# Mathematics Grade 9 ANA Exemplars 2013 Memo

> Grade 9 Mathematics memorandum from the ANA Exemplars 2013, 12 pages. Read online or get the free PDF download, question paper linked when available.

- Page: https://www.hlayiso.com/library/2013-gr-9-maths-exemplar-memo/28b1acfe-73d4-4157-a8a0-45ee9c24ff3c
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 9
- Document type: Memorandum
- Year: 2013
- Exam period: ANA Exemplars
- Curriculum: CAPS
- Pages: 12

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## About this document

Mathematics · Grade 9 · ANA Exemplars · 2013. Memorandum, 12 pages. Read online or download the PDF.

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                                                  ANNUAL NATIONAL ASSESSMENT 2013
                                              GRADE 9 MATHEMATICS EXEMPLAR MEMORANDUM

                KEY
M        Method mark
CA       Consistent Accuracy mark
A        Accuracy mark

1. MULTIPLE CHOICE QUESTIONS

       1.1   B      1.2    D        1.3   C     1.4   C       1.5    D   Give 1 mark for each
 1.                                                                      correct answer.
       1.6   C      1.7    D        1.8   D     1.9   D       1.10   A
                                                                                                  [10]

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2. NUMBERS, OPERATIONS AND RELATIONS

2.1.1   0,0067  A                                                             1 mark    (1)

2.1.2   −16 − 12 − 18 + 2 = −44                                      Substitution:
                                                                              1 mark
                                                                          Simplifying:
                                                                             2 marks
                                                                           Answer: 1
                                                                                 mark    (4)

2.2       7,125 ÷ √25
        = 7,125 ÷ 5  M                                                    5: 1 mark
        = 1,425  CA                                                        Answer:      (2)
                                                                              1 mark
2.3     96:120
        = 8:10                                                                 8:10:
        = 4:5A                                                               1 mark     (2)
                                                                             Answer:
                                                                               1 mark
2.4      =  M                                                               formula:
                                                                               1mark
        80 =  M                                                         substitution:
          = 240 CA                                                           1 mark
          =
                                                                          Answer for
        50 =      M                                                        : 1 mark

          = 4,8ℎ CA or 4 hours 48 minutes
                                                                         substitution:
                                                                               1mark

                                                                          Answer for
                                                                            : 1mark      (5)

2.5              = (1 + )  M                                         formula: 1mark
                = 6 500(1 + 0,075) M                             substituting: 1mark
                = 8 074,93 CA                                 Answer for A: 1 mark
               or                                        Calculating interest: 1 mark
                Year 1: 6 500 × 7,5% = 487,50                        Answer: 1 mark
                Year 2: 6 987,50 × 7,5% = 524,06
                Year 3: 7 511,56 × 7,5% = 563,37   M
                The amount will be R8 074,93 CA

               Interest = R8 074,93 − R6 500M
                        = 1 574,93 CA                                                   (5 )
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2.6.1        20%       = 35 000
                       = 35 000  M                                   = 3500: 1 mark
                       = 175 000 CA                                   Answer: 1 mark         (2)

2.6.2   Amount still to be paid = 175 000 − 35 000
                                = 140000 A                              Answer: 1 mark       (1)

2.6.3     = (1 + )  M                                                     formula: 1mark
          = 140 000(1 + 0,1 × 4) M                           substituting = 4: 1mark
          = 196 000  CA                                      substituting = 0,1: 1mark
        ∴ monthly installment = 196 000 ÷ 48  M                     Answer for A: 1 mark
                              = 4 083,33 CA                     Dividing A by 48: 1 mark
                                                                          Answer: 1 mark
        or                                                                14 000: 1 mark
        10% of 140 000      =       14 000  M                     × 4 years: 1 mark
         14 000 × 4 years   =       56 000      M                       56 000: 1 mark
         140 000 + 56 000 =         196 000M                        Answer for A: 1 mark
         196000 ÷ 48      ℎ =       4083,33       ℎ M/ CA      Dividing A by 48: 1 mark
                                                                          Answer: 1 mark      (6)

2.7     5 8                                                          Answer: 2 marks
         ∶ = 5 ∶ 8
        3 3
                                                                                             (2)
2.8     Amount = 155,50 ×                                      Calculation:2 marks
        = 93,30
                                                                      Answer: 1 mark         (3)

