# Civil Technology Grade 12 NSC November 2016 QP (Eng)

> Grade 12 Civil Technology question paper from the NSC November Exam 2016 (English), 28 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/civil-technology-nov-2016-eng/88c4f96b-fd9e-4d13-9471-d411469e9702
- Updated: 2026-09-27
- Subject: Civil Technology
- Grade: Grade 12
- Document type: Question paper
- Year: 2016
- Exam period: NSC November Exam
- Curriculum: CAPS
- Pages: 28

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## About this document

Civil Technology · Grade 12 · NSC November Exam · 2016. Question paper, 28 pages. Read online or download the PDF.

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                                 GRAAD 12

                                NATIONAL
                           SENIOR CERTIFICATE

                                 GRADE 12

                             CIVIL TECHNOLOGY

                               NOVEMBER 2016

MARKS: 200

TIME: 3 hours

  This question paper consists of 19 pages, 8 answer sheets and a formula sheet.

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Civil Technology                             2                          DBE/November 2016
                                            NSC

REQUIREMENTS:

1.        Drawing instruments

2.        A non-programmable calculator

3.        ANSWER BOOK

INSTRUCTIONS AND INFORMATION

1.        This question paper consists of SIX questions.

2.        Answer ALL the questions.

3.        Answer each question as a whole. Do NOT separate subsections of
          questions.

4.        Start the answer to EACH question on a NEW page.

5.        Do NOT write in the margins of the ANSWER BOOK.

6.        You may use sketches to illustrate your answers.

7.        Write ALL calculations and answers in the ANSWER BOOK or on the
          attached ANSWER SHEETS.

8.        Use the mark allocation as a guide to the length of your answers.

9.        Make drawings and sketches in pencil, fully dimensioned and neatly finished
          off with descriptive titles and notes to conform to the SANS/SABS Code of
          Practice for Building Drawings.

10.       For the purpose of this question paper, the size of a brick should be taken as
          220 mm x 110 mm x 75 mm.

11.       Use your own discretion where dimensions and/or details have been omitted.

12.       Answer QUESTIONS 1.3, 1.8.2, 3.11, 4.3, 5.2, 5.3, 6.1 and 6.2 on the
          attached ANSWER SHEETS using drawing instruments where necessary.

13.       Write your CENTRE NUMBER and EXAMINATION NUMBER on every
          ANSWER SHEET and hand them in with your ANSWER BOOK, whether you
          have used them or not.

14.       Due to electronic transfer, drawings in the question paper are NOT to scale.

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QUESTION 1: CONSTRUCTION, SAFETY AND MATERIAL

1.1       FIGURE 1.1 below shows a person working on a building site.

                                                            [Source: miryaglobalmedia]
                                             FIGURE 1.1

          1.1.1       Study FIGURE 1.1 and describe TWO aspects that the person
                      should have considered to prevent this accident.                           (2)

          1.1.2       Name TWO personal safety items that this person is wearing.                (2)

          1.1.3       Motivate why you think it is appropriate to wear ear protection
                      when working with this power tool.                                         (2)

          1.1.4       Recommend ONE other important safety item that the person
                      should have worn.                                                          (1)

1.2       Freshly cast concrete should be cured.

          1.2.1       Describe what may be used to cure freshly cast concrete.                   (1)

          1.2.2       State the duration of curing.                                              (1)

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1.3       FIGURE 1.3 below shows an incomplete sectional view of a wall and roof
          construction.

          Use ANSWER SHEET 1.3 and complete the sketch by drawing the following:

                  Beam filling
                  The wall plate
                  Corrugated iron sheeting
                  Label any TWO parts of the drawing.

                                            FIGURE 1.3                                     (6)

1.4       Give TWO reasons why a roof covered with concrete tiles is more expensive
          than a roof covered with corrugated iron sheets.                                 (2)

1.5       Recommend ONE material that you would use to finish a plastered wall in
          a bathroom.                                                                      (1)

1.6       Give a reason for your answer to QUESTION 1.5.                                   (1)

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1.7       FIGURE 1.7 below shows a steel profile.

