Ideas for Class 10 Maths Holiday Homework

•  Ideas for Class 10 Maths Holiday Homework

• Complete your notebook.

• Make a project / model on “MATHEMATICS AROUND US”.

• Do 15-15 questions from each chapter (1-3) from previous year question bank.

• Prepare for test after vacation (1st, 2nd and 3rd chapter).

•             Solve previous year board questions based on the chapters

•  Real numbers

•  Polynomialsfrom the attachment file

•      Write these five math lab activity in Lab practical file

• Link is given here: http://www.cbse.nic.in/mathlabx.pdf

•  To obtain the conditions for consistency of a system of linear equations in two variables by graphical method. 

•  To verify that the given sequence is an arithmetic progression by paper cutting and pasting method. 

•  To verify that the sum of first n natural numbers is n(n + 1) / 2, that is Σn = n (n + 1) / 2, by graphical method.

•  To verify the Basic Proportionality Theorem using parallel line board and triangle cut-outs.

•  To verify the Pythagoras Theorem by the method of paper folding, cutting and pasting

• TOPIC: REAL NUMBERS

• Using prime factorization, find the HCM and LCM of 72, 126 and 168. Also show that HCF x LCM ≠ product of the three numbers. 

•  If the HCF of 210 and 55 is expressible in the form 210 × 5 + 55y, find y. 

•  After how many places of decimals, the decimal expansion of 43 2/ 45 3 will terminate? 

•  Check whether 5n can end with the digit 0 for any natural number n.

•  If HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other.

•  Prove that 5 + 2 √ 3 is an irrational number. 

•        C.    TOPIC:  POLYNOMIALS 

• If (x + k) is a factor of 2x² + 2kx + 5x + 10, find k. 

•  If α and β are the zeros of a polynomial p(x) = 3x² – 5x + 6, find (i) (α / β) + (β / α ) (ii) α³ + β³ 

•  Find all the zeroes of the polynomial f (x) = 2x4 – 3x³ – 5x² + 9x – 3, if two of its zeroes are ± √ 3. 

•  Divide (3 – x + 2x² + x³ – 3x4 ) by (2 – x) and verify by division algorithm. 

•  If ‘1’ is one of the zeroes of the polynomial p(x) = 7x – x³ – 6. Find its other zeroes. 

• Find the quadratic polynomial, sum and product of whose zeroes are 2 and – 1 respectively. 

•  Find the quadratic polynomial whose zeroes are 2 3 and −1 4 . 

• Find the polynomial whose zeroes are 2, 1 and – 1. What is its degree? 

• Find the polynomial whose zeroes are reciprocals of the zeroes of the polynomial 2x² + 3x – 6. 

•  Find the ratio of the sum and product of the zeroes of the polynomial 5x² + 2x – 10.

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• 1.NUMBER SYSTEM ➢ The set of Natural numbers ,Whole numbers ,Integers ➢ Even numbers,Odd numbers ➢ Composite numbers ,Prime numbers ,Co-primes ➢ Fundamental theorem of arithmetics- example problems ➢ Rational numbers and Irrational numbers ➢ Definition of Realnumbers 2.Polynomials ➢ Types of polynomials i)Linear polynomial –generalform and examples ii)Quadratic polynomial- generalform and examples 

• 3.Algebraic identities 

• 4.Surface areas and volumes ➢ Cube ,cuboid,cylinder ➢ Cone ➢ Sphere ,hemisphere

•  5.Quadratic equations ➢ General form ➢ Nature of roots ➢ Quadratic formula ➢ Relation between roots and coefficients of the quadratic equation 6.Trigonometry ➢ Pythagorus theorem ➢ Pythagorean triplets ➢ Trigonometric identitie 

•                                     

• What is the HCF of smallest  prime number and smallest composite number ?

• Check whether 4n  ,  6n  can end with the digit 0 for any natural number .

• Show 3  ,   5   ,   and 3 + 5     is irrational .

• If HCF of 45 and 105 is  15 . Write the  LCM  .

•  Prove that the product of any three consecutive positive integers is divisible by 6 .

•  Two positive integers a and b can be written as  a =x3y2  and b = xy3

•                  Find the L.C.M.    of a and b . 

• Find the value of k such that the polynomials 

• x2-k+6x+2(2k-1)

•            has the sum of its zeroes equal to half of their product  .

•    If α and β are the zeroes of the polynomial 2y2+7y+5 ,

• write the value of α+β+αβ

• If zeroes of the polynomial x2+px+q are double in value to the

• Zeroes of 2x2-5x-3, find the value of p and q . 

• Find a quadratic polynomial whose sum of zeroes are 

• 3+2 and 3-2  

• Find all the zeros of the  polynomial 3x3+10x2-9x-4  if one of its zero is 1 .  

•   Find the zeroes of following quadratic polynomials and verify the relation ship between zeroes and the coefficient . 

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•   Solve the following system of linear equations graphically .

• 3x+y-12=0 , x-3y+6=0

• Shade the region bounded by  the lines and x – axis  . Also , find the area of shaded region .

•        For what value of k will the pair of equations has no solution ?

•                3x+y=1 and 2k-1x+k-1y=2k+1

•       Solve the equations .

• 99x+101y=499 and 101x+99y=501

•  The sum of the digits of a two digit number is 12 . The number obtained by interchanging the two digits exceeds the given number by 18 . Find the number .

• The sum of the numerator and denominator of a fraction is 12 . If 1 is added to both numerator and denominator the fraction becomes 34  . Find the fraction .

• 5 pencils and 7 pens together cost Rs. 50 , whereas 7 pencils and 5 pens together cost Rs. 46 . Find the cost of one pencil and that of one pen .

• The largest of two supplementary angle exceeds the smaller by 18 degrees . Find them .

• Five years hence , the age of Jacob will be three times that of his son . Five years ago , Jacob’s age as seven times that of his son . What are their present ages ? 

• Use elimination method to find all possible solutions of the following pair of linear equations :

• 2x+3y=8 and 4x+6y=7

• State and prove B.P.T.