# Mathematics Grade 11 P1 Eastern Cape November 2023 Memo

> Grade 11 Mathematics Paper 1 memorandum from the Eastern Cape November Exam 2023 (Afrikaans), 15 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/maths-p1-gr11-memo-nov-2023-english-afrikaans/84e969c7-880d-4ed8-8946-551447d298f0
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Language: Afrikaans
- Document type: Memorandum
- Year: 2023
- Exam period: Eastern Cape November Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 15

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## About this document

Mathematics · Grade 11 · Eastern Cape November Exam · 2023 · Afrikaans. Memorandum, 15 pages. Read online or download the PDF.

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- [MATHS P1 QP GR11 NOV 2023 Afrikaans D](https://www.hlayiso.com/library/maths-p1-qp-gr11-nov-2023-afrikaans-d/c2f240dc-7fd6-4ceb-81c1-a511d86b6035) — QP · 2023 · Afr

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### Page 1

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                             NATIONAL
                        SENIOR CERTIFICATE/
                             NASIONALE
                         SENIORSERTIFIKAAT

                                GRADE/GRAAD 11

                             NOVEMBER 2023

           MATHEMATICS P1/WISKUNDE V1
          MARKING GUIDELINE/NASIENRIGLYN

MARKS/PUNTE:   150

                     This marking guideline consists of 15 pages./
                     Hierdie nasienriglyn bestaan uit 15 bladsye.

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2                                     MATHEMATICS P1 / WISKUNDE V1                    (EC/NOVEMBER 2023)

NOTE/LET WEL:

•   If a candidate answers a question TWICE, mark the FIRST attempt ONLY.
    Indien ŉ kandidaat ŉ vraag TWEE keer beantwoord, merk SLEGS die EERSTE poging.
•   Consistent accuracy (CA) applies in ALL aspects of the marking guideline.
    Volgehoue akkuraatheid (VA) geld deurgaans in ALLE aspekte van die nasienriglyn.
•   If a candidate crossed out an attempt of a question and did not redo the question, mark the
    crossed-out attempt.
    Indien ŉ kandidaat ŉ poging vir ŉ vraag deurgetrek het en nie die vraag weer beantwoord
    het nie, merk die poging wat deurgetrek is.
•   The mark for substitution is awarded for substitution into the correct formula.
    Die punt vir substitusie word toegeken vir substitusie in die korrekte formule.

QUESTION 1/VRAAG 1

1.1.1    x 2 − 3x = 0
         x( x − 3) = 0                                          factorisation / faktorisering
          x = 0 or / of x = 3                                  answers / antwoorde
                                                                                                        (2)
1.1.2    x(3x + 1) = 5
         3x 2 + x − 5 = 0                                       standard form / standaardvorm
            −b  b 2 − 4ac
         x=
                 2a
             −1  12 − 4(3)(−5)                                 substitution / vervanging
           =
                   2(3)
             −1  61
           =
                 6
           = 1,14 or / of − 1, 47                               answers / antwoorde
                                                                                                        (4)
1.1.3    2 x − 5x + 3  0
            2

         (2 x − 3)( x − 1)  0                                  factors / faktore
         1  x  1   1                       1   112
                      2                                          answer / antwoord (A)
                                                                                                        (3)
1.1.4    2 x + 2 = x −1

         ( 2 x + 2 ) = ( x − 1)
                     2            2
                                                                squaring / kwadreer
         4( x + 2) = x 2 − 2 x + 1
         4x + 8 = x2 − 2x + 1
         x2 − 6 x − 7 = 0                                       standard form / standaardvorm
         ( x − 7)( x + 1) = 0                                   factors / faktore
          x = 7 or / of x  −1                                 both answers / beide antwoorde
                                                                selection / seleksie
                                                                                                        (5)

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(EC/NOVEMBER 2023)                             MATHEMATICS P1 / WISKUNDE V1                                 3

