# Mathematics Grade 11 P2 Eastern Cape November 2023 Memo

> Grade 11 Mathematics Paper 2 memorandum from the Eastern Cape November Exam 2023 (English), 13 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/maths-p2-memo-gr11-nov-2023-afri-english/2a90e6d8-3c93-4f27-b271-c5577c097623
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Language: English
- Document type: Memorandum
- Year: 2023
- Exam period: Eastern Cape November Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 13

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## About this document

Mathematics · Grade 11 · Eastern Cape November Exam · 2023 · English. Memorandum, 13 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Matching paper and memo

- [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) — QP · 2023 · Eng

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### Page 1

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                          NATIONAL
                     SENIOR CERTIFICATE/
                          NASIONALE
                      SENIORSERTIFIKAAT

                           GRADE/GRAAD 11

                         NOVEMBER 2023

           MATHEMATICS P2/WISKUNDE V2
          MARKING GUIDELINE/NASIENRIGLYN

MARKS/PUNTE:   150

                     This marking guideline consists of 13 pages.
                     Hierdie nasienriglyn bestaan uit 13 bladsye.

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 2                                MATHEMATICS P2/WISKUNDE V2                         (EC/NOVEMBER 2023)

 QUESTION 1/VRAAG 1

1.1       6 boys / seuns                                    ✓ answer / antwoord                         (1)
1.2       Skewed to the right / positively skewed           ✓ answer / antwoord
          Skeef na regs / Positief skeef                                                                (1)
1.3       127 – 68 = 59                                     ✓ working out / bewerking
                                                            ✓ answer / antwoord                         (2)
1.4.1     Median/Mediaan = 84 / Remains unchanged /         ✓ answer / antwoord
          Bly onveranderd                                                                               (1)
1.4.2     (87 × 24 + 20) ÷ 24 = 87,8 OR/OF 88               ✓ working out / bewerking
                                                            ✓ answer / antwoord                         (2)
                                                                                                        [7]

 QUESTION 2/VRAAG 2

2.1
                                                    Cumulative
           Time waiting /           Number of
                                                      frequency
               Wagtyd                learners
                                                    Kumulatiewe
          (minutes / minute)      Aantal leerders
                                                     frekwensie          ✓ for / vir 6; 16; 35
              0<𝑥≤4                      6              6
                                                                         ✓ for / vir 50; 55
               4< 𝑥 ≤ 8                  10             16

             8 < 𝑥 ≤ 12                  19             35

            12 < 𝑥 ≤ 16                  15             50

            16 < 𝑥 ≤ 20                  5              55
                                                                                                        (2)

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 (EC/NOVEMBER 2023)                      MATHEMATICS P2/WISKUNDE V2                                 3

2.2

                                                                       ✓ for grounding
                                                                         vir anker

                                                                       ✓ for endpoint
                                                                         vir eindpunt

                                                                       ✓✓ for any 2
                                                                          correct points

                                                                            vir enige 2
                                                                            korrekte punte

                                                                                                        (4)
2.3     55 – 43 = 12 learners / leerders (accept/aanvaar 11 en 13)     ✓ 55 ✓43 ✓12                     (3)
2.4     8 < 𝑥 ≤ 12                                                     ✓ answer /
                                                                         antwoord                       (1)
2.5     IQR / IKW = 14 – 7 = 7                                         ✓ UQ ✓ LQ
                                                                       ✓ answer /
                                                                         antwoord                    (3)
                                                                                                    [13]

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  4                                      MATHEMATICS P2/WISKUNDE V2                        (EC/NOVEMBER 2023)

