# Mathematics Grade 11 P2 Gauteng June 2022 QP (Afr)

> Grade 11 Mathematics Paper 2 question paper from the Gauteng June 2022 (Afrikaans), 9 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/gr11-math-p2-afr-june-2022-question-paper/1fcd90d5-8dba-4271-a9ed-137098dfc983
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper
- Year: 2022
- Exam period: Gauteng June
- Paper: 2
- Curriculum: CAPS
- Pages: 9

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 2022 QP (Afr)](https://www.hlayiso.com/library/gr11-math-p2-afr-june-2022-question-paper/1fcd90d5-8dba-4271-a9ed-137098dfc983)

## About this document

Mathematics · Grade 11 · Gauteng June · 2022. Question paper, 9 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

                  PROVINSIALE EKSAMEN
                               JUNIE 2022
                                GRAAD 11

                                 WISKUNDE
                                 VRAESTEL 2

TYD:        2 uur

PUNTE:      100

7 bladsye en 2 diagramvelle

                                                   b.o.

### Page 2

Downloaded from hlayiso.com

                                               WISKUNDE                                      2
                                               (Vraestel 2)                   GRAAD 11

INSTRUKSIES EN INLIGTING

1.    Hierdie vraestel bestaan uit 3 vrae.

2.    Beantwoord AL die vrae.

3.    Dui ALLE berekeninge, diagramme, grafieke ensovoorts wat jy gebruik het om die
      antwoorde te bepaal, duidelik aan.

4.    Volpunte sal NIE noodwendig aan antwoorde alleen toegeken word NIE.

5.    Gebruik ŉ goedgekeurde wetenskaplike sakrekenaar (nie-programmeerbaar en nie-
      grafies), tensy anders aangedui.

6.    Indien nodig, moet antwoorde afgerond word tot TWEE desimale plekke, tensy anders
      vermeld.

7.    Skryf jou naam en klas op die ANTWOORDBOEK.

8.    Diagramme is NIE noodwendig op skaal geteken NIE.

9.    Nommer die antwoorde korrek volgens die nommeringstelsel wat in die vraestel gebruik
      is.

10.   Skryf netjies en leesbaar.

                                                                                                 b.o.

### Page 3

Downloaded from hlayiso.com

                                                      WISKUNDE                               3
                                                      (Vraestel 2)            GRAAD 11

VRAAG 1

1.1   Die punte D(–1 ; 2), E(4 ; –2), F(–5 ; –3) is die hoekpunte van DEF.

      Bepaal:

      1.1.1 Die gradiënt van DF                                                                  (2)

      1.1.2 Indien lyn DE loodreg is op DF, skryf die gradiënt van DE neer                       (1)

      1.1.3 Die vergelyking van die lyn DE in die vorm y = mx + c                                (3)

      1.1.4 Die vergelyking van die lyn ewewydig aan DE wat deur die punt F gaan in die
            vorm y = …                                                                           (3)

      1.1.5 Indien G(6 ; y) ŉ punt op DE is, bepaal die waarde van y                             (2)

      1.1.6 Toon aan dat die lengte van DF gelyk is aan DE. Watter tipe driehoek is ∆DEF ?       (5)    Commented [PS1]: Change as per English version

      1.1.7 Die oppervlak van driehoek DEF                                                       (2)

1.2   Vierhoek PQRS is hieronder geteken en het die volgende eienskappe:

      •   RQ ‖ SR
      •   Die koördinate van R(–4 ; 1) en S(10 ; 3) is gegee
      •   Die koördinate van Q(–7 ; y) en P(x ; –9) is gedeeltelik gegee

                                                  y
                                                                  S(10 ; 3)
                                  R(–4 ; 1)
                                                                       x
                                              0
                         Q(–7 ; y)

                                                      P(x ; –9)

      Bepaal:

      1.2.1 Watter tipe vierhoek is PQRS?                                                        (1)

      1.2.2 Die waarde van x as RS = 15 eenhede                                                  (5)

      1.2.3 Die koördinate van T, die middelpunt van RS                                          (2)

      1.2.4 Die waarde van y                                                                     (3)

      1.2.5 Die koördinate van W, ŉ punt op SP sodat PQRW ŉ reghoek is                        (3)
                                                                                             [32]
                                                                                                 b.o.

### Page 4

Downloaded from hlayiso.com

                                                         WISKUNDE                               4
                                                         (Vraestel 2)                GRAAD 11

VRAAG 2

2.1   In die diagram is P ŉ punt in die eerste kwadrant sodat 5sin ( 90 −  ) − 3 = 0 .
      R(k ; 6) is ŉ punt in die tweede kwadrant sodanig dat PÔR = 90°.

      In die diagram hieronder:

      •   POˆ R = 90
      •   R(k ; 6) is ŉ punt in kwadrant 2
      •   P is ŉ punt in kwadrant 1 sodanig dat 5sin ( 90 −  ) − 3 = 0

                                                    y
                               R(k ; 6)
                                                                 P
                                    

                                                                         x
                                    Q                0

      Bepaal:

      2.1.1     sin                                                                                (3)

      2.1.2     Die waarde van k                                                                    (3)

2.2   Vereenvoudig volledig, sonder die gebruik van ŉ sakrekenaar:                                         Commented [PS2]: Change as per English version

      2.2.1     tan 315 + cos300
                sin150 + tan135                                                                   (6)

      2.2.2     sin (180 + x ) cos (180 − x ) .sin 50
                tan ( 315 ) .cos 2 ( 360 − x ) .cos140                                           (6)

2.3   Indien x  − 180 ; 180 , bepaal sin ( x + 10 ) − cos ( x − 30 ) = 0 .                   (7)    Commented [PS3]: This is already changed on this version
                                                                                                           – I have changed it on English version

                                                                                                    b.o.

