Mathematics II (English And Urdu) - Solved Model Paper 2022 - For Class X (Science Group)

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Mathematics II
Model Paper 2022
For Class X (Science Group)

SOLUTION
Section 'B'

Q.2: Find the solution set of the following equation.

Q.3: Find the solution set of the following equation. Also verify the answer.

Q.4: Eliminate "Y" from the following equation.

Q.5: prove that

Q.6: Prove that

Q.7: A set of data contains the values as 148, 145, 160, 157, 156, 160, 160, 165 show that mode > median >mean.

Q.8: Find S.D (Standard Deviation) from the following information.

x = 19.5, n = 10, ∑x² = 5555

Q.9: Find all the Values of the trigonometric ratios of 60°.

Q.10: Prove that
^Sinθ /_{1 + Cosθ} + ^{1 + Cosθ} /_Sinθ = 2cosecθ

Q.11: If the sides of a triangle are congruent, the angles opposite to them are also congruent.

THEOREM No.6

OR

The measure of a central angle of a minor arc of a circle is double that of the inscribed angle of the corresponding major arc.

THEOREM No.4

Section 'C'

Q.12: Find the solution set of the following equation graphically (Find three ordered pair for each equation.)
2y - 3x = 12
x + 6 = y

(Note: Find three ordered pairs only as mentioned in question)

Q.13: In any correspondence of two triangle, if one side and any two angles of one triangle are congruent to the corresponding side and the angle of the other, the two triangles are congruent.

THEOREM No.7

Q.14: Take two points P and Q at a distance 7 cm. Draw circles with the radii of 2.8 cm, 1.6 cm and centres at P, Q respectively. Draw direct common tangents of these circles. (Also write the steps of constructions).

Solution:
(i) Take two points P and Q at a distance of 7 cm from each other.
(ii) Join P and Q to draw PQ.
(iii) With centre P and radius = 2.8 cm draw a circle.
(iv) With centre Q and radius = 1.6 cm draw a circle.
(v) Bisect the line segment PQ at point Q.
(vi) Taking 0 as centre and radius = PO or OQ, draw a circle intersecting the previous circles at points D, E, F and G.
(vii) Join D to E and F to G.
(viii) Hence DE and PG are direct common tangents to these circles.
(ix) Line segments joining the points of contact arc = 6.9 cm i.e. DE = 6.9 cm and PG = 6.9 cm.

OR

Opposite side and angles of a parallelogram are congruent. Prove it.

THEOREM No.11