Class : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system

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1 Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following:. Insert rational numbers between. Epress in the decimal form. 8 and.. Epress. as a fraction in the simplest form. 4. Find two irrational numbers lying between and 5. Define an irrational number. 6. Which of the following is irrational? A) 4 9 B) 4 5 C) 7 D) 8 7. Which of the following is irrational? A).4 B).46 C).46 D) An irrational between and.5 is A) B) 5 C).5 D).5 9. Which of the following is irrational? A).5 B).56 C).56 D) The value of.. is A).45 B).4 C).45 D).45

2 p p q are q.. when epressed in the form, int egers, q A) B) C) 999 D) 999 is..4 when epressed in the form p q is A) 99 B) 4 C) D) 99. The number of consecutive zeros in is A) B) C) 4 D) Evaluate = = Simplify

3 Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following:. y. y z. z.. a bc b ac b a a a a b a b c 8 4. If 5. 5 then then , then = in decimal form is 8. a ab b bc c ca b c a 9. the value of =. If 8 what is the value?. If then find the value of.. If y and find. y

4 4. Write the value of The value of is A) 5 B) 5 C) 5 D) A) 4 B) 6 C) 64 D) 56.5 y 7. The value of y when and y is A) 8 B) -8 C) 4 D) If then = 9. The squareroot of 64 divided by cube root of 64 is A) 64 B) C) D) 64 4

5 Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following: y. If 8 64 what is the value of 4. If 64 what is the value of 5. If 8.5 and > then = 6. If then 7. 7 is n 5 5 n n n A) 5 B) 5 C) 5 D) 5 8. If then = 6 A) B) C) 4 D) 8 5. If then = 5 5 A) B) C) 5 D) a b c A) 5a bc B) 5ab c C) 5a bc D) 5a bc 5

6 . The value of is A) B) C) - D) - 4. If 5 n 5 then 64 5 n 5. If A) 5 B) A) M M 4 5 M 4 5 M then 4 C) 65 D) 5 B) C) 4 D) 6. The value of If 8. If 9. = A) 96 B) 89 C) 4 D) then A) B) - C) 7 9 then =.6. 8 D) 4. Prove that a a b a b a b b a 6

7 Class : IX(CBSE) Worksheet - 4 Sub : Mathematics Topic : Rationalisation I. Solve the following:.. a b 5 5. Prove that 4. If 5. If find a and b. simplify find 6. Evaluate: 7. If and y 5, find y 4 5 8, find Write the reciprocal of If a find a. a. If, then find the value of. 5 if A) 5 6 B) 6 5 C) D) = A) 5 6 B) 5 6 C) 5 6 D) 5. The R.F of is 4. The R.F of is A) B) C) D) 7

8 5. 5 then 6. If 7. If A) 5 B) 4 C) D) 5 a b then A) a b B) a b C) a b D) a b 5 4 then 8. The value of is 9. The value of 5 6 is. 9 8 A) B) C) D) 8

9 Class : IX(CBSE) Worksheet - 5 Sub : Mathematics Topic : Algebraic identities I. Solve the following: 4 y.. Epand y. Epand. Epand 4. Epand y 5. Find the product of If y and y find the value of y. 7. If y and y 6 find the value of 9 4y. 8. If 4 y 4 and y 6 find the value of y simplify

10 . a b 4. 5y z =.. 4. y z y z. 5. a b c bc ca ab. 6. a b c a b c simplify. 7. y z y z simplify y 4 y simplify. 9. If y 4 and y find the value of y.. If a b and a b 58 m find the value of a b.

11 Class : IX(CBSE) Worksheet - 6 Sub : Mathematics Topic : Algebraic identities I. Solve the following:. If find... 5 find 98 find.. 4. y and y 6 find 8 7y. 5. y and y find 7 8y 6. Find Find y and 4 y, find 7 8y y.8.6y.49y find product.. y y 4y 4 find the product.. 4.

12 . 4 4 = If a b c then a b c. 5. If a b c 6 and ab bc ca find the value of a b c abc 6. Find the value of a b b c c a a b b c c a If a b 7 and ab, find the value of a b.

