GRADE 12 MATHEMATICS
NOVEMBER EXAMINATION PAPER 1
QUESTION 1
1.1 Solve for x
1.1.1 x 2−9 x +20=0 (3)
1.1.2 x ( x +3 ) −1=0 (correct to 2 decimal points) (3)
1.1.3 x 2+ 7 x <0 (3)
−5
1.1.4 2 x 3 =64 (4)
1.2 Solve simultaneously for x and y if:
2 x− y=8 , and
2 2
x −xy + y =19 (7)
1.3 Solve the expression below without the use of a calculator: (4)
√ 41024 + √ 4 1022
√ 16510
[24]
QUESTION 2
2.1 The terms p ;(2 p+2);(5 p+3) form an arithmetic sequence.
Determine:
2.1.1 The value of p. (4)
2.1.2 The rule in the form of a n=a+(n−1) d . (2)
2.1.3 The 15th term of the sequence. (4)
2.2 x ; y ; 81 is a geometric sequence.
And y=2 x−5
All terms in the sequences are integers.
Calculate the values of x and y . (10)
[20]
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Grade 12 November Paper 1
,QUESTION 3
Given the sequence 2; 6; 10; 14; ….
3.1 What type of sequence is this? Justify your answer by calculation. (2)
3.2 Calculate T 55. (3)
3.3 Which term has a value of 322? (3)
3.4 Determine by calculation if 1204 is a term in the sequence? (4)
QUESTION 4
−3
The sketch below shows the graph of f ( x )= + q. The asymptotes of f intersects at B (−1; y ) .
x+ p
(
The Point D 5 ; 4
1
2)is a point on the graph.
4.1 Determine the value of p. (1)
4.2 Proof that q=5. (2)
4.3 Calculate the x -intercept of f . (2)
4.4 Determine the equation of the vertical asymptote of h if h ( x )=f ( x +4) (2)
4.5 One of the symmetry axes of f is an increasing function. Determine the equation of the
symmetry axis. (3)
4.6 Give the values x for f ( x ) ≥ x +6 . (2)
4.7 Determine the equation of g, the reflection of f in the x-axis and move two units
to the right. (3)
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Grade 12 November Paper 1
, [15]
QUESTION 5
The functions f ( x )=−x2 −2 x +3 and g ( x )=mx+ c are shown below,
with g passing through points E, C and A. A and B are the x-intercepts of f , and CD is the
symmetry axis of f . E is the y -intercept of g .
5.1 Determine the coordinates of C, the turning point of the graph of f. (3)
5.2 Determine the equation of g. (4)
5.3 Calculate the length of CE. (2)
5.4 Determine the set of definitions of f −1 (x). (2)
[11]
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Grade 12 November Paper 1
NOVEMBER EXAMINATION PAPER 1
QUESTION 1
1.1 Solve for x
1.1.1 x 2−9 x +20=0 (3)
1.1.2 x ( x +3 ) −1=0 (correct to 2 decimal points) (3)
1.1.3 x 2+ 7 x <0 (3)
−5
1.1.4 2 x 3 =64 (4)
1.2 Solve simultaneously for x and y if:
2 x− y=8 , and
2 2
x −xy + y =19 (7)
1.3 Solve the expression below without the use of a calculator: (4)
√ 41024 + √ 4 1022
√ 16510
[24]
QUESTION 2
2.1 The terms p ;(2 p+2);(5 p+3) form an arithmetic sequence.
Determine:
2.1.1 The value of p. (4)
2.1.2 The rule in the form of a n=a+(n−1) d . (2)
2.1.3 The 15th term of the sequence. (4)
2.2 x ; y ; 81 is a geometric sequence.
And y=2 x−5
All terms in the sequences are integers.
Calculate the values of x and y . (10)
[20]
1|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 1
,QUESTION 3
Given the sequence 2; 6; 10; 14; ….
3.1 What type of sequence is this? Justify your answer by calculation. (2)
3.2 Calculate T 55. (3)
3.3 Which term has a value of 322? (3)
3.4 Determine by calculation if 1204 is a term in the sequence? (4)
QUESTION 4
−3
The sketch below shows the graph of f ( x )= + q. The asymptotes of f intersects at B (−1; y ) .
x+ p
(
The Point D 5 ; 4
1
2)is a point on the graph.
4.1 Determine the value of p. (1)
4.2 Proof that q=5. (2)
4.3 Calculate the x -intercept of f . (2)
4.4 Determine the equation of the vertical asymptote of h if h ( x )=f ( x +4) (2)
4.5 One of the symmetry axes of f is an increasing function. Determine the equation of the
symmetry axis. (3)
4.6 Give the values x for f ( x ) ≥ x +6 . (2)
4.7 Determine the equation of g, the reflection of f in the x-axis and move two units
to the right. (3)
2|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 1
, [15]
QUESTION 5
The functions f ( x )=−x2 −2 x +3 and g ( x )=mx+ c are shown below,
with g passing through points E, C and A. A and B are the x-intercepts of f , and CD is the
symmetry axis of f . E is the y -intercept of g .
5.1 Determine the coordinates of C, the turning point of the graph of f. (3)
5.2 Determine the equation of g. (4)
5.3 Calculate the length of CE. (2)
5.4 Determine the set of definitions of f −1 (x). (2)
[11]
3|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 1
