# Mathematics Grade 11 P2 North West June 2018 Question Paper

> Grade 11 Mathematics Paper 2 question paper from the North West June 2018, 11 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/mathematics-gr-11-paper-2-1/49e496f7-3959-4248-aafc-0a7605d6f37c
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper
- Year: 2018
- Exam period: North West June
- Paper: 2
- Curriculum: CAPS
- Pages: 11

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## About this document

Mathematics · Grade 11 · North West June · 2018. Question paper, 11 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Document text

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### Page 1

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                                  NATIONAL
                             SENIOR CERTIFICATE

                                         GRADE 11

                                  MATHEMATICS P2
                        MID-YEAR EXAMINATION 2018

MARKS: 100                      JUNE EXAMINATION 2012
TIME:     2 hours

This question paper consists of 8 pages and 3 diagram sheets.

                         Demo
                                 NW/JUNE/MATH/ EMIS/6*******

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Mathematics/ P2                        Mid-Year Examination                          NW/ Jun 2018
                                        NSC- Grade 11

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.       This question paper consists of 6 questions.

2.       AnswerALL the questions.

3.       Number the answers correctly according to the numbering system used in this question paper

4.       Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in
         determining your answers.

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

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

7.       If necessary, answers should be rounded off to TWO decimal places, unless stated
         otherwise.

8.       Diagrams are NOT necessarily drawn to scale.

10.     Write neatly and legibly.

                                                                                                  2
                             Demo
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Mathematics/ P2                         Mid-Year Examination                                 NW/ Jun 2018
                                         NSC- Grade 11

QUESTION 1

1.1     A  1;  1 , B  2;0  and C  5; p  are three points in a Cartesian plane.

        Determine the value(s) of p if:

        1.1.1 A, B and C are collinear.                                                              (2)

        1.1.2 AB is perpendicular to BC.                                                             (3)

        1.1.3 the length of BC is 5 units.                                                           (3)

1.2     In a diagram P  4;5 , Q  4;1 and R  1;  4  are the vertices of a triangle
        in the Cartesian plane with M on PQ. M  2;2  is the midpoint of
        straight line RS.

                                                                  S x ; y 
                                                y

                      P  4;5 

                                                    M  2; 2 
                                                             Q  4;1              x
                                                O

                                R  1;  4 

        1.2.1 Determine the gradient of PQ.                                                          (2)

                         ˆ  90
        1.2.2 Show that PMS                                                                          (3)

        1.2.3 Determine the coordinates of S.                                                        (3)

        1.2.4 Prove that QRS is isosceles.                                                          (3)

        1.2.5 Determine the area of PRS.                                                            (5)

                                                                                                     [24]
                                                                                                           3
                             Demo
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Mathematics/ P2                           Mid-Year Examination                     NW/ Jun 2018
                                           NSC- Grade 11

QUESTION 2

2.1     Given: 17sin  15  0 and 90    270

        With the aid of a sketch and without using a calculator, determine:

        2.1.1 tan                                                                         (3)

        2.1.2 cos   180                                                        (2)

2.2     If tan 70  p, write the following in terms of p :

        2.2.1 tan110                                                                      (2)

        2.2.2 sin 290                                                                     (3)

2.3     Simplify the following without using a calculator:

                           sin150.tan 225
                                                                                           (6)
                          sin  30  .sin 420

                                                                                           [16]

QUESTION 3

3.1    Simplify without using a calculator:

                   cos 390
                             tan  360  x  .cos 180  x  .cos  x  90            (8)
                  cos(30)

3.2    Prove the identity:

                  cos x.tan 2 x
                                 cos x  1                                                (6)
                      1
                          1
                    cos x

3.3    Determine the general solution of

                                  4
               6 cos x  5           ; cos x  0                                   (6)
                                cos x

                                                                                           [20]

