# Mathematics Grade 11 P2 National Exemplar November 2020 Memo

> Grade 11 Mathematics Paper 2 memorandum from the National Exemplar November Exam 2020, 14 pages. Read online or download the free PDF.

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- Updated: 2026-09-28
- Subject: Mathematics
- Grade: Grade 11
- Document type: Memorandum
- Year: 2020
- Exam period: National Exemplar November Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 14

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Mathematics · Grade 11 · National Exemplar November Exam · 2020. Memorandum, 14 pages. Read online or download the PDF.

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### Page 1

NATIONAL
                      SENIOR CERTIFICATE/
                           NASIONALE
                       SENIOR SERTIFIKAAT

                              GRADE/GRAAD 11

                            NOVEMBER 2020

           MATHEMATICS P2/WISKUNDE V2
          MARKING GUIDELINE/NASIENRIGLYN
              EXEMPLAR/EKSEMPLAAR

MARKS/PUNTE:   150

                     This marking guideline consists of 14 pages./
                     Hierdie nasienriglyn bestaan uit 14 bladsye.

### Page 2

2                               MATHEMATICS P2/WISKUNDE V2                      (EC/NOVEMBER 2020)

QUESTION 1/VRAAG 1

    1.1           0  ( 2)    2                          substitution / vervanging
             m PS          
                    36        3                          answer / antwoord
                                OR/OF
            3y  2x  6                                              OR/OF
            3 y  2 x  6
                   2                                          2
            y  x2                                     y  x2
                   3                                          3
                      2
            m PS  
                      3                                   answer / antwoord                     (2)
    1.2              40 4                                    gradient / gradiënt
            mMR           
                    10  3 7                             tan RQX     𝑚
                  ˆ     4
            tan RQX=
                        7                                answer / antwoord
               ˆ
            RQX=29,74                                                                           (4)
    1.3          ˆ =-2
            tan PQX
                        3                                tan PQX
              ˆ =146, 31
            PQX                                           PQX 146,31°
              146,31  29, 74                        answer / antwoord
              116,57                                                                          (3)
    1.4            3                                     𝑚
            mRN 
                   2
                        3     2                          product / produk
            mRN  mPS     1
                        2     3                           1
            RN  PS                                                                              (3)
    1.5
             NR= 10  6    4  2 
                            2            2

                                                         substitution / vervanging
            NR= 52                                       answer / antwoord
            QN = 13                                      length QN / lengte QN
                   1
            Area =  QN  NR
                   2                                     choosing correct sides /
                   1                                       kies korrekte sye
            Area =  13  52                             substitution / vervanging
                   2
            Area = 13 units 2 / eenhede 2
                                                         answer / antwoord
                                                                                                 (6)

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### Page 3

(EC/SEPTEMBER 2020))                    MATHEMATICS P2/WISKUNDE V2                               3

 1.6    y0 4                                             x = 0
              
        x 3 7                                            substitution / vervanging
        7 y  12                                         equation / vergelyking
              12                                          y-coordinate / y-koördinaat
        y
               7

                                OR/OF                                 OR/OF
           4
        y    xc                                         equation / vergelyking
           7
        Subst./vervang (3; 0)
           4
        0=    3  c                                     substitution / vervanging
           7
            12
        c                                               value of c / waarde van c
             7
            12
        y                                               y-coordinate / y-koördinaat
             7

                                                                                                 (4)
                                                                                                [22]

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### Page 4

4                                  MATHEMATICS P2/WISKUNDE V2                      (EC/NOVEMBER 2020)

QUESTION 2/VRAAG 2

    2.1
                      1  4   10  0 
                               2              2
             BC =
                                                            substitution / vervanging
             BC = 25  100
                                                            answer / antwoord
             BC = 125  5 5                                                                           (2)
    2.2            6  0
             mAB                                           substitution / vervanging
                   2  6
                   3
             mAB                                           answer / antwoord
                   4                                                                                  (2)
    2.3                    3
             mCD  mAB                                     gradient / gradiënt
                           4
            y  mx  c
                3
            y  xc
                4
            Sub C  1;10 
                                                            substitution / vervanging
                3
            10    1  c
                4
               43
            c
               4
               3      43
            y  x                                          answer / antwoord                        (3)
               4      4

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### Page 5

(EC/SEPTEMBER 2020))                    MATHEMATICS P2/WISKUNDE V2                                   5

 2.4        M is the midpoint of both BD and AC / is die
            middelpunt van beide BC en AC                   statement / stelling
            Midpoint of AC and BD /Middelpunt van AC
            en BD
                  1  2 10  6 
             M          ;                                 substitution / vervanging
                  2        2 
                  3                                     answer / antwoord
             M  ;2
                  2                                                                                        (3)
 2.5         x  4 3 y  0
                        ;      2                          substitution / vervanging
               2       2   2
            x  4  3; y  0  4
                                                           x- value/waarde y-value/waarde
            x  7; y  4                                  Answer only: Full marks/
                                                           Slegs antwoord: Volpunte                           (3)
                                                                                                             [13]

