# Mathematics Grade 12 Paper 1 NW June 2025 Memo (Afrikaans)

> Grade 12 Mathematics Paper 1 memorandum from the NW June Exam 2025 (Afrikaans), 12 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/grade-12-mathematics-2025-nw-june-exam-question-paper-paper-1-afrikaans/37306e3d-be01-4761-8a1c-8b16873c6847
- Updated: 2026-10-29
- Subject: Mathematics
- Grade: Grade 12
- Language: Afrikaans
- Document type: Memorandum
- Year: 2025
- Exam period: NW June Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 12

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### Page 1

PROVINCIAL ASSESSMENT/
                             PROVINSIALE ASSESSERING

                                        GRADE/GRAAD 12

                            MATHEMATICS P1/WISKUNDE V1
                                         JUNE/JUNIE 2025
                      MARKING GUIDELINES/NASIENRIGLYNE

MARKS/PUNTE: 150

                            This marking guidelines consists of 12 pages.
                            Hierdie nasienriglyne bestaan uit 12 bladsye.

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### Page 2

Mathematics P1/Wiskunde V1                        2                                NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

NOTE:
   If a candidate answers a question TWICE, only mark the FIRST attempt.
   If a candidate has crossed out an attempt of a question and not redone the question, mark
    the crossed-out version.
   Consistent Accuracy applies in ALL aspects of the marking guidelines. Stop marking at
    the second calculation error.
   Assuming answers/values in order to solve a problem is NOT acceptable.

LET WEL:
    Indien ‘n kandidaat ‘n vraag TWEE KEER beantwoord, sien slegs die EERSTE poging na.
    Indien ‘n kandidaat ‘n antwoord van ‘n vraag doodtrek en nie oordoen nie, merk die
     doodgetrekte poging.
    Volgehoue akkuraatheid isdeurgans op ALLE aspekte van die nasienriglyne van
     toepassing. Hou op nasien by die tweede berekeningsfout.
    Aanvaar van antwoorde/waardes om ‘n probleem op te los, word NIE toegelaat nie.

 QUESTION/VRAAG 1

 1.1.1    𝑥 2 − 𝑥 − 12 = 0
          (𝑥 + 3)(𝑥 − 4) = 0                                          factors/faktore
          𝑥 = −3 or/of 𝑥 = 4                                          𝑥 = −3
                                                                      𝑥 = 4                           (3)
 1.1.2    5𝑥 2 + 2𝑥 = 9
          5𝑥 2 + 2𝑥 − 9 = 0                                           std form/vorm
               −2 ± √22 − 4(5)(−9)
          𝑥=                                                          subst
                       2(5)
                                                                      𝑥 = 1,16
           = 1,16 or/of 𝑥 = −1,56
                                                                      𝑥 = −1,56
                                                                                                       (4)
                        2
 1.1.3    18 − 3𝑥 − 𝑥 ≥ 0
          (6 + 𝑥)(3 − 𝑥) ≥ 0                                          factors/faktore
                                                                       critical values/
          −6 ≤ 𝑥 ≤ 3                                                    kritiese waardes
                                                                      answer/antw

          OR/OF                                                       OR/OF

          18 − 3𝑥 − 𝑥 2 ≥ 0
          𝑥 2 + 3𝑥 − 18 ≤ 0
          (𝑥 + 6)(𝑥 − 3) ≤ 0                                          factors/faktore
                                                                       critical values/
          −6 ≤ 𝑥 ≤ 3                                                    kritiese waardes
                                                                      answer/antw

                                                                                                       (4)

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### Page 3

Mathematics P1/Wiskunde V1                        3                                NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 1.1.4    6 − √𝑥 + 4 = 𝑥 + 4
            −√𝑥 + 4 = 𝑥 − 2                                          isolate/isoleer √
                𝑥 + 4 = 𝑥 2 − 4𝑥 + 4                                 square/kwadreer
             𝑥 2 − 5𝑥 = 0                                            std form/vorm
            𝑥(𝑥 − 5) = 0                                             factors/faktore
          𝑥 = 0 or/of 𝑥 ≠ 5                                          𝑥 = 0 or/of 𝑥 = 5
                                                                     𝑥 ≠ 5                            (6)
 1.2      2𝑦 − 𝑥 = 3 . . . . . . . . . ①
          𝑦 2 + 3𝑥 − 2𝑥𝑦 = 0 . . . . ②
          2𝑦 − 3 = 𝑥 . . . . . . . . . ③                             equation/vergelyking

