Mathematics Solved Past Paper 9th Class 2011 Karachi Board

Mathematics Solved Past Paper 9th Class 2011 Karachi Board

Mathematics Solved Past Paper 9th Class 2011 Karachi Board

Mathematics Solved Past Paper 9th Class 2011 Karachi Board

Mathematics Solved Past Paper 9th Class 2011 Karachi Board

SECTION “B” (SHORT-ANSWER QUESTIONS)

NOTE: Answer any Ten questions from this section.

2. If A = (0, 1) , B = {1, 2, 3), find A x B

ANSWER:

Given: A = {0, 1} B = {1, 2, 3}
A xB = {0, 1} x {1, 2, 3}
A x B = ({0,1), (0,2), (0,3), (1,1), (1,2), (1,3)} ans.

Question no.3

Question no.3

4. Find the cube of the following: (2x + 5y)

ANSWER:

(2x + 5y)
Formula used
(a + b)3 = a3 + b³ + 3ab (a + b)
2x + 5y)³ = (2x)³+ (5y) + 3(2x) (5y) (2x + 5y)
= 8x³ + 125y³ + 30xy. (2x + 5y)
= 8x³ + 125y³ + 60x y + 150x²
or 8x³ + 60x²y + 150xy² + 125y³.

Question no.6

Question no.6

7. If p (x) = 2x + 3×3 – X2 – 5, find the value of p (-2)

ANSWER:

P (-2) = 2 (-2) + 3 (-2)3- (-2)²- 5
= (2 x -2) + (3 x -2 x -2 x -2) – (-2) x (-2) -5
= -4 – 24-4- 5
= -37 Ans.

Question no.8

Question no.8

Question no.9

Question no.9

Question no.10

Question no.10

Question no.11

Question no.11

12. Prove that central angle of minor arc of a circle is double (in measure) of me inscribed angle of the corresponding major arc.

ANSWER:

Question no.12

Question no.12

Question no.13

Question no.13

14. Find the value of A + B + C when:
A = 2x³ – 4x² – 5
B = 4x³ – 9x + 8x² – 3
C = -6x³ -3x³ + 2 – 5x

ANSWER:

Adding the expressions of A, Band C
A+B+C = (2x³ – 4x²- 5)+(4x³ – 9x + 8x² – 3)+(-6x² – 3x³ + 2 – 5x)
= 2x³ – 4x²- 5 + 4x³ – 9x + 8x² – 3 – 6x² – 3x³ + 2 – 5x
= 2x³ + 4x³ – 3x³ – 4x²+ 8x² – 6×2 – 9x – 5x – 5 – 3 + 2
= 3x³ -2x²-14x-6 Ans.

Question no.15

Question no.15

17. A man left behind him an inheritance (Tarka) worth Rs.30,000. Distribute the Tarka among his four sons and three daughter. such that each son gets twice as much as a daughter. The deceased left behind him a debt of Rs.8,000.

ANSWER:

Please see Q.no. 18 of 2012

Question no.18

Question no.18

19. Factorize the following:
(i) x² – xy – 3x + 3y
(ii) 4x² + 4xy + y²
(iii) a²x² – 4
(iv) x² + 7x + 12

ANSWER:

(i) x²  ay – 3x + 3y
= x (x – y) -3 (x – y)
= (x – y) (x – 3)

(ii) 4x²+ 4xy + y²
Using formula a² + 2ab + y = (a + b)²
Writing in the farm of formula
= (2x)²+ 2 (2x) (y) + (y)²
= (2x + y)² Ans.

(iii) a²x² – 4
Using the formula a²– b² = (a + b) (a – b)
A²x² – 4 = (ax)² – (2)²
= (ax + 2) (ax – 2) Ans.

(iv) x² + 7x + 12
= x²+ 4x + 3x + 12
= x (x + 4) + 3(x + 4)
= (x + 4) (x + 3).

20.(a) Find the continued product with the help of formula:
(x + y) (x² + y²)(X – y)

ANSWER:

(x + y) (x – y) (x² + Y²)
= (x² – y²) (x² + y²)
= (x²)² – (y²)²
= x4 – y4

Question no.20.(b)

Question no.20.(b)

21. Draw a circle of radius 3cm and take a point P at a distance of 10cm from the centre. Draw the tangent from the external point P . Write the steps of construction.

ANSWER:

Steps of Construction:
(1) Draw a circle of radius = 3 cm
(2) From its centre 0 take a point at a distance of 10 cm and give name P
(3) Join OP and bisect it with compasses. Let the mid point of OP be Q.
(4) With centre Q and radius = QO draw another circle to cut the first circle at T. Join point P to T. Then PT is the required tangent.

Question no.21

Question no.21

Posted on December 17, 2015 in 9th Class 2011 Karachi Board Past Papers

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