# Mathematics Grade 12 P2 Western Cape Mock 2016 QP

> Grade 12 Mathematics Paper 2 question paper from the Western Cape Mock Exam 2016, 14 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/grade-12-mathematics-2016-western-cape-mock-exam-question-paper-paper-2/65f72271-0936-441f-a991-8599bb002886
- Updated: 2026-09-28
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2016
- Exam period: Western Cape Mock Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 14

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## About this document

Mathematics · Grade 12 · Western Cape Mock Exam · 2016. Question paper, 14 pages. Read online or download the PDF.

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## Document text

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### Page 1

YOUR SCHOOL NAME

                                   NATIONAL
                              SENIOR CERTIFICATE

                                        GRADE 12

                                         MATH.2

                                  MATHEMATICS P2

                                   SEPTEMBER 2016

MARKS: 150

TIME: 3 hours

                This question paper consists of 13 pages, 1 information sheet
                                   and an answer book.

### Page 2

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.       This question paper consists of 11 questions.

2.       Answer ALL the questions in the SPECIAL ANSWER BOOK provided.

3.       Clearly show ALL calculations, diagrams, graphs et cetera that you used to determine
         the answers.

4.       Answers only will NOT necessarily be awarded full marks.

5.       If necessary, round off answers to TWO decimal places, unless stated otherwise.

6.       Diagrams are NOT necessarily drawn to scale.

7.       You may use an approved scientific              calculator   (non-programmable    and
         non-graphical), unless stated otherwise.

8.       An INFORMATION SHEET with formulae is included at the end of the question
         paper.

9.       Write neatly and legibly.

                                                                                   Turn over please

### Page 3

Gr 12 Mathematics P2                              3                                   September 2016

QUESTION 1

  Learners were asked the time (to the nearest minute) that they usually take to get from home
 to school each morning. The results are shown in the table below:

                              Time in minutes Number of learners

                                  5 < t  10               160
                                 10 < t  15               150
                                 15 < t  20               110
                                 20 < t  25               60
                                 25 < t  30               45
                                 30 < t  35               15

1.1       Complete the cumulative frequency column in the ANSWER BOOK provided.                            (2)

1.2       Draw the ogive of these data on the grid provided in the ANSWER BOOK.                            (4)

1.3       Calculate the mean time that these learners take to get to school in the morning.                (2)

1.4       Calculate the standard deviation of this data.                                                   (2)

1.5       Use the ogive to determine approximately how many learners would take more than
          one standard deviation from the average time it takes learners to get to school.                 (3)
                                                                                                           [13]

                                                                                        Please turn over

### Page 4

Gr 12 Mathematics P2                               4                               September 2016

QUESTION 2

The table shows the number of athletes and total amount of medals that some countries obtained
during the 2012 Summer Olympics.

(Information according to: http://www.wow.com/wiki/2012_London_Olympics)

                                                 Number of       Number of
                Country
                                                  athletes        medals
                USA                                 530            103
                China                                  396           88
                Great Brittan                          541           65
                Russia                                 436           79
                South Korea                            245           28
                Germany                                392           44
                France                                 330           34
                Australia                              410           35
                South-Africa                           133            6
                Canada                                 277           18
                Netherland                             175           20
                New Zealand                            184           13
2.1       Use the table to determine the equation of the least squares regression line for the
          data.                                                                                         (3)

2.2       Calculate the correlation coefficient for the data.                                           (1)

2.3       How many medals (to the nearest integer) can be predicted, will a country with 350
                                                                                                        (2)
          athletes obtain?

2.4       Comment on the correlation between the number of participating athletes and the
          number of medals obtained by a country.                                                       (1)
                                                                                                        [7]

                                                                                     Please turn over

### Page 5

Gr 12 Mathematics P2                                  5                            September 2016

QUESTION 3

In the diagram below, ABC is an isosceles triangle with A(2;1) and B(4 ; 9). AB = BC and
BC is parallel to the 𝑦-axis.

                                                  𝒚                C

                                                               𝜃

                                                          •K
                                                                   B (4 ; 9)

                                A (–2 ; 1)
                                                                               𝒙

          3.1          Calculate the length of AB.                                                     (2)

          3.2          Calculate the coordinates of C.                                                 (2)

          3.3          Calculate the coordinates of K, the midpoint of AC.                             (2)

          3.4          Determine the equation of AC in the form y = mx + c.                            (3)

          3.5          Calculate the size of 𝜃.                                                        (4)

          3.6          Calculate the area of ABC.                                                     (4)
                                                                                                       [17]

                                                                                    Please turn over

### Page 6

Gr 12 Mathematics P2                                6                                      September 2016

QUESTION 4

The diagram below consists of two circles, which touch each other externally at C (1 ; –2). The
smaller circle has its centre O at the origin. The other circle has centre D(𝑡 ; –6). CA is a
common tangent which intersects the 𝑥-axis at A. CDE is the diameter of the larger circle.

