Mathematics Class Ix

Kulachi Hansraj Model School, Ashok Vihar, Ph-III Holiday Homework- Assignments Grade 9 Number System Q1. Answer the following questions in one word or one sentence. a) A real number is either _____________or ______________. b) Find the number which is a whole number but not a natural number. c) The decimal expansion of a rational number is either __________or__________. d) Find a rational and an irrational number between 1 & 2. e) √ is called the sign of __________. f) What is the conjugate of 3+ . g) Write the order of h) is ________number.(rational /irrational) i) 3.14014001400014……….. is an __________ number .(rational /irrational) Q2. Insert 10 rational numbers between ⅖ and ¾. Q3. Express each of the following in the form p/q. a) b) c) d)

-25.6875 15.7 12 0.05 0.3 178

Q4. Find simplest rationalis ing factor of a) b) c) 2 d) e) Q5. Find a & b so that =

-

=

c)

=

, find the value of 4x3+2x2-8x+7.

Q6. If x=

Q7 (a) Give an example of two irrational numbers whose sum is an irrational number. (b)Give an example of two irrational numbers whose product is a rational number. (c) Give an example of two irrational numbers whose sum is a rational number. (d) Give an example that product of a rational number with an irrational number is a rational number. Q8 Simplify a) (32)2/5 b) 22/3.21/5 c) d) Q9 Represent the following numbers on the number line a) 1+ b) c) d) 3.247 Q10. Visualise 3.5757………. on the number line upto 4 decimal places using successive magnification. find the value of x2 +x y +y2.

Q11. If x=

and y=

Q12.If x =3+

find the value of x2 +

Q13.Simplify the following a) b)

+

.

.

Q14.Prove that

=2

Polynomials Q1. Define a Polynomial. Give an example also. Q2. Define a Quadratic polynomial. Give an example also. Q3. Define a Cubic polynomial. Give an example also. Q4.Fill in the blanks: a) b) c) d) e)

A polynomial of two terms is called as___________. The degree of cubic polynomial is ____________. The degree of √5 y-3 is __________. If a+b+c =0, then a3 + b3 + c 3 =________________. The degree of a non-zero constant polynomial is _______.

f) The coefficient of x2 in 2x2 +x+8 is ________. Q5. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. a) x2 +x b) √2 y-8 c) x10+y Q.6 (a) Find a zero of the polynomial p(x) = 2x + 3. (b) Check whether -2 & 2 are zeroes of polynomial x + 2. Q7. Verify that x3 + y3 + z3 – 3xyz = 1/2(x+y+z) [(x-y) 2 + (y-z) 2 + (z-x) 2] Q8. (a) Evaluate: (998)3 (b)Without calculating the cubes, find the value of (28)3 + (-15)3 + (-13)3 Q9. Find the product of (6z - 3z2 - 1) (4z + 3) (3z3 - 1). Q10. For what value of a, 2y3 + ay2 + 11y + a +3 is exactly divisible by (2y -1)?

Factorisation of Polynomials Q11.Factorise the following:(i)

25 2x - 10x + 1 - 36z2

(ii)

4(x - y) 2 - 12 (x + y) (x - y) + 9 (x + y) 2.

(iii)

x3 - x.

(iv)

1 - 2ab - (a2 + b2)

(v)

x 2 - 7x – 18

(vi)

x 2 - 16xy + 60 y2.

(vii) 9 (a - 2b) 2 - 4 (a - 2b) – 13 (viii) x4 – 81 (ix)

2a5 - 32a

(x)

x 3- 5x2 - 14x.

(xi)

x4 - y4

(xii) 1 - 6x + 9x2 (xiii) a - b - a3 + b3

Problems based on Remainder theorem and Factor theorem Q12. If x 3 + ax 2 + bx + 6 has (x - 2) as a factor and leaves a remainder 3 when divided by x - 3. Find the values a & b. Q13. Factorise the following using Factor theorem: (i) (ii)

x3 + 13x2 + 32x + 20 2y3 + y2 – 2y – 1

Q14. If f(x) = 4x3 - 12 x2 + 14x -3. Use the Remainder theorem to find the remainder when f(x) is divided by x - ½ Q15. The polynomials k x 3 + 3 x 2 - 13 and 2 x 3 - 5 x +k when divided by (x +2) leave the same remainder in each case. Find the value of k? Q16. For what value of ‘a’ is x+3 is a factor of 3x2 + ax + 6? Q17. Check if y + 2 is a factor of 4y3 - 3y2 + 2y – 50 using Factor theorem. Q18. If both (x - 2) and (x - ½) are the factors of px2 + 5x + r, show that p = r. Q19. If ax3 + bx2 + x - 6 has (x + 2) as a factor and leaves a remainder 4 when divided by (x - 2), find the values of a & b. Q20. Show that (x-2), (x+3) and(x-4) are factors of x 3 -3x 2 -10x + 24. Q21.Without actual division, show that 2x4 –6x3 +3x2 +3x – 2 is exactly divisible by x2 – 3x +2. Revision Work: 1. Construct the following angles 60o , 75 o , 90 o, 105 o , 120 o, 135 o and 150 o 2.

