# Mathematics Grade 12 Exemplar Paper 2 June 2011 Memo - DOC by hPU3zn

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```									       MEMORANDUM

MATHEMATICS PAPER 2
JUNE 2011

This memo paper consists of 8 pages.
Grade 12 Mathematics Paper 2             Memorandum                                     June 2011

Question 1

1.1.1    A reflection about the y-axis                         1 for reflection
1 for y-axis                  (2)
1.1.2    A rotation through 900 in an anti clockwise           1 for rotation
direction                                             1 for size and direction      (2)
1.1.3    a rotation through θ in an anti clockwise direction   1 for rotation
1 for size and direction      (2)
1.1.4    An enlargement by a scale factor of 2                 1 for enlargement
1 for the scale factor        (2)
1.2      1.1.4 ( the enlargement). It changes the size.        1 for the correct
transformation
1 for the reason              (2)
1.3                                                            Accept calculator
1 for substitution
1 for values of special
angles
1 for substitution
1 for values of special
angles

[16]

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Grade 12 Mathematics Paper 2             Memorandum                                       June 2011

Question 2

2.1      A reflection in the line y=-x                            1 for reflection             (2)
1 for line of reflection
2.2                                                                                            (2)
2.3      A rotation through 1800                                  1 for rotation               (2)
1 for angle of rotation
2.4                                                                                            (2)
2.5.1    k = 1,5                                                                               (2)
2.5.2    F is ( -4,5 ; -1,5)                                      1 per coordinate             (2)
2.6      Area ΔABC                                                                             (2)
[14]

Question 3

3.1.1                                                             1 for substitution           (2)

3.1.2    the equation of AC will be:                              1 for substitution of
1 for substitution of
point
(3)

3.1.3                                                             1 for tan…
Midpt. of DB is (3;-2).                                  1 for conclusion
Substitute this to check if it is on line AC             1 for reason
LHS = -2                                                 2 for midpoint

RHS =                                                    2 for showing midpoint
on AC                        (7)
So AC bisect DB perpendicularly.

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Grade 12 Mathematics Paper 2            Memorandum                                    June 2011

3.1.5                                     =6,48              2 for AM
2 for BD
2 for area
(6)

3.2.1    M is                                                1 per substitution for
each co-ordinate.
(2)
3.2.2    M is (1;4)                                          1 per gradient                (3)
1 for conclusion

So the points are collinear
3.2.3    Midpoint of AC is (1;4). So diagonals bisect each   1 for midpoint
other.                                              1 for conclusion
So diagonals are perpendicular                      1 for conclusion              (4)
Hence diagonals of ABCD bisect each other
perpendicularly.
[30]

Question 4

4.1                                                            1 for LHS ( completing
the squares)

1 for RHS
1 for final equation
So M is (-2 ; 6) and r = 6                            2 for centre
(6)
4.2.1    When y=2,                                             1 for recognising the
value of y
x = -5 ( from the equation of the line)
1 for the value of x
1 for the value of r
1 for equation in
Hence the circle is
Therefore:                                                                        (6)
1 for expanding
So:

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Grade 12 Mathematics Paper 2           Memorandum                                   June 2011

4.2.2    Let D be

Then                                                  1 for the calculation
of x
And                                                   1 for the calculation
of y
Thus the equation of the tangent is given by:         1 for the gradient of
the tangent
1 for substitution

[18]

Question 5

5.1
1 for simplification
= 0,78 or
(5)
= 0,37
5.2.1                                                        2 per diagram
17            1 for expansion
α
-4                       8             β   1 for substitution
5                       -15

=

5.2.2                                                        1 for expansion
1 for substitution          (3)

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Grade 12 Mathematics Paper 2   Memorandum                          June 2011

5.3                                         1 per reduction             (6)

[19]
Question 6

6.1
1 for getting all to LHS
1 for grouping
1 for factors
1 for roots
1 for working with sinx
only                        (7)

6.2.1                                                                   (4)
6.2.2

2 for numerator
1 for denominator
1 for simplification
1 for simplification

1 for conclusion            (6)

[17]

Question 7

7.1.1           1330                                                    (1)
7.1.2                                       1 for Substitution          (2)
So AC = 183,12

7.1.3                                       1 for substitution          (2)

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Grade 12 Mathematics Paper 2   Memorandum                          June 2011

7.1.4                                       1 substitution
1 for the value of θ

7.2.1                                                                   (1)
7.2.2                                                                   (2)

7.2.3                                       1 for substitution

1 for expanding
compound angle
1 for special angle
values

1 for isolating p
1 for simplification
(5)

[17]

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Grade 12 Mathematics Paper 2    Memorandum                            June 2011

Question 8

8.1.1                                                                      (1)
8.1.2                                                                      (1)
8.1.3    (300 ; 0)                                                         (1)
8.1.4                                                                      (1)

8.2.1    cos graph: (4)                      sin graph: (3)
1 for turning points                1 for turning points
1 for y-intercept                   1 for x-intercept
1 for endpoints                     1 for endpoints              (8)
1 for x-intercepts                  1 for y-intercept

8.2.2                                                                     (1)
8.2.3                                        1 for each endpoint
1 for correct notation       (3)
8.2.4                                        1 for each value
[19]]

8
Grade 12 Mathematics Paper 2   Memorandum          June 2011

Total: 150 marks

9

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