GRADE 12 MATHEMATICS
NOVEMBER EXAMINATION PAPER 2
QUESTION 1
The following frequency table provides the number of goals scored by the Protea netball team
during 50 matches in 2018.
Number of goals Frequency Cumulative Frequency
5< x ≤10 6 b
10< x ≤15 a 14
15< x ≤20 13 27
20< x ≤25 9 c
25< x ≤30 7 43
30< x ≤35 d 48
35< x ≤ 40 e 50
1.1 Determine the values a to e. (5)
1.2 Calculate the average goals scored in 2018. (2)
[7]
QUESTION 2
The table below shows the data for the heartrate per minute of ten males. Their heartrate is
checked before they cycle for 10min (x) and after they have exercised ( y ).
1 2 3 4 5 6 7 8 9 10
Heartrate before 65 50 125 80 85 112 53 118 85 130
Heartrate after 95 100 155 125 135 145 90 175 150 190
2.1 Represent the data a a scatter diagram on the grid provided. (3)
2.2 Calculate the mean heartrate before AND after exercise. (2)
2.3 Determine the formula for the least regression line to 4 decimal places. (2)
2.4 Calculate the correlation coefficient to 4 decimal places AND comment on the
strenght of it. (2)
1|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 2
,2.5 Draw the least squares regression line on your scatter diagram. (1)
[10]
QUESTION 3
The table below shows the distances (in kilometers) travelled daily by a sales representative for
21 working days in a certain month.
3.1 Calculate the mean distance travelled by the sales representative. (2)
3.2 Write down the five-number summary for this data. (4)
3.3 Draw the box-and-whisker diagram for this set of data. (2)
3.4 Calculate the standard deviation of the distance travelled. (2)
[10]
QUESTION 4
4.1 The diagram shows P,A,Q,R and S lies on the circumfrance of the circle with centre O.
SB is a tangent at S and RW=WP. AOWS and RWP are straightlines.
Proof that:
4.1.1 SB∥ RP (4)
4.1.2 SR2=WS . AS (5)
2
RW
4.1.3 AS= +WS (4)
WS
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Grade 12 November Paper 2
, 4.2 AB is the diameter of the circle. D and C are points on the circumfrence of the circle with
DE ⊥ AB. DE and AC intercect one another st T. With ^ ^
D 1= C 2
Proof That:
4.2.1 DA 2= AT . AC (5)
[18]
QUESTION 5
The diagram shows a circle with centre M(1;2). TS is a tangent line to the circle with T(-1;-2) a
point on the circle.
5.1 Determine the equation of the circle with centre at M in the form.
(x−a)2 +( y−b)2=r 2 (3)
5.2 Determine the equation of TS. (5)
5.3 The two circles with centres R and M meet externally at point T.TS is a tangent to both
circles at point T. If MT:TR = 1:4, Determine the coordinates of point R, if the circle with
centre R lies in the 3rd quadrant. (8)
[15]
3|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 2
NOVEMBER EXAMINATION PAPER 2
QUESTION 1
The following frequency table provides the number of goals scored by the Protea netball team
during 50 matches in 2018.
Number of goals Frequency Cumulative Frequency
5< x ≤10 6 b
10< x ≤15 a 14
15< x ≤20 13 27
20< x ≤25 9 c
25< x ≤30 7 43
30< x ≤35 d 48
35< x ≤ 40 e 50
1.1 Determine the values a to e. (5)
1.2 Calculate the average goals scored in 2018. (2)
[7]
QUESTION 2
The table below shows the data for the heartrate per minute of ten males. Their heartrate is
checked before they cycle for 10min (x) and after they have exercised ( y ).
1 2 3 4 5 6 7 8 9 10
Heartrate before 65 50 125 80 85 112 53 118 85 130
Heartrate after 95 100 155 125 135 145 90 175 150 190
2.1 Represent the data a a scatter diagram on the grid provided. (3)
2.2 Calculate the mean heartrate before AND after exercise. (2)
2.3 Determine the formula for the least regression line to 4 decimal places. (2)
2.4 Calculate the correlation coefficient to 4 decimal places AND comment on the
strenght of it. (2)
1|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 2
,2.5 Draw the least squares regression line on your scatter diagram. (1)
[10]
QUESTION 3
The table below shows the distances (in kilometers) travelled daily by a sales representative for
21 working days in a certain month.
3.1 Calculate the mean distance travelled by the sales representative. (2)
3.2 Write down the five-number summary for this data. (4)
3.3 Draw the box-and-whisker diagram for this set of data. (2)
3.4 Calculate the standard deviation of the distance travelled. (2)
[10]
QUESTION 4
4.1 The diagram shows P,A,Q,R and S lies on the circumfrance of the circle with centre O.
SB is a tangent at S and RW=WP. AOWS and RWP are straightlines.
Proof that:
4.1.1 SB∥ RP (4)
4.1.2 SR2=WS . AS (5)
2
RW
4.1.3 AS= +WS (4)
WS
2|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 2
, 4.2 AB is the diameter of the circle. D and C are points on the circumfrence of the circle with
DE ⊥ AB. DE and AC intercect one another st T. With ^ ^
D 1= C 2
Proof That:
4.2.1 DA 2= AT . AC (5)
[18]
QUESTION 5
The diagram shows a circle with centre M(1;2). TS is a tangent line to the circle with T(-1;-2) a
point on the circle.
5.1 Determine the equation of the circle with centre at M in the form.
(x−a)2 +( y−b)2=r 2 (3)
5.2 Determine the equation of TS. (5)
5.3 The two circles with centres R and M meet externally at point T.TS is a tangent to both
circles at point T. If MT:TR = 1:4, Determine the coordinates of point R, if the circle with
centre R lies in the 3rd quadrant. (8)
[15]
3|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 November Paper 2
