# Mathematics Grade 9 BRAILLE 2012 Memo (English)

> Grade 9 Mathematics memorandum from the BRAILLE 2012 (English), 9 pages. Read online or get the free PDF download, question paper linked when available.

- Page: https://www.hlayiso.com/library/grade-9-english-maths-memo-braille/96027be1-21de-423a-b2ba-0fe08d4bf301
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 9
- Language: English
- Document type: Memorandum
- Year: 2012
- Exam period: BRAILLE
- Curriculum: CAPS
- Pages: 9

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## About this document

Mathematics · Grade 9 · BRAILLE · 2012 · English. Memorandum, 9 pages. Read online or download the PDF.

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## Document text

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DEPARTMENT OF BASIC EDUCATION
REPUBLIC OF SOUTH AFRICA

ANNUAL NATIONAL ASSESSMENT 2012
GRADE 9 MATHEMATICS
TEST (BRAILLE)
MEMORANDUM

MARKS: 140
This memorandum consists of 9 pages.

Important Information
        This is a marking guideline. In instances where learners have used different but mathematically sound strategies to solve
         the problems they should be credited.
        Unless stated otherwise, learners who give a correct answer only, should be awarded full marks.
        Apply consistency accuracy and underline errors committed by learners.

                              KEY
           M          Method mark
           CA         Consistent Accuracy mark
           A          Accuracy mark

QUESTION 1

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

QUESTION 2
2.1              3,56 × 10       A                                                                                 Answer: 1 mark       (1 )

2.2.1             (3 ) + 2                                                                                   27    +2    : 1 mark
                  = 27 + 2  A
                  =   29  CA                                                                           Answer = 29      : 1 mark    (2)

2.2.2            a²b² 4a²bc                                                                                       Answer: 2 marks
                     ×
                 ac² 20b³                                                                                                :: 1 mark
                 =               M
                                                                                                                          : 1 mark
                                                                                                                                        (2 )
                 =       

Grade 9 Mathematics Memorandum (Braille)                             1

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2.3.1    4ab (5 ² ²+ 2 −3)                        Distributive law: 1 mark each term
         = 20      +8        − 12      A                         20      : 1 mark
                                                                   8       : 1 mark
                                                                 −12       : 1 mark     (3 )

2.3.2    (2 − 1) − ( + 1)( − 1)                                  Expanding: 1 mark
                                                                 Simplifying: 1 mark
         =4   − 4 + 1 (−       + 1 M                              Answer: 1 mark     (3)
         =3   −4 +2               CA

2.4.1    8 ³+4 ²                                            Common factor: 1 mark
                                                              (2 + 1): 1 mark          (2)
         = 4 ²  (2   + 1) A

2.4.2    9 ²−36 ²
         = 9( ²−4 ²)  M
         = 9( − 2 )( + 2 ) A
         OR
         = (3 − 6 )(3 + 6 ) A
         = 3( − 2 )3( + 2 )
                                                            Common factor: 1 mark
         = 9( − 2 )( + 2 ) A                     Difference of two squares: 1 mark     (2 )

2.4.3      − −2 +2
         = ( − ) − 2( − ) M/A                          Common factor t: 1mark
         = ( − ) ( − 2) M/A                           Common factor 2: 1mark
                                                   Common factor( − ): 2marks
         OR

         = ( − 2) − ( − 2)
         = ( − 2)( − )
                                                                                        (4)

2.5.1    3( + 6) = 12                                          Dividing by 3: 1 mark
             + 6 = 4 M                                              Answer:1 mark
             = −2 CA                                                           OR

         OR                                                 −18 both sides:1 mark
                                                                  Answer:1 mark        (2 )
         3 + 18 = 12
             3 = −6 M
                = −2 CA

2.5.2        −2 = 0                                         Common factor: 1 mark
          ( − 2) = 0 M                                          Answer: 2 marks
                                                               (1 mark per factor)     (3 )
           = 0 or = 2 CA