  QUESTION 3 / VRAAG 3

3.1       𝑚𝐴𝐵 = 𝑚𝐵𝐶
           −8−0          −14−0                                     -8 − 0
                     =                                         ✓ 𝑥 −5 + 8
          𝑥−5 + 8   𝑥+8
           −8     −14                                             −14−0
                =                                              ✓ 𝑥+8
          𝑥+3        𝑥+8
          −8𝑥 − 64 = −14𝑥 − 42                                 ✓ −8𝑥 − 64
          6𝑥 = 22                                              ✓ −14𝑥 − 42
                                                                        11
                11                                             ✓ 𝑥= 3
          𝑥=                                                                                                   (5)
                3
3.2.1          6+0       -2−6                                  ✓ substitution / vervanging
          M(         ;          )
                 2        2                                    ✓ answer / antwoord
          = M(3; -4)                                                                                           (2)
3.2.2                                               2
          AC = √(2 − 0)2 + (10 − (−6))                         ✓ substitution / vervanging
          AC = √4 + 256
          AC = 2√65                                            ✓ answer / antwoord                             (2)
3.2.3     F(−4; 6)                                             ✓ x ✓y                                          (2)
3.2.4
          𝑚𝐴𝐵 =
                     10−(−2)
                                    =
                                        12
                                             = −3              ✓ 𝑚𝐴𝐵
                       2−6            −4                       ✓ 𝑚𝐵𝐶
                     −2+6           4  2
          𝑚𝐵𝐶 =               = =
                     6−0            6    3
                                                               ✓ 𝑚𝐴𝐵 × 𝑚𝐵𝐶 ≠ −1
          𝑚𝐴𝐵 × 𝑚𝐵𝐶 ≠ −1
          ∴ABCF is not a rectangle / is nie ŉ reghoek nie

                                        OR/OF

                                                               ✓𝐴𝐵 = √160 = 4√10
          𝐴𝐶 = √260 = 2√65
                                                               ✓ 𝐵𝐶 = √50 = 5√2
          𝐴𝐵 = √160 = 4√10
                                                               ✓ 260 ≠ 160 + 50
          𝐵𝐶 = √50 = 5√2
          260 ≠ 160 + 50
          𝐴𝐶 2 ≠ 𝐴𝐵2 + 𝐵𝐶 2                                                                                    (3)

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 (EC/NOVEMBER 2023)                           MATHEMATICS P2/WISKUNDE V2                                    5

3.2.5   𝑚𝐴𝐵 = −3                                             ✓ 𝑚𝐴𝐵
        ∴ 𝑦 = −3𝑥 + 𝑐
        10 = −3(2) + 𝑐                                       ✓ substitution / vervanging
        𝑐 = 16
        ∴ 𝑦 = −3𝑥 + 16                                       ✓ equation of AB /
                 10−(−6)                                       vergelyking van AB
        𝑚𝐴𝐶 =                  =8
                      2−0                                    ✓ gradient of AC/gradiënt van AC
        ∴ 𝑦 = 8𝑥 − 6
                                                             ✓ equation of /vergelyking van AC                  (5)
3.2.6   tan AÊX = −3                                               ̂X = −3
                                                             ✓ tan AE
        ∴ AÊX = 108,43°                                     ✓ AÊX
        tan AD̂E = 8                                         ✓ tan AD̂E = 8
        ∴ AD̂ E = 82,87°                                     ✓ AD̂E
        ̂
        A = 108,43° − 82,87° = 25,56°                        ✓✓ answer / antwoord                               (6)
3.2.7       3
        D (4 ; 0)                                            ✓ coordinates of D / koördinate van D
            16
        E ( 3 ; 0)                                           ✓ coordinates of E / koördinate van E
                     55
        ∴ DE = 12 units / eenhede                            ✓ length of DE / lengte van DE

        Perpendicular height / Loodregte hoogte
        = 10 units / eenhede                                 ✓ height / hoogte

                 1        55
        ∴ A = 2 × 12 × 10 = 22, 92 units2/ eenhede2          ✓ answer / antwoord