1.2        x + 3y = 2              (1)
           x 2 − 3 xy = 4          (2)

           x = 2 − 3y              (3)                             x = 2 − 3y
           (2 − 3 y ) 2 − 3 y (2 − 3 y) = 4                        substitution / vervanging
           4 − 12 y + 9 y 2 − 6 y + 9 y 2 = 4                      standard form / standaardvorm
          18 y − 18 y = 0
                2
                                                                   method/factors / metode/faktore
          18 y ( y − 1) = 0                                        both y-values / beide y-waardes
           y = 0 or / of y = 1

                                                                   both x-values / beide x-waardes
           x = 2 − 3(0)         or / of       x = 2 − 3(1)
              =2                               x = −1
                                                                                  OR/OF

                                     OR/OF

           x + 3y = 2                         (1)
           x − 3 xy = 4
            2
                                              (2)
                                                                         2− x
                                                                   y=
                                                                          3
                2− x
           y=                                 (3)
                  3                                                substitution / vervanging
                     2− x
           x 2 − 3x      =4
                     3 
           x 2 − x(2 − x) = 4                                      standard form / standaardvorm
           x2 − 2 x + x2 − 4 = 0
           2x2 − 2 x − 4 = 0
                                                                   factors / faktore
          x2 − x − 2 = 0                                           both x-values / beide x-waardes
          ( x − 2)( x + 1) = 0
           x = 2 or / of x = −1

                 2−2                      2 − ( −1)                both y-values / beide y-waardes
          y =       or / of         y=
                   3                         3
                =0                       =1                                                                (6)

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4                                   MATHEMATICS P1 / WISKUNDE V1                    (EC/NOVEMBER 2023)

1.3     ( x − 3) = p 2 − 4
                  2

         ( x − 3) =  p 2 − 4
                      2
                                                              square root / vierkantswortel
                x − 3 =  p2 − 4
                  x = 3  p2 − 4                             x = 3  p2 − 4
       For non-real roots:
       Vir nie - reëele wortels:            -2   2            p2 − 4  0
       p2 − 4  0                                             factors / faktore
       ( p − 2)( p + 2)  0                                   answer / antwoord
       −2  p  2

                                                                              OR/OF
                                    OR/OF

        ( x − 3) = p 2 − 4
                  2
                                                              expansion / uitbreiding
        x − 6x + 9 = p − 4
         2                2
                                                              standard form / standaardvorm
        x − 6 x + 13 − p = 0
         2                2

        For non-real roots: Vir nie - reëele wortels          b2 − 4ac  0
        b − 4ac  0
         2

        ( −6 ) − 4(1)(13 − p 2 )  0
             2

        36 − 52 + 4 p 2  0
        4 p 2 − 16  0                                       factors / faktore
        (2 p + 4)(2 p − 4)  0                                answer / antwoord
       −2  p  2
                                                                                                     (5)
                                                                                                    [25]

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(EC/NOVEMBER 2023)                              MATHEMATICS P1 / WISKUNDE V1                                    5

QUESTION 2/VRAAG 2

2.1      2n +1 − 8.2n −3 2n.2 − 8.2n.2−3                           numerator / teller
                        =                                          denominator / noemer
              2n − 2           2n.2− 2
                          2n (2 − 8.2−3 )
                        =                                          factorisation / faktoriseering
                              2n.2− 2
                          2 −1
                        = −2
                          2
                        =4                                         answer / antwoord
                                                                                                             (4)
2.2.1     x
              27 = 2187
                                                                       1
                                                                   27 x = 2187
                  1
         27 = 2187x

                    1

         (3 ) = 3
                                                                           1
                                                                   ( 33 ) x = 37 OR/OF 27 x = 37
                                                 −1
                                             27 x = 37
                  3 x   7                                                                        −1
                                    OR /OF
              3
                                                 −1
         3 x = 37                            33 x = 37
            3
          =7                                 3 x −1 = 7          equating exponents
             x                                                      gelyk stel van eksponente
                  3                                 7
         x=                                     x −1 =            answer / antwoord
                  7                                 3
                                                    3
                                                x=
                                                    7                                                        (4)
2.2.2    4 − 16 = 6.2
              x                 x