          ∴ 𝑦 2 + 3(2𝑦 − 3) − 2𝑦(2𝑦 − 3) = 0                         subst
          𝑦 2 + 6𝑦 − 9 − 4𝑦 2 + 6𝑦 = 0
          −3𝑦 2 + 12𝑦 − 9 = 0
          𝑦 2 − 4𝑦 + 3 = 0                                           std form/vorm
          (𝑦 − 1)(𝑦 − 3) = 0                                         factors/faktore
                                                                     y-values/waardes
          𝑦=1             or/of 𝑦 = 3
          𝑥 = 2(1) − 3 or/of 𝑥 = 2(3) − 3
                                                                     x-values/waardes
            = −1                   =3                                                                  (6)
 1.3             1        3    1
          (3 − ) (9 +        + )
                √5       √5 5
                     1 3
          = 33 − ( )                                                 cubes/derdemagte
                    √5
                   1 1     √5                                        rationalise/rasionaliseer
          = 27 − ∙       ×
                   5 √5 √5
                    1                                                𝑎 = 27
          = 27 −      √5
                   25                                                𝑏 = 5
          ∴ 𝑎 = 27 and/en 𝑏 = 5                                                                        (4)
                                                                                                       [27]

 QUESTION/VRAAG 2

 2.1      2; 7; 16; . . . . . . . ; 781; 862
            5 9 13
          ∴ 𝑇4 = 29                                                   29                              (1)
 2.2      2𝑎 = 4; 𝑎 = 2                                                2𝑎 = 4; 𝑎 = 2
          3(2) + 𝑏 = 5; 𝑏 = −1                                         𝑏 = −1
          2 − 1 + 𝑐 = 2; 𝑐 = 1                                        𝑐 =1
          𝑇𝑛 = 2𝑛2 − 𝑛 + 1                                                                             (4)
 2.3      𝑇𝑛 = 2𝑛2 − 𝑛 + 1
          862 = 2𝑛2 − 𝑛 + 1                                           subst
          0 = 2𝑛2 − 𝑛 − 861                                           factorise/faktoriseer
          0 = (𝑛 − 21)(2𝑛 + 41)
                                    41
          𝑛 = 21 or/of 𝑛 = − 2
                                                                      term 21
          ∴ 𝑇21 = 862       N/A                                                                        (3)
                                                                                                       [8]

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### Page 4

Mathematics P1/Wiskunde V1                        4                                NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 QUESTION/VRAAG 3

 3.1.1    2 + 6 + 18 + 54 + . . .

          𝑇𝑛 = 2.3𝑛−1                                                 2.3𝑛−1                          (1)
           𝑚
 3.1.2       2
          ∑ ∙ 3𝑛 = 59 048
             3
          𝑛=1

          ∴ 2 + 6 + 18 + 54 + . . .
                                                                      𝑎; 𝑟
          𝑆𝑚 = 59 048; 𝑎 = 2; 𝑟 = 3

          𝑎(𝑟 𝑚 − 1)
                     = 59 048
            𝑟−1

          2(3𝑚 − 1)                                                   subst
                    = 59 048
            3−1

          3𝑚 = 59 049
          3𝑚 = 310                                                    exp law/eksp wet
          𝑚 = 10                                                      answer/antwoord
                                                                                                       (4)
 3.2.1                  1
          𝑎 = 3; 𝑟 =
                        2
               3 3
          3 +    + + . . .
               2 4
                 3                                                    4
                                                                         3
          ∴ 𝑇3 =                                                                                       (1)
                 4
 3.2.2           𝑎
          𝑆∞ =
                1−𝑟
                 3                                                    subst
             =
                   1
               1−2
                                                                      6
             =6                                                                                        (2)
 3.3      1; 2; 3; 4; . . . . ; 8 000

                   8 000
          𝑆8000 =        (1 + 8 000)
                     2
                 = 32 004 000                                         answer/antwoord

          Powers of 6/Magte van 6:
          6; 36; 216; 1 296; 7 776                                    sequence/ry

               6(65 − 1)                                              subst
          𝑆5 =
                 6−1
             = 9 330

          ∴ 𝑆 = 32 004 000 − 9 330 = 31 994 670                       answer/antwoord
          OR/OF                                                                                        (4)
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### Page 5