                                 OR/OF
                                                             ✓ 𝐴𝐷 = 10,08
        𝐴𝐷 = 10,08
                                                             ✓𝐴𝐸 = 10,54
        𝐴𝐸 = 10,54
                                                             ✓ Formula/formule
                       1
        𝐴𝑟𝑒𝑎 𝑜𝑓 ∆ 𝐴𝐷𝐸 = 𝐴𝐷. 𝐴𝐸 sin 𝐴
                       2
                                1                            ✓ substitution/vervanging
        𝐴𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐷𝐸 =            (10,08)(10,54) sin 25,56
                                2
        𝐴𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐷𝐸 = 22,92 𝑢𝑛𝑖𝑡𝑠/𝑒𝑒𝑛ℎ𝑒𝑑𝑒 2
                                                             ✓answer/antwoord                                 (5)
                                                                                                             [30]

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 6                                MATHEMATICS P2/WISKUNDE V2                          (EC/NOVEMBER 2023)

 QUESTION 4 / VRAAG 4

4.1       tan 𝜃 = 7
                        3                             ✓ correct quadrant / korrekte kwadrant
                                                                 3
          𝑟 2 = (−7)2 + (−3)2                         ✓ tan 𝜃 = 7
          𝑟 2 = 58
          𝑟 = √58                                     ✓ for/vir
          sin θ + cos θ
              2 sin θ
              −3     −7
                  +( )                                ✓ substitution / vervanging
          = √58 −3√58
                  2(        )
                       √58                            ✓ simplification / vereenvoudiging
              −10 √58
          =     ×
            √58   −6                                  ✓ answer / antwoord
            5
          =                                                                                              (6)
              3

4.2.1     tan(−32°)                                   ✓ method used / triangle
          = − tan 32°                                   metode gebruik / driehoek
                𝑝
          =−                                          ✓ − tan 32°
                   2
                  √1−𝑝
                                                      ✓ answer / antwoord
                                                                                                         (3)
4.2.2     sin 418°
          = sin 58°                 = sin(90° − 32)   ✓ sin 58°                   ✓ cos 32°
          = √1 − 𝑝2                 = cos 32°         ✓ answer / antwoord         ✓ answer
                                    = √1 − 𝑝2                                       antwoord
                                                                                                         (2)

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 (EC/NOVEMBER 2023)                                  MATHEMATICS P2/WISKUNDE V2                                  7