Grade 9 Mathematics Memorandum (Braille)      2

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2.5.3         +1            −1                                                             Multiplying by 6: 1 mark
                 –             =1                                                               Expanding: 1 mark
              3             6                                                                       Answer: 1 mark    (3 )

         2( + 1) − ( − 1) = 6 M
            2 + 2 − + 1 = 6 CA
                          = 3 CA

2.5.4    2       = 32                                                                               2 : 1 mark
                                                                               Applying exponential law:1 mark
             2        =2 M
                                                                                              Answer: 1 mark          (3 )
             + 1 = 5 M/ CA
                                                                                                                      [30]
             = 4 CA
QUESTION 3

3.1                           3
         Number of boys = 4  × 240 = 180 M /CA
                                                                                                         3
                                                                                                         : 1 mark
                                                                                                         4
                                                                                                   Answer: 1 mark     (2)

3.2      Speed =              M/ A                                                  Formula / Substitution: 1 mark
         40          /ℎ =
                  × 60        M                                                                 0,225: 1 mark
                                                                                                                      (3)
         OR 0,225 × 60 minutes                                                                     Answer: 1 mark
         = 13,5         CA
3.3          (1 + )  M/ A
             =                             OR
                                                                                                  Formula: 1 mark
         = 12 000(1 + 0,065)  M
         = 16 441,04 CA                   Year 1: 12 000 x 6,5% = 780                         Substitution: 1mark
                                           Year 2: 12 780 x 6,5% = 830,70                                             (3)
                                           Year 3: 13 610,7 x 6,5% = 884,70                        Answer: 1 mark
         OR
                                           Year 4: 14 495,4 x 6,5% = 942,20
                                           Year 5: 15 437,6 x 6,5% = 1 003,44
             =        1+                  There will be R16 441,04 in his account
                                  ,
         = 12 000 1 +                 
         = 16 441,04

3.4.1    15% cash =           × 15 000                                                             Answer: 1 mark     (1)
                        = 2 250 A

3.4.2         = (1 + ) CA from 3.4.1                                                             Formula: 1 mark
              = 12 750[1 + 2(0,1)]
              = 15 300                                                                       Substitution: 2 marks
         OR                                                                                        Answer: 1 mark
                                                                                                               OR
                 =      
                                                                                                  Formula: 1 mark

Grade 9 Mathematics Memorandum (Braille)            3

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                                                                           Substitution: 1mark
                             ( )(     )
              =                                                              Answer: 1 mark
                                                                                                  (4)
                                                                              Answer: 1 mark
                           = 2 250
         Total amount= 12 750 + 2 250
                    = 15 300

3.4.3    Monthly payments = 15 300 ÷ 24 CA from 3.4.1                  15 300 ÷ 24: 1mark
                         = 637,50                                            Answer: 1 mark      (2)

                                                                                                   [15]
QUESTION 4

4.1      18        23 A                                                     Answer: 2marks
                                                                              1 mark per term     (2)

4.2      Add 5 to the last term to get the next. A                   Correct answer: 1mark       (1)

4.3          = 5 − 2 A                                                     Answer: 2 marks      (2)

4.4         = 5 − 2 CA from 4.3                           Substitution into the formula: 1 mark
         38 = 5 − 2 CA                                               Solving equation: 1 mark
         40 = 5  M                                                             Answer: 1 mark     (3)
         ∴8 = A
                                                                                                  [ ]

Grade 9 Mathematics Memorandum (Braille)              4

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QUESTION 5

5.1.1      Parallel A                                     Answer: 1 mark     (1)

5.1.2        = −2 A                                       Answer: 1 mark     (1)

5.1.3      4 A                                            Answer: 1 mark     (1)

5.1.4      Non-linear  A                                  Answer: 1 mark     (1)

5.2.1

X-intercept and Y-intercept: 2 marks per graph +
Gradient: 1 mark per graph+
Correct Labelling of graph: 1 mark per graph +(8)