                                             FIGURE 1.7

          1.7.1         Identify the steel profile.                                               (1)

          1.7.2         Describe ONE effect that the weather will have on exposed,
                        untreated steel profiles.                                                 (1)

          1.7.3         How would you prevent the effect that you have described in
                        QUESTION 1.7.2?                                                           (1)

          1.7.4         State ONE use of the steel profile.                                       (1)

1.8       FIGURE 1.8 below shows the front elevation of a T-junction of a half-brick
          wall with dead ends.

                                                        A     A

                                                        A     A
                   B                                                          B

                                             FIGURE 1.8

          1.8.1         Identify bricks A.                                                        (1)

          1.8.2         Use ANSWER SHEET 1.8.2 and project and draw, from the given
                        front elevation, the plan course of a T-junction of course BB.
                        The position of the T-junction is indicated with a cross (X) on the
                        first course.                                                             (4)

1.9       Name ONE type of material that may be used for ceilings.                                (1)

1.10      Explain why cavity walls must have weep holes.                                          (1)
                                                                                                  [30]

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QUESTION 2: ADVANCED CONSTRUCTION AND EQUIPMENT

Start this question on a NEW page.

2.1       Choose a description from COLUMN B that matches an item in COLUMN A.
          Write only the letter (A–M) next to the question number (2.1.1–2.1.10) in the
          ANSWER BOOK, for example 2.1.11 N.

                            COLUMN A                           COLUMN B
          2.1.1      Key brick               A   adjustable support that may be used
                                                 individually or combined with frames
          2.1.2      Twisted ribbed bar          to support formwork

          2.1.3      Short-bored piles       B   driven into the ground with a drop
                                                 hammer
          2.1.4      Wall ties
                                             C   erecting of scaffolds
          2.1.5      Plywood
                                             D   essential part in the centre of an arch
          2.1.6      Multiprop
                                             E   provides colour and coverage
          2.1.7      Rough arch
                                             F   suitable for use in solid soil
          2.1.8      Dry wall
                                             G part of a dumpy level
          2.1.9      Focusing knob/screw
                                             H   hold the inner and outer walls of the
          2.1.10 Pre-cast concrete pile          cavity wall together

                                             I   construction process that does not
                                                 use bricks

                                             J   used where ground conditions are not
                                                 suitable for normal foundations

                                             K   consists of an uneven number of
                                                 layers of veneer and may be used for
                                                 partitioning

                                             L   reinforcement in concrete

                                             M must be plastered to finish off                   (10)

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2.2     FIGURE 2.2 below shows hand tools that are used on a site and in a workshop.
        Write down the name and ONE use of each of the tools next to the question
        number (2.2.1–2.2.4) in the ANSWER BOOK.

                           2.2.1                                    2.2.2

                           2.2.3                                    2.2.4                          (8)
                                        FIGURE 2.2

2.3       FIGURE 2.3 below shows an incomplete sectional view of a reinforced beam
          and column.

                                        FIGURE 2.3

          2.3.1       Predict TWO negative consequences of not having reinforcement
                      in concrete.                                                                (2)

          2.3.2       Explain why the main bar is placed at the bottom of the beam.               (1)

          2.3.3       Explain why the stirrups in a beam are placed closer to each other
                      near the support.                                                           (1)

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2.4       The accessories below are used to test fresh concrete:

                  Mould with a diameter of 100 mm at the top, 200 mm at the bottom and
                   a height of 300 mm
                  Baseplate 3 mm thick and 600 mm by 600 mm
                  Steel rod 16 mm in diameter and 600 mm long

          2.4.1        Name the test that may be performed with the above accessories.           (1)

          2.4.2        Explain why it is necessary to conduct this test.                         (1)

          2.4.3        How often must this test be carried out?                                  (1)

2.5       Explain TWO advantages of cavity walls.                                                (2)

2.6       FIGURE 2.6 below shows two concrete columns with defects caused by
          forces acting on them.

                                                A

                                                B             C

                                          FIGURE 2.6

          Name the type of forces responsible for the defects at A to C.                         (3)

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2.7       FIGURE 2.7 below shows a type of formwork used in construction.

