# Mathematics Solved Past Paper 10th Class 2012 Karachi Board

SECTION ·A’ MULTIPLE CHOICE QUESTION

1. Choose the correct answer for each from the given options: 2. If U = {x/x∈N . x ≤ 10}. A = (2, 4, 6, 8, 10} B = {3, 6, 9, 10} Prove that {A ∪ B} = A ∩ B 6. Resolve into factors. r² (s – t) + s²(t² – r) + e (r – s)

7. The sum of three consecutive odd numbers is 909. Find the numbers

The sum of these three odd no. will be
X + (x + 2) + (x + 4)
According to given condition
X + x + 2 + x + 4 = 909
3x + 6 = 909
3x = 909 – 6
3x = 903
x = 903/3
1st odd no. is x = 301
2nd no. is x + 2 = 301 + 2 = 303
Then the 3rd odd no.
X + 4 or 301 + 4 = 305
The three odd no. are 301, 303, 305

9. By using Cramer’s rule, solve the

equation  2x + 5y = 9
4x – 2y = 1 10. Find the solution set with the help of
quadratic equation. 2b² – 7b + 5 = 0

11. Prove that the sum of the three angles of a triangle is equal to 180º.

12. Find the relation independent of ‘t’ from the following equation

Similarly

This is an equation independent of t

13. If a transversal intersect two parallel lines, the alternate angles so formed are congruent. Prove it.

Prove that a = b = c

15. If two sides of a triangle are congruent, the angles opposite to them are also congruent. Prove it.

Proof:

16. Prove that cotβ + tanβ = cotβ sec² β.

16. Find the Solution set of the following equations graphically. (Find four ordered pairs of each equation).
4x – y -10 = 0
3x + 5y -19 = 0 19. In a correspondence of triangles if three sides of one triangle are congruent to the corresponding three sides of the other, the two triangles are congruent. Prove it.

Proof:

20.(a) Marks obtained by some students In computer science exam. are given below. Find Median of their numbers

(b) Find the factors of X³ – X² – 14x + 24 with the help of remainder theorem. 21. Draw the transverse common tangents of the two circles with the radII 3cm and 2cm, when the distance b/e their centers
Is 6cm. Write down the steps of construction.

Steps of Construction:

(1) Draw a straight line AB = 6cm
(2) With centre A draw a circle of radius 3 cm and with centre B draw a circle of radius 2 cm.
(3) With centre A draw a big circle of radius 3 + 2 = 5cm
(4) Bisect AB at 0 and with centre 0 and radius = mOA or m OB draw a 4th circle intersecting the big circle at Q and R.
(5) Join A to Q and R, intersecting the given circle at 5 & 5′
(6) Draw BT parallel to AQ and BT’ parallel to AR
(7) Join 5 and T and extend on either sides similarly join 5′ and T’ and extend on either sides. In this way 5T and SiT’ are the required transverse common tangents.

Posted on December 17, 2015 in 10th Class 2012 Karachi Board Past Papers