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:

Mathematics Solved 2012 MCQS

Mathematics Solved 2012 MCQS

Mathematics Solved 2012 MCQS

SECTION “B” (SHORT-ANSWER QUESTIONS)

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

ANSWER:

ANSWER

ANSWER

ANSWER

Simplify

Simplify

ANSWER

ANSWER

Question Answer

Question Answer

ANSWER

ANSWER

Question Answer

Question Answer

6. Resolve into factors. r² (s – t) + s²(t² – r) + e (r – s)

ANSWER: Please see Q.no.6 of 2014.

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

ANSWER

ANSWER

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

Question Answer

Question Answer

9. By using Cramer’s rule, solve the

equation  2x + 5y = 9
4x – 2y = 1

ANSWER:

ANSWER

ANSWER

ANSWER

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

ANSWER: Please see Q.no.9of 2014.

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

ANSWER: Please see Q.no.15of 2014.

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

equation

equation

ANSWER

ANSWER

Similarly

similarly

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.

ANSWER

ANSWER

Question

Question

Prove that a = b = c

ANSWER

ANSWER

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

ANSWER

ANSWER

Proof:

statement bwt reasons

statement bwt reasons

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

ANSWER

ANSWER

SECTION’c’ (DETAILED- ANSWER QUESTION)

Question Answer

Question Answer

ANSWER

ANSWER

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

Answer

Answer

Answer

graph

graph

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.

Answer

Answer

Proof:

statements reasons

statements reasons

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

Question

Question

ANSWER:

Answer

Answer

(b) Find the factors of X³ – X² – 14x + 24 with the help of remainder theorem.

Answer

Answer

Answer

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.

figure

figure

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

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