# Mathematics Grade 11 Paper 2 Gauteng June 2019 Memo > Grade 11 Mathematics Paper 2 memorandum from the Gauteng June Exam 2019, 10 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/gr11-math-p2-afr-eng-june-2019-possible-answers/641902e1-464c-4127-a4d6-a5395f3d42d8 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Document type: Memorandum - Year: 2019 - Exam period: Gauteng June Exam - Paper: 2 - Curriculum: CAPS - Pages: 10 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 11](https://www.hlayiso.com/library/grade-11) › [Mathematics](https://www.hlayiso.com/library/grade-11/mathematics) › [Mathematics Grade 11 Paper 2 Gauteng June 2019 Memo](https://www.hlayiso.com/library/gr11-math-p2-afr-eng-june-2019-possible-answers/641902e1-464c-4127-a4d6-a5395f3d42d8) ## About this document Mathematics · Grade 11 · Gauteng June Exam · 2019. Memorandum, 10 pages. Read online or download the PDF. 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Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com testpapers.co.za GAUTENG DEPARTMENT OF EDUCATION / GAUTENGSE DEPARTMENT VAN ONDERWYS PROVINCIAL EXAMINATION / PROVINSIALE EKSAMEN JUNE 2019 / JUNIE 2019 GRADE 11 / GRAAD 11 MATHEMATICS / WISKUNDE PAPER 2 / VRAESTEL 2 MARKING GUIDLINE / NASIENRIGLYNE 10 Pages / 10 bladsye 1 ### Page 2 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 GAUTENG DEPARTMENT OF EDUCATION / GAUTENGSE DEPARTEMENT VAN ONDERWYS PROVINCIAL EXAMINATION / PROVINSIALE EKSAMEN MATHEMATICS Paper 2 / WISKUNDE Vraestel 2 MARKING GUIDLINE / NASIENRIGLYNE INSTRUCTIONS AND INFORMATION  Consistent accuracy applies as a general rule.  If a candidate answers a question twice and does not delete either, mark the FIRST attempt.  If a candidate answers a question, crosses it out and does not re-do it, mark the deleted attempt. Marks are awarded as per the guideline, and the following symbols are used: A – Accuracy C.A – Continued Accuracy S – Statement R – Reason S. R – Statement and Reason INSTRUKSIES EN INLIGTING  Deurlopende akkuraatheid geld as ʼn algemene reël.  Indien ʼn kandidaat ʼn vraag twee keer beantwoord en nie een van die antwoorde kanselleer nie, merk die EERSTE poging.  Indien ʼn kandidaat ʼn vraag beantwoord en dit doodtrek maar nie oordoen nie, merk die doodgetrekte poging. Punte word toegeken volgens die riglyn en die volgende simbole word gebruik: A – Akkuraatheid D.A. – Deurlopende Akkuraatheid S – Stelling R – Rede S. R – Stelling en Rede 2 ### Page 3 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 QUESTION 1 / VRAAG 1 1.1  correct formula / 1.1.1 =√ – korrekte form.  correct subst. /  (2  (2))2  (1  (2))2 korrekte verv.  25  answer / 5 antwoord (3) 1.1.2 x1  x2 y y ; 1 2 2 2 correct formula / korrekte form. 2= ; 0= correct subst. / 4=1+ ; 0=2+ korrekte verv. 3= ; –2 = D (3 ; –2) answer / antwoord (3) 1.1.3 mAC  mCE – –  equate m. / = gelykstelling m – – – – – =  correct subst. / – – – korrekte verv. 2 1  4 p2  simplification / 2p 4  4 vereenvoudiging 2p  8 (2p – 4 = 4) p4  (4) 1.1.4 quadrilateral ABDE is a kite when: .  