Algebraic Expressions Worksheet

Objective Type Questions

1. State true or false.
   (a) 9pq and –4qp are like terms.
   (b) The coefficient of xz in the term 16xyz is 16.
   
   Multiple Choice Questions
   
   
2. If (b – 1) is a predecessor of a natural number b, then the successor of (b – 1) is
   (a) 1
   (b) b
   (c) (b + 1)
   (d) 0
3. When –d is subtracted from d, we get
   (a) 0
   (b) 2d
   (c) d
   (d) 3d
4. Which of the following is the CORRECT expression for statement “Four times a number when increased by 3 and subtracted from 31”. (Take variable p)
   (a) (4p + 3) – 31
   (b) 4(p + 3) – 31
   (c) 31 – 4(p + 3)
   (d) 31 – (4p + 3)
5. In an expression 8y³ + 7y – 13, –13 is called
   (a) constant
   (b) variable
   (c) numerical coefficient
   (d) literal coefficient
6. Which of the following algebraic statement is TRUE for 15-x/7
   (a) x reduced by 15 and divided by 7.
   (b) One-seventh of x added to 15.
   (c) x reduced by 7 and subtracted from 15.
   (d) Seven times x subtracted from 15.
7. A binomial contains
   (a) one numeric term
   (b) one algebraic term
   (c) two like terms
   (d) two unlike terms
8. The current age of Raghu is ‘m’ years. 8 years ago, his age was
   (a) (m – 8) years
   (b) (m + 8) years
   (c) 8m years
   (d) (m ÷ 8) years
9. What will be the cost of 1 kg potatoes if the cost of 7 kg potatoes is Rs. ‘p’?
   (a) Rs. (p + 7)
   (b) Rs. 7p
   (c) Rs. 7/p
   (d) Rs. p/7
   
10. When –4 is added to the successor of k + 7, the resultant sum is
    (a) k + 3
    (b) k + 4
    (c) k + 2
    (d) k + 1 
11. The length of a rope is ‘42z’ cm. If an equilateral triangle is formed by this rope, the length of each side of a triangle will be
    (a) 42z/3 cm
    (b) 42/3 cm
    (c)  3/42z cm
    (d)  3/42 cm
    
    Subjective Questions
    
    
12. Find the value of  t + 1/11 if  ‘t’ is the smallest 3-digit number.
13. Help Ronit to find the length of part I in the bat.
    
    
14. Find the length of side of a square whose perimeter measures  20/f cm.
15. What will be the previous and the next odd numbers of an odd number ‘y’?
16. Find the total cost of the following items:
    
    
17. Find the value of all variables in the following table
    
18. Find the value of 3a³ -18/a + a - 1 when a = –2.
19. Frame an algebraic expression for statement ‘q subtracted from 3 times 13 and added to number of hours in a day’.
20. Find the value of an unknown variable ‘g’ from the following statement:
    ‘g is the sum of first natural number and number of days in an ordinary year’.

Objective Type Questions

1. State true or false.
   (a) 9pq and –4qp are like terms.
   (b) The coefficient of xz in the term 16xyz is 16.
   Solution:
   (a) True
   Like terms, have same variables.
   (b) False
   The coefficient of xz in the term 16xyz is 16y.
   
   Multiple Choice Questions
   
   
2. If (b – 1) is a predecessor of a natural number b, then the successor of (b – 1) is
   (a) 1
   (b) b
   (c) (b + 1)
   (d) 0
   Correct option: (b) b
   Solution:
   Since (b – 1) is a predecessor of a natural number b, its successor is b.

3.  When –d is subtracted from d, we get
   (a) 0
   (b) 2d
   (c) d
   (d) 3d
   Correct option: (b) 2d
   Solution:
   d – (–d) = d + d = 2d 

