# Mathematics Grade 11 P2 Gauteng June 2023 Memo (Afrikaans) > Grade 11 Mathematics Paper 2 memorandum from the Gauteng June Exam 2023 (Afrikaans), 10 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/gr-11-math-p2-afrikaans-june-2023-possible-answers/63afec40-2b96-4cba-a190-b1602c35bc7d - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Language: Afrikaans - Document type: Memorandum - Year: 2023 - 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 P2 Gauteng June 2023 Memo (Afrikaans)](https://www.hlayiso.com/library/gr-11-math-p2-afrikaans-june-2023-possible-answers/63afec40-2b96-4cba-a190-b1602c35bc7d) ## About this document Mathematics · Grade 11 · Gauteng June Exam · 2023 · Afrikaans. 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 PROVINSIALE EKSAMEN JUNIE 2023 GRAAD 11 NASIENRIGLYNE WISKUNDE (VRAESTEL 2) 10 bladsye ### Page 2 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 INSTRUKSIES EN INLIGTING: A – AKKURAATHEID CA – KONTINUE AKKURAATHEID S – BEWERING  R – REDE S & R – BEWERING met REDE NOTAS:  Indien ʼn kandidaat ʼn vraag TWEE keer beantwoord het, merk slegs die EERSTE poging.  Indien ʼn kandidaat ʼn antwoord doodgetrek het, en dit nie weer gedoen het nie, merk die doodgetrekte antwoord.  Deurlopende akkuraatheid moet op ALLE aspekte van die nasienriglyne toegepas word.  Dit is onaanvaarbaar om waardes/antwoorde aan te neem om probleme op te los. 2 ### Page 3 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 VRAAG 1 1.1 10; 13; 17; 21; 21; 23; 27; 29; 31; 34; 37; 38; 42; 43; 46; 48  Korrekte Min. Q1 en Maks. Min. =10 ; Q1 = 21 ; Maks. = 48  Korrekte Q 2 29  31 38  42 Q2   30 ; Q3   40 2 2  Korrekte Q 3 (3) 1.2  Korrekte Min./ onderste punt Graad 11A  Korrekte Maks./ boonste punt 10 21 30 40 48  Korrekte houer Graad 11B (3) 1.3 480  Breuk x  Antwoord 16 x  30 NB: Antwoord alleen volpunte (2) 1.4 σ = 11,46  Antwoord (2) 1.5 1σ interval: (30 – 11,46 ; 30 + 11,46)  Interval (18,54 ; 41,46)  Antwoord 4 leerders het meer as 41,46 punte behaal. (2) 1.6 Daar is geen verskil in die IKO nie. IKO = 19 vir albei klasse.  Opmerking Alhoewel, die middel 50% van Graad 11B tussen 21 en 40 was in  IKO waarde vergelyking met Graad 11A waar 50% tussen 11 en 30 was. Die houer vir 11B het na regs geskuif. Dus het Graad 11B oor die algemeen beter gevaar. (2) 1.7 75%  Antwoord (1) [15] 3 ### Page 4 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 VRAAG 2 2.1 Vergelyking van EG:  Gradiënt  Antwoord 3x – y + 6 = 0 y = 3x + 6 dan m EG = 3 tan β = 3 β = 71,57° (2) 2.2 x + 3(0) = 8  x=0  Koördinaat vorm x=8  (8 ; 0) (2) 2.3 M DF  M GE hoeklyne halveer mekaar  M DE  M GE  10  8) 6  0   Koördinate van K K ;   x-waarde  2 2   y-waarde K(  1 ; 3) x 1 y9 1  3 2 2 x  3 y  3  E(3 ;  3) (4) 2.4 mDF  mGE  mDF  DF  GE 1  Rede =  3 3 = –1 DF  GE DGFE is ʼn ruit. (hoeklyne halveer mekaar loodreg) (3) [11] 4 ### Page 5 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 VRAAG 3 3.1  Substitusie d x  x )  ( y  y ) 2 1 2 2 1 2 AC  1  (2) 2  5  (1) 2  Antwoord AC  3 5 (2) 3.2 54  Substitusie m BC   Antwoord 1  ( 3) 1 m BC  4 (2) 3.3 m BC  m BD  mCD  Gelyke gradiënte 1 y 5 1 y4  Substitusie  of   y=6 4 5 1 4 5  ( 3) y6 (3) 3.4 m AH  4 (AH  BC)  m AH y  (1)  4 x  (2)   Vervang A  Vergelyking y  4 x  9 (3) [10] VRAAG 4 4.1 4.1.1 x 2  ( 24) 2  25 2  Vervang in Pythagoras  Antwoord x  7 (2) 4.1.2 (a) sin   Antwoord 24  25 (1) (b) cos(180   )  Reduseer   cos   Vereenvoudigde antwoord 7     25  7  25 (2) 5 ### Page 6 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 (c) tan 2 (  )  Reduseer  Vereenvoudigde  tan 2  antwoord 2   24     7  576  49 (2) 4.1.3 (a)  24 y sin    sin   25 15 y  24  Stel sin verhoudings  gelyk 15 25 x  72  cos   y 15 5  Stel cos verhoudings 7 cos   gelyk 25 x 7  15 25  21 x 5 (4) (b) 1  72   Formule vir oppervlak OppΔROT  (12)   van Δ 2  5   Basis = 12 OppΔROT  86, 4 units 2 72  Hoogte = 5 ALTERNATIEF  Oppervlak OT  15 OF  12  OT lengte   253,7397...  