Construct the angle bisector of the following 45 o, 60o and 90 o

PROJECT WORK: Mathematics Project Guidelines: Instructions from CBSE: Every student will be asked to do at least one project, based on the concepts learnt in the classroom. The project should be preferably carried out individually and not in a group. The project may not be mere repetition or extension of the laboratory activities, but should aim at extension of learning to real life situations. Besides, it should also be somewhat open-ended and innovative. The project can be carried out beyond the school working hours. Some sample projects are given in the document but these are only illustrative in nature. The teacher may encourage the students to take up new projects. The weightage of five marks for project work could be further split up as under Identification and statement of the project : 01 mark Design of the project : 01 mark

Procedure/processes adopted Write-up of the project Interpretation of result General Instructions:

: 01 mark : 01 mark : 01 mark

Each student is required to make a handwritten project report according to the project allotted. Please make the project according to your class roll no. Details of projects are given in the end. Roll Number

Project Number

1-10

1

11-20

2

21-30

3

31-40

4

41-50

5

A project has a specific starting date and an end date. General lay-out of the project report has the following format Page Number

Content

1

Your Name, Class, Class Roll No., Title of the project

2

Content – Page description

3

Brief description of project

4-10 (may change)

Procedure (With pictures)

11

Mathematics used /involved

12

Conclusion /Result

13

List of resources (List of encyclopedia ,websites , reference books , journals etc)

14

Acknowledgement

Objective Project1 Useful Link: http://britton.disted.camosun.b Exploring Fibonacci numbers. c.ca/fibslide/jbfibslide.htm http://ewaysmathematics.blog spot.com/search/label/Fibonac ci

Description 1. Fibonacci numbers are a sequence of numbers i.e 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ... .The first number of the sequence is 0, the second number is 1, and next term is equal to the sum of the previous two numbers of the sequence itself. 2. Write the next 20 terms of the sequence generated by it. 3. History of the mathematician who gave this concept. 4. Explore in nature the things that correspond to Fibonacci numbers with pictures. For example: When counting the number of petals of a flower, it is most probable that they will correspond to one of the Fibonacci Numbers. It is seen that: a)White calla lily has one patel b)Euphorbia have two patel c)Trillium have three petals d)Columbine have 5 petals Explore more such examples with pictures from internet.(give atleast 8 examples)

Project 2 Useful Link: http://ptri1.tripod.com/

Objective

Project 3 Useful Link:

Objective

Exploring Pascal’s Triangle

http://www.wikihow.com/Ma Making 3-D Snowflakes ke-a-3D-Paper-Snowflake

Description 1. Pascal’s Triangle: A triangle of numbers in which a row represents the coefficients of the binomial series. The triangle is bordered by ones on the right and left sides, and each interior entry is the sum of the two entries above. 2. History 3. How to construct it 4. Mention about the properties a) The sum of the numbers in any row is 2n, when n is the number of the row. b) Property related to prime number. c) Hockey stick pattern d) Fibonacci sequence located through Pascal’s triangle. e) Powers of 11 5) Make model on Pascal triangle. Description Make a model with project report having contents a) What is 3-D snowflake b) Its applications in daily life. c) Mathematics involved in it. d) Procedure of the model.

Objective Project 4 Useful Link: http://mykhmsmathclass.blogs Making pot.com/search/label/Platonic Platonic Solids %20Solids

Description 1) Introduction 2) Mention about 5 platonic solids and its properties. 3) History 4) Procedure of making Platonic solids. 5) Verify Euler’s Formula for each of the solid.

Project 5 Useful link: http://mykhmsmathclass.blogs pot.com/search/label/Mathem atics%20Around%20us

Objective Exploring Mathematics us.

Description 1. Look around yourself. around In the house... In the garden... In the market... In a bank.... In the nature... so on 2. Click photographs using a digital camera/mobile and explore the hidden mathematics. 3. Click minimum 10 photographs.

Note : If you have any query related to Mathematics Projects, e mail to [email protected]