         ( 2 ) − 6.2 − 16 = 0
                  x 2       x
                                                                   standard form / standaardvorm
         (2 x − 8)(2 x + 2) = 0                                    factors / faktore
          2 x = 8 or / of 2 x  −2                                selection / seleksie
          2 x = 23                                                2 x = 23
         x=3                                                      answer / antwoord

                                        OR/OF                                       OR/OF

         4x – 16 = 6.2x
                                                                   standard form / standaardvorm
         (2x)2 = 6.2x –16 = 0
         Let/Laat k = 2x,
         ∴ k2 – 6k – 16 = 0
                                                                   factors / faktore
              (k – 8)(k + 2) = 0
         ∴ k = 8 or/of k = -2
                                                                   selection / seleksie
         ∴ 2x = 8 or/of 2x ≠ -2
                                                                   2 x = 23
          2x = 23
                                                                   answer / antwoord
         ∴x=3
                                                                                                             (5)

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6                                  MATHEMATICS P1 / WISKUNDE V1                     (EC/NOVEMBER 2023)

           x + 1 ( 3 − 2) + 1
2.3          2
                               2

                =                                            substitution / vervanging
           x −5
                  ( 3 − 2) − 5
             2                 2

                      3 − 4 3 + 4 +1
                  =
                      3− 4 3 + 4−5
                      8−4 3                                       8−4 3
                  =                                         
                      2−4 3                                       2−4 3

                  =
                      (8 − 4 3 )( 2 + 4 3 )                  rationalisation / rasionalisering
                      ( 2 − 4 3 )( 2 + 4 3 )
                    16 + 32 3 − 8 3 − 16.3                   simplification / vereenvoudiging
                  =
                           4 − 16.3
                    24 3 − 32
                  =
                       −44
                    8−6 3                                    answer / antwoord
                  =
                      11
                                                                                                    (5)
                                                                                                   [18]

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(EC/NOVEMBER 2023)                         MATHEMATICS P1 / WISKUNDE V1                                    7

QUESTION 3/VRAAG 3

3.1.1    17 ; 14 ; 11 ; ... ; − 247
         8;5                                                     8     5
                                                                                                         (2)
3.1.2    Tn = 20 − 3n                                             20     − 3n
                                                                                                         (2)
3.1.3    Tn = 20 − 3n
         T17 = 20 − 3(17)                                        substitution / vervanging
                = −31                                             answer / antwoord
                                                                                                         (2)
3.1.4    Tn = 20 − 3n
         −247 = 20 − 3n                                           Tn = −247
         −267 = −3n
          n = 89                                                 answer / antwoord
                                                                                                         (2)
3.2      2 x + 11 ; 2 ; T3 ; 2 x − 4
              2x − 4 − 2                            2 + 2x − 4
         T3 =            +2       OR / OF       T3 =              method / metode
                   2                                     2
              2x − 6                                2x − 2
            =        +2                           =               simplifying / vereenvoudiging
                 2                                     2
            = x −3+ 2                             = x −1
            = x −1                                                T3 = x − 1

          2 − (2 x + 11) = ( x − 1) − 2                          equating / gelykstel
                − 2x − 9 = x − 3
                    − 3x = 6
                       x = −2                                    answer / antwoord

                                  OR/OF                                           OR/OF

         d = 2 − (2 x + 11)
         = −2 x − 9                                               d = −2 x − 9

         2d = 2 x − 4 − 2                                        ✓ 2d = 2 x − 4 − 2
         d = x−3                                                 ✓ d = x −3

          − 2x − 9 = x − 3
                                                                  equating / gelykstel
              − 3x = 6
                  x = −2                                          answer / antwoord
                                                                                                        (5)
                                                                                                       [13]

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8                                 MATHEMATICS P1 / WISKUNDE V1                          (EC/NOVEMBER 2023)

QUESTION 4/VRAAG 4

4.1.1      94       ;     90       ;     82      ;      70

                   -4              -8            -12

                             -4            -4

         54 ; 34                                                    54  and/en 34 
                                                                                                         (2)
4.1.2    2a = −4          3a + b = −4           a + b + c = 94       a = −2
          a = −2         3(−2) + b = −4          2 − 2 + c = 94    b = 2
                                                                     c = 94
                          b=2                      c = 94

