# Mathematics Grade 11 P1 Gauteng June 2023 Memo (English) > Grade 11 Mathematics Paper 1 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-p1-english-june-2023-possible-answers/df728d9d-98d3-4a33-90a1-47ad3e999390 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Language: English - Document type: Memorandum - Year: 2023 - Exam period: Gauteng June Exam - Paper: 1 - 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 P1 Gauteng June 2023 Memo (English)](https://www.hlayiso.com/library/gr-11-math-p1-english-june-2023-possible-answers/df728d9d-98d3-4a33-90a1-47ad3e999390) ## 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. ## 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 1) 10 pages ### Page 2 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD QUESTION 1 1.1 1.1.1 x  {4 ; 5}  answer  answer (2) 1.1.2 x  {0 ; 3}  answer  answer (2) 1.1.3 x  {1 ; 2}  answer  answer (2) 1.2 1.2.1 3x 2  4 x  0  x ( 3 x  4)  0  factors 4 x  0 or  x   answers 3 NOTE: Any other valid method. (3) 1.2.2 3x – 14 = –6x2  standard form  6x2 + 3x – 14 = 0  (3)  (3) 2  4(6)( 14) x=  substitution 2(6)  x = 1,29 or x = –1,79  answers (4) 1.2.3 ( x  1)( x  3)  12 x 2  2 x  3  12  standard form x 2  2 x  15  0 -3 5  factors ( x  5)( x  3)  0  x  5or  x  3  answers (4) 1.2.4 2 x 2 x 2 x  x2 ( 2  x ) 2  ( x  2) 2  squaring both sides 2  x  x2  4x  4 0  x 2  3x  2  standard form 0 = (x – 2)(x – 1)  factors  x = 2 ... or ... x = 1(NA)  answers with rejection (4) 2 ### Page 3 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD 1.2.5 x6  0 x  6  value of x  x  2y  3 6  2y  3  substitution 2y  3 3 y   value of y 2 (3) 1.3 y – 1 = 2x  y = 2x + 1 ………(1)  expression for y x2 + xy – 3x – y + 2 = 0 ………(2)  x2 + x(2x + 1) – 3x – (2x + 1) + 2 = 0  substitution x2 + 2x2 + x – 3x – 2x – 1 + 2 = 0  3x2 – 4x + 1 = 0  standard form (3x – 1)(x – 1) = 0 1 x= ... or ... x = 1  x-values 3 5 y= ... or ... y = 3  y-values 3 (5) 1.4 x 2  px  p 2  2  x 2  px  p 2  2  0   b 2  4ac   ( p ) 2  4(1)( p 2  2)  substitute into    p2  4 p2  8   5 p2  8    5 p2  8  p 2  0 p    5 p 2  0 p    p 2  0 , 5 p 2  0 and 2  5 p  8  0 p   5 p2  8  0  roots are real and unequal. (3) 3 ### Page 4 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD 1.5 The 100 m fencing will make up three sides because the existing wall will make one side. Wall � � � fencing = 2x + y = 100  y = –2x + 100  A  xy  expression for y A = x(–2x + 100) A = –2x2 + 100x  expression for A A = –2(x2 – 50x)  A = –2(x2 – 50x – 625 – 625)  complete square A = –2(x – 25)2 –625) Maximum area: x  25  value of x A  2( 25) 2  100( 25)  value of A  A  1 250  1 250  25 y  y  50  value of y (7) [39] 4 ### Page 5 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD QUESTION 2 2.1 2.1.1 3n2.9n1 27n1 3n2.32n2  32 n  2 and 33n 3 33n3 33n4 33n3 33n43n3  33 n  4  3 n  3 37  answer (3) 2.1.2 x2 1 x (1  3 ) 2   substitution 11 3 1 2 3  3   simplification 2 3 42 3  2 3 2(2  3 ) 2  factorisation  2 3 =2  answer (4) 5 2.1.3 ( a 2  b 2 )  ( a  b) 2 1 ( a  b) 2 5 (a  b)(a  b)  (a  b) 2  ( a  b) 2 1  factorisation 1 1 5 ( a  b) 2 ( a  b) 2  ( a  b) 2  1  simplification ( a  b) 2 1 5 ( a  b) 2  ( a  b) 2  simplification ( a  b) 3 a 3  3a 2b  3ab2  b3  