                                                                      A

                      B                                               B

                                        FIGURE 2.7

          2.7.1       Identify the formwork in FIGURE 2.7.                                        (1)

          2.7.2       Recommend ONE material that may be placed on the inside
                      around part A to give a smoother concrete finish.                           (1)

          2.7.3       What is used to keep parts B together?                                      (1)

          2.7.4       Describe how you would prevent concrete from sticking to the
                      inside of formwork.                                                         (1)

2.8       Distinguish between the installation of a rib and block floor and an in situ
          concrete floor regarding the duration of the installation.                              (1)

2.9       Make a neat, well-proportioned, two-dimensional sketch of a hollow block with
          a rib on either side of the block, as used in a rib and block floor construction.
          Show the reinforcement in the ribs.                                                     (5)
                                                                                                  [40]

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QUESTION 3: CIVIL SERVICES

Start this question on a NEW page.

3.1       Make neat freehand drawings to indicate the difference between a P-trap and
          an S-trap.                                                                               (2)

3.2       Give the diameter of the PVC pipe that you would use for the wastewater at
          a sink.                                                                                  (1)

3.3       FIGURE 3.3 below shows a septic tank. Study the drawing and answer the
          questions that follow.

                                                                                          E
           A

           B                                    C                   D
                                                                                          F

                                                                                          G

                                            FIGURE 3.3

          3.3.1       Label parts A to F.                                                          (6)

          3.3.2       Describe what happens to the raw sewerage in C.                              (1)

          3.3.3       Explain the purpose of G.                                                    (1)

          3.3.4       What is the purpose of F?                                                    (1)

          3.3.5       Describe the liquid level in C and D when the septic tank is filled to
                      capacity.                                                                    (1)

          3.3.6       Explain why you may NOT direct water coming from a bath or sink
                      into a septic tank.                                                          (1)

3.4       Describe the main function of a storm water system.                                      (1)

3.5       Explain why storm water should NOT be directed into a sewerage system.                   (2)

3.6       Explain the purpose of a pressure-reducing valve as used in cold and hot
          water installations.                                                                     (1)

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3.7       Distinguish between the purpose of an elbow and the purpose of a
          tee coupler/T-fitting, as used in water pipe installation.                           (2)

3.8       The temperature of the water in your geyser is too high due to a faulty part.
          Name the faulty part that will cause the water to overheat.                          (1)

3.9       What type of geyser would you use when the pressure of the incoming water
          from the municipality is low?                                                        (1)

3.10      The inside tray of a solar panel is painted a specific colour. Name the colour
          and give a reason for using this specific colour.                                    (2)

3.11      FIGURE 3.11 on ANSWER SHEET 3.11 shows part of a vertical section
          through a building.

          Use ANSWER SHEET 3.11.

          3.11.1      Identify A and B.                                                        (2)

          3.11.2      Complete the drawing by showing the following on the drawing:

                          The incoming electricity cable in a kick pipe connected to
                           a meter box at C
                          Distribution board at D
                          The conduit for the connection from the meter box to the
                           distribution board at D                                             (4)
                                                                                               [30]

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QUESTION 4: QUANTITIES, MATERIALS AND JOINING

Start this question on a NEW page.

4.1        FIGURE 4.1 below shows the front view of a hollow-core flush panel door.
           Study the drawing and complete the incomplete cutting list. Write down the
           answer next to the question number (4.1.1 to 4.1.7) in the ANSWER BOOK.

                                                               50 x 38 mm

                                                               50 x 38 mm

                                                               600 x 50 x 38 mm
                   2 032

                                                               20 x 44 mm

                                                               3 mm

                                                                75 x 38 mm
                                     813

                                        FIGURE 4.1

         MEMBER              QUANTITY UNIT LENGTH    WIDTH    THICKNESS MATERIAL
      4.1.1                     2     mm    2 032      50          38          SA pine
      Top rail                  1     mm     693      4.1.2        38          SA pine
      Lock block                2     mm    4.1.3      50          38          SA pine
      Plywood panel             1     mm    2 032     813         4.1.4        Plywood
      Bottom rail               1     mm    4.1.5      50          38          SA pine
      Cardboard door
                                1     mm    4.1.6      690         38        Cardboard
      filling
      Edging                    1     mm    2 032      44         4.1.7        Meranti        (7)

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4.2       Various options are provided as possible answers to the following questions.
          Choose the answer and write only the letter (A–D) next to the question
          number (4.2.1–4.2.7) in the ANSWER BOOK, for example 4.2.8 C.

          4.2.1       When joining copper pipes using the capillary method, you will ...
                      the two pipes together.