106,26° 1  Vervang in sin OppROT  (15) (12) sin (106,26) oppervlak formule 2  Oppervlakte OppROT  86,4 units 2 (4) 6 ### Page 7 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 4.2 tan 225  sin (180   ) cos (90   )  tan 225° = 1 cos (90   ) sin (  540)  sin (180° – θ) = sin θ  cos (90° + θ) = –sin θ 1  sin  .  sin   sin (–θ –540°) = sin θ sin  .sin   1 – sin2 θ = cos2 θ 1  sin 2  cos 2     tan 2  sin 2  sin  2 cos 2   sin 2   tan 2  (6) [21] VRAAG 5 y 2 1 x O −240º −180º −120º −60º 60º 120º 180º 240º f -1 g -2 5.1 A=2  Antwoord (1) 5.2 Periode = 720°  Antwoord (1) 5.3 a = –1  Waarde van a p = –60°  Waarde van p (2) 5.4 –120° ≤ x ≤ 60° of x = –240° of x = 240°  Interval  –240°; 240° (2) 5.5 p = 30°  Waarde van p (2) [8] 7 ### Page 8 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 VRAAG 6 6.1   r  Substitusie tan     Manipulasie 2 R   R. tan    r 2 (2) 6.2 1 4 1 Vhemisfeer  . R 3  Volume Sfeer 2 3 2 2  Vervang r uit 6.1 Vhemisfeer   R 3  Trek volumes af 3 (Metode) 1 Vkeël   r 2R  Faktore 3 2 1     Vkeël    R.tan    R 3   2  2   Vkeël   .R 3 tan 2   3 2  2 1   Voorblywende   R 3   .R 3 tan 2   3 3 2   R3    Voorblywende   2  tan 2    3   2  (4) 6.3 1   1   Vkeël   .R 3 tan 2    Vkeël  π.R3 tan 2   3 2 3 2 1  36    Vervang  11 tan 2  3 Vkeël   R  11 en   36 3  2   Volume van kerswas Vkeël  147,15 cm 3 (3) [9] VRAAG 7 7.1 7.1.1 Ĉ 2  40 raaklyn koord stelling  S  R (2) 7.1.2 K̂ 1  90  in 'n halwe sirkel  S  R (2) 7.1.3 P̂1  25 buite  van 'n Δ  S  R (2) 7.2 T̂1  65 buite  van Δ  R  R TC  QC sye teen gelyke e (2) [8] 8 ### Page 9 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 VRAAG 8 T U 1 O 2 V 8.1 Konstrueer UO en verleng.  Konstruksie In ΔTOU Oˆ  Tˆ  U ˆ buite  van  1 1  SR Tˆ  U ˆ 1  e teen gelyke radii  SR O ˆ  2Uˆ 1 1 Net so in TOU  Ô 2  2Û 2  S  Ô1  Ô 2  2Û 1  2Û 2   Ô1  Ô 2  2 Û 1  Û 2   Gevolgtrekking TÔV  2TÛV (5) 9 ### Page 10 Downloaded from hlayiso.com WISKUNDE NASIENRIGLYNE (VRAESTEL 2) GRAAD 11 A B 1 2 3 O 2 2x C F 1 1 2 2 M 1 D 8.2 8.2.1 Twee pare aangrensende sye gelyk.  R (1) 8.2.2 (a) midpts = 2  omtreks  R (1) (b) buite  van koordevierhoek  R (1) (c) ooreenkomstige  e, OD MB  R (1) (d) teenoorst e, ruit  R ALTERNATIEF verw  e, OB DM (1) 8.2.3 D̂ 2  x  90 raaklyn  rad  R D̂ 2  90  x B̂ 3  90 raaklyn  rad  S Ĉ  90  x binne e van   SR  D̂ 2  Ĉ albei 90  x  Gevolgtrekking (4) 8.2.4 F̂2  90 ooreenk e, FB DM  SR  S AF  FD lyn van midpt  koord  R AB  BC lyn deur midpt 2 de sy  R (4) [18] TOTAAL: 100 10 ## Related documents - [Gr 11 Math P1 (Afrikaans) June 2023 Question Paper](https://www.hlayiso.com/library/gr-11-math-p1-afrikaans-june-2023-question-paper/3a6596d1-46af-4766-9815-0901dee27aaa) — Mathematics · QP · 2023 · Afr - [MATHS P2 QP GR11 NOV 2023 Afrikaans](https://www.hlayiso.com/library/maths-p2-qp-gr11-nov-2023-afrikaans/17065526-5498-4c8a-b44d-031e45899cfc) — Mathematics · QP · 2023 · Afr - [Gr 11 Mathematics P2 (Afrikaans) June 2024 Question Paper](https://www.hlayiso.com/library/gr-11-mathematics-p2-afrikaans-june-2024-question-paper/4934c5d3-e2a1-4d6b-acf6-d00e0623d46d) — Mathematics · QP · 2024 · Afr - [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 - [MATHS P1 QP GR11 NOV 2023 Afrikaans D](https://www.hlayiso.com/library/maths-p1-qp-gr11-nov-2023-afrikaans-d/c2f240dc-7fd6-4ceb-81c1-a511d86b6035) — Mathematics · QP · 2023 · Afr - [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) — Mathematics · QP · 2024 · Afr ## 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 - [NW 11 MATHEMATICS P2 AB ENGAFR NOV 2024](https://www.hlayiso.com/library/nw-11-mathematics-p2-ab-engafr-nov-2024/8ecc44b8-11a8-4044-8a89-cabd7fafe08c) — Addendum · 2024 - [NW 11 MATHEMATICS P1 QP AFR NOV 2024](https://www.hlayiso.com/library/nw-11-mathematics-p1-qp-afr-nov-2024/f9574947-5433-4acd-b172-fba18e967389) — 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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