# Mathematics Grade 11 P2 Gauteng June 2023 Memo (English) > Grade 11 Mathematics Paper 2 memorandum from the Gauteng June Exam 2023 (English), 10 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/gr-11-math-p2-english-june-2023-possible-answers/7d433fdb-38a7-4d1e-b09f-472448486aa3 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Language: English - 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 (English)](https://www.hlayiso.com/library/gr-11-math-p2-english-june-2023-possible-answers/7d433fdb-38a7-4d1e-b09f-472448486aa3) ## About this document Mathematics · Grade 11 · Gauteng June Exam · 2023 · English. Memorandum, 10 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Matching paper and memo - [Gr 11 Math P2 (English) June 2023 Question Paper](https://www.hlayiso.com/library/gr-11-math-p2-english-june-2023-question-paper/ab59de7d-dca0-4ed6-95a6-dcb8ce60d27d) — QP · 2023 · Eng ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2023 GRADE 11 MARKING GUIDELINES MATHEMATICS (PAPER 2) 10 pages ### Page 2 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 INSTRUCTIONS AND INFORMATION: A – ACCURACY CA – CONSISTENT ACCURACY S – STATEMENT  R – REASON S & R – STATEMENT with REASON NOTES:  If a candidate answered a question TWICE, mark only the FIRST attempt.  If a candidate crossed out an answer and did not redo it, mark the crossed-out answer.  Consistent accuracy applies to ALL aspects of the marking guidelines.  It is unacceptable to adopt values/answers in order to solve a problem. 2 ### Page 3 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 1 1.1 10; 13; 17; 21; 21; 23; 27; 29; 31; 34; 37; 38; 42; 43; 46; 48  Correct Min. Q1 and Max. Min. =10 ; Q1 = 21 ; Max. = 48  Correct Q 2 29  31 38  42 Q2   30 ; Q3   40 2 2  Correct Q 3 (3) 1.2  Correct Min. plot/lower Grade 11A whisker  Correct Max. plot/upper 10 21 30 40 48 whisker Grade 11B  Correct box (3) 1.3 480  Fraction x  Answer 16 x  30 NB: Answer only full marks (2) 1.4 σ = 11,46  Answer (2) 1.5 1σ interval: (30 – 11,46 ; 30 + 11,46)  Interval (18,54 ; 41,46)  Answer 4 learners achieved over 41,46 marks. (2) 1.6 There is no difference in the IQR. IQR = 19 for both classes.  Comment However, the middle 50% for Grade 11B was between 21 and 40  IQR value compared to only 11 and 30 for Grade 11A. The box for 11B is shifted to the right. Thus, Grade 11B generally performed better. (2) 1.7 75%  Answer (1) [15] 3 ### Page 4 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 2 2.1 Equation of EG:  Gradient  Answer 3x – y + 6 = 0 y = 3x + 6 then mEG = 3 tan β = 3 β = 71,57° (2) 2.2 x + 3(0) = 8  x=0  Coordinate form x=8  (8 ; 0) (2) 2.3 M DF  M GE diagonals bisect  M DE  M GE   10  8) 6  0   Coordinates of K K ;   x-value  2 2   y-value 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  Reason =  3 3 = –1 DF  GE DGFE is a rhombus. (diagonals bisect perpendicularly) (3) [11] 4 ### Page 5 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 3 3.1  Substitution d x  x )  ( y  y ) 2 1 2 2 1 2 AC  1  (2) 2  5  (1) 2  Answer AC  3 5 (2) 3.2 54  Substitution m BC   Answer 1  ( 3 ) 1 m BC  4 (2) 3.3 m BC  m BD  mCD  Equal gradients 1 y 5 1 y4  Substitution  or   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)   Substitute A  Equation y  4 x  9 (3) [10] QUESTION 4 4.1 4.1.1 x 2  ( 24) 2  25 2  Substitute into Pythagoras x  7  Answer (2) 4.1.2 (a) sin   Answer 24  25 (1) (b) cos(180   )  Reduction   cos   Simplified answer 7     25  7  25 (2) 5 ### Page 6 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 (c) tan 2 (   )  Reduction  Simplified answer  tan 2  2   24     7  576  49 (2) 4.1.3 (a)  24 y sin    sin   25 15 y  24  Equate sine ratios  15 25 x  cos    72 15 y 5  Equate cosine ratios 7 cos   25 x 7  15 25  21 x 5 (4) (b) 1  72   Formula for area Δ AreaROT  (12)   Base = 12 2  5 72 AreaROT = 86,4 units2  Height = 5 ALTERNATIVE  Area OT  15 OR  12  OT length  106,26°   253,7397...  