                      A   weld
                      B   solder
                      C   glue
                      D   tape                                                                   (1)

          4.2.2       You can join ... pipes using the capillary method.

                      A   copper
                      B   copper and PVC
                      C   copper and galvanised
                      D   copper, PVC and galvanised                                             (1)

          4.2.3       When fixing a cornice to a wall, you will use ...

                      A   panel pins.
                      B   wire nails.
                      C   steel cut nails.
                      D   steel/masonry nail.                                                    (1)

          4.2.4       A compression joint may be used to join ... pipes.

                      A   copper
                      B   PVC
                      C   galvanised
                      D   All of the above                                                       (1)

          4.2.5       ... is used for joining roof trusses to brickwork.

                      A   Hoop iron
                      B   Building line
                      C   Cement
                      D   None of the above-mentioned                                            (1)

          4.2.6       ... may be used to join polyethylene pipes.

                      A   Wood glue
                      B   Insulation tape
                      C   Contact glue
                      D   PVC weld solvent                                                       (1)

          4.2.7       Type of screw used when the head of the screw must be flush to
                      the surface of the timber:

                      A   Coach screw
                      B   Round head screw
                      C   Countersunk head screw
                      D   Round head countersunk screw                                           (1)

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4.3       FIGURE 4.3 below shows the floor plan of a storeroom of which the walls
          need to be plastered.

                                                                         4 000

                                            8 000

                                          FIGURE 4.3

          SPECIFICATIONS:

                  Outside measurements of the storeroom: 8 000 mm x 4 000 mm
                  Height of the walls: 2 700 mm
                  Thickness of the walls: 220 mm
                  Thickness of the plaster: 12 mm
                  Size of the window: 1 200 mm x 900 mm
                  Size of the door opening: 2 100 mm x 900 mm

          Use ANSWER SHEET 4.3 and calculate the:

          4.3.1        Total area of the inside of the building that must be plastered.
                       Ignore the reveals.                                                             (13)

          4.3.2        Volume of plaster needed for the internal walls                                 (3)
                                                                                                       [30]

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QUESTION 5: APPLIED MECHANICS

Start this question on a NEW page.

5.1       FIGURE 5.1 below shows a shaped lamina with a square hole. All dimensions
          are in millimetres.

          Study the lamina and answer the questions that follow by writing only the
          answer with the unit next to the question number (5.1.1–5.1.7) in the
          ANSWER BOOK, for example 5.1.8 2 900 mm².

          HINT: Use the formulae on the FORMULA SHEET.

                                   A

                                                         30
                                          1
                              85

                                                    2

                                                                     80

                              20                    3

                              20

                               B                                     B
                                         20         20     20
                                   A

                                         FIGURE 5.1

          5.1.1       Calculate the area of part 1.                                               (1)
          5.1.2       Calculate the area of part 2 without the hole.                              (1)
          5.1.3       Calculate the area of part 3.                                               (1)
          5.1.4       Calculate the total area of the lamina.                                     (1)
          5.1.5       Calculate the position of the centroid of part 2 from A–A.                  (1)
          5.1.6       Calculate the position of the centroid of part 1 from B–B.                  (2)
          5.1.7       Calculate the position of the centroid of part 2 from B–B.                  (1)

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5.2       ANSWER SHEET 5.2 shows TWO diagrams of a cantilever frame. Use
          ANSWER SHEET 5.2 to answer the following questions.

          5.2.1      Name DIAGRAMS A and B.                                                     (2)

          5.2.2      On DIAGRAM A, indicate the nature of the forces in each member by
                     means of arrows.                                                           (4)

          5.2.3      Complete the table by indicating the nature and magnitude of the
                     forces. (Deduce the information from the drawings given.)                  (6)

5.3       FIGURE 5.3 below shows the space diagram of a beam with a span of
          10 metres with two point loads and a uniformly distributed load. Study the
          diagram and answer the questions that follow.

                                    10 N              10 N/m    20 N

                        A            B          C          D      E           F
                               2m          2m             4m           2m
                        28 N                                                42 N

                                           FIGURE 5.3

          5.3.1      Deduce from FIGURE 5.3 the value of the shear forces at A, B, C, E
                     and F and draw the shear force diagram on ANSWER SHEET 5.3.
                     Indicate the value of the shear forces on the diagram.
                     Use scale 1 mm = 1 N.                                                      (7)

          5.3.2      Calculate the bending moment at D.                                         (3)
                                                                                                [30]

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QUESTION 6: GRAPHICS AND COMMUNICATION

6.1                       FIGURE 6.1 below shows the site plan of a proposed dwelling. Study the
                          drawing and complete the table on ANSWER SHEET 6.1.