4.3        sin 120°.tan 300°                                   ✓ sin 60°
          cos(−60°).tan 225°                                   ✓ − tan 60°
              sin 60° . −tan 60°                               ✓ cos 60°
          =                                                    ✓ tan 45°
                cos 60°.tan 45°
                                                               ✓ for numerator S/A / vir teller
              √3 √3
                .−                                             ✓ for denominator S/A / vir noemer
              2     1
          =    1
                 . 1
               2                                               ✓ answer / antwoord
                 3      2
          = − × = −3                                                                                                 (7)
                 2      1
4.4       cos2 x−cos 𝑥−sin2 x             1           1
                                    =            −
          2 sin 𝑥 cos 𝑥+sin 𝑥            tan 𝑥       sin 𝑥
                             cos2 x−cos 𝑥−(1−cos2 x)
                                                               ✓ 1 − cos2 x
          LHS/LK =
                                 2 sin 𝑥 cos 𝑥+sin 𝑥
                                                               ✓ simplifying / vereenvoudiging
                        2𝑐𝑜𝑠 2 𝑥−cos 𝑥−1                       ✓ factoring the top / faktorisering teller
          LHS =
                     2 sin 𝑥 cos 𝑥+sin 𝑥                       ✓ factoring the bottom /
                     (2 cos 𝑥+1)(cos 𝑥−1)                        faktorisering noemer
          LHS =
                         sin 𝑥(2 cos 𝑥+1)
                     cos 𝑥−1                                      cos 𝑥    1
          LHS =                                                ✓ sin 𝑥 − sin 𝑥
                        sin 𝑥
                     cos 𝑥         1
          LHS =              −
                     sin 𝑥       sin 𝑥
                         1         1
          LHS =              −           = RHS/𝑅𝐾                                                                    (5)
                     tan 𝑥       sin 𝑥
4.5       sin(5𝜃) = cos(𝜃 − 40°)
          sin(5𝜃) = sin[90° − (𝜃 − 40°)]                       ✓ co – function / ko-funksie
          sin(5𝜃) = sin(130° − 𝜃)
          5𝜃 = 130° − 𝜃 + 360°. 𝑘                              ✓ 5𝜃 = 130° − 𝜃 + 360°. 𝑘
          6𝜃 = 130° + 360. 𝑘
          𝜃 = 21,67° + 60°. 𝑘                                  ✓ 𝜃 = 21,67° + 60°. 𝑘
                         OR / OF
          5𝜃 = 180° − (130° − 𝜃) + 360°. 𝑘                     ✓ 5𝜃 = 180° − (130° − 𝜃) + 360°. 𝑘
          4𝜃 = 50° + 360. 𝑘                                    ✓ 4𝜃 = 50° + 360. 𝑘
          𝜃 = 12,5° + 90°. 𝑘 where/waar 𝑘𝜖𝑍                    ✓ 𝜃 = 12,5° + 90°. 𝑘
                         OR / OF
                                                               ✓ co-function /ko-funksie
          0 − 5𝜃 = 360 − (𝜃 − 40) + 360𝑘
                                                               ✓ −6𝜃 = −130 + 360𝑘
          −4𝜃 = 310 + 360𝑘
                                                               ✓ 𝜃 = 21,67 − 60𝑘
          𝜃 = −77,5 − 90𝑘
                                                               ✓90 − 5𝜃 = 360 − (𝜃 − 40) + 360𝑘
                                                               ✓−4𝜃 = 310 + 360𝑘
                                                               ✓ 𝜃 = −77,5 − 90𝑘                                   (6)
                                                                                                                  [29]

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 8                                          MATHEMATICS P2/WISKUNDE V2                      (EC/NOVEMBER 2023)

 QUESTION 5/VRAAG 5

                        𝑥                                                             𝑥
5.1        tan 𝜃 = 𝑄𝑅                                                    ✓ tan 𝜃 = 𝑄𝑅
                    𝑥
           𝑄𝑅 = tan 𝜃                                                    ✓ answer / antwoord
                                                                                                               (2)
                                        2
5.2                                 𝑥                      𝑥             ✓ for the cosine rule
           𝑄𝑆 2 = 𝑥 2 + (tan 𝜃) − 2𝑥 (tan 𝜃) cos 120°
                                                                           vir die cosinusreël
                                𝑥2              2𝑥 2       1
           𝑄𝑆 2 = 𝑥 2 + 𝑡𝑎𝑛2 𝜃 − tan 𝜃 (− 2)                             ✓−
                                                                             1
                                                                             2
                                𝑥2              𝑥2                       ✓ simplification
           𝑄𝑆 2 = 𝑥 2 + 𝑡𝑎𝑛2 𝜃 + tan 𝜃                                     vereenvoudiging

                                        1
           𝑄𝑆 = √𝑥 2 (1 + 𝑡𝑎𝑛2 𝜃 + tan 𝜃)
                                                       1                 ✓ for square rooting
                                                                           vir vierkantswortel
                            1               1
           𝑄𝑆 = 𝑥. √𝑡𝑎𝑛2 𝜃 + tan 𝜃 + 1
                                                                                                               (4)
5.3.1                           1                1                       ✓ substitution / vervanging
           𝑄𝑆 = 15√𝑡𝑎𝑛2 22° + tan 22° + 1
           𝑄𝑆 = 46, 48 m                                                 ✓ answer / antwoord
                                                                                                               (2)
5.3.2      tan 𝑄𝑃̂𝑆 =
                            46,48                                        ✓ for using tan /
                      15
                                                                           vir gebruik van tan
           𝑄𝑃̂𝑆 = 72,11°
                                                                         ✓ answer / antwoord
                                                                                                               (2)
                                                                                                              [10]

