NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.1, 10.2 Solutions
In this page we have provided solutions of the Exercises 10.1, 10.2 of NCERT Class 7 Maths Chapter 10 Algebraic Expressions. These solutions are made by our team of expert teachers. Practice these solutions carefully for a better understanding of the topic which will help in scoring good marks in the examination.
Publishing Organisation |
NCERT |
Class |
7 |
Subject |
Mathematics |
Chapter |
10: Algebraic Expressions |
Exercise |
10.1, 10.2 |
Exercise – 10.1
(1) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
(i) Subtraction of z from y.
Ans:- Y – Z
(ii) One-half of the sum of numbers x and y.
Ans:- 1/2 (x + y)
(iii) The number z multiplied by itself.
Ans:- Z2
(iv) One-fourth of the product of numbers p and q.
Ans:- 1/4 pq
(v) Numbers x and y both squared and added.
Ans:- x2 + y2
(vi) Number 5 added to three times the product of numbers m and n.
Ans:- 3mn + 5
(vii) Product of numbers y and z subtracted from 10.
Ans:- 10 – yz
(viii) Sum of numbers a and b subtracted from their product.
Ans:- ab – (a + b)
(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 + x2
(c) y – y3
(d) 5xy2 + 7x2y
(e) – ab + 2b2 – 3a2
Ans:-
(ii) Identify terms and factors in the expressions given below:
(a) -4x + 5
Ans:- Terms: -4x;5
Factors: -4, x ; 5
(b) -4x + 5y
Ans:- Terms: -4x ; 5
Factors: -4x ; 5
(c) 5y + 3y2
Ans:- Terms: 5y ; 3y2
Factors: 5, y ; 3y2
(d) xy + 2x2y2
Ans:- Terms: xy ; 2x2y2
Factors: x, y; 2, x, x, y, y
(e) pq + q
Ans:- Terms: pq; q
Factors: P,q;q
(f) 1.2 ab – 2.4 b + 3.6 a
Ans:- Terms: 1.2 ab; -2.4 b ; 3.6 a
Factors: 1.2, a, b; – 2.4, b ; 3.6 a
(g) 3/4x + 1/4
Ans:- Terms: 3/4 x ; 1/4
Factors: ¾, x; 1/4
(h) 0.1 p2 + 0.2 q2
Ans:- Terms: 0.1 p2; 0.2 q2
Factors: 0.1, p, p; 0.2, q, p.
(3) Identify the numerical coefficients of terms (other than constants) in the following expressions:
Row |
Expression | Terms | Coefficients |
(i) | 5 – 3t2 | -3t2 |
-3 |
(ii) |
1 + t + t2 + t3 | t
t2 t3 |
1
1 1 |
(iii) | X + 2xy + 3y | X
2xy 3y |
1 2 3 |
(iv) |
100m + 1000n | 100m
1000n |
100
1000 |
(v) | -p2q2 + 7pq | -p2q2
7 pq |
-1 7 |
(vi) |
1.2 a + 0.8 b | 1.2 a
0.8 b |
1.2
0.8 |
(vii) | 3.14r2 | 3.14r2 |
3.14 |
(viii) |
2 (l + b) | 2l
2b |
2
2 |
(ix) | 0.1y + 0.01y2 | 0.1y
0.01y2 |
0.1 0.01 |
(4) (a) Identify terms which contain x and give the coefficient of x.
(i) y2x + y
Ans:-
Terms which Contains xy2x. |
Coefficient of xy2 |
(ii) 13y2 – 8yx
Ans:-
Terms which contains x – 8xy |
Coefficient of x – 8y |
(iii) x + y + 2
Ans:-
Terms which contains xx |
Coefficient of x 1 |
(iv) 5 + z + ZX
Ans:-
Terms which contains xzx |
Coefficient of xz |
(v) 1 + x + XY
Ans:-
Terms which contains xxxy |
Coefficient of x 1y |
(vi) 12xy2 + 25
Ans:-
Terms which contains x12xy2 |
Coefficient of x 12 y2 |
(vii) 7x + xy2
Ans:-
Terms which contains x 7x xy2 |
Coefficient of x 7 y2
|
(b) Identify terms which contain y2 and give the coefficient of y2.