Mathematics P1/Wiskunde V1                        5                                    NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

          1; 2; 3; 4; . . . . ; 8 000
                                                                      OR/OF
                  8 000
          𝑆8000 =       (1 + 8 000)
                    2
                = 32 004 000

          Powers of 6/Magte van 6:
          6; 36; 216; 1 296; 7 776                                    answer/antwoord

          𝑆5 = 6 + 36 + 216 + 1296 + 7776
             = 9 330                                                  series/ry

          ∴ 𝑆 = 32 004 000 − 9 330                                    add terms to 9 330/
              = 31 994 670                                             tel terme op na 9 330

                                                                      answer/antwoord
                                                                                                       [12]

 QUESTION/VRAAG 4

 4.1.1    𝑇17 = 3 × 17 − 14                                           3 x 17
              = 37                                                     − 14                           (2)
 4.1.2    White tiles/wit teëls
          5; 7; 9; . . .
          ∴ 𝑇𝑛 = 5 + (𝑛 − 1)2
               = 2𝑛 + 3                                               2𝑛         3                   (2)
 4.1.3    Black tiles/Swart teëls:
          1 + 2 + 3 + . . . + 25
                 𝑛                         𝑛
          ∴ 𝑆𝑛 =   [𝑎 + 𝑙]              =    [2𝑎 + (𝑛 − 1)𝑑]
                 2                         2
                 25                       25                          subst
           𝑆25 =    (1 + 25)            =     [2(1) + 24(1)]
                  2                        2
               = 325                    = 325                         325

          White tiles/Wit teëls:
          5 + 7 + 9 + . . . + 53
                  𝑛                      𝑛
          ∴ 𝑆𝑛 = [𝑎 + 𝑙]               = [2𝑎 + (𝑛 − 1)𝑑]
                  2                      2
                  25                     25                           subst
           𝑆25 =      (5 + 53)         =    [2(5) + 24(2)]
                   2                      2
               = 725                  = 725                           725
          ∴Tiles all together/Teëls altesaam = 1 050                  1 050                           (5)
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### Page 6

Mathematics P1/Wiskunde V1                        6                                NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

          OR/OF

          6 + 9 + 12 + . . . . 25 terms/terme                         series/reeks
          𝑎 = 6; 𝑑 = 3                                                a d
                25
          𝑆25 =    [2(6) + (25 − 1)(3)]                               subst
                 2
              = 1 050
                                                                      1 050
 4.2               1       2
          19 + 18 + 17 + . . .
                   5       5
                4                                                     𝑎; 𝑑
          𝑑 = − ; 𝑎 = 19
                5
                              4                                       subst
          𝑇𝑛 = 19 + (𝑛 − 1) (− )
                              5
                     4    4
             = 19 − 𝑛 +
                     5    5
               99 4
             =    − 𝑛
                5 5
          99 4                                                           99   4
             − 𝑛<0                                                    5 − 5𝑛 < 0
           5 5
                4𝑛       99
             −      <−
                 5        5
                  𝑛 > 24,75                                            𝑛 > 24,75
          ∴First negative term is/Eerste negatiewe term is T25        answer/antwoord                 (5)
                                                                                                       [14]

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### Page 7

Mathematics P1/Wiskunde V1                        7                                NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 QUESTION/VRAAG 5

 Given/Gegee: 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 8 and/en
              𝑔(𝑥) = 𝑚𝑥 + 𝑐