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 (EC/NOVEMBER 2023)                      MATHEMATICS P2/WISKUNDE V2                                9

 QUESTION 6 / VRAAG 6

6.1

      For f : ✓ shape ✓ endpoints ✓ TP and/en x-intercepts
      Vir f : ✓ vorm ✓ eindpunte ✓ DP and/en x-afsnitte

      For g: ✓ asymptote ✓ shape ✓ y-intercept
      Vir g: ✓ asimptoot ✓ vorm ✓ y-afsnit
                                                                                                       (6)
6.2.1 0° < 𝑥 < 90°                                           ✓ answer / antwoord
                                                                                                       (1)
6.2.2 −45° ≤ 𝑥 ≤ 0° or/of 45° ≤ 𝑥 < 90°                      ✓✓✓ for each answer
                    or/of 90° < 𝑥 ≤ 180°                         vir elke antwoord
                                                                                                       (3)
6.3   1 ≤ 𝑦 ≤ 3 or/of 𝑦𝜖[1; 3]                               ✓✓ for the answer
                                                                vir die antwoord                     (2)
                                                                                                    [12]

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10                               MATHEMATICS P2/WISKUNDE V2                         (EC/NOVEMBER 2023)

QUESTION 7 / VRAAG 7

 7.1

 7.1.1    𝑂𝑅 = 3𝑥                                             ✓ answer / antwoord                   (1)
 7.1.2    UR = 20 cm (line from centre perpendicular…)        ✓S✓R
                       (lyn vanaf middelpunt loodreg …)       ✓ S and/en R
          (3𝑥)2 = (2𝑥)2 + 202 (Pythagoras)
          9𝑥 2 = 4𝑥 2 + 400                                   ✓ simplification
          5𝑥 2 = 400                                            vereenvoudiging
          𝑥 2 = 80
                                                              ✓ answer / antwoord
          𝑥 = √80 = 4√5                                                                             (5)
 7.2

 7.2.1    𝑂̂1 = 54° (alt s / verw. e, OD ∥ AB)                          ✓S✓R
          𝐴̂2 = 27° ( at centre) / (middelpunts )                       ✓S✓R
                                                                                                    (4)
 7.2.2    𝐶̂ = 153° (opp. s of a cq) / (teenoorst. e van k.v)           ✓S✓R
                                                                                                    (2)
 7.2.3    𝐴̂ = 54° (s opp = sides) / (e teenoor = sye)                  ✓ S and/en R
          𝐴̂2 = 27° (proven) / (reeds bewys)                              ✓S
          ∴ 𝐴̂1 = 27°                                                     ✓S
          ∴DA bisects OÂ B / DA halveer OA
                                          ̂B                                                       (3)
                                                                                                  [15]

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(EC/NOVEMBER 2023)                       MATHEMATICS P2/WISKUNDE V2                                     11

QUESTION 8 / VRAAG 8

 8.1

          Let /Laat 𝐴̂1 = 𝑥
          ∴ 𝐴̂2 = 90° − 𝑥 (tan ⊥ rad) / (raaklyn ⊥ radius)                      ✓S✓R
          𝐹𝐶̂ 𝐴 = 90° ( in a semi-circle) / ( in semi-sirkel)                 ✓ S and/en R
          𝐶̂2 = 90° − 𝑥 (s in the same segment) / (e in dies. segment)
                                                                                ✓ S and/en R
          ∴ 𝐶̂1 = 𝑥
              ̂B = BĈ A                                                        ✓S
          ∴ DA                                                                                        (5)
 8.2

