# Mathematics Grade 11 Paper 1 Gauteng June 2016 Memo > Grade 11 Mathematics Paper 1 memorandum from the Gauteng June 2016, 11 pages. Read online or get the free PDF download, question paper linked when available. - Page: https://www.hlayiso.com/library/gr11-math-p1-june-2016-possible-answer/8abf9959-f0c5-4918-94fd-aa3ebabec0f5 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Document type: Memorandum - Year: 2016 - Exam period: Gauteng June - Paper: 1 - Curriculum: CAPS - Pages: 11 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 1 Gauteng June 2016 Memo](https://www.hlayiso.com/library/gr11-math-p1-june-2016-possible-answer/8abf9959-f0c5-4918-94fd-aa3ebabec0f5) ## About this document Mathematics · Grade 11 · Gauteng June · 2016. Memorandum, 11 pages. 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Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION JUNE 2016 GRADE 11 MATHEMATICS P1 MEMORANDUM 11 pages ### Page 2 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) GAUTENG DEPARTMENT OF EDUCATION− PROVINCIAL EXAMINATION MATHEMATICS (Paper 1) MEMORANDUM QUESTION 1 1.1  4  OR x   3 (2) 1.2 1.2.1 = x+4  Squaring ( both sides  Standard form 2–x = + 8x +16 2  Factors x + 8x +16 + x – 2 = 0  Answers x2 + 9x +14 = 0  x= –2 only (x + 2)(x + 7) =0 x = –2 OR x = –7 NA (5) 1.2.2 2x( x - 3) = 1  Standard form 2x2 - 6x – 1 =0  Substitution a = 2; b = -6; c = -1  Answer  answer x = x= x= x = 3,2 OR x = -0,2 (4) 2 ### Page 3 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) 1.2.3 >0  x 1  x3  Critical values in >0 context of an inequality >0  correct notation Only focus on -3 < < -1 or > 1 numerator OR (-3 ; -1)  (1 ; ) (4) 1.3  Divide by 2 73  2 16  Finding square root 2 ( )  x = 2,89 2 =  x = -1,39 Use of quadratic x = formula max 2/5 for the two correct answers. x= OR x= x = 2,89 OR x = -1,39 (5) [20] 3 ### Page 4 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) QUESTION 2 2.1  Expansion  33 3  4.9 =  3x 1  3  Answer = = If k-method is used exactly the same mark = allocation = 16 OR (4) 2.2 2.2.1   5  10 5  2    5  10 5  2  5 2 5 52 5  simplification  5  10 5  20   5 5 2 5  52 5 5  2 55 25  10 5  52 5  answer   552 5  5  2 55 5 OR  + Rationalizing the denominator = +   Rationalizing the denominator =5 - 2  Simplification  Answer =5 - 2 =5 (4) 4 ### Page 5 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) 2.2.2 (  7 2008  7 3  71 =(  (7 =( +  Answer =(7 - =(7 =343 OR 2009 2.2.2 (  7 2 cont.  (7–1)  (7 =( + )2  Answer = + )2 = (7 = (49)(7) = 343 (4) 2.3 from: 2 . 4y = 1 x  2 2y 2x . 22 y = 20  x + 2y = 0 x + 2y = 0 OR x = –2y................. x= –2y subst  into (4y)x =  substitution (4y)–2x =  same bases on either 2 4 y  2 4 side 2 –4y2 = –4  y = 1 y = 1  x = 2 subst y =  1 into  y= 1 x = –2 y = –1 x =2 OR (6) 5 ### Page 6 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) 2 x .4 y  1  22 y 2 x .2 2 y  2 0  x + 2y = 0 x  2 y  0.......... .1 OR   4y  x 1 16 x= –2y  22xy  24 2  2 4 2 xy  2 xy  4 2 xy  4 2  y = 1 y   .......... ...... 2 x  x = 2  2 x  2    0  x x2  4  0 x  2x  2  0 x  2 or x  2 2 y x 2 2  or  2 2 y  1 y 1 [18] 6 ### Page 7 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) QUESTION 3 3.1 3.1.1 Roots are non-real (imaginary) Non-real roots therefore  < 0. OR   < 0 (2) 3.1.2 Roots are real and equal,  Roots are real = 0  Roots equal (2) 3.2  2 = (2k -1) – 4(k)(k-1)  Substitution = 4k2 – 4k +1 -4k2 +4k  Simplification =1  Value of 1 1 is a perfect square, the coefficients  Perfect square are rational, so the roots are rational. (4) [8] QUESTION 4 4.1 4.1.1 -1; 8; 23; .........  –1 8 23 (3) 4.1.2 2 3k – 4 = 71 3k2 – 4 = 71 k2 = 25  k2 = 25 or k = 5 k  5k  5 k = 5  k=5 No marks for k =  5 (3) 4.2 4.2.1 Quadratic number pattern  Quadratic  second difference is 0 ; 5 ; 12 ; 21; .... constant or illustration 5 7 9 2 2 If the learner only Quadratic number pattern show the pattern without justification OR/OF only 1 mark Quadratic number pattern The first difference is not constant but the second difference is constant. (2) 7 ### Page 8 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) 4.2.2 2a = 2 a = 1 a = 1 3a + b = 5 3(1) + b = 5 b = 2 b = 2 T1 = a + b + c 0 = 1 + 2 +c c = –3 c = –3 Tn = an2 + bn + c Tn = n2 + 2n -3 Tn = n2 + 2n -3 (4) 4.3 4.3.1 Row 4  Row 4 = 22 7  6  5  4  22 2 2 2 2 Row 20 Row 20 = 86 23  22  21  20  86 2 2 2 2 (2) 4.3.2 (n  3)  (n  2)  (n  1)  n  4n  6  a  n  3 2 2 2 2  b  n  2; c  n  1; d  n  Tn  4n  6 If only the general term was given 1/3 (3) [17] QUESTION 5 5.1 x = –2 and y = 1  x = –2  y=1 Both has to be in equation form. If not 0/2 If p  2 and q  1 0/2 (2) 5.2 Sub B = (0; -2) in y = +1  Substitution of (0 ; –2) and q = 1 -2 = +1 -2 = +1 –3 = then k = -6  y= +1  k value  Answer (3) 8 ### Page 9 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) 0 = +1  y=0 5.3  x26 –1 =  x=4 (x +2) = 6  Writing Point D in x = 4 coordinate form. D(4 ; 0) (4) 5.4 C(–2 ; 0) and B(4 ; 0) CA from 5.3 y = a(x+ 2)(x – 4)  x2 –2 = a(0+2)(0 – 4)   x  4 –2 = a (–8)  Sub. B (0; –2) =a  a = y = (x + 2)(x – 4)  answer in any form y = -2x – 8) = – x–2 (5) 5.5  Shape  Coordinates of (0 ; 4) y  Graph not crossing the x- axis (0; 4) x (3) 5.6 y=  y = (2) 5.7 y is real ,  y is real, (y R) both condition (1) [20] 9 ### Page 10 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) QUESTION 6 6.1 [0 ; 4]  0 OR 4 0 x4 (2) 6.2 h( x)  ( x2  4x  4  4)  a = –1.   x  2   4 2  p = –2.  q = –4. (3) 6.3 CA from 6.1 y y (2 ;4)  (2;4) h(x)  Shape (neg graph)  Turning point  y-intercept. 2 4 x  positive y-values 0 only. 0 4 x (4) 6.4 h(x) = - x + 4x2  Sub x with x  5 = –( x – 5 )2 + 4( x – 5)  Simplification = – (x2 – 10x +25) + 4x -20  Answer = – x2 +10x –25 + 4x -20 h(x – 5) = – x2 + 14x -45 OR OR y = – (x – 2)2 + 4  (x – 2 – 5)2 = – (x – 2 – 5)2 + 4 = – (x – 7)2 + 4 = – (x2 – 14x + 49) + 4  Simplification = – x2 + 14x – 49 + 4 = – x2 + 14x – 45  Answer (3) 10 ### Page 11 Downloaded from hlayiso.com MATHEMATICS Grade 11 MEMORANDUM (Paper 1) 6.5 k(x) = x2 – 4x  x2  –4x (2) 6.6 9 9 p(–3) = 2  p(–3) = 2 1 1 p(–1) = 2  p(–1) = 2 Average gradient  Answer = = Average gradient of p = –2 (3) [17] 11 ## Related documents - [Gr11 Math P1 June 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p1-june-2016-question-paper/c0be92f8-5b2d-42a2-beef-6c5ca8029155) — Mathematics · QP · 2016 - [Gr11 Math P1 (Afrikaans) June 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p1-afrikaans-june-2016-question-paper/7ea1ce61-afcd-483b-a4fa-ea2b49b96e56) — Mathematics · QP · 2016 · Afr - [Gr11 MATH P1 (AFR) June 2022 Possible Answers](https://www.hlayiso.com/library/gr11-math-p1-afr-june-2022-possible-answers/31eae199-9c0b-4a71-ab81-f769f84c7ccd) — Mathematics · Memo · 2022 · Afr - [Gr11 Math P1 June 2017 Possible Answers](https://www.hlayiso.com/library/gr11-math-p1-june-2017-possible-answers/19ca7dfb-d358-4c42-bbfc-c68d580cfe21) — Mathematics · Memo · 2017 - [Gr11 Math P1 (Afrikaans) June 2017 Possible Answers](https://www.hlayiso.com/library/gr11-math-p1-afrikaans-june-2017-possible-answers/b8504619-0cb6-476d-944d-f53d2ea22f72) — Mathematics · Memo · 2017 · Afr - [Gr11 Math P2 June 2016 Question Paper](https://www.hlayiso.com/library/gr11-math-p2-june-2016-question-paper/aa2249f8-80f3-42ba-b4b6-0ebec49b6fc6) — Mathematics · QP · 2016 ## 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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