### Page 5

Downloaded from hlayiso.com

                                                WISKUNDE                             5
                                                (Vraestel 2)              GRAAD 11

2.4   In die vierhoek hieronder:

      •   AB            ˆ D = 80°, BD
            ˆ C = 36°, CB           ˆ C = 60°
      •   Lyn AB = 74 m en lyn BC = 52 m

                        A                74 m               B
                                                    36°
                                                          80°

                                         52 m

                                                                60°
                                                                      D
                                     C

      Bereken:

      2.4.1   Die waarde van B ˆCD                                                       (1)

      2.4.2   Die lengte van lyn CD                                                      (2)

      2.4.3   Die lengte van diagonaal AD                                                (4)

      2.4.4   Die oppervlakte van vierhoek ABCD                                       (4)
                                                                                     [36]

                                                                                         b.o.

### Page 6

Downloaded from hlayiso.com

                                                 WISKUNDE                                          6
                                                 (Vraestel 2)                   GRAAD 11

VRAAG 3

3.1   In die skets hieronder is O die middelpunt van die sirkel. Koord PQ is loodreg op OM by M.

                                                          Q
                                             O

                                                     M

                                            P

      Bewys die stelling wat beweer dat die lyn wat uit die middelpunt van die sirkel loodreg op
      die koord getrek word, halveer die koord.                                                        (5)

3.2   In die skets hieronder:

      •   O is die middelpunt van die sirkel
      •   AB = 10 cm en is loodreg op OC by punt D
      •   C is ŉ punt op die omtrek van die sirkel
      •   Die radius van die sirkel is 13 cm

                                                     O

                                                 D
                                       A                        B

                                                     C

      Bereken die lengte van lyn DC.                                                                   (5)

3.3   Bereken die oorblywende oppervlak van die sirkel indien die oppervlak van ∆OAB
      uitgesluit is.                                                                                   (3)

                                                                                                       b.o.

### Page 7

Downloaded from hlayiso.com

                                                   WISKUNDE                                7
                                                   (Vraestel 2)             GRAAD 11

3.4   In die skets hieronder:

      •   PQRS is ŉ koordevierhoek
      •   Lyn AB is ŉ raaklyn aan die sirkel by punt S
      •   PQ = QR
      •   PR = SR
      •   PQ ║ SR
      •    ˆR= x
          BS

                                              P
                                A                                 Q
                                             12   3

                                        12                        1 2
                                    S                                   R
                                         3

                                              B

      3.4.1   Bepaal met redes, VYF hoeke wat gelyk is aan BŜR.                           (10)

      3.4.2   Bereken die waarde van Ŝ1 in terme van x asook TWEE ander hoeke wat gelyk
              is aan Ŝ1 .                                                                     (6)

      3.4.3   Bewys dat PS = QR.                                                               (3)
                                                                                           [32]

                                                                              TOTAAL:      100

                                                  EINDE

### Page 8

Downloaded from hlayiso.com

                                       WISKUNDE                  8
                                       (Vraestel 2)   GRAAD 11

DIAGRAMVEL 1

VRAAG 3

3.1

                                   Q
                   O

                           M

               P

3.2

                       O

                   D
           A                   B

                       C

### Page 9

Downloaded from hlayiso.com

                                        WISKUNDE                  9
                                        (Vraestel 2)   GRAAD 11

DIAGRAMVEL 2

3.3
                      P
      A                                Q
                      1       3
                          2

              1                         2
          S       2                    1
                  3                         R

                          B

## Related documents

- [Gr11 MATH P2 (ENG) June 2022 Possible Answers](https://www.hlayiso.com/library/gr11-math-p2-eng-june-2022-possible-answers/1a429955-227a-4c34-aec9-9e119d0c4bc5) — Mathematics · Memo · 2022 · 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
- [Gr11 Math P2 June 2017 Question Paper](https://www.hlayiso.com/library/gr11-math-p2-june-2017-question-paper/64687c17-ca24-4dad-9367-5ed08ba6ca70) — Mathematics · QP · 2017
- [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
- [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 P2 June 2018 Question Paper Errata](https://www.hlayiso.com/library/gr11-math-p2-june-2018-question-paper-errata/c33250f1-b917-4589-ae55-a60bdee9309d) — Mathematics · Errata · 2018

## More from Grade 11 Mathematics

- [Grade 11 Mathematics P1 November 2026 Mock Memo](https://www.hlayiso.com/library/grade-11-mathematics-2026-november-mock-exam-memorandum-paper-1/470265ad-99e7-4e3e-af02-0c28a273b390) — Memo · 2026 · Eng
- [MATHS P1 MEMO GR11 NOV 2025 E+A watermark](https://www.hlayiso.com/library/maths-p1-memo-gr11-nov-2025-e-a-watermark/5af2bd74-cc9d-4651-895a-310a59d8ce25) — Memo · 2025
- [MATHS P2 MEMO GR 11 NOVEMBER 2025 (ENG & AFR) watermark](https://www.hlayiso.com/library/maths-p2-memo-gr-11-november-2025-eng-afr-watermark/6bc83e22-926c-4a81-95ea-4dee0141ce24) — Memo · 2025 · Afr
- [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 P2 GRADE 11 NOV 2024 ENG AFR MARKING GUIDELINE watermark](https://www.hlayiso.com/library/maths-p2-grade-11-nov-2024-eng-afr-marking-guideline-watermark/0f16be7d-4a28-41e1-9e8d-57c649490c1c) — Memo · 2024 · Eng

## 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. When citing, link the page URL above, not a PDF or /api/ URL.