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### Page 6

6                               MATHEMATICS P2/WISKUNDE V2                       (EC/NOVEMBER 2020)

QUESTION 3 / VRAAG 3

    3.1
                                              y

                                        B             x
                                            O

                    (– 12; – 5)                           diagram / diagram
            Therefore/d.w.s: r = 13                       value of r / waarde van r
            sin B  cos B
              5 12
                                                        substitution / vervanging
              13 13
              17                                         answer / antwoord
            
               13                                                                                        (5)
    3.2     sin 43  p
    3.2.1   cos133
            cos(90  43)
              sin 43                                     sin 43
                                                          answer / antwoord
             p                                                                                         (2)
    3.2.2   tan( 43)
              tan 43                                     tan 43
                       p
                                                        answer / antwoord
                      1  p2                                                                             (3)
    3.3.1    sin(360  x )
                              tan( x  180)
              sin(90  x )
                 sin x                                     sin x
                        tan x                            cos x
                cos x
                                                           tan x
               tan x  tan x                              tan x
              1                                          answer / antwoord                            (5)
    3.3.2     sin 210.cos150.tan 25
             tan 205.cos 315.sin135
                 sin 30.  cos 30.tan 25                 sin 30
                                                           cos30
                 tan 25.cos 45.sin 45                   tan 25
               1 3                                         cos 45
                 .
              2     2                                     sin 45
               1 1
                   .
                2 2                                       special angles / spesiale hoeke
                  3
                                                         answer / antwoord
                 2                                                                                       (7)
                                                                                                         [22]

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### Page 7

(EC/SEPTEMBER 2020))                          MATHEMATICS P2/WISKUNDE V2                                7

QUESTION 4 / VRAAG 4

 4.1         sin   cos  .sin 
                                     tan 
             cos   (1  sin 2  )

                     sin  (1  cos  )                         factorising / faktorisering
            LHS =
                      cos   cos 2                             cos2 
                    sin  (1  cos  )
                 =                                              common factor / gemene faktor
                    cos  (1  cos  )
                                                                answer / antwoord
                 = tan                                                                                         (4)
 4.2        2sin x cos x  cos 2 x  0
            cos x(2sin x  cos x)  0                           factors / faktore
                                                                 cos x  0
            cos x  0 or/of 2sin x  cos x                                1
                                                                 tan x 
                                        1                                 2
            cos x  0 or/of tan x 
                                        2
            x  90  360.k or/of x  270  360.k             x  90  360.k
            or/of x  26,57  180.k                            x  270  360.k
                                                                 x  26,57  180.k
                                                                                                                (6)
 4.3        2. sin   1
                      1
              sin  
                      2                                                 1
                                                                sin  
                    1                                                   4
            sin  
                    4                                             14, 48
              14, 48 or/of   165,52                         165,52                                     (3)
 4.4              x y                               3          x y
                                                                        45
             tan         1 and/en cos( x  y )                  2
                  2                                 2
                                                                 x  y  30
             x y
                     45          and/en x  y  30
               2                                                setting up equations/
             x  y  90 ...............(1)                      opstel van vergelykings
             x  y  30 ...............(2)
             2 x  120
             x  60                                             x-value/waarde
             y  30                                            y-value/waarde                                  (5)
                                                                                                                [18]

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### Page 8

8                              MATHEMATICS P2/WISKUNDE V2                          (EC/NOVEMBER 2020)

QUESTION 5 / VRAAG 5

    5.1.1     0  y 1    or    0;1                      0    1
                                                                                                            (2)
    5.1.2    Period = 720                                 answer                                          (1)
    5.2

     shape / vorm
     x-intercept / x-afsnit
     y-intercept / y-afsnit
     turning points / draaipunte
                                                                                                            (4)
    5.3       180  x  150      or/of 30  x  180    180  x  150
                                                            30  x  180                                 (3)
                                                                                                           [10]

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### Page 9

(EC/SEPTEMBER 2020))                        MATHEMATICS P2/WISKUNDE V2                                 9

QUESTION 6 /VRAAG 6

 6.1                   PQ
            sin 60 
                       PS
                        8
            sin 60                                                                          8
                       PS                                                          sin 60 
                                                                                             PS
                      8
            PS =                                                                            8
                  sin 60                                                          PS =
                                                                                         sin 60
                  16 3
            PS =                                                                         16 3
                     3                                                             PS =
                                                                                           3               (3)
 6.2                            PQ
             In PQS: tan 60 
                                QS                                                            8
                                                                                   QS =
                                                                                          tan 60
                                   8      8 3
                         QS =                m                                          8 3
                                tan 60    3                                       QS =        m
                                                                                           3
                            8 3
                         QR =     m                                                       8 3
                             3                                                     QR =         m
                                                                                             3
             In RQS: RS2  QR 2  QS2  2.QR.QS.cos100
                                                                                  formula /
                                        2          2         2       2
                                8 3  8 3           8 3  8 3                formule
                             = 
                                  3
                                       
