MATHEMATICS II - FOR CLASS X (Science Group) - GUESS PAPER 2024 - By Sir Sajjad Akber Chandio

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Mathematics II
For Class X (Science Group)
Guess Paper 2024

By Sir Sajjad Akber Chandio

Sets And Functions

Q.1: If A = {1,2,3,4…..10 }, B={2,4,6,8,10}, U= {1,2,3…….12 } verify Demorgan’s law (AUB)’= A'∩B'
Q.2: Find x and y (x+5, 8) and (9, y-6)
Q.3: A = {1,2,5}, B = {2,4,6}, C= {2,4}. Then prove that:

1. A∆B = (AUB) - (A∩B)
2. A∩B x B∩C

Q4: A = {1,2,3……6}, B = {2,4,6,8,10}, U = {1,2,3……12}. Verify Demorgan’s law (A∩B)’ = A'UB'

Variations

Matrices And Determinants

Basic Statistics

Q1: find the mean, Mode, Medium, G.M, H.M, of electricity consumption (in kWh) of a shop for 60 days.

Q2: If x= 51,55,52,54,58,60,61,62,52,57,52,64. Find mean, median, mode, valiance, range, G.M, H.M.

Pythagoras’s Theorem

Q1: a=15cm, b=12cm, c= 13cm

Introduction To Trigonometry

Q1: from the top of a light house 102m high a measure of the angle of depression of a ship is 18°30’. How far is the ship from the light house?
Q2: A ladder makes angle 60° with the ground and reached the height of 6m on the wall, find the length of the ladder?
Q3: Find the angle of elevation when a 6m high bamboo makes a shadow of length 2√3 m?
Q4: Find the remaining trigonometric functions ∫ ratios: if,

Theory Of Quadratic Equations

Q1: Show that:

1. (1+Ɯ)(1+ Ɯ²)(1+ Ɯ⁴)(1+ Ɯ⁸) = (Ɯ + Ɯ²)⁴
2. (a+ Ɯb+ Ɯ²c)(a+ Ɯ²b+ Ɯc) = a²+b²+c²-ab-ba-ca

Q2: Sum of the roots of equation 2x²-3x+4m=0 is 6 times the product of its roots.
Q3: The roots of the equation on 5x²-7x+k-2 = 0 satisfy the relation 2α+5β= 1.

Practical Geometry Circles

Q1: Construct the ∆ABC and draw its circumcircle in each case.

1. mAB = 5.5cm, mAC = 6 cm and m∠A = 50°
2. mAB = 6cm, mBC = 4.5cm and mAC = 5cm

Q2: Draw two equal circles each of radius 3.3cm with centres at the points A and B such that mAB=7.8cm
a)Draw direct common tangent to this circle.
b) Draw transverse common tangents to these circles.

Partial Fraction

1. x² + 7x + 3/x²(x + 3)
2. 6x – 5 / (x² + 10) (x + 1)

Theorem

Long
1: If the square of one side of triangle is equal to the sum of the squares of the other two sides, then the triangle is a right angled triangle. Prove it. (23.2 pg. 177)
2: If two circles touch externally, the distance between their centres is equal to the sum of their radii. Prove it. (26.4 case a pg. 217)

Short
1: Prove that one and one circle can pass through three vertices of triangle. (Example 1 chap 25 pg. 198)
2: Perpendicular from the centre of the circle to chord bisect it (25.3 pg. 200)
3: The angled in a segment greater than the semi-circle is less than a right angle. (28.3b pg. 237)
4: If the angles subtended by two chords of a circle (or congruent circles) at the Centres (corresponding centres) are equal, the chords are equal. Prove it.
5: A line parallel to one side of triangle and intersecting the other two sides, divides them proportionally. Prove it.