 5.1      𝑝 = (−6)2 + 2(−6) − 8
             = 16                                                        16                           (1)
 5.2      𝑥 −intercepts/afsnitte: 𝑦 = 0
          𝑥 2 + 2𝑥 − 8 = 0                                               𝑓(𝑥) = 0
          (𝑥 + 4)(𝑥 − 2) = 0                                             factorise/faktoriseer
          𝑥 = −4 or/of 𝑥 = 2
          ∴ 𝐴(−4; 0)                                                     𝐴(−4; 0)
          ∴ 𝐵(2; 0)                                                      𝐵(2; 0)
                                                                                                       (4)
 5.3      Turning point/draaipunt:
                  𝑏       2
          𝑥=−       =−        = −1                                       𝑥 −value/waarde
                2𝑎       2(1)
          𝑦 = (−1)2 + 2(−1) − 8 = −9                                     𝑦 −value/waarde
          ∴ 𝐷(−1; −9)                                                                                  (2)
 5.4      𝑐 = −8                                                         𝑐 = −8
          𝑚 = −2                                                         𝑚 = −2                       (2)
 5.5      𝑚 = 𝑓 ′ (𝑥) = 2𝑥 + 2                                           𝑓 ′ (𝑥) = 2𝑥 + 2
          𝑚 = 𝑓 ′ (0)                                                    subst
            = 2(0) + 2
            =2
          Subst 𝑚 = 2 and/en 𝐶(0; −8) into/in 𝑦 = 𝑚𝑥 + 𝑐
          ∴ 𝑦 = 2𝑥 − 8                                                   equation/vergelyking         (3)
 5.6      (−∞; 9]                                                        values/waardes
                                                                         notation/notasie
          OR/OF                                                          OR/OF

          𝑦 ≤ 9; 𝑦 ∈ ℝ                                                   answer/antwoord             (2)
 5.7      𝑓(𝑥) − 𝑔(𝑥) > 0
          𝑓(𝑥) > 𝑔(𝑥)
          ∴ 𝑥 < −4 or/of 𝑥 > 0                                            𝑥 < −4
                                                                         𝑥>0                          (2)
           2
 5.8      𝑥 + 2𝑥 + 𝑘 = 0
          𝑥 2 + 2𝑥 − 8 = −𝑘 − 8
          ∴ −𝑘 − 8 < −9
          ∴        𝑘>1                                                   answer/antwoord             (2)
                                                                                                       [18]

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### Page 8

Mathematics P1/Wiskunde V1                           8                                NW/June/Junie 2025
                                 Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 QUESTION/VRAAG 6
                             6
 Given/Gegee: ℎ(𝑥) = 𝑥−2 − 1

 6.1 𝑥 = 2                                                                   𝑥 = 2
     𝑦 = −1                                                                  𝑦 = −1                           (2)
 6.2 𝑥 −intercept/afsnit: 𝑦 = 0
           6                                                                 ℎ(𝑥) = 0
     0=        −1
         𝑥−2
           6
     1=
         𝑥−2
     𝑥−2=6
         𝑥=8
     ∴ (8; 0)                                                                 (8; 0)
     𝑦 −intercept/afsnit: 𝑥 = 0
          6
     𝑦=      −1
         −2
       = −4
     ∴ (0; −4)                                                                (0; −4)                         (3)
 6.3

                                                                             shape/vorm
                                                                             asymptotes/asimptote
                                                                             x- and y-
                                                                              intercept/afsnit

                                                                                                               (3)
 6.4 ℎ(𝑥) < 0; 𝑥 ∈ [0; ∞)
     ∴ 0 ≤ 𝑥 < 2 or/of 𝑥 > 8                                                 0 ≤ 𝑥 < 2
                                                                             𝑥 > 8                            (2)
                                                                                                               [10]

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### Page 9

Mathematics P1/Wiskunde V1                           9                                NW/June/Junie 2025
                                 Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 QUESTION/VRAAG 7

 Given/Gegee: 𝑝(𝑥) = 𝑏 𝑥 and/en 𝑝−1 (𝑥)
              S(27; -3) lies on 𝑝−1 /lê op 𝑝−1
              K(-3; 27) lies on 𝑝/lê op 𝑝

 7.1      𝑝(𝑥) = 𝑏 𝑥
          27 = 𝑏 −3                                                      subst (27; -3)
           1
              = 27
           𝑏3
                 1
           𝑏3 =
                27
                1                                                        𝑏 = 3
                                                                                 1
          ∴𝑏=                                                                                             (2)
                3
                             𝑥
 7.2                    1
          𝑓(𝑥) = 𝑦 = ( )
                        3
                         1 𝑦
          𝑓 −1 (𝑥): 𝑥 = ( )                                              swapping/omruil
                         3
          𝑦 = log 1 𝑥                                                    equation/vergelyking
                   3                                                     Answer only: 2/2                 (2)
 7.3      𝑄(0; 1)                                                        𝑄(0; 1)
          𝑅(1; 0)                                                        𝑅(1; 0)                         (2)
 7.4.1    0 < 𝑝(𝑥) ≤ 1
          ∴𝑥≥0                                                           𝑥 ≥ 0                           (1)
 7.4.2    log 1 𝑥 < −3
             3                                                           𝑥 > 27
          ∴ 𝑥 > 27                                                                                        (1)
 7.5      𝑇(27; 1)                                                       T(27; 1)
          ∴ 𝑇𝑄 = 27; 𝑇𝑆 = 4                                              TQ; TS
                        1
          ∴ Area ∆𝑄𝑇𝑆 = 2 ∙ 𝑇𝑄 ∙ 𝑇𝑆
                        1
                      = × 27 × 4                                         subst
                        2
                      = 54 units2/eenh2
                                                                         answer/antwoord                 (4)
                                                                                                          [12]