                                                                                                 4
                               Demo
                                       NW/JUNE/MATH/ EMIS/6*******

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Mathematics/ P2                     Mid-Year Examination                NW/ Jun 2018
                                     NSC- Grade 11

QUESTION 4

                                                            ˆ  106.
                                      ˆ  26, AB  DC and EOC
O is the centre of circle ABCDE with DEC

       Calculate the size of:

4.1     ˆ
       BCA                                                                      (2)

4.2    Â1                                                                      (2)

4.3     ˆ
       OCD                                                                      (6)

                                                                                [10]

                                                                                  5
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Mathematics/ P2                      Mid-Year Examination                             NW/ Jun 2018
                                      NSC- Grade 11

QUESTION 5

5.1     Complete the missing information in the theorem below:

        The angle subtended by the diameter at the circumference of the circle is …           (1)

5.2     Given: Circle centre O, tangent CPT at P chord PM and the point B on the
        major arc.

Complete the proof:

                            ˆ  ˆ
        Required to proof: MPT PBM

        Construction: Draw diameter PA and join AM

        Proof:

        …………………………………………………………………………..

        …………………………………………………………………………...

        …………………………………………………………………………..                                                        (5)

                                                                                                    6
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Mathematics/ P2                                            Mid-Year Examination   NW/ Jun 2018
                                                            NSC- Grade 11

5.3                                                     ˆ  x. BC // PQ.
        PA and PB are tangent to circle M with AC  BC. A 2

                                       M
        A
                1
            2
            x                                      1             B
                          1
                                                   2         4
                      C       2                        3

                                   1
                              S4       2
                                   3
                                                                                      Q
                                               2
                                                       3
            1                              1
                  2
                                               R
        P

        5.3.1 Determine with reasons FOUR other angles equal to x.                        (8)

        5.3.2 Prove that ABRP is a cyclic quadrilateral                                   (2)

        5.3.3 Prove that AP  BQ                                                          (3)

                                                                                          [19]

                                                                                                7
                                       Demo
                                                   NW/JUNE/MATH/ EMIS/6*******

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Mathematics/ P2                      Mid-Year Examination        NW/ Jun 2018
                                      NSC- Grade 11

QUESTION 6

Refer to the diagram below, ST is a diameter of the circle.
                      ˆ
OS // PN, TO bisects STP.

Prove that
6.1      PUNK is a cyclic quadrilateral                                         (5)
6.2      SO is a tangent to circle KUST                                         (6)
                                                                         [11]

                                       TOTAL:       [100]

                                                                           8
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Mathematics/ P2                        Mid-Year Examination              NW/ Jun 2018
                                        NSC- Grade 11

NAME: …………………………………………………..                                       CLASS: ………….

                                      DIAGRAM SHEET 1

QUESTION 1.2

                                              S  x; y
                             y

     P  4;5

                                 M  2; 2 
                                          Q  4;1          x
                             O

             R  1;  4 

QUESTION 4

                                                                                   9
                             Demo
                                    NW/JUNE/MATH/ EMIS/6*******

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Mathematics/ P2                                        Mid-Year Examination             NW/ Jun 2018
                                                        NSC- Grade 11

NAME: …………………………………………………..                                                      CLASS: ………….

                                                       DIAGRAM SHEET 2

QUESTION 5.2

QUESTION 5.3

                               M
 A
          1
      2
      x                                    1           B
                  1
                                           2       4
              C       2                        3

                           1
                      S4       2
                           3
                                                                                       Q
                                       2
                                               3
      1                            1
          2
                                       R
  P

                                                                                                 10
                                           Demo
                                                   NW/JUNE/MATH/ EMIS/6*******

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Mathematics/ P2                 Mid-Year Examination               NW/ Jun 2018
                                 NSC- Grade 11

NAME: …………………………………………………..                                 CLASS: ………….

                                DIAGRAM SHEET 3

QUESTION 6

                                                                            11
                       Demo
                              NW/JUNE/MATH/ EMIS/6*******

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