13 Class : IX(CBSE) Worksheet - 7 Sub : Mathematics Topic : Factorization of algebraic epressions I. Solve the following: a a y a y z z factorize.. 4 9y 6z y 4yz 6z factorize y factorize a a factorize 5. 6 factorize 6. y y 7 5 factorize 7. a b c b c a a b cb c a factorize. 8. factorize a.6 factorize. factorize 9 9. y factorize y y factorize 4. a a a a factorize a b 5b factorize factorize 6 4 p p p

14 Class : IX(CBSE) Worksheet - 8 Sub : Mathematics I. Solve the following:. Topic : Factorization of algebraic epressions a 8b 7c 8 abc factorize. a b ca b c ab ac bc =.. 5y 49 5y 5y y 6 =. 4. y y z z factorize 5. p q r q r p r p q 6. factorize z y 5 y 4 z y z factorize 8. The factors of a are. 9. The factors of 4 5 are.. Factors of 4y 4y 4y 8 are.. Factors of 7 6 are.. Factors of y y y are.. The epression a b b c c a 4. If a b c factorize., then the value of a b c a b c. 5. If 6 y y y y ky then k 6. If 7 a b c, then a+b+c=. 7. The value of is. 8. The value of is 9. If p a prove that a 6ap p 8. a b c 6abc factorize 4

15 Class : IX(CBSE) Worksheet - 9 Sub : Mathematics Topic : Factorization of Polynomials I. Solve the following:. Coefficient of in 4 6 is. find f. If f ( ) 7.. Integral roots of the pollynomial 6 6 is. 4. f 7 find f. 5. The remainder when is divided by is. eactly divisible by 6. For what values of a is a a 7. If both and are factors of p 5 r show that p=r.? 8. 5 is a factor of a then the value of a. 9. The value of a if -4 is a factor of 5 7 a 8.. The value of k if - is a factor of k k k k. Find & if + and + are factors of k.. If a b is divisible by, find a & b.. If both + and - are factors of a b, find the value of a and b. 4. Factorize using factors theorem. 5. Factorize Factorize Factorize Factorize 9. Factorize. If + is a factor of a find a. 5

16 Class : IX(CBSE) Worksheet - Sub : Mathematics I. Solve the following: Topic : Factorization of Polynomials. If - is a factor of a a, then a =.. If 6 4 k is eactly divisible by then k =.. If a is a factor of a a 6, then the value of b. 4. If 4 5 k is divisible by, then k =. 5. If and are the factors of m n then m =, n =. 6. Let f is a polynomial such that 6 f, then factor of f. 7. When a b is divided by, the reminder is - 6, the value of a & b is. 8. One factor of 4 is 5 the other factor is. 9. If is a factor of f but not g then it must be a factor of. f g g A) f g B) f g C) f g D). is a factor of 4 only if.. If is a factor of a 5 then a =.. If is a factor of a 5 then a =.. If is a factor of 8 8 5k then k =. 4. If 5 5 is divisible by the reminder is. 5. If is a factor of polynomial k, then k =. 6. If a is a factor of 4 a 6a, then a =. 7. The value of k for which is a factor of 4 4 k is. 8. If both and are factors of p 5 r, then. 9. If is a factor of 4 a b c d e, then.. If is a factor of k 5, then k =.

17 Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Introduction to Euclid s Geometry, Lines and angles I. Answer the following:. How many least number of distinct points determine a unique line?. How many lines can be drawn through both the given points?. How many lines can be drawn through the given point? 4. In how many points two distinct lines can intersect? 5. How many least number of distinct points determine a unique plane? 6. How many planes can be made to pass through two points? 7. How many planes can be made to pass through three distinct points? 8. Find the measure of an angle which is complement of it self? 9. Two supplementary angles differ by 4. Find the angles.. An angle is equal to five times its complement. Find the measure?. Write the complement of each of the following angles:, 5, 9, 77,. If an angle is 8 lessthan its complement find the measure of angle.. If the angles and 5 are complementary angles find? 4. The measure of an angle is twice the measure of its supplementary angle. Find its measure. M P 5. Lines XY and MN intersect at O if POY and a b 9 : : find c. X b a c O N Y 7

18 6. Find also find BOC, COD, AOD D C A + A + B 7. If a > b by one third of right angle find a and b. C A a b B 8. Show that AB EF. B 57 A E F C 5 45 D 9. Define complementary angle.. Define supplementary angel. 8

19 Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Lines and angles I. Answer the following:. One angle is equal to three times its supplement. The measurement of the angle is.. Two complementary angles such that two times the measure of one is equal to three times the measure of the other, the measure of the smaller angle is.. Two stright lines AB & CD intersect one another at the point O if AOC COB BOD 74 then AOD =. 4. Two stright lines AB and CD cut each other at O, if BOD 6, then BOC. 5. Given POR and QOR, if POQ is a stright line then the value of =. C D 6. AOB is a stright line if AOC BOD 85, then COD A O B 7. The value of y = y 9

20 y 8. If 5 z and 4, then the value of is y z 9. The value of =. Two lines AB and CD intersect at O if AOC COB BOD 7, then AOC =. If l m what is the value of? +5. If lines l and m are parallel, then =. y y+5 l m 65 A B. If AB CD, then = P 48 C l D m 4. If lines l and m are parallel lines then = 7

21 5. If l m then = l 65 m 4 6. If lines l and m are parallel then the value of is 5 l m 7. CP BQ, the measure of = Q P B 5 5 A y z 8. If 5 4 then find = y z