                                             3
                                                 2. 
                                                          3
                                                             . 
                                                                    3  cos100
                                                                         substitution /
                             = 50,0756......                                       vervanging
                          RS = 7,08 m                                            simplification/
                                                                                 vereenvoudiging
                                                                                 answer /
                                                                                   antwoord
                                                                                                            (7)
                                                                                                           [10]

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### Page 10

10                             MATHEMATICS P2/WISKUNDE V2                                 (EC/NOVEMBER 2020)

QUESTION 7 / VRAAG 7

                                                 B

                                                       D

                                                                        C
                                                           O

                                           A

 7.1              ˆ =x
         Let/Laat A
           ˆ = x (angles opp = sides)/(hoeke teenoor  sye)
         BAD                                                                        S and/en R
           ˆ
         ADO = 2 x (angle at the centre)/(middelpuntshoek )                         S and/en R
         Similarly, if you let / Net so, as jy: Cˆ = y;
                    ˆ = 2y
         then/dan: CDO                                                              S
             ˆ = 2 x  2 y = 2( x  y )
          ADC
                       ˆ
                  = 2 ABC                                                           S and conclusion
                                                                                     en gevolgtrekking            (5)
 7.2.1   B̂3  10 (angles opp = sides; DB = DF)                                    S R
                    (hoeke teenoor  sye; DB = DF)
         D̂ 2  20 (exterior angle of a BDF)                                      S and/en R
                    (buitehoek van BDF)                                                                          (3)
 7.2.2    ˆ = 90 (angles in a semi-circle)
         ABD                                                                        S R
                      (hoek in halwe sirkel )
         Â = 70 (angles of a triangle)                                            S R
                  (hoeke van ' n driehoek )                                                                       (4)
 7.2.3   Ô2  140 (angle at the centre) / (middelpuntshoek )                      S R
                                                                                                                  (2)
 7.2.4   Ĉ1  110 (opposite angles of a c.q.)/(teenoorst. hoeke van k .v)         S R
               OR / OF
                                                                                          OR / OF
         ˆ O
         O  ˆ O ˆ  220 (angles around a point/(omwenteling )
          1   4    3

                                                                                    S and/en R
         Ĉ1  110 (angle at the centre)/(middelpuntshoek )
                                                                                    S and/en R                   (2)

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### Page 11

(EC/SEPTEMBER 2020))                    MATHEMATICS P2/WISKUNDE V2                                  11

 7.2.5   Ê = 70 (angles in the same segment)/(hoeke in dieselfde segment ) S R
                               OR/OF
                                                                               OR/OF
         Ê = 70 (opposite angles of a c.q.)/(teenoorst. hoeke van k .v)

                                                                                S R                  (2)
 7.2.6   Ĉ2  70 (ext.  of a c.q.)/ (buitehoek van k .v)                     S R
                          OR/OF                                                     OR/OF
         Ĉ2  110  180 (s on a straight line)/(hoeke op ' n reguitlyn)
                                                                                S R
         Ĉ2  70                                                                                     (2)
 7.2.7   Oˆ O  ˆ  140 (vertically opp. s)/(regoorstaande e)                S R
           4     2

                                                                                                       (2)
                                                                                                      [22]

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### Page 12

12                             MATHEMATICS P2/WISKUNDE V2                      (EC/NOVEMBER 2020)

QUESTION 8 / VRAAG 8

                                              P

                                                         E
                                A

                                              O

                          C                                       D
                                              F

 8.1       ENG                                               construction
           Draw diameter FP and join PA
                ˆ =x
           Let EFD                                           S and R
            ˆ = 90 (tan  radius)
          OFD
             ˆ = 90  x
           OFE                                              S and R
             ˆ = 90  x (angles in the same segment)
           PAE                                              S and R
            ˆ = 90 (angles in a semi circle)
          PAF
             ˆ =x
           EAF                                              conclusion
                ˆ =x
             ˆ =A
           EFD

 8.1       AFR
 AFR       Teken middellyn FP en verbind PA                   konstruksie
                  ˆ =x
           Laat EFD
            ˆ = 90 (raaklyn  radius )
          OFD                                                 S en R
             ˆ = 90  x
           OFE
           ˆ
           PAE = 90  x (hoeke in dieselfde segment )        S en R
                                                              S en R
           ˆ = 90 (hoeke in ' n halwe sirkel )
          PAF
             ˆ =x
           EAF
                                                              gevolgtrekking
                ˆ =x
             ˆ =A
           EFD                                                                          (5)