vierhoek ABDE is ʼn vlieër wanneer: – – . – – – – –  correct subst. / . korrekte verv. – – – . ( )  –1 –1 since the product of the gradients = –1 / produk van van gradiënte = –1  explanation / AC BC verduideliking ABDE is a kite (diagonals intersect 90 / ABDE is ʼn vlieër (hoeklyne deursny 90 (4) 3 ### Page 4 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 1.2 1.2.1 P(0 ; 4) answer / antwoord (1) 1.2.2 R(4 ; 0) answer / antwoord (1) 1.2.3 = tan 45 =1  =1 y = mx + c 4 = 1(0) + c 4=c g(x) = x + 4 answer / antwoord (2) 1.2.4.1 = –1  = –1 = tan (–1) = 180 – 45  answer / = 135 antwoord (2) 1.2.4.2 PR̂Q  45 (supplementary angles) (suppl. hoeke)  S.R = 180 – 90 (sum of angles of a / (som van hoeke in driehoek)  answer / = 90 antwoord (2) [22] 4 ### Page 5 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 QUESTION 2 / VRAAG 2 2.1 2.1.1 y correct sketch / korrekte skets 2 5 x θ x2  y 2  r 2 application Pyth. / x 2  (5)2  (2)2 Pythagoras x 2  16 x  4 ……..restriction / beperking (90;270) choose / kies  x  4 x  4 x 4 answer / cos   r 5 antwoord (4) 2.2 2.2.1 cos2 45  sin330.tan 2 210  cos2 45  sin(360  30).tan 2 (180  30) correct expansion / korrekte  cos2 45  sin30.tan 2 30 uitbreiding. 2  2 1  1  2 correct reduction /     .  korrekte reduksie  2  2  3 substitution / 1  vervanging 3 answer / antwoord (6) 2.2.2   cos x cos x.( tan x)( cos x)   tan x  1.( sin x)   sin x  sin x  sin x cos x    (cos x) cos x   cos x   sin x simplification / sin x.cos x  vereenvoudiging  sin x answer / antwoord   cos x (6) 5 ### Page 6 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 2.3 √ – – – –tan √ – –  tan √  identity / identiteit simplification / √ vereenvoudiging answer / antwoord sec (5) 2.4 x  0 answer / antwoord x  90 answer / antwoord answer / antwoord x  180 (3) [24] 6 ### Page 7 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 QUESTION 3 / VRAAG 3 3.1 3.1.1  answer / antwoord  answer / antwoord  answer / antwoord (3) 3.2 3.2.1 answer / antwoord x = 325 answer / antwoord (2) 3.2.2 90 x 325 corr. critical value / korr. kritieke waarde corr. inequality korr. ongelykhede (2) 3.3 4  asymptotes / asimptote 3  shape / vorm 2 x-intercepts / x-afsnitte 1 y-intercept / y-afsnit 0 45° 90° 135° 180° 225° 270° -1 -2 -3 -4 (4) [11] 7 ### Page 8 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 QUESTION 4 / VRAAG 4 4.1 ... twice angle at circumference / twee keer die hoek op die omtrek.  answer / antwoord (1) 4.2 Construction / konstruksie: Join CO and produce it./ lyn CO verleng  construction / konstruksie Proof / bewys: In ACO: Oˆ 2  Aˆ  Cˆ 2 (exterior angle of a triangle is   SR equal to sum of int. opp. angles / buite hoek van ) but / maar Aˆ  Cˆ 2 (OA  OC ) (radii / radius)  Ô2 = Ĉ2+ Ĉ2 Ô2 = 2 Ĉ2 Similarly we can prove that / kan ook bewys word dat: Ô1= 2Ĉ1 S Ô2+ Ô1= 2 Ĉ2+ 2 Ĉ1  equating /  AÔB = 2 AĈB gelykstelling  substitution / vervanging (6) [7] 8 ### Page 9 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 QUESTION 5 / VRAAG 5  answer / 5.1 ... supplementary / suppl. antwoord (1) 5.2 5.2.1 Ŝ  Q̂  x (subt. by same arc / omtrekshoeke onderspan deur dieselfde boog)  S.R  S.R QR̂S  Q̂  x (alternate angles/ verwisselende binnehoeke: PQ || RS)  S.R Ŝ  QP̂S  x (alternate angles: verwisselende binnehoeke PQ || RS) (6) 5.2.2 PT̂R  x  x (ext. angle of sum of int. opp. angles / buitehoek van )   S.R  2x  answer / antwoord (3) 5.2.3 PT̂R  2 x (ext. angle of sum of int. opp. angles / buitehoek van )  SR PÔR  2 x (angle at centre th. / middelpunt stelling)  SR Line PR subtends equal angles at PT̂R and PÔR conclusion / gelyke omtrekshoeke onderspan deur dieselfde koord gevolgtrekking quadrilateral PTOR is concyclic / (3) PTOR is ʼn koordevierhoek [13] QUESTION 6 / VRAAG 6 6.1 6.1. SR = (midpoint Th. / middelpunt stelling) substitution / = vervanging = conclusion / AE = EC gevolgtrekking (4) 6.2 Eˆ 1  90 (line from