Q1: If Aftab’s age is represented by “a”, and Shabnam is 5 years older than Aftab, write an algebraic expression for Shabnam’s age.
Ans:
Shabnam’s age = Aftab’s age + 5. The algebraic expression is “a + 5”.
Q2: Simplify the expression 3x + 5x – 2x.
Ans:
Combine like terms:
(3x + 5x – 2x) = (3 + 5 – 2)x = 6x.
Q3: A shop sells pencils for “c” each and erasers for “d” each. If a customer buys 4 pencils and 3 erasers, write an expression for the total cost.
Ans:
Total cost = Cost of pencils + Cost of erasers
Total cost = 4c + 3d.
Q4: The perimeter of a square is 4 x side. If the side length is “q”, write the simplified algebraic expression for the perimeter.
Ans:
Perimeter = 4 x q = 4q.
Q5: If m = 4, find the value of the expression 5m + 3.
Ans:
Substitute m = 4:
5 x 4 + 3 = 20 + 3 = 23.
Q6: A rectangle has length “l” and breadth “b”. Write the simplified expression for its perimeter.
Ans:
Perimeter = 2 x (l + b) = 2l + 2b.
Q7: Simplify Tp – p + 5q – 2q.
Ans:
Combine like terms:
(Tp – p) + (5q – 2q) = (T – 1)p + 3q = Tp – p + 3q.
Q8: If a number machine follows the rule “3a – b”, find the output when a = 5 and b = 2.
Ans:
Output = 3 x 5 – 2 = 15 – 2 = 13.
Q9: A snail climbs “u” cm during the day and slips back “d” cm at night. Write an expression for its net progress after 5 days and 5 nights.
Ans:
Net progress = 5 x (u – d).
Q10: A train stops for 2 minutes at each of 3 stations. If the travel time between stations is “t” minutes, write an expression for the total journey time.
Ans:
Total time = Travel time + Stop time = 3 x t + 6 minutes.
Q11: Simplify 4(x + y) – y.
Ans:
Distribute and combine like terms:
4x + 4y – y = 4x + 3y.
Q12: If 10y – 3 and 10(y – 3) are two expressions, compare their values when y = 4.
Ans:
10y – 3 = 10 x 4 – 3 = 37.
10(y – 3) = 10 x (4 – 3) = 10.
They are not equal.
Q13: Subtract 9a – 6b + 14 from 6a + 9b – 18.
Ans:
(6a + 9b – 18) – (9a – 6b + 14) = -3a + 15b – 32.