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### Page 13

(EC/SEPTEMBER 2020))                        MATHEMATICS P2/WISKUNDE V2                                  13

                        A

                                                    E
                                                1
                                                    2       3

                                                                                B

                                                                O

                                        1
                                            2
                                    D                                   2
                                            x                       1
                                                                            C

                                                        F

8.2.1 A = 𝑥 corresponding angles; AB                                                S R
                    ∥ DC / 𝑜𝑜𝑟𝑒𝑒𝑛𝑘𝑜𝑚𝑠𝑡𝑖𝑔𝑒 ℎ𝑜𝑒𝑘𝑒; AB || DC
      E    𝑥 tan-chord / 𝑟𝑎𝑎𝑘𝑙𝑦𝑛-𝑘𝑜𝑜𝑟𝑑                                              S R
      D    𝑥 angles opposite = sides / ℎ𝑜𝑒𝑘𝑒 𝑡𝑒𝑒𝑛𝑜𝑜𝑟       sye                      S R
      E    𝑥 alternate angles, AB                                                   S R
                    ∥ DC / 𝑣𝑒𝑟𝑤𝑖𝑠𝑠𝑒𝑙𝑒𝑛𝑑𝑒 ℎ𝑜𝑒𝑘𝑒; AB || DC
      C       E    𝑥 exterior angle of a c.q. / 𝑏𝑢𝑖𝑡𝑒ℎ𝑜𝑒𝑘 𝑣𝑎𝑛 ′𝑛 𝑘. 𝑣               S R           (10)
8.2.2 B = 180° 𝑥 opposite angles of a c.q.                                          S R
                   𝑡𝑒𝑒𝑛𝑜𝑜𝑟𝑠𝑡. ℎ𝑜𝑒𝑘𝑒 𝑣𝑎𝑛 ′𝑛 𝑘. 𝑣
      A+B=𝑥        180° 𝑥       180°
      ∴ AD ∥ BC co-interior angles formed =
                  𝑘𝑜-𝑏𝑖𝑛𝑛𝑒 ℎ𝑜𝑒𝑘𝑒 𝑔𝑒𝑣𝑜𝑟𝑚 = 180                                       R
      ∴ ABCD is a parallelogram opp. sides ∥
        ABCD is ′n parallelogram 𝑡𝑒𝑒𝑛𝑜𝑜𝑟𝑠𝑡. 𝑠𝑦𝑒 ||                                  R               (4)
                                                                                                    [19]

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### Page 14

14                             MATHEMATICS P2/WISKUNDE V2                              (EC/NOVEMBER 2020)

QUESTION 9 / VRAAG 9

9.1.1 perpendicular to the chord / loodreg op die koord              answer/antwoord          (1)
9.1.2 interior opposite angle / teenoorstaande binnehoek             answer/antwoord          (1)
9.2

                                   F

                                   1
                                  x

                                                         O
                                                    1
                                                        2 3

                                                        1 2
               L
                                   C                     E           H

9.2.1   E     E    90° line from centre                              S R
                     𝑙𝑦𝑛 𝑣𝑎𝑛𝑎𝑓 𝑑𝑖𝑒 𝑚𝑖𝑑𝑑𝑒𝑙𝑝𝑢𝑛𝑡
        FCH 90° angles in a semi-circle                              S R
                  ℎ𝑜𝑒𝑘𝑒 𝑖𝑛 '𝑛 ℎ𝑎𝑙𝑤𝑒 𝑠𝑖𝑟𝑘𝑒𝑙
        ∴ FCH E
        ∴ FC ∥ OE corresponding angles formed are                    R
            𝑜𝑜𝑟𝑒𝑒𝑛𝑘𝑜𝑚𝑠𝑡𝑖𝑔𝑒 ℎ𝑜𝑒𝑘𝑒 𝑤𝑎𝑡 𝑔𝑒𝑣𝑜𝑟𝑚 𝑤𝑜𝑟𝑑 𝑖𝑠                                              (5)
9.2.2    ˆ
        LFO = 90 (tan  radius) / (raaklyn  radius )               S and/en R
        Ê 2  90 (proven) / (reeds bewys )                         S and/en R
         OFLE is a c.q. (converse exterior angle of a c.q.)         R
                         (omgekeerde buitehoek van k .v stelling )                               (3)
9.2.3   Ĥ  x (tan - chord) / (raaklyn - koord )                    S
                                                                     R
        Ô1  2 x (angle at the centre)                              S
                   (middelpuntshoek )                                R                          (4)
                                                                                                [14]

                                                                     TOTAL/TOTAAL:              150

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