Download maths-ix-x-vikas - Kendriya Vidyalaya No.1

KENDRIYA VIDAYALYA NO-1 AHMEDNAGAR
Holiday Home Work
MATHEMATICS
Class – IX
1. The cost of a pen is four times the cost of a pencil express the statement as a
linear equation in two variables.
2. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the
quadrilateral.
3. Show that a median of a triangle divides it into two triangle of equal area.
4. Find the value of a if (-1, 1) is a solution of the equation 3x-ay=5.
5. ABCD is a rectangle in which diagonal AC bisects as well as . Show that ABCD is a
square.
6. Show that the diagonals of a parallelogram divides it into four triangles of equal
area.
7. Draw the graph of each of the equations 5x+4y+1=0 and 2x-3y=-5 find the
coordinates of the point where the lines meet.
8. If a line is parallel to the base of a trapezium and bisects one of the non-parallel
sides, then prove that it bisects either diagonal of the trapezium.
9. Parallelogram ABCD and rectangle ABEF are on the same base and have equal
areas. Show that perimeter of the parallelogram is greater than that of
rectangle.
10. Write three solutions for the equation 7x-8y=13.
11. Prove that the straight line joining the mid-points of the diagonals of a trapezium
is parallel to the parallel sides and is equal to half their difference.
KENDRIYA VIDAYALYA NO-1 AHMEDNAGAR
Holiday Home Work
MATHEMATICS
Class – X
1.
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3.
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5.
If a = 5 , d = 3 and = 50 , then find n.
Find term from end of the AP : 17 , 14 ,11…………-40.
For what value of ‘k’ the equation 2x 2 + kx + 3 = 0 has equal roots?
Find the roots of the quadratic equation x2+7x+12=0.
Using quadratic formula, determine the roots of the following equation: x23x-1=0.
6. Find the sum of all natural numbers between 250 and 1000 which are exactly
divisible by 3.
7. Find the value of k for which roots of the equation x2-8kx+2k=0.
8. How many terms are there in the sequence 3, 6, 9, 12, ……111?
9. A two digit number is such that the product of the digit is 35, when 18is added to
the number, the digits inter change their places. Find the number.
10. From a point 20 m away from the foot of the tower, the angle of elevation of the
top of the tower is 300 , find the height of the tower.
11. Solve for x:
1
2
4
+ x+2 = x+4 ; x≠ −1, −2.
x+1
12. From a point on the ground the angles of elevation of the bottom and top of a
transmission tower fixed at the top of 420m high building are 450 and 600
respectively. Find the height of the tower.
13. A tree breaks due to storm and the broken part bends so that the top of the tree
touches the ground making an angle 300 with it. The distance between the foot
of the tree to the point where the top touches the ground is 8m. Find the height
of the tree.
14. Find the sum of the following A.P 2,7,12,… to 10 terms.
15. Two poles of equal heights are standing opposite each other on either side of the
road, which is 80m wide. From a point between them on the road the angles of
elevation of the top of the poles are 60◦ and 30◦. Find the heights of pole and the
distance of the point from the poles.
16. A train travels 360km at a uniform speed. If the speed had been 5 km/h
more, it would have taken 1 hour less foe the journey. Find the speed of the
train.