(i) 8 – xy2
Ans:-
Terms which contains y2 – xy2 |
Coefficient of y2 – x
|
(ii) 5y2 + 7x
Ans:-
Terms which contains y2 5y2 |
Coefficient of y2 – 5
|
(iii) 2x2 – 15xy2 + 7y2
Ans:-
Terms which contains y2 – 15 xy2 7y2 |
Coefficient of y2 – 15 × 7
|
(5) Classify into monomials, binomials and trinomials.
(i) 4y – 7z
Ans:- Binomial
(ii) y2
Ans:- Monomial
(iii) x + y – XY
Ans:- Trinomial
(iv) 100
Ans:- Monomial
(v) ab – a – b
Ans:- Trinomial
(vi) 5 – 3t
Ans:- Binomial
(vii) 4p2q – 4pq2
Ans:- Binomial
(viii) 7mn
Ans:- Monomial
(ix) z2 – 3z + 8
Ans:- Trinomial
(x) a2 + b2
Ans:- Binomial
(xi) z2 + z
Ans:- Binomial
(xii) 1 + x + x2
Ans:- Trinomial
(6) State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
Ans:- Like
(ii) -7x, 5/2 x
Ans:- Like
(iii) -29x, – 29y
Ans:- Unlike
(iv) 14xy, 42yx
Ans:- Like
(v) 4m2p, 4mp2
Ans:- Unlike
(vi) 12xz, 12x2z2
Ans:- Unlike
(7) Identify like terms in the following:
(a) –xy2, -4yx2, 8x2, 2xy2, 7y, – 11x2, – 100x, – 11yx, 20x2y, -6x2, y, 2xy, 3x
Ans:- -xy2, 2xy2, -4yx2, 20x2y, 8x2, -11x2, -6x2, 7y, 7, -100x, 3x, -11xy, 2xy
(b) 10pq, 7p, 8q, -p2q2, -7qp, -100q, -23, 12q2p2, -5p3, 41, 2405p, 78ap, 13p2q, qp2, 701p2
Ans:- 10pq, -7qr, 78qp, 7p, 2405p, 8q, -100q, -p2q2, 12 p2 q2, -23, 42, -5p2, 701p2, 13p2q, qp2
Exercise – 10.2
(1) If m = 2, find the value of:
(i) m – 2
Ans:- m – 2 = 2 – 2 = 0
(ii) 3m – 5
Ans:- 3m – 5 = 3 × 2 – 5 = 6 – 5 = 1
(iii) 9 – 5m
Ans:- 9 – 5m = 9 – 5 × 2 = 9 – 10 = -1
(iv) 3m2 – 2m – 7
Ans:- 3 (2)2 – 2 (2) – 7
(v) 5m/2 4
Ans:- 5 × 2/2 – 4 = 5 4 = 1
(2) If p = – 2, find the value of:
(i) 4p + 7
Ans:- 4 × (-2) + 7
= – 8 + 7
= -1
(ii) -3p2 + 4p + 7
Ans:- -3 (-2) × (-2) + 4 × (-2) + 7
= -12 – 8 + 7
= -13
(iii) -2p3 – 3p2 + 4p + 7
Ans:- -2 (-2) × (-2) × (-2) – 3 (-2) × (-2) + 4 × (-2) + 7
= 16 – 12 -8 + 7
= 3
(3) Find the value of the following expressions, when x = –1:
(i) 2x – 7
Ans:- 2 × (-1) – 7
= -9
(ii) –x + 2
Ans:- – (-1) + 2
= 1 + 2
= 3
(iii) x2 + 2x + 1
Ans:- (-1) × (-1) + 2x (-1) + 1
= 1 – 2 + 1
= 0
(iv) 2x2 – x – 2
Ans:- 2 (-1) × (-1) – (-1) -2
= 2 + 1 – 2
= 1
(4) If a = 2, b = – 2, find the value of:
(i) a2 + b2
Ans:- (2)2 + (2)2
= 4 + 4
= 8
(ii) a2 + ab + b2
Ans:- (2)2 + (2) (-2) + (-2)2
= 4 – 4 + 4
= 4 + 4 – 4
= 8 – 4
= 4
(iii) a2 – b2
Ans:- (2)2 – (-2)2
= 4 – 4
= 0
(5) When a = 0, b = – 1, find the value of the given expressions:
(i) 2a + 2b
Ans:- 2 (0) + 2 (-1)
1 Put a = 0, b = 1
= 0 – 2
= -2
(ii) 2a2 + b2 + 1
Ans:- 2 (o)2 + (-1)2 + 1
= 0 + 1 + 1
= 2
(iii) 2a2b + 2ab2 + ab
Ans:- 2 (0)2 – (-1) + 2 (0) (-1)2 + (0) (-1)
= 0 + 0 + 0
= 0
(iv) a2 + ab + 2
Ans:- (o)2 + (0) (-1) + 2
= 0 + 0 + 2
= 2
(6) Simplify the expressions and find the value if x is equal to 2.
