GRADE 12 MATHEMATICS PAPER 2JUNE 2015Page 1 of 22

GRADE 12 MATHEMATICS PAPER 2JUNE 2015Page 1 of 22

GRADE 12 MID-YEAR EXAMINATIONS

June 2015
MATHEMATICS PAPER 2

Examiner: K Moffat Marks: 150 Moderator: N Vazzana Time: 3 hours
______

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY.

1. This paper consists of 22 pages, including a two page formula sheet.
   
2. Answer all the questions on the question paper.
   
3. You may freely use an approved, non-programmable, and non-graphics calculator. Answers must be rounded off to two decimal places unless otherwise as stated in each question.

1. Show all your working details, write legibly and present your work neatly.

All writing must be in black or blue pen. Only sketches may be drawn in pencil.

1. Diagrams are not necessarily drawn to scale.

1. Use your time wisely: spend no more than half an hour on every 25 marks.

SECTION A: [78]

QUESTION 1: [14]

has vertices and

(a)Determine the equation of the line that is the perpendicular bisector of (2)

(b)Find the midpoint of (2)

(c)Find the gradient of (2)

(d)Find the equation of the line that is the perpendicular bisector of (3)

(e)Find the point of intersection, , of lines and(2)

(f)Calculate the inclination of line (3)

QUESTION 2: [10]

(a)Simplify:(5)

(b)If and find by using a sketch,
the value of . (5)

QUESTION 3: [14]

The following are the ages (x) and the blood pressures (y) of 12 women.

Age (x) / 57 / 43 / 73 / 61 / 69 / 43 / 39 / 50 / 56 / 48 / 64 / 37
Blood Pressure (y) / 148 / 126 / 161 / 156 / 153 / 141 / 116 / 146 / 151 / 129 / 150 / 119

(a)Make a scatter plot on the axes provided below.(3)
(b)Evaluate
(1)(2)

(2)(2)

(c)Give the equation of the line of best fit below and draw the line of best fit onto

the scatter plot, going through the point .(5)

(d)Use your line to predict the blood pressure of a 55 year-old woman, correct to

the nearest integer.(2)

QUESTION 4: [11]

The graph below shows graphs of and over the interval . Use the graph to answer the questions that follow.

(a)Find the values of a, b and c.(4)

(b)Find a value forxif .(2)

(c)Find the values of x for which .(2)

(d)Find the value(s) of x for which .(3)

QUESTION 5: [12]

(a)Complete the statements below by filling in the missing word (s) so that the statement is correct:

(1)The exterior angle of a triangle is equal to ______
______(1)

(2)The exterior angle of a cyclic quad is equal to ______
______(1)

(b)In the figure is the centre of the circle and .

and are straight lines.

Find, with reasons, the magnitude of the following angles:

(1)(3)

(2)(3)

(3)(2)

(4)(2)

QUESTION 6: [17]

(a)Prove the theorem stated below:
The opposite angles of a cyclic quadrilateral are supplementary. (5)

Given: Circle centre O passing through the vertices of cyclic quad ABPQ.

RTP: and

(b)In the diagram below, parallelogram KLMN is given. isnot the centre of the circle.
and . Determine the size of .(5)

(c) and .
.
Prove that P, K, T and M are concyclic.(7)

SECTION B: [72]

QUESTION 7: [10]

(a)Determine the centre of the circle with the equation
(4)

(b)Determine the length of the tangent drawn from to its point of
contact with the circle(6)

QUESTION 8: [20]

(a)Solve for: for (8)

(b)Now sketch accurately on the sheet provided (labelling all intercepts, minima and maxima and endpoints) the graph of and
for the interval (8)

(c)Use the graph to determine where (4)

QUESTION 9: [8]

Prove the following identity:

(8)

QUESTION 10: [6]

In, show that the exact value of is .(6)

QUESTION 11: [13]

(a)Mr Browne is trying to compare his 2009 matric classes (27 students) results from the school trial and the final (IEB) examinations. The box plot is the summary of the trial examination whilst the cumulative frequency graph summarizes the results from the IEB examination.

(1)Use the ogive and read off the value of the 60th percentile(2)

(2)Draw the box and whisker plot for the IEB examination and indicate on
this diagram the values of the 5 number summary.(3)

(3)How do the two sets of results compare?(3)

(b)Let and be integers such that and

• The mode of these four numbers is
  
• The range of these four numbers is
  
• The mean of these four numbers is
  

Calculate the values of and (5)

QUESTION 12: [8]

In , and

Determine, with reasons, the numerical values of

(a)(4)

(b)(4)

QUESTION 13: [7]

is a tangent to the circle with centre .

Prove that:

(a)is cyclic (3)

(b)(4)

MATHEMATICS
INFORMATION SHEET

PAGE 1

/ Where is the first term of the first difference and is the first term of the second difference.

MATHEMATICS
INFORMATION SHEET

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