2.9      . . =         
                                                                     Formula: 1 mark
        3000( )(0,8) = 960      
           =4                          or                       Substitution: 1mark
                                                                      Answer: 1 mark
              = (1 + )
        3960 = 3000(1 + 0,08 )
         0,32 = 1 + 0,08
        0,32 = 0,08                                                                          (3)
          = 4

2.10       = (1 + )                                               Formula: 1 mark
           = 10 000(1 + 0, 1)                                   Substitution: 1mark
                                                                                             (3)
           = R13 310,00                                            Answer: 1 mark

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3. PATTERNS, FUNCTIONS AND ALGEBRA

3.1.1     (2 ) + 3
         =4 +3  M                                                      4 : 1 mark
         = 7  CA                                                     Answer: 1 mark
                                                                                         (2)
3.1.2           2            ×                                    Numerator: 1 mark
                                                                Denominator: 1 mark
         =  A
                                                                                         (2 )
3.1.3
            (   )

        =      M                                                     4     : 1 mark
        = 4  CA                                                          4 : 1 mark
                                                                      Answer: 1 mark
        = 64  A
                                                                                         (3)
3.2.1    3                       (3 − 4 − )                     1 mark for each term
        =9                        − 12   −3       A
                                                                                         (3)
3.2.2     (2 − 3)( + 1)                                            Answer: 2 marks
        = 2 − − 3 A                                        (deduct a mark for each
                                                                               error)    (2 )
3.2.3              .                                                       : 1 mark
        =                                                          Answer:1 mark        (2)
3.3.1     10 − 5                                                         5 : 1 mark
        = 5 (2 − 1)  A                                             2 − 1: 1 mark
                                                                                         (2)
3.3.2     81 − 100                                                 9 − 10 : 1 mark
        = (9 − 10 )(9 + 10 )A                                    9 + 10 : 1 mark
                                                                                         (2 )
3.4.1               2 − 5 = 5 + 16                                     −3  : 1 mark
                    −3  = 21  M                                        21: 1 mark
                          = −7  A                                    Answer:1 mark
                                                                                         (3)
3.4.2                   ( − 2) (2 + 1) 5
                              +       =
                          4       3     3
         × 12
             12      + 12(   ) = 12 ×
                                                                  3( − 2): 1 mark
         3( − 2) + 4(2 + 1) = 4 × 5 M
                                                                 4(2 + 1): 1 mark
                3 − 6 + 8 + 4 = 20  M
                                                                     4 × 5: 1 mark
                           11 = 22                               Simplifying: 1 mark
                              =2 A                                 Answer: 1mark        (5 )

3.5     −16 − 12 − 18 + 2 = −44                          Substitution: 1 mark
                                                             Simplifying: 2 marks        (4)
                                                                Answer: 1 mark
3.6     20                   +8        − 12                   20       : 1 mark
                                                                   8      : 1 mark
                                                                      −12     :1 mark
                                                                                         (3)
3.7.1   (               )(        )=                            (         ): 1 mark
                                                                              : 1 mark   (2)

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3.7.2        +                                      Answer: 2 marks
                                                                           (2 )

3.7.3                                           Simplifying: 2 marks
                                                     Answer: 1 mark
         = 8                                                              (3)
3.7.4      −2     −3                              Simplifying: 4 marks
              –
          2      3                                   Answer: 1 mark
              (   ) (           )
         =                          
         =                     
         =       
                                                                           (5 )
         =            

3.7.5             ×            =                 Simplifying: 1 mark
                                                      Answer: 1 mark
                                                                           (2)
3.7.6    (       )(       )                         Difference of two
             (        )
                          
                                                            squares:
         =                                                    1 mark
                                                Common factor: 1 mark
                                                     Answer: 1 mark        (3 )

3.8.1    3 (          − 3 − 2)                  Common factor3 : 1
                                                               mark
                                                                           (2 )
                                                  Factor − 3 − 2: 1
                                                               mark

3.8.2    ( + )(4 − )                              Common factor: 2
         = ( + )(2 + )(2 − )                                  marks
                                                     Difference of two
                                                             squares:      (4 )
                                                              2 marks