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### Page 10

Mathematics P1/Wiskunde V1                        10                                   NW/June/Junie 2025
                               Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 QUESTION/VRAAG 8

 8.1      𝑓(𝑥) = 3𝑥 2 − 2
          𝑓(𝑥 + ℎ) = 3(𝑥 + ℎ)2 − 2
                       = 3𝑥 2 + 6𝑥ℎ + 3ℎ2 − 2                          𝑓(𝑥 + ℎ) value/waarde
                           𝑓(𝑥 + ℎ) − 𝑓(𝑥)
          𝑓 ′ (𝑥) = lim
                       ℎ→0        ℎ
                        3𝑥 2 + 6𝑥ℎ + 3ℎ2 − 2 − 3𝑥 2 + 2                subst
                  = lim
                    ℎ→0               ℎ
                                                                       simplification/vereenv
                        ℎ(6𝑥 + 3ℎ)
                  = lim
                    ℎ→0      ℎ
                  = lim (6𝑥 + 3ℎ)                                      factors/faktore
                       ℎ→0

                  = 6𝑥
                                                                       answer/antwoord                 (5)
 8.2.1                    1
          𝑓(𝑥) = 3𝑥 4 − 𝑥 2 + 5
                          2                                            12𝑥 3
          𝑓 ′ (𝑥) = 12𝑥 3 − 𝑥
                                                                       −𝑥                              (2)
 8.2.2        √𝑥    1
          𝑦=     −
               2   9𝑥 3
              1 1 1                                                       1   1
                                                                                        1
            = 𝑥 2 − 𝑥 −3                                               2 𝑥 2         9 𝑥 −3
              2     9
                                                                                  1
            𝑑𝑦 1 − 1 1 −4                                                 1                 1
          ∴    = 𝑥 2 + 𝑥                                               4 𝑥 − 2       + 3 𝑥 −4
            𝑑𝑥 4         3                                                                              (4)
 8.2.3             2𝑥 2 − 3𝑥 − 5
          𝑓(𝑥) =
                       𝑥+1
                   (2𝑥 − 5)(𝑥 + 1)
                 =                                                     factors/faktore
                        (𝑥 + 1)
                                                                       2𝑥 − 5
                 = 2𝑥 − 5
                                                                       𝑓 ′ (𝑥) = 2
               ′ (𝑥)
          ∴𝑓           =2                                                                               (3)
                                                  1
 8.3      𝑦 = −𝑥 2 + 4𝑥    and/en 𝑦 = 2𝑥 − 4                           𝑦 ′ = −2𝑥 + 4
                                                                       𝑚⊥ = −2
          𝑚 = −2𝑥 + 4             ∴ 𝑚⊥ = −2
                                                                       eqauting/Vergelyk
          ∴ −2 = −2𝑥 + 4
                                                                       𝑥 = 3
          ∴ 𝑥=3
          𝑦 = −(3)2 + 4(3) = 3
                                                                       (3; 3)
          ∴ (3; 3) and/en 𝑚 = −2
          ∴ 3 = −2(3) + 𝑐
                                                                       subst
          ∴𝑐=9                                                         answer/antwoord
          ∴ 𝑦 = −2𝑥 + 9                                                                                 (7)
                                                                                                        [21]

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### Page 11

Mathematics P1/Wiskunde V1                       11                                   NW/June/Junie 2025
                              Grade/Graad 12 – Marking Guidelines/Nasienriglyne

 QUESTION/VRAAG 9

 Given/Gegee: 𝑓(𝑥) = −2𝑥 3 + 5𝑥 2 + 4𝑥 − 3

 9.1      𝑓(𝑥) = −2𝑥 3 + 5𝑥 2 + 4𝑥 − 3
             0 = −(2𝑥 3 − 5𝑥 2 − 4𝑥 + 3)
          2𝑥 − 5𝑥 2 − 4𝑥 + 3 = 0
             3

