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.
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 .
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.
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