3.9.1    8 + 3 = 3 − 22                             Simplifying:1 mark
         8 − 3 = −22 − 3                              Answer: 1 mark
            5 = −25
               = −5                                                       (2)

3.9.2           −1                                  Multiplying by 2: 1
             −        =3                                          mark
                2
             2 − + 1 = 6                           Simplifying:1 mark
                  + 1 = 6                            Answer: 1 mark       (3 )
                      = 5

3.9.3        3 =3                                Applying exponential
             + 1 = 4                                     law: 2 marks
                = 3                                   Answer: 1 mark      (3 )

3.10.1   13A , 17A                                     1 mark per term   (2)

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3.10.2   The number of sides increase by 4 to get the next diagramA    Correct deduction: 1 mark    (1)
3.10.3        = 4 + 1A                                                              4 :1 mark
                                                                                      +1: 1 mark     (2)

3.11.1
                                                                             Answer: 2 marks
          1        2          3
          6        9          12
                                                15 matches                                         (2)

3.11.2   Tn = 3n + 3                                                            3n: 1 mark
                                                                                    3:1 mark
                                                                            (1 mark per term)        (2)

3.11.3        = 3(20) + 3 = 63                                         Substitution: 1 mark
                                                                            Answer :1 mark           (2)

3.12       = 2 −3 +5
           = 2(−1) − 3(−1) + 5M                                              substitution: 1 mark
           = 10CA                                                               Answer: 1 mark      (2)

3.13.1     = 2A                                                                 Answer: 1 mark      (1)

3.13.2     = 2 A                                                              Answer: 2 marks      (2)

3.13.3   (2; −2)A                                                                    2: 1 mark
                                                                                      −2: 1 mark     (2)

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3.14.1

                                                                          y=3x+1

                                                                                     y=3x-2
                                                                           .
                                                                           .4
                                                                          .3              = 3 + 1
                                                                           .2                  = 3 − 2
                                                                             .1
                              -5            -4    -3    -2       -1                .0         1   2     3     4
         5
                                                                 1         2
                                      .-1
                                                                 3         3
                                                                          .-2
                                                                           .-3
                                .-4
                              .-5

         X-intercept: 1 mark per graph+A
         Y-intercept: 1 mark per graph+A
         Correct labelling of graph: 1 mark per graph +A
                                                                                                                            (6)

3.14.2   The lines are parallel or the lines will never cut.A                                                              (1)

3.15         (3; 3)                                                                                    Answer: 1 mark     (1)

3.16.1                                =          = −2                              = −2    +              −2 : 1 mark
                                                                                                             4:1 mark
         4
                                                             4
                                                        =       = −2
                                                             −2
                                      = −2 − 4
                                                                                                          −2 : 1 mark
                                                                                                            −4:1 mark      (4)

3.16.2   AD || BC                                                                                  AD || BC : 1 mark
         (because the Gradient of AD = Gradient of BC)                                               Reason :1 mark       (2)

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4. SPACE AND SHAPE

4.1          = 95° − 30°               (ext. ∠ of ∆   ) M/ A          correct statement with reason:1 mark
             = 65° A                                                                 Answer for : 1 mark
        or
                         = 180° − 95°    (ext. ∠ of ∆  )
                         = 85°
             + 85° + 30° = 180° (sum of ∠s of ∆= 180°) M/ A
                 + 115° = 180°
                         = 65° A
                                                                       correct statement with reason:1 mark
                     + = 180° (co - interior <s AB || CD) M/ A
                                                                                      Answer for : 1 mark      (4)
                         = 115° A

4.2           In ∆                 ∆
                          =                  (Common) A              correct statement with reason:1 mark
                          =            = 90° (Given) A               correct statement with reason:1 mark
                          =                   (Given) A               correct statement with reason:1mark
              ∴∆          ≡∆                  (90°Hyp S) A            correct deduction and reason:1 mark     (4)

4.3.1         +    +       + = 180° (co-int ∠ ; || ) A              Correct statement with reason: 1 mark
        But       =       and =       (given) A                     Correct statement with reason: 1 mark
                                                                                 Correct deduction: 1 mark
                  ∴2      + 2 = 180°A                                               Simplification: 1 mark
                           + = 90°A                                 Correct deduction with reason: 1 mark
                              = 90°(sum of ∠ of ∆= 180°)                                                      (5)