                                      𝒚

                                                                           𝒙
                                       O                      A

                                               C (1 ; –2)

                                                        D (𝑡 ;–6)

                                                               E

4.1       Give a reason why the points O, C and D lie on a straight line.                                      (2)

4.2       Calculate the gradient of OC.                                                                        (2)

4.3       Hence, show that the value of 𝑡 = 3.                                                                 (2)

4.4       Determine the equation of the tangent AC in the form y = mx + c.                                     (3)

4.5       Calculate the coordinates of E.                                                                      (2)

4.6       Determine the equation of a circle passing through the points A(5 ; 0), C and E in the
          form ( x  a)2  ( y  b)2  r 2 .                                                                   (6)

4.7       If a circle centre D with equation ( x  3)2  ( y  6)2  r 2 has to cut the circle centre O
          twice, give all possible values of r.                                                                (4)
                                                                                                               [21]

                                                                                            Please turn over

### Page 7

Gr 12 Mathematics P2                                  7                                 September 2016

QUESTION 5

5.1       If sin 34° = 𝑝, determine the value of each of the following in terms of 𝑝,
          WITHOUT USING A CALCULATOR.

          5.1.1        sin 214°                                                                             (2)

          5.1.2        cos 34° . cos(− 22°) + cos56°. sin 338°                                              (4)

          5.1.3        cos 68°                                                                              (2)

5.2       Determine the value of each of the following expressions:

          5.2.1               cos(90  2 ).sin 
                       sin 2 (180   ). cos(720   )                                                    (6)

          5.2.2           1             1
                          2
                                 
                       sin 2 x       tan 2 2 x                                                              (4)
                                                                                                            [18]

                                                                                         Please turn over

### Page 8

Gr 12 Mathematics P2                                 8                                    September 2016

QUESTION 6

In the diagram, the graph of 𝑓(𝑥) = −sin 2𝑥 is drawn for the interval 𝑥 𝜖 [−90°; 180°].

                                         y

                                     1

                                                                            f

                                                                                                              x
      -90       -60       -30        0          30         60        90         120       150        180

                                    -1

6.1         Draw the graph of 𝑔, where 𝑔(𝑥) = cos(𝑥 − 60°), on the same system of axes for
            the interval 𝑥 𝜖 [−90°; 180°] in the ANSWER BOOK.                                                 (3)

6.2         Determine the general solution of 𝑓(𝑥) = 𝑔(𝑥).                                                    (5)

6.3         Use your graphs to solve 𝑥 if 𝑓(𝑥) ≤ 𝑔(𝑥) for 𝑥 𝜖 [−90°; 180°]                                    (3)

6.4         If the graph of f is shifted 30° left, give the equation of the new graph which is
            formed.                                                                                           (2)

6.5         Which transformation must the graph of g undergo to form the graph of h, where
            h(x) = sin x?                                                                                     (2)
                                                                                                              [15]

                                                                                           Please turn over

### Page 9

Gr 12 Mathematics P2                                9                                   September 2016

QUESTION 7

In the diagram below, D, B and C are points in the same horizontal plane. AC is a vertical pole
and the length of the cable from D to the top of the pole, A, is 𝑝 meters. AC ⊥ CD. AD̂ C= θ ;
DĈ B = (90° − 𝜃) en CB  ̂ D = 2𝜃.

                                              A

                                p

                                              C

                                          90° − 𝜃

                           𝜃

                                                                      2𝜃
                       D                                                      B

7.1       Prove that:
                 p cos
          BD 
                 2 sin                                                                                     (5)

7.2       Calculate the height of the flagpole AC if  = 30° and 𝑝 = 3 meters.                              (2)

7.3                                                                         ̂ B = 70°
          Calculate the length of the cable AB if it is further given that AD                               (5)
                                                                                                            [12]

                                                                                         Please turn over

### Page 10

Gr 12 Mathematics P2                              10                                       September 2016

Give reasons for all statements and calculations in QUESTION 8, 9, 10 and 11.