 8.2.1    ̂
          R1 = 39° ( subtended by diameter)/ ( onderspan deur middellyn)           ✓S✓R             (2)
 8.2.2    ̂1 = 78° ( at centre) / (Middelpunts )
          O                                                                          ✓S✓R
                                                                                                      (2)
 8.2.3    ̂ 1 = 51° (s opp = sides) / (e teenoor gelyke sye)
          Q                                                                          ✓S✓R
                                                                                                      (2)
 8.2.4    ̂1 = 68° (s in the same segment) / (e in dieselfde segment)
          U                                                                          ✓S✓R
                                                                                                     (2)
                                                                                                    [13]

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12                               MATHEMATICS P2/WISKUNDE V2                          (EC/NOVEMBER 2023)

QUESTION 9 / VRAAG 9

 9.1.1      ̂F = 𝑥
           AB         (tan-chord theorem) / (raaklyn-koord stelling)         ✓S✓R
                                                                                                   (2)
 9.1.2     BĈD = 𝑥 (corresponding angles, BF∥CD)                            ✓S✓R
                    (ooreenkomstige hoeke ; BF || CD)
                                                                                                   (2)
 9.2       Exterior angle = interior opp. angle                              ✓R
           Buitehoek = teenoorstaande binnehoek.
                                                                                                   (1)
 9.3        ̂ C = 𝑥 (angles in the same segment) /
           BD                                                                ✓S✓R
                    (hoeke in dieselfde segment)

            ̂ D = 𝑥 (alternate angles BF∥CD)
           FB
                      (verwissellende hoeke BF || CD)                        ✓S✓R
                                                                                                   (4)
                                                                                                   [9]

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(EC/NOVEMBER 2023)                      MATHEMATICS P2/WISKUNDE V2                                      13

QUESTION 10 / VRAAG 10

 10.1      𝐷̂ = 𝐶̂3 (s opp. = sides) / (e teenoor = sye)                        ✓ S and/en R
           𝐷̂ = 𝐵̂1 (ext.  of a cq) / (buite  van k.v)                          ✓S✓R
           𝐶̂3 = 𝐵̂2 (s in the same segment) / (e in dieselfde segment)         ✓ S and/en R
           𝐵̂1 = 𝐵̂2
                                                                                                        (4)
 10.2      𝐶̂1 + 𝐶̂2 = 𝐷
                       ̂ (tan-chord theorem) / (raaklyn-koord stelling)           ✓ S and/en R
           But/Maar 𝐷  ̂ = 𝐵̂2 (proven) / (reeds bewys)
           ∴ 𝐵2 = 𝐶1 + 𝐶̂2 (ext  = int opp.angle) /
              ̂      ̂                                                            ✓ S and/en R
                             (buite  = teenoorst. binnehoek)                     ✓R
           BECH is a c.q. / BECH is ŉ kv (converse. ext.  of a cq) /
                           (omgekeerde buite  van kv)
                                                                                                        (3)
 10.3      𝐵̂2 = 𝐴̂3 + 𝑇̂1 (ext  of a triangle) / (buite  van driehoek)         ✓ S and/en R
           But/Maar 𝐵̂2 = 𝐶̂1 + 𝐶̂2 (proven) / (reeeds bewys)                     ✓ S and/en R
           And/ En AT = CT (tangents from the same point)                         ✓ S and/en R
                               (raaklyne vanaf dieselfde punt)                    ✓ S and/en R
           ∴ 𝐶1 + 𝐶2 = 𝐴3 + 𝐴̂2 (s opp. = sides) / (e teenoor = sye)
              ̂     ̂     ̂                                                       ✓ S and/en R
           𝐴̂3 + 𝐴̂2 = 𝐴̂3 + 𝑇̂1 (conv. tan-chord) /
                                 (omgekeerde raaklyn-koord)
           ∴ 𝐴̂2 = 𝑇̂1
           CA is a tangent to circle ABT / CA is ŉ raaklyn aan sirkel ABT)                             (5)
                                                                                                      [12]

                                                                           TOTAL/TOTAAL:              150

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