          (𝑥 + 1)(2𝑥 2 + 𝑘𝑥 + 3) = 0                                  method to factorise/
                                                2      2        2      faktoriseer metode
                                             2𝑥 + 𝑘𝑥 = −5𝑥
                                                    𝑘𝑥 2 = −7𝑥 2
          (𝑥 + 1)(2𝑥 2 − 7𝑥 + 3) = 0
          (𝑥 + 1)(𝑥 − 3)(2𝑥 − 1) = 0
                                       1
          𝑥 = −1 or/of 𝑥 = 3 or/of 𝑥 = 2                              each 𝑥 −value/
                                                                         elke 𝑥 −waarde                (4)
 9.2      𝑓(𝑥) = −2𝑥 3 + 5𝑥 2 + 4𝑥 − 3
          𝑓 ′ (𝑥) = −6𝑥 2 + 10𝑥 + 4 = 0                               𝑓 ′ (𝑥) = 0
          3𝑥 2 − 5𝑥 − 2 = 0
          (𝑥 − 2)(3𝑥 + 1) = 0                                         factors/faktore
          𝑥 = 2 or/of 𝑥 = − 3
                               1                                      𝑥 −values/waardes
          𝑓(2) = −2(2)3 + 5(2)2 + 4(2) − 3
                 =9
                 1          1 3        1 2 1
          𝑓 (− ) = −2 (− ) + 5 (− ) + 4 (− ) − 3
                 3          3          3   3
                       100                                                        1     100
                   =−                                                  𝐵 (− 3 ; − 27 )
                        27
                   1    100
          ∴ 𝐵 (− 3 ; − 27 ) and/en 𝐸(2; 9)                             𝐸(2; 9)
                                                                                                       (5)
 9.3      𝑓(𝑥) = −2𝑥 3 + 5𝑥 2 + 4𝑥 − 3
          𝑓 ′ (𝑥) = −6𝑥 2 + 10𝑥 + 4
          𝑓"(𝑥) < 0                                                   𝑓"(𝑥) < 0
          ∴ −12𝑥 + 10 < 0                                             𝑓"(𝑥) = −12𝑥 + 10
                   −12𝑥 < −10
                           5
          ∴           𝑥>                                                      5
                           6                                          𝑥 >6                            (3)

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### Page 12

Mathematics/P1                                   12                                  NW/June 2025
                              Grade/Graad 12– Marking Guidelines/Nasienriglyne

 9.4      𝑥. 𝑓 ′ (𝑥) > 0
                                1                                     0 < 𝑥 < 2
          0 < 𝑥 < 2 or/of 𝑥 < − 3
                                                                             1
                                                                      𝑥 < −3                  (3)
 9.5      2𝑥 3 − 5𝑥 2 − 4𝑥 + 3 = 𝑘
          ∴ −𝑓(𝑥) = 𝑘
              𝑓(𝑥) = −𝑘                                               𝑓(𝑥) = −𝑘
               100
          ∴−       < −𝑘 < 9
               27
                        100                                           notation/notasie
          ∴ −9 < 𝑘 <                                                  values/waardes          (3)
                        27
                                                                                               [18]

 QUESTION/VRAAG 10

 10.1

          Q is the maximum t.pt/maksimum dr.pt                        Q max/maks
          P is the minimum t.pt/minimum dr.pt                         P minimum               (2)
 10.2     𝑥>𝑎
          ∴ 𝑓(𝑥) is increasing/stygend                                increase/stygend       (2)
 10.3     𝑓 ′ (𝑥) = 3𝑝𝑥 2 + 2𝑞𝑥 + 𝑟                                   𝑓′(𝑥)
          ∴ (𝑜; 𝑟)                                                    coordinate/koőrdinaat   (2)
 10.4     If 𝑥 = 𝑏        ⇒ 𝑓 ′ (𝑥) = 0                               𝑓 ′ (𝑥) = 0
          ∴turning point/draaipunt Q                                  Q t.pt/dr.pt            (2)
 10.5       𝑎+𝑏
          (        ; 0)
               2                                                      answer                 (2)
                                                                                               [10]

                                                                            TOTAL/TOTAAL: 150

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