Integer and Polynomial X2
DELHI PUBLIC SCHOOL
BOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2011-2012
Class: X
REAL 1. 2. 3.
Subject : Mathematics
Assignment No. 1
4. 5. 6. 7. 8. 9. 10.
11. 12.
NUMBERS Show that square of any odd integer is of the form of 4p+1 for some integer p. Show that (12)n, where n is a natural number cannot end with the digit 0 or 5. Prove that each of the following are irrational : 1 a] 7 − 3 2 b] c) 3 + 5 5 +2 Use Euclid’s division algorithm, to find the HCF of a] 455 & 42 b] 392 & 267540 Express each of the following as a non-terminating recurring decimal a] 1/7 b] 13/44 c] 1/15 d] 1/370 Find the HCF and LCM of 30,72 and 432 by using the fundamental theorem of arithmetic. Show that one and only one out of p, p + 4, p + 8,p +12 and p + 16 is divisible by 5, where p is any positive integer. Check whether the following are composite or not i) 3 × 4 × 7 × 11 × 7 + 7 ii) 5 × 3 × 11 × 23 × 5 × 23 + 11 Prove that there is no rational number whose square is 8. Express the numbers p i) 0.3 178 ii) 2. 31 in the form . q Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively. If the HCF (210,55) is expressible in the form 210 ×5 + 55y, find y.
POLYNOMIALS 1. Find a quadratic polynomial when the sum and product of zeros of the polynomial are given as 2 1 −3 1 a] ,− b) ,− c] 0 & -10/3 d] − 2 & 3 2 3 3 2 5 2. Find the zeroes of the polynomial, also verify the relationship between the zeros and its coefficients 1 1 c] t2 - 2 a] 4x2+5√2x–3 b] y2 – d] √3x2 – 11x + 6√3 y+ 2 16 3. If one of the zeroes of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the other, find the value of k. 4. Verify whether the given numbers are zeros of the cubic polynomial or not. Also verify the relationship between the zeros and the coefficients in each case. a] x3 – x; 0,1 & -1 b] 2x3 – 5x2 + x + 2; 1, 2 & -1/2 5. Find all the zeros of the polynomial 2x4 – 10x3 + 5x2 + 15x – 12, if two zeros are √(3/2) and -√(3/2). 6. If the zeroes of
BOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2011-2012
Class: X
REAL 1. 2. 3.
Subject : Mathematics
Assignment No. 1
4. 5. 6. 7. 8. 9. 10.
11. 12.
NUMBERS Show that square of any odd integer is of the form of 4p+1 for some integer p. Show that (12)n, where n is a natural number cannot end with the digit 0 or 5. Prove that each of the following are irrational : 1 a] 7 − 3 2 b] c) 3 + 5 5 +2 Use Euclid’s division algorithm, to find the HCF of a] 455 & 42 b] 392 & 267540 Express each of the following as a non-terminating recurring decimal a] 1/7 b] 13/44 c] 1/15 d] 1/370 Find the HCF and LCM of 30,72 and 432 by using the fundamental theorem of arithmetic. Show that one and only one out of p, p + 4, p + 8,p +12 and p + 16 is divisible by 5, where p is any positive integer. Check whether the following are composite or not i) 3 × 4 × 7 × 11 × 7 + 7 ii) 5 × 3 × 11 × 23 × 5 × 23 + 11 Prove that there is no rational number whose square is 8. Express the numbers p i) 0.3 178 ii) 2. 31 in the form . q Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively. If the HCF (210,55) is expressible in the form 210 ×5 + 55y, find y.
POLYNOMIALS 1. Find a quadratic polynomial when the sum and product of zeros of the polynomial are given as 2 1 −3 1 a] ,− b) ,− c] 0 & -10/3 d] − 2 & 3 2 3 3 2 5 2. Find the zeroes of the polynomial, also verify the relationship between the zeros and its coefficients 1 1 c] t2 - 2 a] 4x2+5√2x–3 b] y2 – d] √3x2 – 11x + 6√3 y+ 2 16 3. If one of the zeroes of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the other, find the value of k. 4. Verify whether the given numbers are zeros of the cubic polynomial or not. Also verify the relationship between the zeros and the coefficients in each case. a] x3 – x; 0,1 & -1 b] 2x3 – 5x2 + x + 2; 1, 2 & -1/2 5. Find all the zeros of the polynomial 2x4 – 10x3 + 5x2 + 15x – 12, if two zeros are √(3/2) and -√(3/2). 6. If the zeroes of