Question

Mathematics/Grade 12 QUESTION 1 3 May 2024 1.1 Given $x^2 + y^2 - 6x - 2y + 1 = 0$ is the equation of the circle, centre N. M($p$;7) is a point outside the circle and the length of the tangent to the point T on the circle is $2\sqrt{13}$ units. NO $2\sqrt{13}$ - M 3 1.1.1 Determine the coordinates of the centre and the length of the radius, TN of the circle. 1.1.2 Calculate the value(s) of $p$. (4) (6) 1.2 A(2;5) and B(4; -1) are the two points on a circle. C($a$;$b$) is the centre of the circle. The centre of the circle lies on the $2x - y + 1 = 0$. AB is a chord of the circle with $AD = \frac{1}{2}AB$. A(2;5) D C($a$;$b$) B(4;-1) 1.2.1 Give a reason as to why $CD \perp AB$. 1.2.2 Determine the equation of the tangent to the circle at B. Assignment Ximhungwe Circuit (1) (5) Mathematics/Grade 12 May 2024 1.2.3 Determine the equation of the circle. (5) [21] QUESTION 2 Given $f(x) = -2x^2 + 1$ 2.1 Show that the average gradient of the graph of $f$ between the point $x = 3$ and $x = 3 + h$, ($h \ne 0$), is $-12 - 2h$ 2.2 Hence, use your answer in question 2.1 above, to calculate $f'(3)$ from first principles. 2.3 Determine the numerical value of the gradient of the graph of $f$ at $x = 0$. (4) (2) (2) [8]

          Mathematics/Grade 12
QUESTION 1
3
May 2024
1.1 Given $x^2 + y^2 - 6x - 2y + 1 = 0$ is the equation of the circle, centre N. M($p$;7) is a point outside the
circle and the length of the tangent to the point T on the circle is $2\sqrt{13}$ units.
NO
$2\sqrt{13}$
- M
3
1.1.1 Determine the coordinates of the centre and the length of the radius, TN of the
circle.
1.1.2 Calculate the value(s) of $p$.
(4)
(6)
1.2 A(2;5) and B(4; -1) are the two points on a circle. C($a$;$b$) is the centre of the circle. The centre of the
circle lies on the $2x - y + 1 = 0$. AB is a chord of the circle with $AD = \frac{1}{2}AB$.
A(2;5)
D
C($a$;$b$)
B(4;-1)
1.2.1 Give a reason as to why $CD \perp AB$.
1.2.2 Determine the equation of the tangent to the circle at B.
Assignment
Ximhungwe Circuit
(1)
(5)
Mathematics/Grade 12
May 2024
1.2.3 Determine the equation of the circle.
(5)
[21]
QUESTION 2
Given $f(x) = -2x^2 + 1$
2.1 Show that the average gradient of the graph of $f$ between the point $x = 3$ and $x = 3 + h$,
($h \ne 0$), is $-12 - 2h$
2.2 Hence, use your answer in question 2.1 above, to calculate $f'(3)$ from first principles.
2.3 Determine the numerical value of the gradient of the graph of $f$ at $x = 0$.
(4)
(2)
(2)
[8]

Mathematics/Grade 12
QUESTION 1
3
May 2024
1.1 Given x^2 + y^2 - 6x - 2y + 1 = 0 is the equation of the circle, centre N. M(p;7) is a point outside the
circle and the length of the tangent to the point T on the circle is 2√(13) units.
NO
2√(13)
- M
3
1.1.1 Determine the coordinates of the centre and the length of the radius, TN of the
circle.
1.1.2 Calculate the value(s) of p.
(4)
(6)
1.2 A(2;5) and B(4; -1) are the two points on a circle. C(a;b) is the centre of the circle. The centre of the
circle lies on the 2x - y + 1 = 0. AB is a chord of the circle with AD = (1)/(2)AB.
A(2;5)
D
C(a;b)
B(4;-1)
1.2.1 Give a reason as to why CD ⊥ AB.
1.2.2 Determine the equation of the tangent to the circle at B.
Assignment
Ximhungwe Circuit
(1)
(5)
Mathematics/Grade 12
May 2024
1.2.3 Determine the equation of the circle.
(5)
[21]
QUESTION 2
Given f(x) = -2x^2 + 1
2.1 Show that the average gradient of the graph of f between the point x = 3 and x = 3 + h,
(h 0), is -12 - 2h
2.2 Hence, use your answer in question 2.1 above, to calculate f'(3) from first principles.
2.3 Determine the numerical value of the gradient of the graph of f at x = 0.
(4)
(2)
(2)
[8]

Added by Jennifer V.

Question

Please give Ace some feedback