# Mathematics Solved Past Paper 10th Class 2011 Karachi Board

SECTION ‘A’ MULTIPLE CHOICE QUESTION

1. Choose the correct answer for each from the given options: 2. If A = {1,2,3,4} and B = {2,4,6,8}, show that (A ∩ B) – (A ∪ B) = A ∇, B.

L.H.S. (A U B) – (A  B) 5. Resolve into factors: x² (y – z) + y² (z – x) + z² (x-y):

6. Find the solution set of x² + 8x + 15 = 0 with the help of quadratic equation 10. Find the relation independent of ‘x’ the following equation 11. If two angles of a triangle are congruent, the sides opposite to them are also congruent. Prove.  14. If a perpendicular is drawn from the centre to a chord of a circle, it  bisects the chord. Prove

Proof:

15. Prove that sin ²θ + cos ²θ = 1.

SECTION ‘C’ (DETAILED – ANSWER QUESTIONS)

Q.no.19 which is compulsory.

17. Factorize the following:-
(i) 18 x²  + 9x – 20
(ii) a 4 + 64

(iii) a³ – a² + 2
(iv) 27 x³ – 1 + 8 y 6 + 18 xy²

18. Find the solution set of the following equations graphically: (Find four ordered pairs for each equation.)

x – 2y = -3
2x + Y = 14

19. In – any correspondence of two fight angles, if their hypotenuses are congruent and one more side of one triangle is congruent to the corresponding side of the other, the two triangles are congruent. Prove it.

Proof:

21. Take two points p & q at a distance of 7cm. Draw circles with the radii of 2.8 cm, and 1.6cm with centres p & q. Draw direct common tangent to these circles & write steps of construction

STEPS OF CONSTRUCTION:

(i) Draw a line segment PQ = 7cm
(ii) With centre P draw a circle of radius 2.8 cm and at Q draw a circle of radius 1.6 cm.
(iii) Taking P as centre draw a third circle of radius 2.8 – 1.6 = 1.2 cm
(iv) Bisect line segment PQ at point O.
(v) Taking centre 0 and radius equal to OP or OQ draw a 4th circle intersecting.
(vi) Join P to C and produce it to meet the bigger circle at O. Repeat the same process with the lower point C.
(vii) Draw QE parallel to PO and QF parallel to PO’
(viii) Now join D and E and produce it on both sides similarly draw D’E’ and produce on both sides DE and DE are the required direct common tangents .

Posted on December 17, 2015 in 10th Class 2011 Karachi Board Past Papers