Math Class X

Section A

·         With the help of table find the value of (0.96)(87.5) ² / 4850

·         If a + b=9 and ab=20 find  (a-b)

·         Factorize any four of following

o        8a³-1 +b³ + 6ab

o        16a²-40ab+25b²

o        6x²-5xy-6y²

o        a²+8b³+c³+6abc

o        1+2ab-(a² + b²)

o        12x² –17xy+6y²

·         Find graphically the solution set of the following equations, make four ordered pair of each

o        3x – 2y = -4

o        x + 2y = 12

·         If a/b = c/d prove that a² /b² = c² / d² = 2ac/bd

·         Find the solution of the following equation, with the help of matrices

o        x+2y = 5

o        x +3y = 7

•          If A=⌠6  2│ , Find A^-1 ; and verify that AA^-1 =1

•               │4  3│          

·         Simplify 1/a-b – b/a² –b²  - a/ a²+ b²  

·         Find the relation independent of X from the following equations:

o        X² + 1/x² = m² , x⁴ +1/x⁴ =x⁴  

·         Factorize 2x³ +9x²+19x +12 by reminder theorem.

·         Find the Solution Set of any two of the following equations

o        =⌠2x-1/3│ + 4 = 11

o        √4(3x-1) = 2√ x + 8

o        5 x² – 13x + 6 = 0

Section B

^·          Convert a Triangle ABC in which m AB(bar) = 6.21cm, m BC(bar) = 7.4cm , m AB(bar). Draw a circumscribed circle round the given triangle and  write the steps of Construction

^·          IF two Chords of Circle are congruent, then prove that they are the equidistant from the center.

^·          Prove that the sum of measures of three angle of triangle is 180^o

^·          Prove that an exterior angle of a triangle is greater in measure then either of the non-adjacent angles of the triangle

·         Prove that the measure of the square of the hypotenuse of a right angle triangle is equal to the sum of the measures of the squares of other two sides.

·         Draw two circle of radii 3cm and 1.5cm.The distance between their centers is 6.5cm. Draw their direct common tangents. Also write the steps of construction.

·         Prove that the opposite angles of the parallelogram are congruent.

·         If the diameter of a circle is perpendicular to a chord, prove that it bisects the chord.

Section C

•          Prove that Sinθ/1-Cosθ = 1+Cosθ/Sinθ

•          Find the Standard deviation from the following Information.

                       x(bar) =19.5, ɛx=195, ɛx²=5555

•          Find the values of all the trigonometric ratios of 30^o

•          The following are the percentages of the marks obtained by 10 Students in maths.

X|23|15|48|41|5|8|9|11|51|35|

                    Find the median of the marks  of the Students.

•          Find the variance of the following set of numbers

X=13,5,7,9,11,19,20,16,25

•          A tree of 90dm height Situated on the back of the river makes a angle of 30^o at a point directly on the opposite side of the river, find the width of the river.

------------GOOD LUCK------------