TECH MATHS P2 MG AFR ENG JUNE 2025

[Type here] [Type here] [Type here] PROVINCIAL ASSESSMENT/ PROVINSIALE ASSESSERING GRADE 12/GRAAD 12 TECHNICAL MATHEMATICS P2/ TEGNIESE WISKUNDE V2 JUNE/JUNIE 2025 MARKING GUIDES/ NASIENRIGLYNE MARKS/ PUNTE: 150 A Accuracy/Akkuraatheid AO Answer only/Antwoord alleenlik CA Consistent Accuracy/Volgehoue Akkuraatheid I Identity/Identiteit M Method/Metode NPR No Penalty for Rounding/Geen penalisering vir Afronding NPU No Penalty for Units omitted/Geen penalisering vir eenhede weggelaat R Rounding/Afronding RE Reason/Rede S Simplification / Vereenvoudiging F Formula/Formule SF Substitution in correct Formula/Vervanging in korrekte formule ST/RE Statement with reason/Bewering met rede This marking guideline consists of 16 pages./Hierdie nasienriglyne bestaan uit 16 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 2 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne GENERAL GUIDELINES FOR MARKING/ALGEMENE RIGLYNE OM TE MERK  If a learner makes more than one attempt at answering a question and does not cancel any of them out, only the first attempt will be marked irrespective of which of the attempt(s) may be the correct answer./As ‘n leerder meer as een poging aanwend om ‘n vraag te beantwoord en nie een van hulle word uitgeskakel nie, sal slegs die eerste poging gemerk word ongeag watter van die poging(s) die regte antwoord kan wees.  Consistent accurate marking regarding calculations will be followed in the following cases / Volgehoue akkurate nasiening met betrekking tot berekeninge sal in die volgende gevalle gevolg word: o Sub question to sub question: When a certain variable is incorrectly calculated in one sub question and needs to be substituted into another sub question full marks can be awarded for the subsequent sub questions provided the methods used are correct and the calculations are correct./ Subvraag na subvraag: Wanneer ‘n sekere veranderlike verkeerd in een subvraag bereken word en in‘n ander subvraag vervang moet word, kan volpunte toegeken word vir die daaropvolgende subvrae, mits die metodes wat gebruik is, en die berekeninge korrek is. o Assuming values/answers to solve a problem is unacceptable./ Aanvaarding van waardes/antwoorde om ‘n probleem op te los, is onaanvaarbaar.  If a learner did a question in pencil, and did not write it over in pen, the pencil must be marked. Draw a line through and make note of it./ As ‘n leerder ‘n vraag in potlood gedoen het en dit nie in pen oorgeskryf het nie, moet die potlood gemerk word. Trek ‘n lyn deur en maak ‘n nota daarvan. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 3 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne QUESTION 1 / VRAAG 1 1.1 1.1 𝑦𝐶 − 𝑦𝐵 𝑚𝐵𝐶 = 𝑥𝐶 − 𝑥𝐵  SF = −4−(−3)  answer/antwoord A 3−(−3) CA Only CA with correct 1 = −6 formula/ CA slegs met korrekte formule (2) 1.2 𝑦 − 𝑦𝐶 = 𝑚(𝑥 − 𝑥𝐶 ) can also use B(-3;-3)  SF A 𝑦 − (−4) = − 6 (𝑥 − 3) 1  answer/antwoord CA 1 −4 = − 6 (3) + 𝑐 1 1 𝑦 = −6𝑥 + 2 − 4 1 7 𝑦 = − 6 𝑥 − 2 or/of -3,5 OR/OF use B(-3;-3) 1 𝑦=− 𝑥+𝑐 6 7 𝑐=− 2 1 7 ∴𝑦=− 𝑥− 6 2 (2) 1.3 − = 1 4−3 OR/OF 𝑥 − (−2) = 7  SF A 7 −2−𝑥  answer/antwoord A 𝑥+2=7 −7 = −2 − 𝑥 𝑥=5 𝑥 = −2 + 7 AO: full marks/volpunte 𝑥=5 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 4 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 1.4 𝑚𝐵𝐶 ≠ 𝑚𝐴𝐷  reason/rede A ∴ 𝐵𝐶 ∦ 𝐴𝐷  answer/antwoord A (2) 1.5 𝑥1 + 𝑥2 𝑦1 + 𝑦2 𝑀𝐴𝐵 = ( ; ) 2 2  SF  answer/antwoord A −2+(−3) 4+(−3) =( ; ) 2 2 CA 5 1 = (− ; ) or/of (−2,5; 0,5) 2 2 (2) 1.6 𝑦 − (−4) = 6(𝑥 − (−1))  correct gradient/ A 𝑦 + 4 = 6𝑥 + 6 korrekte gradiënt 𝑦 = 6𝑥 + 2 𝑚=6  substitute/vervanging A (-1;-4)  answer/antwoord CA (3) 1.7 𝑡𝑎𝑛 𝜃 = 𝑚  tan 𝜃 = 𝑚 7  gradient of/gradiënt A 𝑡𝑎𝑛𝜃 = van DC CA 2 CA from/vanaf 1.3 A 𝜃 = 74,05° accept/aanvaar 74°  answer/antwoord (3) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 5 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne QUESTION 2 / VRAAG 2 2.1.1 𝑥2 + 𝑦2 = 𝑟2 (2) + (−3)2 = 𝑟 2 2  SF A 13= 𝑟 2  answer/antwoord CA ∴ 𝑥 2 + 𝑦 2 = 13 AO: full marks/volpunte (2) 2.1.2 (−√13; 0) or/of (−3.61; 0)  x-value/waarde A  y-value/waarde A (2) 2.1.3 3  correct gradient/ A 𝑚𝑂𝐶 = − korrekte gradiënt 2 (1) 2.1.4 𝑦 − 𝑦𝐶 = 𝑚(𝑥 − 𝑥𝐶 ) OR/OF 𝑦 = 𝑚𝑥 + 𝑐 2 CA the gradient from/die gradiënt −3 = 3 (2) + 𝑐 2 13 vanaf 2.1.3 A 𝑦 − (−3) = 3 (𝑥 − 2) 𝑐=− 3 A  correct gradient/korrekte gradiënt CA 2 4 2 13 𝑦 = 3𝑥 − 3− 3 ∴ 𝑦 = 3𝑥 − 3  substitute/vervanging (2; -3)  answer /antwoord 2 13 1 𝑦 = 3𝑥 − 3 or/of -4,33 or/of −4 3 (3) 2.1.5 𝑦 = 2 𝑥 − 13 3 3 CA equation from/vergelyking vanaf 2 13 2.1.4 CA 0= 𝑥− CA 3 3  substitute/vervanging 𝑦 = 0 13 3 × =𝑥  coordinates/koördinate 3 2 OR/OF x-value/waarde 13 13 =𝑥 ∴ 𝐷 ( 2 ; 0) or/of (6,5 ; 0) (2) 2 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 6 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 2.2  correct x-intercept A korrekte x-afsnit  correct y-intercept A korrekte y-afsnit  shape/vorm CA (3) [13] QUESTION 3 / VRAAG 3 3.1.1 3 cos 𝛽 = 5  𝛽 = 53,13° A 3 𝛽 = cos−1 5  correct rounded answer/ A 𝛽 = 53,13° korrek afgeronde antwoord ∴ 53° (2) 3.1.2 𝜋 180° ×  answer/antwoord 6 𝜋 A = 30° (1) 3.1.3 sin(2 × 53°) − sec(30°) OR/OF 53,13°  substitution/vervanging CA 1 CA from 3.1.1 and 3.1.2/ = sin(106°) − CA vanaf 3.1.1 en 3.1.2 A cos(30°) = −0,19  correct identity/korrekte identiteit CA  answer/antwoord CA with the values of 𝜷 𝒂𝒏𝒅 𝜶 from above/met die waardes van 𝜷 𝒆𝒏 𝜶 vanaf bo NPR (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 7 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 3.2.1  diagram (correct quadrant)/ A (korrekte kwadrant) (1) 3.2.2 𝑟 = √(−5)2 + (4)2 (pyth)  correct value of r/ 𝑟 = √41 korrekte waarde van r A 𝑐𝑜𝑠 2 𝜃 + 𝑠𝑖𝑛2  substitution/vervanging CA −5 2 4 2 =( ) +( )  answer /antwoord CA √41 √41 no decimals/geen desimale. 25 16 if calculator was used NO marks/ = + as sakrekenaar gebruik is, GEEN punte. 41 41 =1 (3) 3.3 8 cos 𝑥 − 2 = 2  simplifying ratio/ 1 vereenvoudig verhouding A cos 𝑥 = 2 𝑥 = 60°  first correct value of x / OR/OF eerste korrekte waarde vir x CA 𝑥 = 360° − 60°  second correct value of x/tweede CA 𝑥 = 300° korrekte waarde vir x NPR (3) [13] QUESTION 4 / VRAAG 4 4.1 cos(𝜋 + 𝜃). tan(180° + 𝜃). 𝑠𝑖𝑛2 (180 − 𝜃)  −cos 𝜃 A 1  tan 𝜃 A − tan(180° − 𝜃). sin 𝜃 . cos(180 − 𝜃) . sec 𝜃  𝑠𝑖𝑛2 𝜃 A  −(−𝑡𝑎𝑛𝜃) 𝒐𝒓/𝒐𝒇 tan 𝜃 A − cos 𝜃. tan 𝜃. sin 𝜃. sin 𝜃  − cos 𝜃 A = 1 tan 𝜃 . sin 𝜃. − cos 𝜃. cos 𝜃  𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦/𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑒𝑖𝑡 sec 𝜗 = 𝑐𝑜𝑠𝜃 A = tan 𝜃  tan 𝜃 answer/antwoord A (7) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 8 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 4.2 𝑠𝑖𝑛2 𝜃 𝑐𝑜𝑠 2 𝜃 1 + =  𝑡𝑎𝑛2 𝜃 A 𝑐𝑜𝑠 𝜃 𝑐𝑜𝑠 𝜃 𝑐𝑜𝑠 2 𝜃 2 2 LHS/RK:  1 A 𝑡𝑎𝑛2 𝜃 + 1 = 𝑠𝑒𝑐 2 𝜃  𝑠𝑒𝑐 2 𝜃 A 1 = 1 A 𝑐𝑜𝑠 2 𝜃  𝑐𝑜𝑠2 𝜃 (4) [11] QUESTION 5/ VRAAG 5 5.1 5.1.1 𝑥 = 90° or/of 𝑥 = 270°  𝑥 = 90° A  𝑥 = 270° (2) 5.1.2 180°  correct answer/ A korrekte antwoord (1) 5.1.3 𝑥 = 45°  correct answer/ A korrekte antwoord (1) 5.1.4 (180°; 0)  notation/Notasie A  correct answer/ korrekte antwoord (2) 5.2 5.2.1 𝑎=1  answer/antwoord A (1) 5.2.2 180°  answer/antwoord A (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 9 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 5.2.3 (90°; −1)  90° A  -1 A (2) 5.3.1 (90°; 180°)  correct values/ A korrekte waardes (2)  notation/notasie 5.3.2 (45°; 135°)  correct values/ A korrekte waardes (2)  notation/notasie 5.4 −1 ≤ 𝑦 ≤ 1 OR/OF [−1; 1]  values/waardes A  notation/notasie (2) [16] QUESTION 6/ VRAAG 6 6.1.1 𝐶̂1 = 70° Alternate/Verwisselende ∠s/e AF║BD  statement/bewering A OR/OF Interior/Binne ∠’s/e of/van Δ  reason/rede A (2) 6.1.2 𝐴̂2 = 70° − 63°  answer/antwoord A = 7° (1) 6.2 110 𝐴𝐶 110 sin 70° = 𝐴𝐶 OR/OF = sin 90° sin 70°  SF A  AC=117,06 A 110 𝐴𝐶 = sin 70° AC= 117,06𝑚 𝐴𝐶 = 117,06𝑚 Learners can determine BC and use pyth to get AC./ Leerders kan BC bepaal en AC bepaal d.m.v. Pyth NPR (2) BC = 40,0367 6.3 𝐶𝐷 117,06 =  method/metode sin 7° sin 63° A CD = 16,01  63° A OR/OF  answer/antwoord CA 𝐶𝐷 𝐴𝐷 123,46 = = sin 7° sin 110° sin 110° CA if ∠ values are wrong from 6.1. / 𝐶𝐷 = 16,01 CA as ∠ waardes verkeerd is vanaf 6.1. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 10 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne OR/OF 110 110 NPR BC = tan 70° and/en BD = tan 63° = 40,04 = 56,05 ∴ CD = 56,06 − 40,04 CD = 16,01 (3) 6.4 AD = c  SF A 𝑐 2 = 𝑎2 + 𝑑 2 − 2𝑎𝑑 cos 𝑐  answer/antwoord CA 𝑐 = √(16,01)2 + (117,06)2 − 2(16,01)(117,06) cos 110 ° = 123,46 CA if sides are wrong OR/OF from 6.2 and 6.3./CA as sye C =√(110)2 + (56,05)2 − 2(110)(56,05) cos 90 ° verkeerd is vanaf 6.2 en 𝑐 = 123,46 6.3. NPR (2) [10] QUESTION 7/ VRAAG 7 7.1 7.1.1 any three angles/enige drie hoeke:  ST A 𝐸̂ = 35° tangent chord/raaklyn koord  R A 𝐴̂ = 35° ∠’s subt by equal chords/∠’e onderspan deur gelyke koorde  ST A ̂ 𝐷2 = 35° alternate/verwisselende ∠’s/e AC║ FD  R A ̂4 = 35° 𝐷 tangent chord/raaklyn koord  ST A  R A (6) 7.1.2 ̂ 𝐻 = 70° 𝐴𝐷  ST A (1) 7.1.3 𝐶̂ = 70° tangent chord/raaklyn koord  ST CA  R A (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 11 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 7.1.4 𝐶𝐷 ̂ 𝐹 = 180° − 70° co interior/ko-binne ∠s/e AC║FD  ST CA = 110°  R (2) 7.1.5 𝐷̂3 = 45° interior/binne ∠’s/e of ∆ OR/OF  ST A ̂ 𝐸𝐷 𝐺 = 65° 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 𝑐ℎ𝑜𝑟𝑑/𝑟𝑎𝑎𝑘𝑙𝑦𝑛 𝑘𝑜𝑜𝑟𝑑  R A ∴ 𝐷 ̂3 = 45° ∠’s on a str line/∠’e op ‘n reguit lyn (2) 7.1.6 any two statements:/enige twee bewerings:  ST/R A 𝐴̂ = 𝐷̂2 alternate/verwisselende ∠’s/e AC║FD  ST/R A ̂𝐽1 = 𝐽̂2 vertical opp ∠’s /regoorstaande ∠’e 𝐵̂1 = 𝐹̂ alternate/verwisselende ∠’s/e AC║FD  reason/rede A ∠;∠;∠ ∆𝐽𝐴𝐵 ⫴ ∆𝐽𝐷𝐹 (∠;∠;∠) (3) 7.2 7.2.1 ̂1 = 80° 𝑁 exterior ∠ of a cyclic quad/  ST A buite∠ van koordevierhoek  R A (2) 7.2.2 𝑃̂1 = 60° opposite interior ∠’s of cyclic Quad./  ST A teenoorstaande binne ∠’e van koordevierhoek  R A (2) 7.2.3 ̂ = 90° 𝐾 ∠ in a half circle/semi-circle/  ST A ∠ in halwe sirkel/semi-sirkel  R A (2) 7.2.4 𝐿̂2 = 