4. Which of the following is the CORRECT expression for statement “Four times a number when increased by 3 and subtracted from 31”. (Take variable p)
   (a) (4p + 3) – 31
   (b) 4(p + 3) – 31
   (c) 31 – 4(p + 3)
   (d) 31 – (4p + 3)
   Correct option: (d) 31 – (4p + 3)
   Solution:
   Four time a number = 4p
   Increased by 3 = 4p + 3
   Subtracted from 31 = 31 – (4p + 3) 
5. In an expression 8y³+ 7y – 13, –13 is called
   (a) constant
   (b) variable
   (c) numerical coefficient
   (d) literal coefficient
   Correct option: (c) constant
   Solution:
   –13 is called a constant term.
6. Which of the following algebraic statement is TRUE for 15-x/7
   (a) x reduced by 15 and divided by 7.
   (b) One-seventh of x added to 15.
   (c) x reduced by 7 and subtracted from 15.
   (d) Seven times x subtracted from 15.
   Correct option: (c) x reduced by 7 and subtracted from 15.
   Solution:
   x reduced by 7 = x/7
   x reduced by 7 and subtracted from 15 = 15 -  x/7
7. A binomial contains
   (a) one numeric term
   (b) one algebraic term
   (c) two like terms
   (d) two unlike terms
   Correct option: (d) two unlike terms
   Solution:
   A binomial contains two unlike term.
   Example: 5xy + 3x²
8. The current age of Raghu is ‘m’ years. 8 years ago, his age was
   (a) (m – 8) years
   (b) (m + 8) years
   (c) 8m years
   (d) (m ÷ 8) years
   Correct option: (a) (m – 8) years
   Solution:
   Current age of Raghu = m
   8 years ago, Raghu’s age = (m – 8) years
9. What will be the cost of 1 kg potatoes if the cost of 7 kg potatoes is Rs. ‘p’?
   (a) Rs. (p + 7)
   (b) Rs. 7p
   (c) Rs. 7/p
   (d) Rs. p/7
   
   Correct option: (d) Rs. 
   Solution:
   Cost of 7 kg potatoes = Rs. p/7
   Then, cost of 1 kg potatoes = Rs. p/7
10. When –4 is added to the successor of k + 7, the resultant sum is
    (a) k + 3
    (b) k + 4
    (c) k + 2
    (d) k + 1
    Correct option: (b) k + 4
    Solution:
    Successor of k + 7 = (k + 7) + 1 = k + 8
    Now, required sum = (k + 8) + (–4) = k + 8 – 4 = k + 4 
11. The length of a rope is ‘42z’ cm. If an equilateral triangle is formed by this rope, the length of each side of a triangle will be
    (a) 42z/3 cm
    (b) 42/3 cm
    (c)  3/42z cm
    (d)  3/42 cm
    Correct option: (a) 42z/3  cm
    Solution:
    Length of a rope = 42z cm
    All sides of an equilateral triangle are equal.
    Therefore, length of each side of an equilateral triangle = 42z/3 cm
    
    Subjective Questions
    
    
12. Find the value of  t + 1/11 if  ‘t’ is the smallest 3-digit number.
    Solution:
    t = smallest 3-digit number = 100
    Then,  
13. Help Ronit to find the length of part I in the bat.
    
    
    Solution:
    Length of a bat = 72 cm
    Length of part II = b cm
    Therefore, length of part I = Length of a bat – Length of part II = (72 – b) cm
14. Find the length of side of a square whose perimeter measures  20/f cm.
    Solution:
    Perimeter of a square = 20/f cm
    4 × side of a square = 20/f cm
    Side of a square =  cm
15. What will be the previous and the next odd numbers of an odd number ‘y’?
    Solution:
    Odd number = y
    Then,
    Previous odd number = y – 2
    Next odd number = y + 2
16. Find the total cost of the following items:
    
    
    Solution:
    Total cost = Rs. v + Rs. 15 + Rs. 24 = Rs. (v + 15 + 24) = Rs. (v + 39)
17. Find the value of all variables in the following table
    
    Solution:
    
18. Find the value of 3a³-18/a + a - 1 when a = –2.
    Solution:
    
    = 3(–8) + 9 – 2 – 1
    = –24 + 9 – 3
    = –27 + 9
    = –18
19. Frame an algebraic expression for statement ‘q subtracted from 3 times 13 and added to number of hours in a day’.
    Solution:
    3 times 13 = 3 × 13 = 39
    q subtracted from 3 times 13 = 39 – q
    Number of hours in a day = 24
    Then,
    q subtracted from 3 times 13 added to number of hours in a day = (39 – q) + 24 
20. Find the value of an unknown variable ‘g’ from the following statement:
    ‘g is the sum of first natural number and number of days in an ordinary year’.
    Solution:
    First natural number = 1
    Number of days in an ordinary year = 365
    Therefore, g = 1 + 365 = 366