q̂ 1 = 2P̂2 ̂1 = ̂ Q P2 ✓S PB is a tangent angle between line and chord/hoek tussen lyn ✓R en koord (6) 9.1.2 ̂ Q1 + ̂ Q2 = ̂ P1 + ̂ P2 given/gegee ✓S/R ̂ 2 = 2P 2Q ̂2 ̂2 = ̂ Q P2 ✓S ADPQ is a cyclic quad AD subtends equal ∠'s/AD onderspan ✓R gelyke ∠'e (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 21 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 21 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne 9.2 9.2 AP AQ PQ 4 = = = proportionality theorem PQ ∥ BC / ✓S✓R AB AC BC 7 𝑒𝑤𝑒𝑟𝑒𝑑𝑖𝑔ℎ𝑒𝑖𝑑𝑠𝑠𝑡𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑄 ∥ 𝐵𝐶 1 𝐴𝑟𝑒𝑎 𝛥𝐴𝑃𝑄 2 AP. AQ. 𝑠𝑖𝑛 𝐴 ✓correct = formula/korrekte 𝐴𝑟𝑒𝑎 𝛥𝐴𝐵𝐶 1 AB. AC. 𝑠𝑖𝑛 𝐴 2 formule AP. AQ = AB. AC 4.4 ✓substitution/ = substitusie 7.7 16 = ✓answer/antwoord 49 (5) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 22 Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 22 FS/VS/September 2024 Grade/Graad 12 Prep. Exam./Voorb. Eksam. Marking Guidelines/Nasienriglyne QUESTION/VRAAG 10 10.1 ̂ 2 = 90° D angle in semi-circle/ℎ𝑜𝑒𝑘 𝑖𝑛 ℎ𝑎𝑙𝑓𝑠𝑖𝑟𝑘𝑒𝑙 S/R In ΔADC and ΔBDA ̂1 = ̂ A B tan chord theorem/𝑡𝑎𝑛𝑘𝑜𝑜𝑟𝑑 𝑠𝑡𝑒𝑙𝑙𝑖𝑛𝑔 S/R ̂1 = D D ̂ 2 = 90° angles on str. line/ℎ𝑜𝑒𝑘𝑒 𝑜𝑝 𝑟𝑒𝑔𝑢𝑖𝑡𝑙𝑦𝑛 S/R ̂C = A ̂2 ′ sum of int ∠ 𝑠 of Δ/𝑠𝑜𝑚 𝑣𝑎𝑛 𝑏𝑖𝑛𝑛𝑒∠′𝑒 𝑣𝑎𝑛Δ 𝛥ADC /// ΔBDA [∠∠∠] S AD DC AC = = similar Δ's/𝑔𝑒𝑙𝑦𝑘𝑣𝑜𝑟𝑚𝑖𝑔𝑒 Δ′𝑒 BD DA BA S/R AD2 = BD. DC S = 3𝑥. 2𝑥 = 6𝑥 2 (6) 10.2 𝐴̂1 + A ̂ 2 = 90° radius ⊥ tangent/𝑟𝑎𝑑𝑖𝑢𝑠 ⊥ 𝑟𝑎𝑎𝑘𝑙𝑦𝑛 2 2 2 CB = AC + AB pythagoras' theorem/𝑠𝑡𝑒𝑙𝑙𝑖𝑛𝑔 (5𝑥)2 = AC 2 + AB 2 25𝑥 2 = AC 2 + AB 2 S AC 2 + AB 2 + AD2 S = 25𝑥 2 + 6𝑥 2 Simplify/ = 31𝑥 2 vereenv √AC 2 + AB 2 + AD2 = √31𝑥 2 S = 𝑥√31 (4) [10] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ## Related documents - [G12 Maths P2 Sept Free State 2024](https://www.hlayiso.com/library/g12-maths-p2-sept-free-state-2024/b81ee450-da0b-40b1-84a9-e4089f8e3d30) — Mathematics · QP · 2024 - [LP Maths Grade 12 June 2024 P2 and Memo](https://www.hlayiso.com/library/lp-maths-grade-12-june-2024-p2-and-memo/ae975968-03fb-478d-83f9-e424fe245c15) — Mathematics · Memo · 2024 - [FS Gr 12 Sept 2024 Afr en Eng P1](https://www.hlayiso.com/library/fs-gr-12-sept-2024-afr-en-eng-p1/4d7be3dc-5f53-4da3-a833-8fa9c4d73be1) — Mathematics · QP · 2024 · Eng - [MATHS P2 ANSWER BOOK GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-answer-book-gr12-june-2024-afr-english/4a71e975-4ac4-4f55-8e23-0b8155a5b0c6) — Mathematics · Addendum · 2024 · Eng - [MATHS P2 GR12 QP JUNE 2024 English](https://www.hlayiso.com/library/maths-p2-gr12-qp-june-2024-english/f19338aa-ae27-4fb7-9f1b-e60b2b91eb8c) — Mathematics · QP · 2024 · Eng - [MATHS P2 QP GR12 SEPT 2024 Afrikaans](https://www.hlayiso.com/library/maths-p2-qp-gr12-sept-2024-afrikaans/8572c34f-22e2-48bc-9d8a-f78c7e29781d) — Mathematics · QP · 2024 · Afr ## More from Grade 12 Mathematics - [MATHS P1 ANSWER BOOK GR12 SEPT 2025 English Afrikaans watermark](https://www.hlayiso.com/library/maths-p1-answer-book-gr12-sept-2025-english-afrikaans-watermark/d78c3fd3-dcd5-4f3f-911b-e5635b4686cc) — Addendum · 2025 · Afr - [Maths Grade 12 NSC P2 QP September 2025 Gauteng](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-qp-september-2025-gauteng/1d6bf7fd-d288-4a01-99f7-2c87e247760c) — QP · 2025 - [Maths Grade 12 NSC P2 QP September 2025 Afr Limpopo](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-qp-september-2025-afr-limpopo/f2f8d481-5d87-4e89-bb21-6077bbcf403d) — QP · 2025 · Afr - [Maths Grade 12 NSC P1 QP September 2025 Afr Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p1-qp-september-2025-afr-northern-cape/f5b3a4ce-fa91-4475-96e0-0654a87e1405) — QP · 2025 · Afr - [Maths Grade 12 NSC P2 QP September 2025 Eng Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-qp-september-2025-eng-northern-cape/4ede8207-ca82-4419-bae1-fae734498cc7) — QP · 2025 · Eng - [MATHS P2 QP GR12 SEPT 2024 Sesotho](https://www.hlayiso.com/library/maths-p2-qp-gr12-sept-2024-sesotho/f11751b2-1b49-4f07-90d1-83c261b8a1f5) — QP · 2024 · Sesotho ## Collection - [Grade 12 past papers](https://www.hlayiso.com/grade-12/past-papers) --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. 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