Grade 9 Mathematics Memorandum (Braille)               5

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5.2.2   At point of intersection:−2 + 1 =    − 2                                              Equation:1mark
                                               −3 = −3                                         Answer: 1 mark          (2)
                                                    =1
                                     = (1) − 2 = −1
                                    ∴ (1; −1)
        OR

             = −2 + 1            = 1; = (−2(1) + 1) = −1
             = −2               = 1; = 1− = −1

        Therefore, this point lies on both graphs and it must be the point of intersection                             [14]

QUESTION 6

6.1     6.1.1     2 + 3 + 4 = 180° (TQ S is a straight angle) M/ A                                     Statement: 1 mark
                          9 = 180°                                                                         Reason: 1 mark
                             = 20° A                                                                                           (3)
                                                                                                           Answer: 1 mark

        6.1.2      = 3  (alternate Ls ;PQ|| RS) M                                                       Statement: 1mark
                   = 60°  CA for 6.1.1                                                                     Reason: 1 mark
                                                                                                            Answer: 1 mark      (3)

         6.1.3        =          (corresponding Ls; PQ|| RS
                                                        =2 °
                      = 40° M

                  OR

                      +     +    = 180° (sum of Ls of ∆ = 180 ) M
                                              4 + + = 180°
                                            80° + 60° + = 180°
                                                  = 180° − 140
                                                 = 40° A
                  OR

                       +      =         +  (ext L of    = sum ofintoppLs) M
                  2 +3 = +
                  5 = 60° +                                                                              Statement: 1 mark
                  100° = 60° +                                                                             Reason: 1 mark
                   = 40° A                                                                                Answer: 1 mark       (3)

6.2      ∆       ≡∆                (S, <, S) A                        Statement with vertices in the correct order: 1 mark
                                                                                                           Reason : 1 mark      (2)

         6.3.1    In ∆ ABD and ∆ ACD                                                Correct statement with reason: 1 mark
                       AB = AC       (given)  A                                    Correct statement with reason: 1 mark
                                                                                    Correct statement with reason: 1 mark
                          BD = CD        (given) A                                Correct deduction and reason : 1 mark        (4)
                         AD = AD   ( common side) A
                      ∆ ABD ≡ ∆ ACD (s,s,s) A

Grade 9 Mathematics Memorandum (Braille)                  6

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                  OR
                  In ∆ ABD and ∆ ACD
                   ABD =  ACD (opposite angles of a kite)
                  AB = AC               (given) 
                  BD = CD      (given)
                   ∆ ABD ≡ ∆ ACD (s,  , s)

         6.3.2    In ∆ ABE and ∆ ACE
                  AB = AC              (given)  A
                  AE = AE      (common side) A
                       =     corr. <s of congr. ∆s/ bisecting diagonals)  A
                   ∆ ABE≡ ∆ ACE (s,L,s) A

                  OR

                  In ∆ ABE and ∆ ACE
                  AB = AC              (given) 
                                                                                          Correct statement with reason: 1 mark
                            =                (L opp = sides of )                         Correct statement with reason: 1 mark
                            =         corr. <s of congr. ∆s) or BE=EC (AD bisects BC)    Correct statement with reason: 1 mark
                                                                                          Correct deduction and reason: 1 mark             (4)
                      ∆ ABE≡ ∆ ACE (L, L,s)

         6.3.3              +         = 180°( B C is str L) A                            Correct statement with reason: 1 mark
                                                                                          Correct statement with reason: 1 mark
                      But         =        (corr. <s of congr. ∆s) A                                       Conclusion: 1 mark             (3)
                       ∴          =         = 90° A

                  OR
                  BC  AD  (diagonals of a kite) 

         6.3.4    AE is perpendicular to BC A                                                                   Answer: 1 mark            (1)

