Coefficient refers to a number or quantity placed with a variable. The Worksheet on Coefficients available here has questions for finding the numerical coefficient as well as the literal coefficient in each term. The key point to be remembered while solving the problems on Identifying Coefficients is that it always comes with a variable.
Check out the Free Math Printable Coefficient Worksheet as a quick guide and learn how to solve similar kinds of problems. Download the Practice Worksheet on Coefficient and try to solve the problems on your own to understand your grip on the concept.
Read More: Worksheet on Degree of a Polynomial
Numerical and Literal Coefficient Worksheet with Answers
I. Write down the coefficient of x in each of the following:
(i) x
(ii) –x
(iii) –3x
(iv) – 7ax
(v) (1/5)xy
(vi) cx/z
Solution:
(i)The coefficient of x is 1.
(ii) The coefficient of x is -1.
(iii) The coefficient of x is -3.
(iv) The coefficient of x is -7a.
(v) The coefficient of x is (1/5)y.
(vi) The coefficient of x is c/z.
II. Write down the numerical and literal coefficients in each of the following terms:
(i) 34m3n
(ii) -5p/q
(iii) 2/7 xy2
(iv) -13/y
(v) 1/7mn2
(vi) 25 ab
Solution:
(i) The numerical coefficient is 34.
The literal coefficient is m3n.
(ii) The numerical coefficient is -5.
The literal coefficient is p/q.
(iii) The numerical coefficient is 2/7.
The literal coefficient is xy2
(iv) The numerical coefficient is -13.
The literal coefficient is 1/y.
(v) The numerical coefficient is 1/7.
The literal coefficient is mn2.
(vi) The numerical coefficient is 25.
The literal coefficient is ab.
III. Write down the coefficient of pq2 in each of the following:
(i) -pq2
(ii) 3pq2
(iii) -5pq2
(iv) (1/3)pq2
(v) 4pq2y
(vi) (-2a/b) pq2
Solution:
(i) The coefficient of pq2 is -1.
(ii) The coefficient of pq2 is 3.
(iii) The coefficient of pq2 is -5.
(iv) The coefficient of pq2 is 1/3.
(v) The coefficient of pq2 is 4y.
(vi) The coefficient of pq2 is (-2a/b).
IV. Write the coefficient of the following:
(i) a in -2ab
(ii) a in -ap
(iii) b in -b
(iv) b in (2/p) b
(v) ab in -7abc
(vi) ab in -ab
(vii) a2b in -5pa2b
(viii) ab2 in 7pab2
(ix) x2y in -10x2y
(x) x2y in 7abx2y
Solution:
(i) The coefficient of a in -2ab is -2b.
(ii) The coefficient of a in -ap is -p.
(iii) The coefficient of b in -b is -1.
(iv) The coefficient of b in (2/p)b is 2/p
(v) The coefficient of ab in -7abc is -7c.
(vi) The coefficient of ab in -ab is -1.
(vii) The coefficient of a2b in -5pa2b is -5p.
(viii) The coefficient of ab<sup>2</sup> in 7pab<sup>2</sup> is 7p.
(ix) The coefficient of x2y in -10x2y is -10.
(x) The coefficient of x2y in 7abx2y is 7ab.
V. State the numerical coefficient of each of the following:
(i) 8mn
(ii) 2xyz
(iii) abc
(iv) -5m/n
(v) 2/7 mn2
(vi) -12xy/5z
(vii) -7a ÷ b
(viii) -2x ÷ (7y)
(ix) x/-y
(x) –m/-n
Solution:
(i) The numerical coefficient in 8mn is 8.
(ii) The numerical coefficient in 2xyz is 2.
(iii) The numerical coefficient in abc is 1.
(iv) The numerical coefficient in -5m/n is -5.
(v) The numerical coefficient in 2/7 mn2 is 2/7.
(vi) The numerical coefficient in -12xy/5z is -12/5.
(vii) The numerical coefficient in -7a ÷ b is -7.
(viii) The numerical coefficient in -2x ÷ (7y) is -2/7.
(ix) The numerical coefficient in x/-y is -1.
(x)The numerical coefficient in –m/-n is 1.
VI. In 4xy2z3, write the coefficient of the following:
(i) 4
(ii) x
(iii) y2
(iv) z3
(v) 4x
(vi) xy2
Solution:
(i)The coefficient of 4 is xy2z3.
(ii) The coefficient of x is 4y2z3.
(iii) The coefficient of y2 is 4xz3.
(iv) The coefficient of z3 is 4xy2.
(v) The coefficient of 4x is y2z3.
(vi) The coefficient of xy2 is 4z3.
VII. State whether the following statement is true or false:
(i) The coefficient of x in 35x is 35x.
(ii) The coefficient of mn in –2mn is -2.
(iii) The coefficient of b in -4ab is -4.
(iv) In product 9pq, 9 is the numerical coefficient of pq.
(v) In product 4abc, b is the literal coefficient of 4a.
Solution:
(i) False
(ii)True
(iii) False
(iv) True
(v) False