22 Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Triangles and its angles I. Answer the following:. In a ABC if A 55, B 4 find C.. If the angles of a triangle are in the ratio : : determine three angles.. The angles of a triangle are 4, and, find? 4. ABC is a triangle in which A 7 the internal bisects of angles B and C meet in O. Find BOC 5. In ABC ABC ACB and the bisects of ABC and ACB intersect at O. Such that BOC, show that A B C An eterior angle of a triangle is and one of the interior opposite angle is, find the other two angles of the triangle. 7. ABC is a triangle the bisector of the eterior angle at B and the bisector of C intersect each other at D. Prove that D A. 8. In ABC, AD bisects A and C B prove that ADB ADC. 9. Define a triangle.. Write the sum of the angles of an obtuse triangle.. If the angles of a triangle are in the ratio : :. Then find the measure of smallest angle.. State eterior angle theorem.. If all the three angles of a triangle are equal, then each one of them is equal to.

23 4. If two acute angles of a right triangle are equal, then each acute angle is equal to. 5. In ABC B C and ray AX bisects the eterior angle DAC if DAX 7, then ACB =. 6. In ABC if A AD bisects A and AD BC, then B. 7. In ABC if A 55 B 4 find C. 8. In ABC if A 6 B 8 and the bisectors of B and C meet at O, then BOC =. 9. Line segments AB and CD intersect at O such that AC DB, if CAB 45 and CDB 55 then BOD.. If + y = 8 4 O y 7

24 Class : IX(CBSE) Worksheet - 4 Sub : Mathematics I. Answer the following: Topic : Co-ordinate geometry. The point of intersect of the co-ordinate aes is.. The abscissa and ordinate of the origin are.. The measure of the angle between the co-ordinate aes is. 4. A point whose abscissa and ordinate are and -5 respectively lies in quadrant. 5. Points 4, and 7, lie ais. 6. The ordinate of any point on X-ais is. 7. The abscissa of any point on Y-ais is. 8. The abscissa of a point is positive in the quadrant. 9. A point whose abscissa is - and ordinate lies in quadrant.. Two points having same abscissae but different ordinates lie on.. The perpendicular distance of the point P 4, from X-ais is.. The perpendicular distance of the point P 4, from Y-ais is.. The distance of the point P 4, from the origin is. 4. The area of the triangle formed by the points A, B,5 and R, 4 is. 5. The area of the triangle formed by the points P, Q,5 and R, 4 is. 6. Plot the following points on the graph paper i),4 ii), iii) 5, iv) 4, 7. In which quadrant following points lie 4,,5, 5 8. Co-ordinates of origin is. 9. Distance between, and,4. Abscissica of, is.. 4

25 Class : IX(CBSE) Worksheet - 5 Sub : Mathematics I. Answer the following: Topic : Heron s Formula. Find the area of triangle whose sides are cm, 4cm and 5cm.. Area of triangle who s sides are 5cm, cm and cm is.. The perimeter of a triangular field is 54m and its sides are in the ratio 5 : 7 :. Find the area of triangle. 4. A triangle has sides, 5cm, 54cm, 6cm long find area and altitude. 5. The sides of a quadrangular field taken in order are 6m, 7m, 7m are 4m respectively find area. 6. Two parallel sides of a trapezium are 6cm and 77cm and other sides are 5cm and 6cm. Find the area of trepezium. 7. Find the perimeter and area of quadrilateral ABCD in which AB = 7cm, AD = 9cm, CD = cm, ACB 9, AC = 5cm. 8. Find the area of triangle whose base is 5cm altitude is 4cm respectively. 9. Find area of an isosceles triangle having a base cm and one side y com.. Find area of an equilateral triangle having each side 4cm.. The area of an equilateral triangle having each side of cm.. Find the area of an equilateral triangle having altitude h cm.. Let tri If each side of a triangle is doubled find percentage increase in its area. 5. The sides of a triangle are 6cm, cm, 4cm its area is. 6. The base of an isosceles right triangle is cm its area is. 7. If the area of an isosceles right triangle is 8cm what is perimeter of triangle is. 8. If the length of medium of an equelateral triangle is cm then area is. 9. The length of each side of an equilateral triangle of area 4 cm is.. The sides of triangle are 5cm, 78cm and cm the smallest altitude is. 5

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CLASS IX : CHAPTER - 1 NUMBER SYSTEM

MCQ WORKSHEET-I CLASS IX : CHAPTER - 1 NUMBER SYSTEM 1. Rational number 3 40 is equal to: (a) 0.75 (b) 0.1 (c) 0.01 (d) 0.075. A rational number between 3 and 4 is: (a) 3 (b) 4 3 (c) 7 (d) 7 4 3. A rational