centre of a circle bisecting the chord is to chord) S  R (lyn van middelpunt van koord na middelpunt van sirkel loodreg) (3) 6.3 OE 2  102  82 (Theorem of Pythagoras / Pythagoras Stelling) S R OE  6cm OE = 6cm ED  4cm answer / antwoord (4) [11] 9 ### Page 10 Downloaded from hlayiso.com MATHEMATICS / WISKUNDE MEMORANDUM Paper 2 / Vraestel 2 Grade / Graad 11 QUESTION 7 / VRAAG 7 7.1. Let: = x = = x (tan / chord / raaklyn / koord) S R = = x (alternate angles / verwisellende hoeke, DR║ PS) S R but / maar = (given / gegee) = = x (v.o.a / teenoorstande hoeke) S R hence / dus = =x TS is a tangent (angle between tang. and chord is to angle in alter. seg.) R TS is ʼn raaklyn(tussen lyn en koord) (6) 7.1.2 T̂2  D̂ 2 (angles subt. by the same chord / omtrekshoeke onderspan  S R deur dieselfde koord)  S R but / maar D2  PŜT (tan / chord / raaklyn / koord)  S R PŜT  T2 (alternate angles / verwisselende binnehoeke ) TW || PS (6) [12] TOTAL / TOTAAL: 100 10 ## Related documents - [Gr11 Math P2 (Afrikaans) November 2019 Possible Answers](https://www.hlayiso.com/library/gr11-math-p2-afrikaans-november-2019-possible-answers/d5138457-8292-415c-8ae5-52ff1920ee97) — Mathematics · Memo · 2019 · Afr - [Gr 11 Math P2 (English) June 2023 Possible Answers](https://www.hlayiso.com/library/gr-11-math-p2-english-june-2023-possible-answers/7d433fdb-38a7-4d1e-b09f-472448486aa3) — Mathematics · Memo · 2023 · Eng - [Gr11 Math P1 (Afrikaans) June 2019 Question Paper](https://www.hlayiso.com/library/gr11-math-p1-afrikaans-june-2019-question-paper/8a92fc2a-58f8-4c91-9d87-bc71603b08cd) — Mathematics · QP · 2019 · Afr - [Gr11 Math P1 (English) June 2019 Question Paper](https://www.hlayiso.com/library/gr11-math-p1-english-june-2019-question-paper/9e010e98-da6e-4074-a4f9-ae653c922762) — Mathematics · QP · 2019 · Eng - [G11 Math P2 (Afrikaans) November 2019 Question Paper](https://www.hlayiso.com/library/g11-math-p2-afrikaans-november-2019-question-paper/ef5d8a14-92a5-4e9c-ba98-30f5140b04de) — Mathematics · QP · 2019 · Afr - [Mathematics GR 11 Paper 2](https://www.hlayiso.com/library/mathematics-gr-11-paper-2/d067d79e-bc2e-41a9-af62-97830243ae5c) — Mathematics · QP · 2019 ## More from Grade 11 Mathematics - [FS Maths Grade 11 June 2025 P1 only](https://www.hlayiso.com/library/fs-maths-grade-11-june-2025-p1-only/82015d8f-bcc0-478e-ad47-d3b295dabb01) — QP · 2025 - [FS Maths Grade 11 June 2025 P2 only](https://www.hlayiso.com/library/fs-maths-grade-11-june-2025-p2-only/5d0e7dd8-cb37-419c-8fe2-0aee27fbdc84) — QP · 2025 - [KZN Maths Grade 11 November 2025 P2 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-11-november-2025-p2-and-memo/a2aac931-a969-41c8-bde2-85d23035d042) — QP + Memo · 2025 - [MATHS P2 ANSWER BOOK GR11 2024 ENG AFR D watermark](https://www.hlayiso.com/library/maths-p2-answer-book-gr11-2024-eng-afr-d-watermark/91fd4f6b-a252-4d30-b6b1-f8f546015336) — Addendum · 2024 · Afr - [MATHS P1 QP GR11 NOV2024 ENG D watermark](https://www.hlayiso.com/library/maths-p1-qp-gr11-nov2024-eng-d-watermark/739068f1-b085-4977-8a45-18f9bb927644) — QP · 2024 · Eng - [Gr 11 Mathematics P1 (Afrikaans) June 2024 Question Paper](https://www.hlayiso.com/library/gr-11-mathematics-p1-afrikaans-june-2024-question-paper/1a0f4a9d-f18a-4aca-af77-5a81acfb8e0c) — QP · 2024 · Afr ## Collection - [Grade 11 past papers](https://www.hlayiso.com/grade-11/past-papers) --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. 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