PODAR INTERNATIONAL SCHOOL, SANGLI

HOLIDAY HOMEWORK MATHS (2016-17)

CLASS-IX

NUMBER rational no’s between a SYSTEM

1. Find 4 rational numbers between 2 and 3.2. Find three and b (a < b).

3. Find 5 rational number between 35 and

45 .

4. Find two irrational number between √2 and √3 .5. Plot ,√2 ,√3,√ 5,√ 6 on a number line.6. Represent √8.3 on the number line.

7. If x= 3 +√ 8 and y = 3 - √8 then 1X2

+ 1Y 2

= ?

8. If 3+√73−√7

= a + b√3 then (a,b) = ?

9. The product of √3 and 3√5 is : --------

10. The exponential from of√√2X √2 X √2 is : _______________

11. If x = 5−√212

show that .( X3 + 1X3

) -5(X2 + 1X2

) +( X + 1X ) = 0.

12. Express the following numbers in pq forms

i. 2.023232323…. …………… ii. ii. 0.0012012012………. iii. iii. 0.49494949………

13. Find the value of k if x – 3 is a factor of k2x3 – kx2 + 3kx – k.14. Check whether g(x) is factor of f(x) or not in the following polynomials using factor

theorems.i. f(x) = 3x3 + x2 – 20x + 12, g(x) = 3x – 2ii. f(x) = x3 - 6x2 – 19x + 84, g(x) = x – 7

15. Factorize each of the following polynomials by using factor theoremi. Y3 – 7y + 6ii. X3 – 3x2 – 9x – 5iii. X3 – 2x2 –x + 2

POLYNOMIAL

16. If x2 + 1X2

= 23, find the value of ( x + 1x ).

17. Evaluate : (i) (107)2 (ii) (94)2 (iii) (0.99)2

18. If x - 1x = 5, find the value of x3 -

1x3

.

19. Prove that : (x - y)3 + (y - z)3 + (z - x)3 = 3(x - y) (y - z) (z - x).20. Find the value of (28)3 - (78)3 + (50)3 .21. If a + b + c = 9 and ab + bc + ac = 26, find the value of a3 + b3 + c3 - 3abc.22. Factorise : x4 + x2y2 + y4 .

23. If a4 + 1a4

= 119 , then find the value of − 1a3

.

24. Factorise : x12 - 1.

HERON’S FORMULA

25. Find the percentage increase in the area of a triangle if its each side is doubled.26. Calculate the area of the triangle whose sides are 18 cm, 24 cm and 30 cm in length.

Also, find the length of the altitude corresponding to the smallest side of the triangle.27. The sides of a triangle are 10 cm, 24 cm and 26 cm. Find its area and the longest

altitude. 28. Two sides of a triangular field are 85 m and 154 m in length, and its perimeter is 324

cm. Find (i) the area of the field, and (ii) the length of the perpendicular from the opposite vertex on the side measuring 154 cm.

29. The sides of a triangular field are 165 cm, 143 cm and 154 cm. Find the cost of ploughing it at 12 paise per sq. m.

30. The base of an isosceles triangle measures 80 cm and its area is 360 cm2 . Find the perimeter of the triangle.

31. The perimeter of an isosceles triangle is 42 cm and its base is 112 times each of the equal

sides. Find (i) the length of each side of the triangle, (ii) the area of the triangle, and (iii) the height of the triangle.

32. The perimeter of a right angle triangle is 40 cm. Its hypotenuse is 17 cm. Find the sides containing the right angle. Also find the area of the triangle.

33. Find the area and perimeter of an isosceles right-angled triangle, each of whose equal sides measures 10 cm. Take √2 = 1.414.

34. The area of a square field in 8 hectares. How long would a man take to cross its diagonal by walking at the rate of 4 km per hour ?

35. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting ?

ANSWERS

1.) 4+1=5

3/1*5/5=15/5

4/1*5/5=20/5

15/5 ( 16/5,17/5,18/5,19/5 ) 20/5

2.)

3.)5+1=6

3/5*6/6=18/30