Substitute sine area 1 formula Area ROT  (15) (12) sin (106,26) 2  Area Area ROT  86,4 units 2 (4) 6 ### Page 7 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 4.2 tan 225  sin (180   ) cos (90   )  tan 225° = 1 cos (90   ) sin (   540)  sin (180° – θ) = sin θ 1  sin  .  sin  cos (90° + θ) = –sin θ   sin (–θ –540°) = sin θ sin  .sin   1 – sin2 θ = cos2 θ 1  sin 2  cos 2   sin 2    tan 2  sin  2 cos 2   sin 2   tan 2  (6) [21] QUESTION 5 y 2 1 x O −240º −180º −120º −60º 60º 120º 180º 240º f -1 g -2 5.1 A=2  Answer (1) 5.2 Period = 720°  Answer (1) 5.3 a = –1  Value of a p = –60°  Value of p (2) 5.4 –120° ≤ x ≤ 60° or x = –240° or x = 240°  Interval  –240°; 240° (2) 5.5 p = 30°  Value of p (2) [8] 7 ### Page 8 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 6 6.1   r  Substitution tan    2 R  Manipulation   R. tan    r 2 (2) 6.2 1 4 1 Vhemisphere  . R 3  Volume Sphere 2 3 2 2  Substitute r from 6.1 Vhemisphere  R 3 3  Subtract volumes 1 (Method) Vcone  r 2 R  Factors 3 2 1     Vcone    R. tan    R 3   2  2   Vcone   .R 3 tan 2   3 2 2 1   Vremaining  R 3   .R 3 tan 2   3 3 2 R 3     Vremaining   2  tan 2    3   2  (4) 6.3 1   1   Vcone   .R 3 tan 2    Vcone  π.R3 tan 2   3 2 3 2 1  36   Substitute Vcone   11 tan 2  3  R  11 and   36 3  2   Volume of wax Vcone  147,15 cm 3 (3) [9] QUESTION 7 7.1 7.1.1 Ĉ 2  40 tan chord theorem  S  R (2) 7.1.2 K̂ 1  90 ' s in a semi circle  S  R (2) 7.1.3 P̂1  25 ext  of a Δ  S  R (2) 7.2 T̂1  65 ext  of Δ  R  R TC  QC sides opp equal ' s (2) [8] 8 ### Page 9 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 8 T U 1 O 2 V 8.1 Construct UO and extend.  Construction In ΔTOU Ô1  T̂  Û 1 exterior  of   SR T̂  Û 1 ' s opp equal radii  SR  Ô1  2Û 1 Similarly in TOU  Ô 2  2Û 2  S  Ô1  Ô 2  2Û 1  2Û 2   Ô1  Ô 2  2 Û 1  Û 2   Conclusion TÔV  2TÛV (5) 9 ### Page 10 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 A B 1 2 3 O 2 2x C F 1 1 2 2 M 1 D 8.2 8.2.1 Two pairs of adjacent sides equal.  R (1) 8.2.2 (a)  at centre = 2   at circumference  R (1) (b) ext  of cyclic quad  R (1) (c) corr ' s, OD MB  R (1) (d) opp ' s, rhombus  R ALTERNATIVE alt ' s, OB DM (1) 8.2.3 D̂ 2  x  90 tan  rad  R D̂ 2  90  x B̂3  90 tan  rad  S Ĉ  90  x int s of   SR  D̂ 2  Ĉ both 90  x  Conclusion (4) 8.2.4 F̂2  90 corr s, FB DM  SR  S AF  FD line from centre  chord  R AB  BC line through midpt to 2 nd side  R (4) [18] TOTAL: 100 10 ## Related documents - [MATHS P2 AB GR11 NOV 2023 Afri+English](https://www.hlayiso.com/library/maths-p2-ab-gr11-nov-2023-afri-english/eee869d2-4e88-4265-9665-6bcf4b2cfc27) — Mathematics · QP · 2023 · Eng - [Gr 11 Mathematics P2 (English) 2023 Question Paper](https://www.hlayiso.com/library/gr-11-mathematics-p2-english-2023-question-paper/b8f6a489-3cb4-476d-8c5a-3c2de035fcf8) — Mathematics · QP · 2023 · Eng - [MATHS P1 QP GR11 NOV 2023 English](https://www.hlayiso.com/library/maths-p1-qp-gr11-nov-2023-english/11b74f81-704a-47bc-b151-d2eea1003c3c) — Mathematics · QP · 2023 · Eng - [1 MATHS P1 QP GR11 NOV 2023 English (28 09 2023)](https://www.hlayiso.com/library/1-maths-p1-qp-gr11-nov-2023-english-28-09-2023/54f88191-f662-4aed-b968-fcd43f78efee) — Mathematics · QP · 2023 · Eng - [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 - [Gr 11 Mathematics P2 (English) November 2022 Question Paper](https://www.hlayiso.com/library/gr-11-mathematics-p2-english-november-2022-question-paper/130a0fe0-0914-40c3-aedd-67a7e297f1cd) — Mathematics · QP · 2022 · Eng ## 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 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 - [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 - [ALTERNATIVE ANSWERS TO SOME QUESTIONS](https://www.hlayiso.com/library/alternative-answers-to-some-questions/589e5071-8eca-4868-96d4-89372a4d874b) — QP · 2023 ## 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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