(i) x + 7 + 4 (x – 5)
Ans:- x + 7 + 4x – 20
= x + 4x +7 – 20
= (5 × 2) – 13
= 10 – 13
= -3
(ii) 3 (x + 2) + 5x – 7
Ans:- 3x + 6 + 5x – 7
= 3x + 5x + 6 – 7
= 8x – 1
= (8 × 2) – 1
= 16 – 1
= 15
(iii) 6x + 5 (x – 2)
Ans:- 6x + 5x – 10
= 11x – 10
= (11 × 2) – 10
= 22 – 10
= 12
(iv) 4 (2x – 1) + 3x + 11
Ans:- 8x – 4 + 3x + 11
= 11x + 7
= (11 × 2) + 7
= 22 + 7
= 29
(7) Simplify these expressions and find their values if x = 3, a = – 1, b = – 2.
(i) 3x – 5 – x + 9
Ans:- 3x – x – 5 + 9
= 2x + 4
= (2 × 3) + 4
= 10
(ii) 2 – 8x + 4x + 4
Ans:- 2 + 4 – 8x + 4x
= 6 – 4x
= 6 – (4 × 3)
= 6 – 12
= 6
(iii) 3a + 5 – 8a + 1
Ans:- 3a – 8a + 5 + 1
= -5a + 6
= -5 × (-1) + 6
= 5 + 6
= 11
(iv) 10 – 3b – 4 – 5b
Ans:- 10 – 4 – 3b – 5b
= 6 -8b
= 6 – 8 × (-2)
= 6 + 16
= 22
(v) 2a – 2b – 4 – 5 + a
Ans:- 2a + a – 2b – 4 – 5
= 3a – 2b – 9s
= 3 × (-1) – 2 (-2) – 9
= -3 + 4 – 9
= – 8
(8) (i) If z = 10, find the value of z3 – 3 (z – 10).
Ans:- z3 – 3z + 30
= (10)3 – 3 (10) + 3 1 Put z = 10
= 1000 – 30 + 30
= 1000
(ii) If P = -10, find the value of p2 – 2p – 100
Ans:- (-10)2 – 2(-10) – 100
= 1 Put P = -10
= 100 + 20 – 100
= 120 – 100
= 20
(9) What should be the value of a if the value of 2x2 + x – a equals to 5, when x = 0?
Ans:- 2x2 + x –a = 5, when x = 0
(2 × 0) + 0- a
= 5
0 – a = 5
a = -5
(10) Simplify the expression and find its value when a = 5 and b = – 3.
2 (a2 + ab) + 3 – ab
Ans:- 2a2 + 2ab + 3 – ab
= 2a2 + 2ab – ab + 3
= 2a2 + ab + 3
= 2 (5)2 + (5) (-3) + 3
1 Put a = 5, b = 3
= 50 – 15 +3
= 50 + 3 – 15
= 53 – 15
= 38
Chapter 8 Rational Numbers