answer (4) 5 ### Page 6 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD 2 8 2.2 RTP: – = 2 1 2 8 2 8 – 1 2 8 2 8  2 2  – 1 2 2 2 2(2 2 )  8(1  2 )   2 2(1  2) 2 2 (1  2 ) 4 2 88 2  2 2 2 4 4 2 88 2  2 2 4 4 2 8   simplification 2 2 4 4 2 2   factorisation 2 2 2  2 (4) 2.3 MK  LM  2  MK= 2 JM 2  (2  3) 2  22 pythag  substitution JM 2  4  4 3  3  4  simplification JM 2  4 3  3 JM  4 3  3  JM 1 A  (4) 4 3  3  substitution into area formula 2 A  6,3 units2  answer (6) [21] 6 ### Page 7 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD QUESTION 3 3.1 T2  T1  T3  T2 4 x  5  x  10 x  5  ( 4 x  5)  method 3x  5  10 x  5  4 x  5 3x  5  6 x  10  3x  15 x  5  answer (2) 3.2 3.2.1  3n  20  106  equating 3n  126  n  42  answer (2) 3.2.2  3n  20  0  Tn  0 20  3n 20  n 3 n  7  answer (2) 3.2.3 Odd valued terms: 17; 11; 5; ………..  sequence General term: Tn  6n  23  Tn Tn  6( 20)  23  Tn  97  answer (3) 3.3 3; a; 10; b; 21  1st differences a  3; 10  a; b  10; 21  b 1st difference 2nd differences: 10  a  a  3  1  equating 2nd difference in  2a  13  1 terms of a, then b.  2a  12 a  6  value of a and 21  b  b  10  1  2b  31  1  2b  30  b  15  value of b (4) [13] 7 ### Page 8 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD QUESTION 4 y D(6 ; 7) C(–1 ; 0) B x O A(2 ; y) 4.1 B(5; 0)  answer NOTE: Must be in coordinate form. (2) 4.2 y  a ( x  x1 )( x  x2 )  7  a (6  (1))(6  5)  substitute roots and 7  7a point D(6;7) a  1  value for a  y  1( x  1)( x  5) y  x 2  5x  x  5  y  x 2  5x  x  5  y  x2  4x  5 (3) 4.3 B(5 ; 0) C(0 ;  5) 50 mBC  05 5 mBC   mBC 5  mBC  1  mh   1  mh  y  y1  m( x  x1 ) y  (1)  1( x  0) pt (1;0)  y  x 1  answer (3) 8 ### Page 9 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD 4.4 1  x  0  all critical values (independent) x5  answers OR x  [–1 ; 0] or [5 ; ]  all critical values NOTE: Deduct 1 mark if brackets are incorrect in the (independent) alternative solution.  answers (2) [10] QUESTION 5 5.1  asymptotes 2  intercepts  shape NOTE: If the candidate calculates the intercepts and lists the asymptotes but does not sketch the graph, award 2 marks. (3) 5.2 tan 135 = –1  m  1 y – y1 = m(x – x1) y – (–1) = –1(x – (–2))  subs. point (2;–1) y + 1 = –x – 2 y = –x – 3  answer (3) 5.3 x  2  answer (1) 5.4 5.4.1 5 units right  answer NOTE: Accept an answer of 5 units. (1) 5.4.2 3 units up  answer NOTE: Accept an answer of 3 units. (1) [9] 9 ### Page 10 Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 1) GRAD QUESTION 6 6.1 6.1.1 y  6  answer (1) 6.1.2 h( x)  3.2 x  6 0  3.2 x  6  equate to 0 6  3.2 x 2  2x x 1  answer (2) 6.1.3 h( x )  3.2 x  6 y = 3.2 – 6 y = –3  answer (1) 6.1.4 x >1  answer (1) 6.2 y  x-intercept x O  asymptote –1  shape (3) [8] TOTAL: 100 10 ## Related documents - [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 - [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) — 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 - [Maths Grade 11 November 2023 P1 and Memo](https://www.hlayiso.com/library/maths-grade-11-november-2023-p1-and-memo/59d9512d-30fd-4836-9eda-81b77787e852) — Mathematics · Memo · 2023 ## 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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