6.4    =     (proportional sides of similar∆ ) A                                       Proportional sides and reason: 2 marks
                                                                                                             substitution: 1 mark
        =        A                                                                                              Answer: 1 mark
                                                                                                                                     (4)
         (15)(6)
       =
           10
       = 9    A
                                                                                                                              [27]

QUESTION7

7.1         (−1; 1)            ′(1; 1) A                                                                   Answer:2 marks
                                                                                               1 mark per pair of co-ordinates         (2)

7.2         (1; 7)         ′(1; 1) A                                                                       Answer:2 marks
                                                                                               1 mark per pair of co-ordinates         (2)

Grade 9 Mathematics Memorandum (Braille)                         7

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7.3        The perimeter = (3 + 1,5 + 1 + 1 + 2 + 0,5)               =9                        Length of reduced sides: 1 mark
           M/A                                                                                                   Answer: 1 mark            (2)
           OR
           (6+3+2+2+4+1)÷2= 9 units

7.4        Area of fig. P: Area of reduced fig = 4: 1 M/ A                                                  Answer: 2marks
           OR                                                                             (Dimensions halved:Area of original)            (2)
           Area of fig P to Area of reduced Fig = 1:0,25 or 1:
           OR
           Area of fig P to Area of reduced Fig = 10:2,5

                                                                                                                                          [8]

QUESTION 8

8.1
             3-D figure           Name of figure          No. of       No. of vertices    No. of      1 mark
                                                          faces                           edges       for each
                                                                                                      answer

                                Cylinder             3 faces        No vertices        2
                                                                                         edges

      Shape of the faces: Circles and a rectangle
                                                                                                                  (6)

8.2        The surface area of a rectangular prism is:                                   Formula/ substitution into the correct
           = 2( × ) + 2( × ℎ) + 2( × ℎ)                                                                     formula: 3 marks
           = 2(7,2 × 5) + 2(7,2 × 3,32) + 2(5 × 3,32)                M/ A                               Calculation: 1 mark       (5)
                                                                                                              Answer: 1 mark
           = (72 + 47,808 + 33,2)               CA
                                                                                                    Wrong formula: 0 marks
           = 153, 01       CA
           OR

           2 + 2( + )ℎ
           = 2(7,2 × 5) + 2(7,2 + 5)3,32
           = 72 + 81,01       
           = 153,01 

8.3       Volume of a cylinder = 1 000                                                        Formula &substitution: 2 marks
                           ℎ = 1 000     M                                                            Calculation: 1 mark
                 (2,82) ℎ = 1 000       M                                                                 Answer: 1 mark           (4)
                           ℎ = 40     
                           ℎ = 40,0268             ≈ 40              CA
                                                                                                                                        [15]

Grade 9 Mathematics Memorandum (Braille)                        8

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QUESTION 9

9.1.1       Class Interval                 Tally marks       Frequency   1 mark per interval

               1 – 10                         ___               0

              11 – 20                                           2        
                                               II
              21 – 30                                           12       
                              IIIIIIIIII
              31 – 40                                           9        
                              IIII IIII
              41 – 50                                           7        
                              IIII II
                                                                         A                                               (4)

9.1.2 (a)         Modal class is 11 – 20                                                        answer                  (1)

9.1.2 (b)         A=9                                                                           answer                  (1)

9.1.2 (c)         B = 20                                                                        answer                  (1)

9.1.2 (d)         16                                                                            answer                  (1)

9.2.1        Range = 10 − 5 = 5  A                                                             Range: 1 mark
                 5 5 6 7 8 9 9 9 9 10                                                           Median: 1 mark           (2)
             Median = 8 A

9.2.2        Mode = 5                                                                             Answer: 1 mark        (1)

9.2.3        Mean=                            M                                                   Formula:1 mark
                                                                                                   Answer: 1 mark   (2)

                 = 6 A

                                                                                                                        [13]

                                                                                                          TOTAL: 140

Grade 9 Mathematics Memorandum (Braille)                 9

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