Mathematics Paper 2 Grade 12 - St Stithians College
Mathematics Paper 2
Grade 12
Preliminary Examination 2017
DURATION: MARKS: Date:
180 min 150 15 September 2017
EXAMINER:
R. Obermeyer
MODERATOR: A. Janisch
External Moderator: I. Atteridge
INSTRUCTIONS:
See overleaf for Instructions. This paper consists of 25 pages (including cover) and an information sheet.
NAME: ____________________________________
Question
1 2 3 4 5 6
7 8 9 10 11 12
Level Tested
1 ? 4 1 ? 4 1 ? 4 1 ? 4 1 ? 4 1 ? 4
1 ? 4 1 ? 4 1 ? 4 1 ? 4 1 ? 4 1 ? 4
ASSESSMENT
Topic
Time Allocation
SECTION A
Analytical Geometry
22 mins
Trigonometry Graphs
10 mins
Trigonometry
28 mins
Euclidean Geometry
16 mins
Euclidean Geometry
11 mins
Statistics
16 mins
SECTION B
Analytical Geometry Statistics Trigonometry Measurement Euclidean Geometry Euclidean Geometry
26 mins 12 mins 10 mins 6 mins 19 mins 6 mins
TOTAL:
Possible mark
18 8 23 13 9 13
22 10 8 5 16 5 150
PERCENTAGE:
Actual mark
Teacher's Signature: ________________________ Controller's Signature: _______________________ Moderator's Signature: _______________________
Mathematics Paper 2 Preliminary Exam 2017
Grade 12 Examiner: Ms. R. Obermeyer
Instructions
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 25 pages (including the cover page) and an Information Sheet of 2 pages. Please check that your question paper is complete.
2. Read the questions carefully. 3. Answer ALL the questions on the question paper and hand this in at the end of the
examination. 4. Diagrams are not necessarily drawn to scale. 5. You may use an approved non-programmable and non-graphical calculator, unless
otherwise stated. 6. All necessary working details must be clearly shown. 7. Round off your answers to one decimal digit where necessary, unless otherwise stated. 8. Ensure that your calculator is in DEGREE mode. 9. It is in your own interest to write legibly and to present your work neatly.
Page 2 of 25
Mathematics Paper 2 Preliminary Exam 2017
Grade 12 Examiner: Ms. R. Obermeyer
Question 1
SECTION A
In the figure below, is a quadrilateral with (4; 10); (1; 1); (4; 0) and (8; 2).
a. Determine the gradient of and .
(4)
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b. Determine the length of in simplest surd form.
(2)
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Page 3 of 25
Mathematics Paper 2 Preliminary Exam 2017
Grade 12 Examiner: Ms. R. Obermeyer
c. Show that .
(2)
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d. A is a point in the first quadrant. Determine the coordinates of to make a rectangle. (2)
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e. Prove that is a cyclic quadrilateral.
(3)
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f. Determine the equation of the circle passing through ; ; and .
(5)
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[18] Page 4 of 25
Mathematics Paper 2 Preliminary Exam 2017
Question 2 Given: () = sin 2 for [-135?; 135?]
Grade 12 Examiner: Ms. R. Obermeyer
a. Sketch () = - tan( + 45?) for the given domain on the same axis as ().
(4)
b. Find the value of (90?) - (0?).
(2)
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c. If the equation = sin( + ) represents the graph of () reflected over the -axis
and shifted 60? to the right, find the values of and .
(2)
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[8]
Page 5 of 25
Mathematics Paper 2 Preliminary Exam 2017
Grade 12 Examiner: Ms. R. Obermeyer
Question 3
a. Simplify the following without the use of a calculator:
cos 25? . sin 55? - cos 65? . sin 35?
(5)
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b. Prove that:
1-cos 2 sin 2
=
tan
(4)
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c. Determine the general solution of:
sin . cos
=
1 3
(5)
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Page 6 of 25
Mathematics Paper 2 Preliminary Exam 2017
Grade 12 Examiner: Ms. R. Obermeyer
d. In the photograph below, a bridge is supported by a tower which is not perpendicular to the ground.
In the diagram, the tower PQ is shown and stays (steel ropes), PR and PS, help keep
the tower stable. (There are also other cables). From base Q of the tower a vertical line
QT is shown. = 30, = 10, = 31? and = 39,7?.
1. Why is 1 = 8,7? ?
(1)
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2. Show that = 34,05 .
(2)
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3. Determine the length of the tower PQ correct to one decimal place.
(2)
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Page 7 of 25
Mathematics Paper 2 Preliminary Exam 2017
Grade 12 Examiner: Ms. R. Obermeyer
4. Now find the angle marked , the inclination of the tower from the vertical.
(4)
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[23]
All statements must have reasons in Question 4 ? 5
Question 4
a. Use the diagram below to prove the theorem that states:
The line from the centre of a circle perpendicular to a chord bisects the chord.
(6)
Page 8 of 25
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