Unit Test (Solutions): Algebraic Expressions | Mathematics (Maths) Class 7 (Old NCERT) PDF Download

Time: 1 hour M.M. 30 

Attempt all questions. 

• Question numbers 1 to 5 carry 1 mark each. 
• Question numbers 6 to 8 carry 2 marks each. 
• Question numbers  9 to 11 carry 3 marks each. 
• Question numbers 12 & 13 carry 5 marks each.

Q1: The algebraic expression for "two less than the product of x and y" is:  (1 mark)
(a) x + y
(b) xy
(c) xy - 2
(d) x - y
Ans: (c)
Sol:
"Product of x and y" is xy, and "two less than" means -2.
Therefore, the algebraic equation becomes xy - 2

Q2: Simplify: 5x + 2y - 3x + 4y.  (1 mark)
(a) 6x + 2y
(b) 2x + 6y
(c) 2x + y
(d) 2x + 6y
Ans: (d)
Sol:
Combine the 'x' terms and the 'y' terms separately:
5x - 3x = 2x, and 2y + 4y = 6y.
Therefore, the algebraic equation becomes 2x + 6y.

Q3: The algebraic expression for "three times a number increased by 4" is:  (1 mark)
(a) 3x + 4
(b) 4x + 3
(c) 3x - 4
(d) 4x - 3
Ans: (a)
Sol:
"Three times a number" is 3x, and "increased by 4" means +4.
Therefore, the algebraic equation becomes 3x + 4.

Q4: Add 5pq and -12pq.  (1 mark)
Ans: Adding the coefficients of the given terms will give the sum of the two terms, that is,
5pq + (-12pq)
= (5 - 12)pq
= -7pq
Thus, the sum is -7pq.

Q5: Subtract 12pq from 5pq.  (1 mark)
Ans: Subtracting the coefficients of the given terms will give the difference between the two terms, that is,
5pq - 12pq
= (5 - 12)pq
= -7pq
Thus, the difference is -7pq.

Q6: Subtract 5a - 3ab + 4 from 14a - 6ab + 7b - 2.  (2 marks)
Ans: Subtract 5a - 3ab + 4 from 14a - 6ab + 7b - 2:
= 14a - 6ab + 7b - 2 - (5a - 3ab + 4)
= 14a - 6ab + 7b - 2 - 5a + 3ab - 4
= 14a - 5a - 6ab + 3ab + 7b - 2 - 4
= 9a - 3ab + 7b - 6
Thus, the result is:
9a - 3ab + 7b - 6

Q7: Add (10x² + 3x + 4y) and (5x² - 2x + 6y).  (2 marks)
Ans:
Adding (10x² + 3x + 4y) and (5x² - 2x + 6y), we get:
= (10x² + 3x + 4y) + (5x² - 2x + 6y)
= 10x² + 3x + 4y + 5x² - 2x + 6y
= (10x² + 5x²) + (3x - 2x) + (4y + 6y)
= 15x² + x + 10y
Thus, the sum is:
15x² + x + 10y

Q8. Find the value of  (2 marks)
(a) 4p² + 3q² - 7, when p = 4 and q = -1
(b) x³ - 2x²y + 5xy² + 7x + 10, when x = 2 and y = -1
Ans:
(a) 4p² + 3q² - 7
Substituting p = 4 and q = -1,
= 4(4)² + 3(-1)² - 7
= 4(16) + 3(1) - 7
= 64 + 3 - 7
= 60

(b) x³ - 2x²y + 5xy² + 7x + 10
Substituting x = 2 and y = -1,
= (2)³ - 2(2)²(-1) + 5(2)(-1)² + 7(2) + 10
= 8 - 2(4)(-1) + 5(2)(1) + 14 + 10
= 8 + 8 + 10 + 14 + 10
= 50

Q9: Simplify 4(3x + 2) + 5x + 10 when x = -2.  (3 marks)
Ans:
We are given the equation:
4(3x + 2) + 5x + 10

Substituting x = -2,
= 4[3(-2) + 2] + 5(-2) + 10
= 4[(-6) + 2] + (-10) + 10
= 4(-4) - 10 + 10
= -16 - 10 + 10
= -16
Thus, the simplified value is -16.

Q10: Simplify:   
10x - 5y + 8xy + 3x - 4y - 6xy + 2 - 7   (3 marks)
Ans:
10x - 5y + 8xy + 3x - 4y - 6xy + 2 - 7
= (10x + 3x) - (5y + 4y) + (8xy - 6xy) + (2 - 7)
= (13x) - (9y) + (2xy) - 5
= 13x - 9y + 2xy - 5
Therefore, the simplified expression is:
13x - 9y + 2xy - 5

Q11: A rope of length (3x + 4) metres is cut into two parts, one measuring (7x - 2) metres. What will be the length of the other part?      (3 marks)
Ans: The length of the other part = (total length of the rope) - (length of the cut part)
= (3x + 4) - (7x - 2)
= 3x + 4 - 7x + 2
= -4x + 6

The length of the other part will be -4x + 6 metres.

Q12: From the sum of 7p + 3q + 11 and 4p − 2q − 5, subtract 3p − q + 11.  (5 marks)
Ans: By adding coefficients of similar terms of the first two expressions we get,

By subtracting coefficients of similar terms of the above expression and third expression we get,

​Q13: Simplify the polynomial and write it in standard form:       (5 marks)
(x³ - 2)(2x² - 3x + 4) + 3x(4x - 5)
Ans:
(x³ - 2)(2x² - 3x + 4) + 3x(4x - 5)
= 2x⁵ - 3x⁴ + 4x³ - 4x² + 12x - 8 + 12x² - 15x
= 2x⁵ - 3x⁴ + 4x³ + (12x² - 4x²) + (12x - 15x) - 8
= 2x⁵ - 3x⁴ + 4x³ + 8x² - 3x - 8
Thus, the simplified polynomial is:
2x⁵ - 3x⁴ + 4x³ + 8x² - 3x - 8