Students can Download Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

Question 1.

Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations

- Subtraction of z from y.
- One-half of the sum of numbers x and y?
- The number z multiplied by itself
- One-fourth of the product of numbers p and q
- Numbers x and y both squared and added.
- Number 5 added to three times the product of numbers m and n.
- Product of numbers and z subtracted from 10.
- Sum of numbers a and b subtracted from their product.

Solution:

- y – z
- \(\frac{x+y}{2}\)
- z × z = z
^{2} - \(\frac{p \times q}{4}=\frac{p q}{4}\)
- x
^{2}+ y^{2 } - mn + 5
- 10 – yz
- ab – (a + b)

Question 2.

(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.

(a) x – 3

(b) 1 + x + x^{2}

(c) y – y^{3}

(d) 5xy^{2} + 7x^{2}y

(e) – ab + 2b^{2} – 3a^{2}

Solution:

(a) x – 3

(b) 1 + x + x^{2}

(c) y – y^{3}

(d) 5xy^{2} + 7x^{2}y

(e) – ab + 2b^{2} – 3a^{2}

(ii) Identify terms and factors in the expressions given below:

(a) – 4x + 5

(b) – 4x + 5y

(c) 5y + 3y^{2}

(d) xy + 2x^{2}y^{2}

(e) pq + q

(f) 1.2 ab – 2.4 b + 3.6 a

(g) \(\frac{3}{4}\) x + \(\frac{1}{4}\)

(h) 0.1p^{2} + 0.2q^{2}

Solution:

Question 3.

Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t^{2}

(ii) 1 + t + t^{2} + t^{3}

(iii) x + 2xy + 3y

(iv) 100m + 1000n

(v) – p^{2}q^{2} + 7pq

(vi) 1.2 a + 0.8 b

(vii) 3.14 r^{2}

(viii) 2 (l + b)

(ix) 0.1 y + 0.01y^{2}

Solution:

Question 4.

(a) Identify terms which contain x and give the coefficient of x.

(i) y^{2}x + y

(ii) 13y^{2} – 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(v) 1 + x + xy

(vi) 12xy^{2} + 25

(vii) 7x + xy^{2}

Solution:

(b) Identify terms which contain y^{2} and give the coefficient of y^{2}.

(i) 8 – xy^{2}

(ii) 5y^{2} + 7x

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Solution:

Question 5.

Classify into monomials, binomials and trinomials.

(i) 4y – 7z

(ii) y^{2}

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p^{2}q – 4pq^{2}

(viii) 7mn

(ix) z^{2} – 3z + 8

(x) a^{2} + b^{2}

(xi) z^{2} + z

(xii) 1 + x + x^{2}

Solution:

Question 6.

State whether a given pair of terms is of like or unlike terms.

- 1,100
- -7x, \(\frac{5}{2}\)x
- -29x, -29y
- 14xy, 42yx
- 4m
^{2}p, 4mp^{2} - 12xz, 12x
^{2}z^{2}

Solution:

- Like
- Like
- Unlike
- Like
- Unlike
- Unlike

Question 7.

Identify like terms in the following:

(a) – xy^{2}, – 4yx^{2}, 8x^{2}, 2xy^{2}, 7y, – 11x^{2}, – 100x, 11yx, 20x^{2}y, – 6x^{2}, y, 2xy, 3x

Solution:

– xy^{2}, 2xy^{2}, – 4yx^{2}, 20x^{2}y; 8x^{2}, – 6x^{2}, – 11x^{2}, 7y, y, – 100x, 3x, – 11yx, 2xy

(b) 10pq, 7p, 8q, – p^{2}q^{2}, – 7qp, – 100q, – 23, 12q^{2}p^{2}, – 5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}

Solution:

10pq, – 7pq, 78qp, 7p, 2405p, 8q, – 100q, – p^{2}q^{2}, – 23, 41, – 5p^{2} , 701p^{2}, 13p^{2}q, qp^{2}

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