QUESTION 8

In the diagram, O is the centre of the circle. A, B, C, D and E are points on the circumference of
the circle. Chords BE and CD produced meet at F. Ĉ = 100°, F̂ = 35° and AÊB  55

                                                                                       F

                                                                                 35°

                                 A
                                                                 E
                                                           55°       2
                                                                 1

                                                                             1
                                                                         2       D

                                                  O

                                                                 100°
                                 1                                       C
                                     2
                             B

8.1       Calculate, giving reasons, the size of each of the following angles:

          8.1.1        Â                                                                                      (2)

          8.1.2        Ê1                                                                                     (2)

          8.1.3        D̂1                                                                                     (2)

8.2       Prove, giving reasons, that AB || CF.                                                                (4)
                                                                                                               [10]

                                                                                            Please turn over

### Page 11

Gr 12 Mathematics P2                                 11                               September 2016

QUESTION 9

9.1                                                          ̂ =D
          In the diagram below, ∆ABC and ∆DEF are given with A  ̂ ;B ̂=E ̂ and Ĉ = F̂ . Use
                                                                               DE DF
          the diagram in the ANSWER BOOK to prove the theorem that states that            .
                                                                               AB AC
                                                                                                           (7)
                                                     A                  D
                                                                        •
                                                 •

                                                                E   *   # F

                       B
                             *                            # C

9.2       In the diagram, ABC is a tangent to the circle at B. BDEF is a cyclic quadrilateral with
          DB = BF. BE is drawn and ED produced meets the tangent at A.

                                    C

                                             F

                               B
                                                                        E

                                    D

                       A
          Prove that:

          9.2.1        B̂1  Ê 2                                                                          (3)

          9.2.2        BDA ||| EFB                                                                       (4)

          9.2.3        BD 2  AD. EF                                                                       (2)
                                                                                                           [16]

                                                                                        Please turn over

### Page 12

Gr 12 Mathematics P2                             12                                   September 2016

QUESTION 10

In the diagram, P, S, G, B and D are points on the circumference of the circle such that
PS || DG || AC. ABC is a tangent to the circle at B. GB̂ C = 𝑥.

                                        P                         S

                          D                                 F                   G
                                            E

                              A                                                C
                                                  B
10.1      Give a reason why Ĝ1  x .                                                                         (1)

10.2      Prove that:

          10.2.1              BP . BF
                       BE 
                               BS                                                                             (2)

          10.2.2       BGP ||| BEG                                                                          (4)

          10.2.3       BG 2 BF
                           
                       BP 2 BS                                                                                (3)
                                                                                                              [10]

                                                                                           Please turn over

### Page 13

Gr 12 Mathematics P2                                 13                         September 2016

QUESTION 11

In the diagram, ABC with points D and F on BC and E a point on AC such that EF || AD and

                                     AE 5
DE || BA. Further it is given that      and DF = 20 cm.
                                     EC 4

                                             A

                                                                  E

       B                                         D        20 𝑐𝑚       F                  C

11.1       Calculate, giving reasons, the length of:

           11.1.1      FC                                                                           (3)

           11.1.2      BD                                                                           (4)

11.2       Determine the following ratio:

           Area ∆ ECF
                      =                                                                      (4)
           Area ∆ ABC
                                                                                             [11]
                                                                                         TOTAL: 150

                                                                                 Please turn over

### Page 14

Gr 12 Mathematics P2                                                                                           September 2016
                                             INFORMATION SHEET

          b  b 2  4ac
    x
               2a
    A  P(1  ni)            A  P(1  ni)               A  P(1  i) n                              A  P(1  i) n

    Tn  a  (n  1)d                Sn 
                                            n
                                              2a  (n  1)d 
                                            2

    Tn  ar n1                      Sn 
                                              
                                             a r n 1  ; r 1                            S 
                                                                                                    a
                                                                                                        ; 1  r  1
                                               r 1                                                1 r

    F
           
         x 1  i   1
                     n
                                              P
                                                    x[1  (1  i)n ]
                i                                           i
                    f ( x  h)  f ( x )
    f ' ( x)  lim
               h 0          h
                                                            x  x2 y1  y 2 
     d  ( x 2  x1 ) 2  ( y 2  y1 ) 2                M  1     ;         
                                                            2         2 

                                                                                       y 2  y1
     y  mx  c                      y  y1  m( x  x1 )                         m                         m  tan 
                                                                                       x 2  x1

     x  a 2   y  b2  r 2
                     a     b     c
    InABC:                  
                   sin A sin B sin C

                             a 2  b 2  c 2  2bc. cos A
                                                        1
                             oppervlakte ABC            ab. sin C
                                                        2
    sin     sin  . cos   cos .sin                      sin     sin  . cos   cos .sin 
    cos     cos . cos   sin  . sin                     cos     cos . cos   sin  . sin 
             cos2   sin 2 
             
    cos 2  1  2 sin 2                                        sin 2  2 sin  . cos
             2 cos2   1
             
                                                                              n            2

        fx                                                                   x  x 
                                                                                   i
    x                                                              i 1
                                                                        2

           n                                                                       n
               n( A )
    P(A)                                                         P(A of B) = P(A) + P(B) – P(A en B)
               nS

     yˆ  a  bx                                                  b
                                                                             x  x ( y  y )
                                                                              (x  x)         2

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