                                                           25 000

                                                                                     RE

                                       3 000
                                                                                                            1

                                                  SH        B       WC

                                       8 000
                                                                                                                2
                                                       Proposed dwelling

   LONG STREET
                                                                                                   PLOT 81

                 30 000                                                                                         3
                                       10 000
                                                                                 S
PLOT 77

                                                   8 000                 6 000       3 000 2 000
                                       5 000                                     MH                         4

                                                         PLOT 79

                                                                                                            5
                                                 THABO STREET

                                                        SCALE 1 : 200

                                                         FIGURE 6.1                                                 (15)

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6.2       FIGURE 6.2 below shows a line diagram of the floor plan of an office with
          a storeroom.

                         3 000              2 000                          3 500

                                            W2                              W1
                           S                WC

                                                      WHB
3 000
                                        BATHROOM
                        KITCHEN

              W1                                 D1
                                                                    STOREROOM

                               OFFICE

3 000                                                       D1

                                                 D1

                                        FIGURE 6.2

          Study FIGURE 6.2 and develop and draw, on ANSWER SHEET 6.2, to
          scale 1 : 50, the FLOOR PLAN of the building. Use the specifications below
          and on the next page. (Use the assessment criteria on ANSWER SHEET 6.2
          as a guideline for your drawing.)

          SPECIFICATIONS:

                  The measurements indicated    on     the      drawing    are    the   inside
                   measurements of each room.
                  Windows and doors:

                      WINDOWS AND DOORS             WIDTH                  HEIGHT
                     Window 1 (W1)                  1 500                   1 200
                     Window 2 (W2)                   900                     600
                     Door 1 (D1)                     900                    2 100

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                  All windows are positioned in the middle of the external wall of each
                   room.
                  All doors are positioned 300 mm from the wall to the right of the door.
                  The door of the storeroom is positioned in the middle of the wall shared
                   by the office and the bathroom.
                  All external walls of the house are 220 mm wide.
                  All internal walls are 110 mm wide.

          The following must also be shown on the floor plan:

                  The drawing symbols for a hand basin, water closet and double-bowl
                   sink, as indicated by the abbreviations on the line diagram
                  The total internal dimensions of the office on the western side of the
                   building
                  The dimensions of the thicknesses of the walls and sizes of rooms on
                   the western side of the office
                  Labels for the floor coverings for each room
                  The windows and doors in the spaces, as indicated on the line diagram

          THREE marks will be allocated for the application of the scale.

          Start the drawing from corner A, as indicated in the bottom left-hand corner of
          ANSWER SHEET 6.2.                                                                     (25)
                                                                                                [40]

                                                                                  TOTAL:        200

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CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 1.3

  ASSESSMENT CRITERIA           MARK CANDIDATE'S
                                        MARK
Roof covering correctly drawn    1
Beam filling correctly drawn     2
Wall plate correctly drawn       1
Any two labels                   2
TOTAL                            6

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CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 1.8.2

1.8.2

                   B                                    B

         ASSESSMENT             MARK   CANDIDATE'S
           CRITERIA                       MARK
    Stretcher course             2
    Header course                1
    Correctness of T-junction    1
    TOTAL                        4

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CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 3.11

                              A

                                  D          C

                              B

A:        ________________________________                           (1)

B:        ________________________________                           (1)

   ASSESSMENT          MARK   CANDIDATE'S
     CRITERIA                    MARK
Incoming cable          2
Meter box               1
Distribution board      1
TOTAL                   4

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CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 4.3

Complete your answers in the spaces indicated with _____________.