         Tn = −2n 2 + 2n + 94                                       Tn = −2n 2 + 2n + 94
                                                                                                         (4)
4.1.3    First differences / Eerste verskille:
         t n = − 4n                                                  method / metode
         −136 = −4n
              n = 34                                                n = 34
         Tn = −2n 2 + 2n + 94
           T34 = −2(34) 2 + 2(34) + 94
                = −2150                                              T34 = −2150
         T35 = −2(35) 2 + 2(35) + 94
                = −2286                                              T35 = −2286

                                   OR/OF                                          OR/OF
         Tn +1 − Tn = −136
         −2 ( n + 1) + 2(n + 1) + 94 − ( −2n 2 + 2n + 94 ) = −136
                    2

                                                                     method / metode
         −2(n 2 + 2n + 1) + 2n + 2 + 94 + 2n 2 − 2n − 94 = −136
         −2n 2 − 4n − 2 + 2n + 2 + 94 + 2n 2 − 2n − 94 = −136
         −4n = −136
                                                                     n = 34
             n = 34
            n + 1 = 35
         Tn = −2n 2 + 2n + 94
           T34 = −2(34) 2 + 2(34) + 94
                                                                     T34 = −2150
                = −2150
         T35 = −2(35) 2 + 2(35) + 94
                = −2286                                              T35 = −2286
                                                                                                         (4)

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(EC/NOVEMBER 2023)                      MATHEMATICS P1 / WISKUNDE V1                                 9

4.2      Tn = an 2 + bn − 15
         T1 = a + b − 15
         T2 = 4a + 2b − 15                                     𝑇1 and/en 𝑇2 and/en T3
         T2 − T1 = 3a + b = 3                                 3a + b = 3
         T3 = 9a + 3b − 15
         T3 − T2 = 5a + b = 7                                  5a + b = 7
          5a + b = 7
          3a + b = 3
            2a = 4
              a = 2                                           value for a / waarde van a
                 b = −3                                        value for b / waarde van b
                                                                                                  (5)
                                                                                                 [15]

QUESTION 5/VRAAG 5

5.1      p=3                                                p =3
         q = −1                                             q = −1
                                                                                                   (2)
5.2                a
          f ( x) =      +q
                 x+ p
                   a
               =       −1                                   substituting for p and q
                 x+3                                        vervanging vir p en q
                      a
              0=          −1                                substituting for x and y
                   −5 + 3                                   vervanging vir x en y
                    a
               1=
                   −2
              a = −2                                       answer / antwoord
                                                                                                   (3)
5.3               a
          f ( x) =    +q
                 x+ p
                  −2
              =       −1
                 x+3
                 −2
            y=       −1                                     substituting x = 0
                0+3                                          vervang x = 0
                  5                                         answer / antwoord
              =−
                  2                                                                                (2)
5.4      𝑥 ∈ ℝ, but/maar 𝑥 ≠ -3                             𝑥 ∈ ℝ  x  −3
                                                                                                   (2)
5.5       y = −( x + 3) − 1                                 y = −( x + 3) −1
            = −x − 3 −1
                                                            answer / antwoord
            = −x − 4
                                                                                                   (2)
5.6      −5  x  −3                                        answer / antwoord (A)
                                                                                                   (2)

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10                              MATHEMATICS P1 / WISKUNDE V1                            (EC/NOVEMBER 2023)

 5.7     f is reflected in the x-axis and then shifted 4 units    reflected / gereflekteer
         to the right.                                            x-axis / x-as
         f is gereflekteer in die x-as en dan 4 eenhede na        4 units / 4 eenhede
         regs geskuif.                                            right / regs
                                                                                                        (4)
                                                                                                       [17]

 QUESTION 6/VRAAG 6

 6.1     (0;3)                                                    answer / antwoord
                                                                                                         (1)

 6.2      y =1                                                    answer / antwoord
                                                                                                         (2)
 6.3

                                                                  y-intercept / y-afsnit

                                                                  asymptote / asimptoot

                                                                  shape (must be increasing)
                                                                   vorm (moet stygend wees)