4.3.2   ∆         ||| ∆            (      )A                      Correct statement with reason: 2 marks     (2)

4.3.3        =       =         (prop. sides of similar ∆ ) A        Correct statement with reason: 1 mark
                                                                     Correct statement with reason: 1 mark
                                                                                           Answer: 1 mark
              =                (       =2      ) A

        1   4
          =
        2
                                                                                                               (3)
              =8          A

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4.4.1         (−5; 4) A                                            Correct pair of co – ordinate:1 mark each
               (−4; 2)A                                                                                         (2)

4.4.2

          A                                    B          B’                        A’

                  D                C                           C’           D’

correct shape: 1 mark A
correct coordinates of the image: 1 mark A
                                                                                                                 (2)
4.4.3         (5; 4)                                                               1 mark per co - ordinate
              (4; 2)                                                                                            (2)

4.5        No .of faces : 5A                                                      1 mark per correct answer
           No. of vertices : 6A
                                                                                                                 (3)
           No. of edges : 9A
4.6        In ∆AEW :
              +       = 110° (sum of <s of ∆ = 180°)
           but    =      (angles opp. equal sides of ∆)                 Statement with reason: 1 mark
                                                                        Statement with reason:1 mark
                                       = 55°                            Statement with reason:1 mark            (3)
              =       = 55° (alt <s ; CS || HW)

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4.7.1   In ∆ ABD and ∆ ACD                                            statement with reason: 1 mark
            AB = AC          (given)                           statement with reason: 1 mark
                                                             statement with reason: 1 mark
            BD = CD          (given)                                          Correct case: 1 mark
           AD = AD           ( common side)
        ∴∆ ABD ≡ ∆ AC         (s,s,s)
                                                                                                           (4)
4.7.2     = (corr<s of congruent ∆s)                         Correct statement with reason:1 mark
        DA bisects BÂC                                                         Conclusion:1 mark          (2)

4.8             + 50° + 2 − 20° = 180°                               Statement with reason: 1 mark
                                                                     Statement with reason:1 mark
              (co-interior<e; AB || CD)
                   3 + 30° = 180°                                                         : 1 mark
                       3 = 150°                                            : 1 mark
           = 50° 
           + + 50° = 180°
          (co-interior <e; AC || BD)
                     + 100° = 180°
           = 80°                                                                                          (4)

5. MEASUREMENT

5.1     Surface area = 6 M/ A
                     = 6(6  )                                              Formula/ substitution: 1 mark
                     = 216  A                                                         Answer: 1 mark
                                                                                                            (2)

5.2.1   Volume of cylinder =       ℎM                                                 Formula: 1 mark

                            =   × 9 × 100      M                                   Substitution: 1 mark

                            = 25 446,90       CA                                       Answer: 1 mark      (3)

5.2.2   Volume of rectangular = ℎ M                                                   Formula: 1 mark
                               = 30 × 14 × 8   M                                   Substitution: 1 mark
                               = 3 360     CA                                          Answer: 1 mark
                                                                                                            (3)

5.2.3   Number of rectangular prisms      =                  M
                                                    ,
                                                                                      Formula: 1 mark
                                          =        M                              Substitution: 1 mark
                                          = 7,573 …
                                          = 7 CA                                      Answer: 1 mark       (3)

                                                        10

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5.3              = 12 + 5         (    ℎ)                         Formula/substitution:
                 = 169                                                          1 mark
                = 13                                               Calculation: 1 mark
                                                                       Answer: 1 mark
                                                                                              (3)
5.4     Volume = 5000                                                  Formula:1 mark
           ℎ = 5000                                                Substitution: 1 mark
         (20) ℎ = 5000                                                Answer: 1 mark
                ℎ = 4,0       
                                                                                              (3)

6. DATA HANDLING

6.1.1    24 passengers A                                                  Answer: 1 mark     (1)

