# Mathematics Solved Past Paper 10th Class 2013 Karachi Board

SECTION ‘A’ MULTIPLE CHOICE QUESTION

1. Choose the correct answer for each from the given options SECTION “B” SHORT-ANSWER QUESTIONS

2. If A = {1, 2, 3, 4} B = {2, 4, 5, 6} and C = {2, 3, 6, 8} then find (A – B) x (B – C)

ANSWER:

(A _ B) = {1, 2, 3, 4} – {2, 4, 5, 6}
(A – B) = {1, 3}
(B _ C) {2, 4, 5, 6} – {2, 3, 6, 8}
(B – C) = {4, 5}
(A _ B) x (B – C) = {1, 3} x {4, 5}
= {(1, 4), (1, 5), (3, 4), (3, 5)} ANSWER:

6. Resolve into factors. a² (b – c) + b² (c – a) + c² (a – b)

7. If a transversal intersects two coplanar lines such that the pair of alternate angles are congruent. Prove that the lines are parallel.

Proof: If AB and CO are not parallel, then being .coplanar, they will meet at point (say at R) and PQR will be a triangle.

What should be added to 4a4 + 4a³ + 5a² + 2a + 5 so that it becomes a perfect square?

9. Solve, if possible by using Cramer’s rule:

2x + 3y =-3
4x + 3y = 5 10. Solve the equation 2X² – 7x + 6 = 0 by using quadratic equation

11. Find all the trigonometric ratios of 45°. 12. Eliminate ‘y’ from the equations:

13. If two angles of a triangle are congruent, prove that the sides opposite to them are also congruent

Please see Q.no. 15 of 2012

15. If a perpendicular is drawn from the centre to a chord of a circle. Prove that it bisects the chord

16. A pole 14 metres high· on the bank of a stream makes an angle of 30° with a place on the opposite bank. Find the breadth of the stream.

SECTION ‘C’ (DETAILED – ANSWER QUESTION)

17. Factorize the following:

(i) X4+ 4y4
(ii) 18y² + 9y – 20
(iii) x³ – x – 2y + 8y³
(iv) a³ – 8b³ + 27c³ + 18abc 18. Find the Solution set of the following equations graphically. (Find four ordered pairs of each equation).

2x- y = 5
x – 2y = 1 19. In a correspondence of two right angled triangles. If their hypotenuses are congruent and more side of one triangle is congruent to the corresponding sides of the other, the two triangles are congruent. Prove it.

ANSWER: Please see Q.no. 19 of 2011

20.(a) Find the variance the following set of
observation :x= 11,-13, 25,15,12,18,17,23,20,16

20.(b) Find the factors of x³ – 4X² + 5x – 2 by means of Remainder Theorem. 21. Construct a triangle ABC in which mAB = 4cm, mBe = 5cm, and mLB = 60°. Draw the circum circle of the triangle and write the steps of construction.

ANSWER:

STEPS OF CONSTRUCTION:

(i) Draw a line segment BC = 5cm
(ii) At point B make angle of 60° and ray Bx
(iii) With centre B cut off BA = 4cm Join A to C
(iv) Draw right bisectors of sides BC and AC and let them intersect at 0
(v) Join 0 to any vertex say C and with centre 0 and radius – \ . = OC draw a circle. It is the circumscribed circle

Posted on December 16, 2015 in 10th Class 2013 Karachi Board Past Papers

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