                                        1

                                                                                                         (3)
 6.4      y  −5                                                 answer / antwoord (A)
                                                                                                         (2)
                                                                                                         [8]

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(EC/NOVEMBER 2023)                         MATHEMATICS P1 / WISKUNDE V1                                11

 QUESTION 7/VRAAG 7

 7.1    x = 12                                                 answer / antwoord
                                                                                                      (1)

 7.2    x  12                                                 answer / antwoord
                                                                                                      (1)
 7.3    Average gradient / Gemiddelde gradiënt
            4−6                                                method / metode
        =
           −1 − 0                                              answer / antwoord
        =2                                                                                            (2)
 7.4    g ( x) = mx + q
              y2 − y1
        m=
              x2 − x1
            6−4
          =
          1 − (−1)
         =1                                                    m =1
       y = x+q
        6 = 1 + q or / of         4 = −1 + q                   substituting a point
                                                                vervanging van ’n punt
        q = 5                                                 q=5
        g ( x) = x + 5
                                                                                                      (3)
 7.5    f ( x) = ax + bx + c
                     2

                                                               c=6
        c=6
        f ( x) = ax 2 + bx + 6
              4 = a(−1) 2 + b(−1) + 6
                                                               both substitutions /
                 6 = a(1) 2 + b(1) + 6                          beide vervangings

              −2 = a −b
                0 = a+b                                        method / metode
               2a = −2
               a = −1
                 b =1
                                                               values of a and b
        f ( x) = − x 2 + x + 6
                                                                waardes van a en b
                                                                                                      (4)

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12                                  MATHEMATICS P1 / WISKUNDE V1                     (EC/NOVEMBER 2023)

 7.6    g ( x) = x + 5
           0 = x+5                                            substitution / vervanging
          x = −4
          S(0; − 4)                                           S(0 ; –4)
        f ( x) = − x 2 + x + 6
            0 = − x2 + x + 6
           x2 − x − 6 = 0
          ( x − 3)( x + 2) = 0                                factors / faktore
            x = −2 or / of x = 3                             both x-intercepts
            U(3;0)                                            beide x-afsnitte
        SU = 3 − (−4)
               = 7 units/eenhede                              answer / antwoord
                                                                                                      (5)

 7.7    x  −1 or / of x  1                                  x  −1  x  1
                                                                                                      (2)
 7.8    yV − yW = f ( x) − g ( x)
                 = (− x 2 + x + 6) − ( x + 5)                 f ( x) − g ( x)
                 = − x2 + x + 5 − x − 5
              = − x2 + 1                                      answer / antwoord
        Max.length of VW is 1 unit                           interpretation / interpretasie
         Maks. lengte van VW is 1 eenheid                                                            (3)
                                                                                                    [21]

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(EC/NOVEMBER 2023)                          MATHEMATICS P1 / WISKUNDE V1                                    13

 QUESTION 8/VRAAG 8

                                 m
 8.1                 i 
         ieff + 1 = 1 + nom                                    formula / formule
                        m 
                              12
                0, 093                                         substitution / vervanging
             = 1 +      −1
                    12 
             = 0, 09707
             = 9, 71%                                            answer / antwoord
                                                                                                            (3)
 8.2     A = P(1 + i )    n

            = R312000 (1 + 0, 0691)                              n = 5 substitution / vervanging
                                        5

            = R 435 758,88                                       answer / antwoord
                                                                                                            (3)
                                                                         0,0925
 8.3.1               0, 0925 
                                      12
                                           0, 082       24
                                                                i =               and/en 𝑛 = 12
         A =  23000 1 +       + 13500  1 +     
                                                                            4
                         4                 12             i =
                                                                         0,082
                                                                                  and/en 𝑛 = 24
                                                                         12
           = R51 530,18                                                     0, 0925 
                                                                                        12
                                                                                                  
                                                                     23000 1 +       + 13500 
                                                                                 4             
                                                                                    24
                                                                        0,082 
                                                                        1 +    
                                                                            12 
                                                                 answer / antwoord
                                     OR/OF                                                                  (5)
                                                                                         OR/OF
                        0, 0925 
                                   12
                                              
            A =  23000 1 +         + 13500 
                            4                                         0,0925
                                                              i=                and/en 𝑛 = 12
                                                                             4
               = R 43760, 23                                    i=
                                                                          0,082
                                                                         and/en 𝑛 = 24
                                            24                        12
                             0, 082                            R51530,18
            A = R 43760, 23 1 +     
                                12                                           0,082 
                                                                                                      24

              = R51530,18                                        R43760, 23 1 +     
                                                                                  12 
                                                                 answer / antwoord
                                                                                                            (5)
 8.3.2   A = P (1 + i )   n
                                                                    i
                                             36                  12 and/en n = 36
                                   i 
         64 487, 24 = 51530,18 1 + 
                                12                             substituting / vervang
                                                                A = R64487, 24
                         64 487, 24 
                  i =  36         − 1  12
                         51530,18                              substituting into correct formula
                    = 0, 075                                      vervanging in korrekte formule
         rate/koers = 7,5%

                                                                 answer / antwoord
                                                                                                            (4)
                                                                                                           [15]

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14                              MATHEMATICS P1 / WISKUNDE V1                       (EC/NOVEMBER 2023)

 QUESTION 9/VRAAG 9

 9.1.1 For mutually exclusive events:
       Vir onderling uitsluitende gebeurtenisse:

         P(A or B) = P(A) + P(B)                               formula / formule
             0, 61 = 0, 35 + P(B)                               substitution / vervanging
            P( B) = 0, 61 − 0,35
                    = 0, 26                                     answer / antwoord
                                                                                                    (3)
 9.1.2 For independent events:
       Vir onafhanklike gebeurtenisse:

         P(A or/of B) = P(A) + P(B) − P(A and/en B)             formula / formule
               0, 61 = 0,35 + P(B) − P(A).P(B)                  substitution / vervanging
               0, 61 = 0,35 + P(B) − 0,35  P(B)                0,61 = 0,35 + P(B) − 0,35  P(B)
               0, 61 = 0,35 + 0, 65  P(B)
          0, 65  P(B) = 0, 26
                            0, 26
                 P(B) =
                            0, 65
                          = 0, 4                                answer / antwoord
                                                                                                    (4)

 9.2.1   a = 28, b = 86,    c = 216                             a = 28  b = 86  c = 216
                                                                                                    (3)
         216 9
 9.2.2      =   or / of 0,36                                    answer / antwoord
         600 25                                                                                     (1)
 9.2.3 P(not defective) + P(Axisphones and defective)
       P(nie foutief) + P(Axis Phones en foutief)

             514   58
         =       +                                                 514    58
             600 600                                                  +
                                                                   600    600
             572 143
         =      =    or/of 0,95                                 answer / antwoord
             600 150                                                                               (3)
                                                                                                  [14]

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(EC/NOVEMBER 2023)                              MATHEMATICS P1 / WISKUNDE V1                                     15

 QUESTION 10/VRAAG 10

 10.1
                                                                      4            R
                                                                    x −1

                                            5              R
                                            x
                                                                    x −5
                                                                    x −1          G
                                                                 5                 R
                                                               x −1
                                        x −5
                                          x                G

                                                                   x−6
         CA only if proper fractions are used and -1 for           x −1            G
         2nd pick
         VA slegs as egte breuke gebruik word en –1 vir
         tweede keuse.

         P(GG) = P(G)  P(G)
                      x −5 x −6
                   =                                              x −5 x −6
                        x     x −1                                    
           x −5 x −6 3                                               x   x −1
                         =                                                    3                   3
              x      x − 1 11                                   equating to      / stel gelyk aan
         11( x − 5)( x − 6) = 3x( x − 1)                                       11                  11

         11( x 2 − 11x + 30) = 3x 2 − 3x                        getting rid of fractions
                                                                 raak ontslae van breuke
         11x 2 − 121x + 330 = 3x 2 − 3x
          8 x 2 − 118 x + 330 = 0
          4 x 2 − 59 x + 165 = 0                                standard form / standaardvorm

                                                                                                                [4]

                                                                                    TOTAL/TOTAAL:              150

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