6.1.2    Range = (70 − 1)             = 69   A                            Answer: 1 mark     (1)

6.1.3   Mean age =                                                               Formula/
            (                                                 )
                                                                              substitution:
        =                                                           M             1 mark
        =            M                                                      Calculations:
                                                                                   1 mark
        = 26,71                                                            Answer: 1 mark
        = 27         CA                                                                      (3)

6.2.1   Amount = 19% of 105
               =   × 105       M                                  × 105         : 1 mark
                                                                           Answer: 1 mark      (2)
               = 19,95      CA

6.2.2   Percentage = 17% + 14% = 31% A                                    Answer: 1 mark      (1)

6.2.3   Amount = (19% + 11%) of 105
               = 30% of 105      M                           30% of 105       : 1 mark
               = 31,5       A                                           Answer: 1 mark
        or                                                                           or
        Amount = 19% of 105       + 11% of 105              19% of 105       + 11% of
               = 11,55        + 19,95       M                       105       : 1 mark
               = 31,5       A                                           Answer: 1 mark        (2)

6.3.1

                  Stem                  Leaves
                    0         3 5 6 7 9                A
                    1         0 1 1 1 3 3 4 5 7        A
                    2         0 1 2 3 3 6              A                                      (3)

6.3.2   Range = 26 − 3 = 23 A                                             Answer: 1 mark      (1)

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6.3.3     Median mark = 13 A                                                                     Answer: 1 mark      (1)

6.3.4     Modal mark = 11 A                                                                      Answer: 1 mark      (1)

6.4.1                                          Win (W)                  Draw (D )            Loss (L )
                  Win                           WW                        WD          WL                  A
                  Draw                          DW                         DD         DL                  A
                  Loss                           LW                        LD         LL                  A          (3)

6.4.2.1    A                                                                                     Answer: 1 mark      (1)

6.4.2.2    A                                                                                     Answer: 1 mark      (1)

6.4.2.3    A                                                                                     Answer: 1 mark
                                                                                                                      (1)
6.5.1
                                                                                              For each correct
           Class-interval         Tally marks                 Frequency
                                                                                              interval: 2 marks
           140-144                ||||                           4
           145-149                |||                            3
           150-154                |||| ||||                      9
           155-159                |||| |                         6
           160-164                |||| ||||                      10
           165-169                ||||                           5
           170-174                |||                            3
                                                                                                                     (14)
6.5.2     Range = 174 − 140 
                                                                                               Answer:2 marks
                = 34                                                                                                 (2)
6.5.3     160 − 164                                                                                                 (2)
                                                                                               Answer: 2marks
6.5.4                               <                         <
                                                                                               Answer: 2marks
          Class-interval 155 - 159                                                                                  (2)

7. PROBLEM SOLVING

            A     :      B    :           C      :   Total
            4     :      3
                         4    :           3
           16     :      12   :           9      :       37

          A’s share =    × 148 = 64 A                                              Each correct statement: 1 mark
          B’s share =    × 148 = 48 
          C’s share =    × 148 = 36 
          or

          C’s share = R148 − R112
                    = R36                                                                                            (3)
                                                                  END
                                                                  12

Grade 9 Mathematics Exemplar Memorandum

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- [KZN Zululand Maths Grade 9 March 2025 QP and Memo](https://www.hlayiso.com/library/kzn-zululand-maths-grade-9-march-2025-qp-and-memo/a5d0e368-52a3-4816-b3aa-3597ee4f5a9f) — QP + Memo · 2025
- [Maths Grade 9 June 2025 QP and Memo](https://www.hlayiso.com/library/maths-grade-9-june-2025-qp-and-memo/1c92dc3a-8522-46ea-9bc2-251685906fd8) — QP + Memo · 2025
- [2024 G9 Mock June Test Free State](https://www.hlayiso.com/library/grade-9-mathematics-2024-free-state-june-exam-question-paper/3628eaa4-69bb-4e63-a6b9-8c072d118cdb) — QP · 2024
- [2024 G9 Mock June Test Free State.docx](https://www.hlayiso.com/library/grade-9-mathematics-2024-free-state-june-exam-question-paper/7d033d41-fed7-4c04-a7cc-78d6c025aa9b) — QP · 2024

## Collection

- [Grade 9 past papers](https://www.hlayiso.com/grade-9/past-papers)

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Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.