Download Class X Assignment 1 - KV HVF , AVADI Chennai

KENDRIYA VIDYALAYA, HVF AVADI (2014-15)
Class X
Assignment 1: Real Numbers
Section A
1. HCF of 48 and 120 is
(a) 8
(b) 12
(c) 24
(d) 16
2. For some integer m, every even integer is of the form
(a) m
(b) 2m
(c) m+1
(d) 2m+1
3. If HCF of a and b is 15 and a x b = 4500, then LCM of a and b is,
(a) 300
(b) 900
(c) 600
(d) none of these
4. The product of a non-zero rational and an irrational number is
(a) Always rational
(b) always irrational
(c) either rational or irrational
(d) one
5. The product or two irrational numbers is
(a) Always rational
(b) always irrational
(c) one
(d) always non-zero
6. Euclid’s Division Lemma states that for any two positive integers a and b, there exits
unique integers q and r such that a = bq + r, where r must satisfy
(a) 1 < r < b
(b) 0 < r < b
(c) 0 r < b
(d) 0 < r b
7. The decimal expansion of the rational number
(a) one decimal place
(c) three decimal places
will terminate after
(b) two decimal places
(d) four decimal places
Section B
8. Show that 12 x 17 x 19 x 23 + 13 x 23 is a composite number.
9. Without actually performing the long division, find if
will have terminating or non-
terminating (repeating) decimal expansion.
10. Find the HCF of 344 and 60 by the prime factorization theorem.
11. If 0.2316 is expressed in the form of p/(2n x 5m) for smallest values of whole numbers n
and m. Write these values of n and m.
12. Prove that 3 +
is an irrational number
13. Prove that
is an irrational number
14. Prove that
-2
is an irrational number
15. Show that square of any odd integer is of the form 4q + 1 for some integer q.
16. Show that (12)n cannot end with digit 0 or 5 for any natural number n.
17. Prove that
is an irrational number.
18. If n is an odd integer, prove that n2 – 1 is divisible by 8.
19. Find the HCF of 456 and 120 by prime factorization method. Hence, find their LCM.
20. Find HCF of 120, 105 and 150 using prime factorization method. Also find the LCM of
these numbers.
Assignment 2: Polynomials
Section A
1. Quadratic polynomials having zeros -1 and 2 is
(a) x2 – x + 2
(b) x2 + x – 2
(c) x2 – x – 2
(d) none of these
2
2. If one of the zeros of the quadratic polynomial (k-1) x + kx + 1, k 1, is -3, then the
value of k is
4
4
2
2
(a)
(b) (c)
(d) 3
3
3
3
3. If α, β are the zeros of the quadratic polynomial 5x2 + 2x – 1, then the value of α + β + αβ
is
1
3
3
1
(a)
(b) (c)
(d) 5
5
5
5
2
4. If the zeros of the quadratic polynomial x + (a+1)x + b is 2 and -3, then
(a) a = -7, b = -1
(b) a = 5, b = -1
(c) a = 2, b = -1
(d) a = 0, b = -6
5. Sum of the zeros of the quadratic polynomial is -14 and the product of its zeros is 5. The
quadratic polynomial is
(a) x2 – 14x + 5
(b) x2 – 14x – 5
(c) x2 + 14x + 5
(d) none of these
Section B
6. If α, β are the zeros of the quadratic polynomial ax2 + bx + c, a 0, then prove that a(xα)(x-β) is equal to ax2 – bx + c.
7. Prove that both zeros of the quadratic polynomial x2 + 99x + 127 are negative
8. Find the zeros of the polynomial x2 + 2x + 1
9. Represent the zero of the linear polynomial 2x – 9 graphically.
10. Find the zeros of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship
between the zeros and the coefficients of the polynomial.
11. Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence,
find the zeros of the polynomial.
12. Find the zeros of the quadratic polynomial x2 +13x + 36 and verify the relations between
the zeros and the coefficient of the polynomial.
13. If the polynomial 6x4 + 8x3 +17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1,
the reminder comes out to be ax + b, find a and b.
14. If 1 is a zero of polynomial p(x) = ax2 - 3(a-1)x – 1, then find the value of a and also the
other zero of the polynomial
15. For what value of k, -4 is a zero of polynomial x2 – x – (2k+2)? Also find the other zero of
the polynomial.
x2 – 7x - 6
16. Find the zeros of the polynomial
the zeros and the coefficients of the polynomial.
17. Find the zeros of the polynomial 3 x2 + 13x - 2
and verify the relationship between
and verify the relationship between
the zeros and the coefficients of the polynomial.
18. Find the zeros of the polynomial x3 + 3x2 - 2x – 6, if two of its zeros are 3
2
and
19. Find the zeros of the polynomial x - 6x + 11x – 6, if two of its zeros are 1 and 2
20. If one zero of the polynomial 3x2 + (2k+7)x – 4 is negative of the other, find the value of
k and hence find the zeros.
21. Find the other zeros of the polynomial x4 – 5x3 + 2x2 + 10x – 8 if it is given that two of its
zeros are - and
Project
1. Prepare a mathematical model (working/PPT).
or
2. Prepare an album on Golden Ratio and its usage.
or
3. History of Indian Mathematicians
Write about their lives, achievements, contributions, research work etc.