4.3.1        A         B          C                                     D
                                             Area to be plastered:
                                             Length of ONE short wall:
                                             = ______ – 2/________
                                             = ______
                                             Length of ONE long wall:
                                             = _____ – 2/________
                                             = _______
                                             Total length of one short and one long wall
                                             = _____________ + _____________
                                             = _____________                                            (3)

           2/        _______                 Area of internal walls before deductions:
                     _____     _____ m   2                                                              (2)

           1/        _______                 Area of window opening:
                     _______   _____ m   2                                                              (2)

           1/        _______                 Area of door opening:
                                         2                                                              (2)
                     _____     _____ m

                                             Total wall area to be plastered
                                             = _____________ - _____________ - ______________
                                             =_______________ m2                                        (4)

4.3.2                                        Volume of plaster needed:
           1/        ______
                     ______    ________                                                                 (3)

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CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 5.2

                                                      A

                                  60°    8N               60°

                                                  D         B

                                                                60 N
                                   C
                                        60°

                                   DIAGRAM A __________________________ (1)

                              a               d

                          b                                       c
                                    DIAGRAM B ________________________ (1)

                                  SCALE: 1 mm = 1 N

                          MEMBER NATURE MAGNITUDE
                          BC
                          CD            ---
                          DA
                          BD            ---                                    (6)

Tolerance of 1 N to either side

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### Page 25

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Civil Technology                                                        DBE/November 2016
                                              NSC

CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 5.3

                          10 N              10 N/m   20 N

            A              B           C       D      E            F
                     2m          2m           4m            2m
           28 N                                                  42 N

        5.3.1

 ASSESSMENT CRITERIA                  MARKS CANDIDATE'S
                                               MARK
Drawing correct                         5
Indicate all values of shear
                                        1
forces on drawing
Correct application of scale            1
TOTAL                                   7

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### Page 26

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Civil Technology                                                      DBE/November 2016
                                              NSC

CENTRE NUMBER:

EXAMINATION NUMBER:

ANSWER SHEET 6.1

NO.                   QUESTIONS                             ANSWERS            MARKS

  1     Name the scale used for the site plan.                                    1
        State the colour that you would use to
  2     indicate the proposed dwelling on the                                     1
        site plan.
  3     Identify number 1.                                                        1

  4     Identify the line at number 2.                                            1

  5     Identify number 3.                                                        1
        Determine the distance from the
  6     boundary line to the proposed dwelling                                    1
        to the right of the building.
  7     Identify number 4.                                                        1

  8     Identify number 5.                                                        1

        Draw the roof line of a hipped roof for
  9                                                                               4
        the building.

        Calculate the perimeter of the
 10                                                                               2
        proposed dwelling.
        Which elevation will be closest to Long
 11                                                                               1
        Street?
                                                    TOTAL                         15

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### Page 27

Civil Technology
                          Downloaded from hlayiso.com                  DBE/November 2016
                                      NSC

    CENTRE NUMBER:

                                                    ASSESSMENT CRITERIA            MARKS   LM
    EXAMINATION NUMBER:
                                                    External walls                   4

    ANSWER SHEET 6.2                                Internal walls                   3
                                                    Windows                          3
                                                    Doors                            3
                                                    Wash basin                       1
                                                    Water closet                     1
                                                    Double-bowl sink                 1
                                                    Dimensions                       4
                                                    Floor coverings                  2
                                                    Application of scale
                                                    One or two incorrect     =3
                                                    Three or four incorrect  =2
                                                    More than five incorrect = 1
                                                    No measurement correct = 0       3
                                                    TOTAL                           25

A

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### Page 28

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Civil Technology                                                          DBE/November 2016
                                               NSC

                                     FORMULA SHEET

IMPORTANT ABBREVIATIONS

SYMBOL         DESCRIPTION        SYMBOL         DESCRIPTION         SYMBOL DESCRIPTION
   c             Centroid            b           Breadth/Width          r      Radius
   ℓ              Length             s               Side               A       Area

FORMULAE

   AREA OF                FORMULA                  FORMULA              FORMULA FOR THE
                          (in words)              (in symbols)        POSITION OF CENTROIDS
                                                                        X-axis       Y-axis
                                                                          s            s
Square                    side × side                  s×s
                                                                          2            2
                                                                           ℓ           b
Rectangle              length × breadth                ℓ×b
                                                                          2            2
Right-angled                                                              b            h
                      ½ x base × height               ½b × h
triangle                                                                  3            3
Equilateral
triangle/                                                                 b               h
                      ½ x base × height               ½b × h
Isosceles                                                                 2               3
triangle

                                               (A1  d)  (A2  d)
                      Position of centroid =
                                                  Total area

                                               OR

                                          Y
                                                 Ay
                                                A

                                               OR

                                          X
                                                 Ax
                                                A

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