60° alternate/verwisselende ∠’s/e KL║PN  ST/R A 𝑥 = 30° int ∠’s of Δ / binne ∠’e van Δ OR/OF  ST/R A 𝑥 = 30° Co interior/Ko-binne ∠’s/e KL║PN (2) [24] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 12 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne QUESTION 8/ VRAAG 8 8.1 equal / gelyk  answer/antwoord A (1) 8.2 8.2.1 𝑂̂1 = 80° ∠ at the centre 2 × ∠ at circumf/  ST A ∠ by middelpunt = 2 × ∠ op omtrek  R A (2) 8.2.2 𝐴̂1 = 90° rad ⏊ tangent or tan ⏊ rad /  ST A rad ⏊ raaklyn of raaklyn ⏊ rad  R A (2) 8.2.3 𝐴̂2 = 50° ∠’s opposite equal sides  ST A ∠’e teenoor gelyke sye  R A (2) 8.2.4 𝐴̂3 = 40°  ST A (1) 8.2.5 AC = CB  ST CA 𝐴̂3 = 𝐵̂3 = 40° ∠’s opp equal sides/  ST/R A ∠’e teenoor gelyke sye  ST/R CA 𝐶̂ = 100° int ∠’s of Δ / binne ∠’e van Δ both statements correct without reasons. ONE mark only./ beide bewerings korrek sonder redes. Slegs EEN punt. (3) [11] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 13 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne QUESTION 9/ VRAAG 9 9.1 9.1 half the length/die helfte van die lengte (1) 9.2.1 𝑎 = 10 midpoint theorem/middelpuntstelling  ST A  R A (2) 9.2.2 𝑏=6  ST A (1) 9.2.3 𝑥 = 45° corresp./ooreenkomstige ∠’s/e PR║ST  ST A  R A (2) 9.2.4 2c  ST A (1) [7] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 14 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne QUESTION 10/ VRAAG 10 10.1.1 𝜔 = 2𝜋𝑛  formula/formule A 20  substitution of/vervanging A = 2𝜋 van 20 60 2𝜋 = 3 or/of 2,09𝑟𝑎𝑑  ÷ 60 A  answer/antwoord CA NPR & NPU (4) 10.1.2 𝑣 = 𝜔𝑟  formula/formule A 2𝜋 = 3 × 0,6 2𝜋  SF CA = 5 or/of 1,26  r = 0,6 OR/OF A ÷ 60 for 2nd option/ OR/OF vir 2de opsie  answer/antwoord CA 𝑣 = 𝜋𝐷𝑛 20 = 𝜋 × 1,2 × 60 2𝜋 NPR & NPU = 5 or/of 1,26 (4) 10.1.3 𝑠 = 𝑟𝜃 60𝜋  F A = 0,6 (180 )  SF A 1 = 5 𝜋 𝑜𝑟/𝑜𝑓 0,628  conversion of/herlei van A 𝑟𝑠 60° 𝐴𝑟𝑒𝑎/𝑂𝑝𝑝𝑒𝑟𝑣𝑙𝑎𝑘𝑡𝑒 =  answer/antwoord CA 2 0,6 × 0,628 = 2 = 0,19 OR/OF 𝑟2𝜃 𝐴𝑟𝑒𝑎/𝑂𝑝𝑝𝑒𝑟𝑣𝑙𝑎𝑘𝑡𝑒 = 2 𝜋 0,6 × 60° × = 180 2 3𝜋 = 5 or/of 0,19 NPR & NPU (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 15 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 10.2 4ℎ2 − 4𝑑ℎ + 𝑥 2 = 0  F A 4ℎ2 − 4(30)ℎ + 182 = 0  SF A 4ℎ2 − 120ℎ + 324 = 0 ÷4 2 ℎ − 30ℎ + 81 = 0  method/metode A −(−30) ± √(−30)2 − 4(1)(81) ℎ= 2 ℎ=3  answer h=3/antwoord h=3 CA ℎ ≠ 27 OR/OF 𝑂𝐶 = √(15)2 − (9)2 = 12 𝐷𝐶 = 15 − 12 = 3 (4) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 16 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne QUESTION 11/ VRAAG 11 11.1.1 𝑥 = 15  𝑥 = 15 A OR/OF 14,5 𝐴𝑇 = 𝑎(𝑚1 + 𝑚2 + 𝑚3 + ⋯ 𝑚4 ) A = 4(15 + 15,5 + 14,5 + 𝟏𝟒, 𝟓 + 14 + 12,5)  F A = 4(86)  value of a/ = 344 𝑚2 waarde van a CA OR/OF  SF 𝑜1 + 𝑜𝑛 CA 𝐴𝑇 = 𝑎 ( + 𝑜2 + 𝑜3 + 𝑜4 + ⋯ 𝑜𝑛−1 )  answer/antwoord 2 14+12 = 4( + 16 + 15 + 14 + 15 + 13) 2 2 = 344 𝑚 NPU (5) 11.2.1 𝑉 = (𝑙𝑥𝑏𝑥ℎ) + (𝑙𝑥𝑏𝑥ℎ)  adding A volumes/ 𝑉 = (40 × 16 × 26) + (40 × 20 × 8) optel van volumes 𝑉 = 23040𝑐𝑚2  first volume/ A eerste volume  second A volume/ tweede volume  total volume/ totale volume A (4) 11.2.2 𝐴 = (16 × 40) + 2(26 × 16) + 2(26 × 40)  SF A  answer/ = 3552𝑐𝑚2 antwoord CA  answer/ 𝐴 = (20 × 40) + 2(8 × 20) + 2(8 × 40) antwoord A 2 CA only for correct = 1760𝑐𝑚 formula/CA slegs vir CA korrekte formule NPR (3) 11.2.3 𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎/𝑇𝑜𝑡𝑎𝑙𝑒 𝑂𝑝𝑝𝑒𝑟𝑣𝑙𝑎𝑘𝑡𝑒 = 3552 + 1760  total area/ CA totale = 5312𝑐𝑚2 oppervlakte (1) [13] TOTAL/TOTAAL:150 Copyright reserved/Kopiereg voorbehou

Technical Mathematics/P2/Tegniese Wiskunde/V2 17 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne TECH MATHS GR 12 JUNE 2025 PAPER 2 VRAAG/ KNOWLEDGE ROUTINE COMPLEX PROBLEM SOLVING QUESTION LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Q 1: ANALYTICAL GEOMETRY 1.1 2 1.2 2 1.3 2 1.4 2 1.5 2 1.6 3 1.7 3 Q 2: HALF CIRCLE , TANGENT & ELLIPSE 2.1.1 2 2.1.2 2 2.1.3 1 2.1.4 3 2.1.5 2 2.2 3 Q 3: TRIG RATIO’S 3.1.1 2 3.1.2 1 3.1.3 3 3.2.1 1 3.2.2 3 3.3 3 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 18 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne Q 4: TRIG IDENTITIES & REDUCTION FORMULA 4.1 7 4.2 4 Q 5: TRIG GRAPHS 5.1.1 2 5.1.2 1 5.1.3 1 5.1.4 2 5.2.1 1 5.2.2 1 5.2.3 2 5.3.1 2 5.3.2 2 5.4 2 Q 6: TRIG RULES 6.1.1 2 6.1.2 1 6.2 2 6.3 3 6.4 2 Q 7: GEOMETRY 7.1.1 6 7.1.2 1 7.1.3 2 7.1.4 2 7.1.5 2 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 19 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne 7.1.6 3 7.2.1 2 7.2.2 2 7.2.3 2 7.2.4 2 Q 8: GEOMETRY 8.1 1 8.2.1 2 8.2.2 2 8.2.3 2 8.2.4 2 8.2.5 3 Q 9: MIDPOINT T. & CONCRUENCY & SIMULARITY 9.1 1 9.2.1 2 9.2.2 1 9.2.3 2 9.2.4 1 Q 10: ANGULAR MOVEMENT, VELOCITY, SECTORS , RADIANS & SEGMENT HEIGHT 10.1.1 4 10.1.2 4 10.1.3 4 10.2 4 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Technical Mathematics/P2/Tegniese Wiskunde/V2 20 NW/June/Junie 2025 Grade/Graad 12 Marking Guidelines/Nasienriglyne Q 11: IRREGULAR SHAPE, VOLUME & SURFACE AREA 11.1 3 2 11.2.1 4 11.2.2 3 11.2.3 1 TOTAL 64 49 21 16 PERCENTAGE 42,67% 32,67% 14% 10,67% TOTAL OF PAPER 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief