# Mathematics Grade 12 Paper 1 Eastern Cape Mock 2020 Memo

> Grade 12 Mathematics Paper 1 memorandum from the Eastern Cape Mock Exam 2020, 16 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/gr-12-ec-maths-p1-memo-sep-2020/411f1d16-f302-46a4-88ab-36d8c0d25076
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Memorandum
- Year: 2020
- Exam period: Eastern Cape Mock Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 16

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Mathematics · Grade 12 · Eastern Cape Mock Exam · 2020. Memorandum, 16 pages. Read online or download the PDF.

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### Page 1

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                              NATIONAL
                         SENIOR CERTIFICATE/
                              NASIONALE
                          SENIOR SERTIFIKAAT

                             GRADE 12/GRAAD 12

                              SEPTEMBER 2020

          MATHEMATICS P1/WISKUNDE V1
         MARKING GUIDELINE/NASIENRIGLYN

MARKS/PUNTE:   150

                     This marking guideline consists of 16 pages./
                     Hierdie nasienriglyn bestaan uit 16 bladsye.

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2                                    MATHEMATICS P1/WISKUNDE V1                          (EC/SEPTEMBER 2020)

    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 applies in ALL aspects of the marking guideline.
        Volgehoue akkuraatheid 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 vir substitusie in die korrekte formule toegeken.

    QUESTION 1/VRAAG 1

    1.1.1     2x2  x  3  0
              (2 x  3)( x  1)  0                                   factorisation / faktorisering
                        3
              x              or / of      x 1                               3
                        2                                             x         x 1
                                                                                2
                                                                                                           (3)
    1.1.2      x(7 x  2)  1
              7 x2  2 x 1  0                                       standard form / standaardvorm
                     b  b 2  4ac
              x
                          2a
                  2  22  4(7)(1)                                  substitution / vervanging
                
                        2(7)
                   2  32
                 
                       14
                  0, 26  or / of           0,55                     0,26         0,55
                                                                                                           (4)
    1.1.3      x2  x  2  0                           y

              x2  x  2  0                                          x2  x  2  0
              ( x  2)( x  1)  0                                    x2  x  2  0
               x  2 or / of x  1                2   1       x
                                                                      x  2  x  1

                                          OR/OF                                      OR/OF
                                                         y

               x2  x  2  0                                        1 x
              (1  x)( x  2)  0                                     factorisation / faktorisering
                                                 2          1   x
               x  2      or / of       x 1                        x  2       x 1
                                                                                                           (4)

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(EC/SEPTEMBER 2020)                  MATHEMATICS P1/WISKUNDE V1                                              3

 1.1.4                  17
             2 x  22 x 
                          2
                      2 x
             2.2  2.2  17
                x

                   23
             2.2  x  17
                 x

                   2
             2.2  17.2 x  8  0
                2x
                                                                   standard form / standaardvorm
             Let / Laat k  2 ,  x

              2k 2  17 k  8  0                                 substitution / vervanging k  2 x
             (2k  1)(k  8)  0                                   factorisation / faktorisering
                  1
             k        or / of k  8
                  2
              2 x  21 or / of     2 x  23                      2x  21 and/en      2x  3

              x  1         or / of      x3                      both answers / beide antwoorde

                                        OR/OF                                     OR/OF

                        17
             2 x  22 x 
                          2
                      2 x
             2.2  2.2  17
                x

                     23
             2.2 x      17
                     2x
             2.22 x  17.2 x  8  0                               standard form / standaardvorm
             (2.2 x  1)(2 x  8)  0                              factorisation / faktorisering
              2 x  21     or / of     2 x  23                  2 x  2 1      2x  3

              x  1         or / of      x3                      both answers / beide antwoorde
                                                                                                 (5)

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4                                      MATHEMATICS P1/WISKUNDE V1                      (EC/SEPTEMBER 2020)

1.2
                                       y

                                                         ●
                                                             B

            A
                         ●                   ●
                                   O                             x

           ( x  2) 2  y 2  25                 1
            x  3  3y  0                        2
            x  3y  3                             3                x  3y  3

           (3 y  3  2) 2  y 2  25                                 substitution / vervanging
           (3 y  5) 2  y 2  25
           9 y 2  30 y  25  y 2  25
                                                                     standard form / standaardvorm
           10 y 2  30 y  0
                                                                      factorisation / faktorisering
           10 y ( y  3)  0
            y  0 or / of         y3
                                                                      x and y values / x en y waardes
            x  3       or / of       x6
            A(3;0)         and/en        B(6;3)                     both sets of coordinates
                                                                       beide stelle van koördinate

                                           OR/OF                                    OR/OF

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(EC/SEPTEMBER 2020)                     MATHEMATICS P1/WISKUNDE V1                                            5

             ( x  2) 2  y 2  25                    1
             x  3  3y  0                            2
              y  13 ( x  3)                          3            y  13 ( x  3)

                                        2
                         x                                          substitution / vervanging
             ( x  2)    1  25
                      2

                         3 
                             x2 2x
             x  4x  4  
               2
                                        1  25  0
                              9     3
             9 x 2  36 x  36  x 2  6 x  216  0
             10 x 2  30 x  180  0                                 standard form / standaardvorm
             x 2  3 x  18  0
             ( x  3)( x  6)  0                                     factorisation / faktorisering
              x  3         or / of           x6
                                                                      x and y values / x en y waardes
             y 0     or / of     y3
              A(3 ; 0)     B(6 ; 3)                                 both sets of coordinates /
                                                                       beide stelle koördinate
                                                                                                           (6)
 1.3         ( x  m)( x  n)  p           2

             x 2  nx  mx  mn  p 2  0
             x 2  (m  n) x  (mn  p 2 )  0                        x 2  (m  n) x  (mn  p 2 )  0
             For real roots / Vir reele wortels:                      (m  n) 2  4(1)(mn  p 2 )  0
             b 2  4ac  0
              (m  n) 2  4(1)(mn  p 2 )  0
              m 2  2mn  n 2  4mn  4 p 2  0
              m 2  2mn  n 2  4 p 2  0                             m  n  (2 p) 2  0
                                                                                2

               m  n   (2 p)2  0                                  explanation / verduideliking
                          2

             Now/Maar: (m  n) 2  0 and/en (2 p) 2  0
               0                                                                                      (4)
                                                                                                        [26]

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6                                    MATHEMATICS P1/WISKUNDE V1                                       (EC/SEPTEMBER 2020)

 QUESTION 2/VRAAG 2

 2.1         86      ;   119         ;     150      ;    179      ;    206   ;      231

                    33               31           29              27         25

                      2                    2               2        2
 2.1.1       206 ; 231                                                            206      231                       (2)
 2.1.2       2 a  2
              a  1                                                             a  1
             3a  b  33
             3  b  33
                                                                                  b  36
                   b  36
             a  b  c  86
             1  36  c  86
                                                                                  c  51
                      c  51
                                                                                  Tn  n 2  36n  51                (4)
             Tn   n 2  36n  51

 2.1.3       326  n 2  36n  51                                                substitution / vervanging
             n 2  36n  275  0
             (n  11)(n  25)  0                                                 method / metode
              n  11      or / of         n  25                                 answers / antwoorde                 (3)

 2.1.4       86 +k ; 119 +k              ; 150 +k ; 179 +k

                   33             31                    29

                         2                  2
             2a  2
              a  1

             3a  b  33
             3  b  33
              b  36                                                             a  1 and/en b  36

             a  b  c  86  k
             1  36  c  86  k
                                                                                  c  51  k
              c  51  k

             Tn  k   n 2  36n  (51  k )
                                                                                                                       (2)

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(EC/SEPTEMBER 2020)                 MATHEMATICS P1/WISKUNDE V1                                           7

 2.2.1       2y 1 ; 4y 1 ; 6y 1
             d  4 y  1  (2 y  1)
                2y                                           d = 2y
              Tn  2 yn  1                                   2 yn  1
             T30  2 y (30)  1
                  60 y  1                                   60 y  1
                                       OR/OF                                OR/OF
              Tn  a  (n  1)d
             T30  (2 y  1)  (30  1)(2 y )                 d = 2y
                                                              substitution / vervanging
                  2 y  1  58 y                             answer / antwoord
                  60 y  1                                                                        (3)

 2.2.2
             Sn 
                    n
                      2a  n  1d 
                    2
                                                              d  2y
             S 30 
                    30
                        2(2 y  1)  292 y                substitution into correct formula
                     2
                                                              vervanging in die korrekte formule
                   15(4 y  2  58 y )
                   15(62 y  2)
                                                              equating to  2820 /
              2820  15(62 y  2)                            stel gelyk aan – 2820
                  188  62 y  2
                  186  62 y
                     y  3                                  answer / antwoord

                                   OR/OF                                    OR/OF
                  n
             Sn   a  l                                    d  2y
                  2
                  30                                          substituting a and l /
             S30   2 y  1  60 y  1                       vervanging van a en l
                   2
             2820  15  62 y  2                           equating to  2820
             188  62 y  2                                   stel gelyk aan – 2820
             186  62 y
                                                              answer / antwoord
              y  3                                                                              (4)
                                                                                                  [18]

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8                                          MATHEMATICS P1/WISKUNDE V1                      (EC/SEPTEMBER 2020)

 QUESTION 3/VRAAG 3

 3.1         1  4  4 2  43  ...  4 n1
             Tn  4 n1                                                 Tn  4 n1
                                       7
             Sum/Som :               4         n 1
                                                                              7
                                      n 1                                4 n1
             For original sequence:/Vir oorspronklike ry:                   n 1
                             5 000
             Sum/Som:  n
                                                                            5000
                                                                         n
                              n 1
                                                                             n 1
                    5 000        7
             Sn :  n   4             n 1
                                                                         answer / antwoord
                    n 1       n 1
                                                                                                             (4)
 3.2                 1
             S 
                    ar

                                           1
             1  x  x 2  x 3  ...         and/en                      1
                                         1 x                           
                                           1                              1 x
                1  x  x 2  x 3  ...                                   1
                                          1 x                          
                                                                          1 x
                                  1       1
             Sum/Som :                 
                                1 x 1 x
                                 1 x 1 x
                              
                                (1  x)(1  x)
                                   2
                                                                              2
                                1  x2                                  
                                                                            1  x2
                          2
                              8                                        equating sum to 8
                       1  x2
                                                                          stel som gelyk aan 8
                       8  8x 2  2
                             8 x 2  6
                                             3
                                x2 
                                             4                                3
                                      3                                  x2 
                                 x                                          4
                                     2                                   answer / antwoord
                                                                                                            (6)
                                                                                                           [10]

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(EC/SEPTEMBER 2020)                  MATHEMATICS P1/WISKUNDE V1                                              9

 QUESTION 4/VRAAG 4

 4.1                       a
              f ( x)          3,
                         x 1

             x  1;       y 3                                     x 1         y3
                                                                                                        (2)
 4.2               a
              y      3
                 0 1
                3 a                                              3a
                   a
             0        3                                          y0
                 x 1
                     a
             3 
                   x 1
             3 x  3  a
                         a         3 a                                      a       3a
             x  1        or / of                                 x  1     or/of
                         3          3                                        3        3
                                                                                                        (3)
 4.3
                                                                   asymptotes / asimptote

                                                                   y-intercepts / y-afsnitte

                                                                   x-intercepts / x-afsnitte

                                                                   shape / vorm

                                                                                                        (4)

 4.4                      a                      1                x + 2  +1
              f ( x)         1 or/of f ( x)      1
                         x2                    x2                                                    (2)
                                                                                                      [11]

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10                                  MATHEMATICS P1/WISKUNDE V1                         (EC/SEPTEMBER 2020)

 QUESTION 5/VRAAG 5

 5.1         (0 ;  7)                                           y  7                               (1)
 5.2         q  8                                              q  8                               (1)
 5.3         g ( x)  b x  8
              5  b1  8                                        substituting (1 ; – 5) /
                                                                  vervanging van (1;  5)
             b  3

             At turning point of f: / By die draaipunt van f:
                    b     3                                               b
             x                                               x
                   2a     4                                               2a
                                                                     b     3
             
                   3
                      
                         3                                           
                  2a     4                                          2a     4
              6a  12                                        b=3
                                                                 simplifying / vereenvoudiging
                  a2
              5  2(1) 2  3(1)  c                            f (1)  5
               c  10                                                                                 (6)
 5.4         y  8 ; y  ℝ                                      y  8
                                                                  (accuracy) / (akkuraatheid) (2)
 5.5         y  9 x   28
             y  9 x  28
             y  2 x 2  3 x  10
              2 x 2  3 x  10  9 x  28                      2 x 2  3x  10  9 x  28
             2 x 2  12 x  18  0                              standard form / standaardvorm
             x 2  6x  9  0                                    factorisation / faktorisering
             ( x  3)( x  3)  0                                x  3
              x  3
             y  2(3) 2  3(3)  10                            y  1
                 1
              T (3 ;  1)

                                         OR/OF                                  OR/OF

             y  9 x  28                                       m  9
              m  9
              f ( x)  2 x 2  3 x  10                          f ' x   4 x  3
              f '  x   4 x  3  9                           equating gradients /
              4 x  12                                          stel gradiënte gelyk
                 x  3
                                                                 x  3
             y  9(3)  28
                1
                                                                 y  1
             T (3 ;  1)                                                                             (5)

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(EC/SEPTEMBER 2020)                MATHEMATICS P1/WISKUNDE V1                                       11

 5.6         y  log 3 x                                      y  log 3 x
                                                                                                   (2)
 5.7          p( x)  f ( x)  1
                    2 x 2  3 x  10  1
                    2 x 2  3x  9
                                                             p ( x)  2 x 2  3 x  9
                    (2 x  3)( x  3)
             when/wanneer: y  0,
                  3
             x     or / of  3                              x-intercepts / x-afsnitte
                  2

                                              3
              x  3 or / of         0 x
                                              2              x  3
                                                                        3
                                                             0 x       (accuracy/akkuraatheid)
                                                                        2
                                                                                                (4)
                                                                                              [21]

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12                                     MATHEMATICS P1/WISKUNDE V1                       (EC/SEPTEMBER 2020)

 QUESTION 6/VRAAG 6

 6.1         A  P (1  i ) n
             1                                                      1
               x  x (1  i ) 4                                      x  x (1  i) 4
             3                                                      3
             1
                (1  i ) 4
             3
                   1
               
             3 4  1  i
              0,24  i
              i  0,24
                                                                 i  0,24
              r  24%                                           answer / antwoord
                                                                                                        (3)
 6.2.1           x[(1  i )  1]
                              n
             F                                                       0,095
                        i                                        i
                                  0,095 72                         12
                              x 1          1               n  72
                                    12                     F  R 596 458,10
             R 596 458,10 
                                      0,095                      substitution into correct formula /
                                       12                        vervanging in die korrekte formule
                                              0,095
                             R 596 458,10 
                         x                    12
                                0,095    72
                                                 
                               1         1
                                   12                      answer / antwoord
                                 R 6178,13
                                                                                                        (5)
 6.2.2
             P
                       
                 x 1  1  i 
                                  n
                                       
                         i
                               0,095  72                    n  72
                 R 6178,131  1        
                                   12                      substitution into correct formula /
                                                                vervanging in die korrekte formule
                                0,095
                                 12
                R 338 070,29

                           A  P (1  i ) n
                               0,095 
                                               5
                                                                 A  R 338 070,29
             R 338 070,29  P1        
                                  12                           n5
                                                                 substitution into correct formula /
                          R 338 070,29
                    P               5
                                                                 vervanging in die korrekte formule
                           0,095 
                          1                                   answer / antwoord
                               12 
                         R 325 000

                                                                                                        (6)
                                                                                                       [14]

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### Page 13

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(EC/SEPTEMBER 2020)                      MATHEMATICS P1/WISKUNDE V1                                      13

 QUESTION 7/VRAAG 7

                                 𝑓 (𝑥+ℎ)−𝑓(𝑥)
              f ' x  = lim
 7.1
                           ℎ→0                ℎ

                                 −2(𝑥+ℎ)2 −(−2𝑥2 )
                      = lim                       ℎ                substitution / vervanging
                           ℎ→0
                                     −2(𝑥 2 +2𝑥ℎ+ℎ2 )+2𝑥 2
                      = lim
                           ℎ→0                        ℎ            expansion / uitbreiding
                                 −2𝑥 2 −4𝑥ℎ−2ℎ2 +2𝑥 2
                      = lim
                           ℎ→0                        ℎ
                                                                   −2𝑥 2 − 4𝑥ℎ − 2ℎ2 + 2𝑥 2
                                 ℎ(−4𝑥−2ℎ)
                      = lim                                        factorisation / faktorisering
                           ℎ→0            ℎ

                      = lim (−4𝑥 − 2ℎ)
                           ℎ→0

                      = − 4𝑥                                        4x
                                              OR/OF
                                                                                 OR/OF
             𝑓(𝑥) = −2𝑥 2

             𝑓(𝑥 + ℎ) − 𝑓(𝑥) = −2(𝑥 + ℎ)2 − (−2𝑥 2 )
                             = −2𝑥 2 − 2𝑥ℎ − 2ℎ2 + 2𝑥 2
                                                                   −2𝑥 2 − 2𝑥ℎ − 2ℎ2 + 2𝑥 2
                             = −4𝑥ℎ − 2ℎ2
                                                                   −4𝑥ℎ − 2ℎ2
                                 𝑓 (𝑥+ℎ)−𝑓(𝑥)
              f ' x  = lim
                           ℎ→0                ℎ

                                 −4𝑥ℎ−2ℎ2
                      = lim                                        substitution / vervanging
                           ℎ→0            ℎ
                                 ℎ(−4𝑥ℎ−2ℎ)
                      = lim                                        factorisation / faktorisering
                           ℎ→0                ℎ

                      = lim (−4𝑥ℎ − 2ℎ)
                           ℎ→0
                                                                    4x
                   = − 4𝑥                                                                                (5)
 7.2                   2
             y  7x4 
                       x3
                                     3
                                                                          3
                 7x  2x
                       4             2                                 
                                                                   2x 2
                                          5                                            5
               dy                                                                 
                  28 x 3  3 x 2                                 28x 3   3x 2                      (3)
               dx
 7.3            1       5       
             Dt  gt 2   3g 
                2        t      
                  1                                              5t 1
              Dt  gt 2  5t 1  3g 
                  2                  
              gt  5t 2                                          gt   5t 2
                                                                   Dt(3g) = 0                          (4)
                                                                                                       [12]
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### Page 14

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14                                     MATHEMATICS P1/WISKUNDE V1                     (EC/SEPTEMBER 2020)

 QUESTION 8/VRAAG 8

 8.1         (0 ; 9)                                             (0 ; 9)
                                                                                                        (1)
 8.2          f  x   2 x  x  12 x  9
                            3     2

              f (1)  2(1)3  (1) 2  12(1)  9                  method / metode
                       0
              f  x   ( x  1)(2 x 2  3x  9)                2 x 2  3x  9
                                                                 factorisation / faktorisering
                   0  ( x  1)( x  3)(2 x  3)
                                                    3
              x  1 or / of x  3 or / of x 
                                                    2
                                3                                                     3 
             D(3;0), E(1;0), F  ;0                            D(3; 0)  E(1; 0)  F ; 0 
                                2                                                     2 
                                                                                                        (6)

 8.3         For concave down / Vir konkaaf afwaarts             f ''  x   0
              f ' ' x   0
              f '  x   6 x 2  2 x  12                       f ' x   6 x 2  2 x  12
                                                                 f ' ' x   12 x  2
              f ' '  x   12 x  2
             12 x  2  0                                                1
                            1                                    x
                        x                                               6
                            6
                                                                                                       (4)

 8.4         6 x 2  2 x  12  0
                 b  b 2  4ac
             x
                      2a
                   2  2 2  4(6)(12)                          substitution into correct formula
                                                                vervanging in die korrekte formule
                           2.6
                 2  292                                        x-values / x-waardes
               
                     12
                1,59 or / of 1, 26
                                                                 answer / antwoord
                1,59  x  1, 26                                 (accuracy / akkuraatheid)
                                                                                                       (4)
                                                                                                      [15]

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(EC/SEPTEMBER 2020)               MATHEMATICS P1/WISKUNDE V1                                         15

 QUESTION 9/VRAAG 9

                                     1     1
           Area of/van ∆PBA           bh   t  12  6t cm 2       Area of/van ∆PBA
                                     2     2

                                     1             7    t2
           Area of/van ∆ACS           t (7  t )  t     cm 2      Area of/van ∆ACS
                                     2             2    2

                                     1                   7t
           Area of/van ∆BQC           (12  t )7  42     cm 2     Area of/van ∆BQC
                                     2                   2

           Area of rectangle/van reghoek: PBQS  12  7  84 cm 2

           ∴ Area of/van ∆ABC:                                       subtracting from 84 /
                                                                      trek van 84 af
                              7t t 2     7t
           A(t)  84  6t        42 
                              2 2        2

             1
            t 2  6t  42
             2
           a  0, so A  t  is a min graph / is ' n min grafiek
                                A ' t   t  6                     A ' (t )  0
                                At min / By min : A '(t )  0
                                t 6  0
                                        t 6

           Smallest area / Kleinste oppervlakte:
            A 6  6  6(6)  42
                   1 2
                   2
                 24 cm 2                                            smallest area / kleinste area
                                                                                                     (6)
                                                                                                     [6]

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16                                 MATHEMATICS P1/WISKUNDE V1                              (EC/SEPTEMBER 2020)

 QUESTION 10/VRAAG 10

 10.1                                                         S =135    Correct entries of:
                                                                        Korrekte waarde van:
                M                                                  P
                                        12                               12
                                                      y
                       2y+3
                                                                         5 ; 12 ; 24
                                        x
                               5                 24                      2y+3 ; y ; y

                                        y                               x
                                                              12
                                        A
                                                                                                              (4)
 10.2        x  y  5  24  60                                         x + y + 5 + 24 = 60
             x  y  31
            2 y  3  x  5  12  x  y  12  24                       2 y  3  x  5  12  x  y  12  24
            2 y  x  20  x  y  36
                   y  16 and/en x  15                                 y = 16 and/en  x = 15              (4)
 10.3                                2 y  3  5  12  x  24
            P(M or/of (P and/en A))=
                                                135                      2 y  3  5  12  24
                              35  5  12  15  24
                            
                                       135
                                91
                             =        or / of 0 , 67                     answer / antwoord
                               135
                                                                                                             (3)
                                                                                                            [11]

 QUESTION 11/VRAAG 11

 11.1       7!= 5 040 ways / maniere                                      7!                                (2)
 11.2       Sample space/Steekproefruimte:

               5       4       2        3    1            2        1     arrangement / rangskikking

            Possible outcomes/Moontlike uitkomste:

               3       2       2        2    1            1        3     arrangement / rangskikking

                                               3  2  2  2 11 3
            Probability/Waarskynlikheid =
                                               5  4  2  3 1 2 1
                              72                                         3 2  2  2 11 3 and/en
                                                                        5  4  2  3 1 2 1
                             240
                              3                                          answer / antwoord
                                0,3
                             10                                                                              (4)
                                                                                                              [6]

                                                                               TOTAL/TOTAAL:                 150
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