Solved Questions on Variables and Constants
1. Which of the following represents a constant?
a) x
b) y
c) π
d) z
Answer: c) π (pi)
Explanation: π is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is a fixed value and does not change.
2. What does a variable represent?
a) A fixed value
b) An unknown quantity that can change
c) A mathematical operation
d) A constant value
Answer: b) An unknown quantity that can change
Explanation: Variables are symbols or letters used to represent unknown values or quantities that can vary. They are not fixed and can take on different values.
3. In the equation 5x + 9 = 22, what does “x” represent?
a) A constant
b) A variable
c) A mathematical operation
d) A known value
Answer: b) A variable
Explanation: In the equation, “x” represents an unknown quantity that we need to determine. It is a variable because its value can vary.
4. Which of the following is a variable in the expression 2a + 5b + 13?
a) 2
b) a
c) 5
d) 13
Answer: a) 2
Explanation: In the expression, both “a” and “b” represent variables. They are letters used to represent unknown quantities that can change. Therefore, the required answer is “a”.
5. What role does a constant play in mathematical calculations?
a) It represents an unknown value.
b) It changes throughout the calculation.
c) It provides stability and consistency.
d) It is denoted by letters or symbols.
Answer: c) It provides stability and consistency
Explanation: Constants are fixed values that remain unchanged throughout a mathematical calculation. They ensure that specific relationships or properties hold and provide a reference point for calculations.
Questions to Practice on Variables and Constants
1. In the equation y = 2x + 5, what does “y” represent?
a) Constant
b) Variable
c) Mathematical operation
d) Known value
Answer: b) Variable
2. Which of the following is a variable in the expression 4x – 3y = 10?
a) 4
b) 10
c) -3
d) y
Answer: d) y
3. What does a constant value indicate?
a) It changes frequently
b) It is unknown
c) It remains fixed throughout
d) It depends on other variables
Answer: c) it remains fixed throughout
4. Which of the following is an example of a variable?
a) The value of “π”
b) The number “7”
c) A fixed quantity
d) The letter “z”
Answer: d) The letter “z”
5. Which of the following is a constant in the equation y = 2x + b?
a) y
b) 2
c) x
d) b
Answer: b) 2
6. What role does a variable play in mathematical modelling?
a) It represents a fixed value
b) It establishes standardized values
c) It allows for generalization and flexibility
d) It provides stability and consistency
Answer: c) It allows for generalization and flexibility
7. Which of the following is an example of a constant term in a polynomial expression?
a) 3x2
b) 5
c) 2x
d) 7x3
Answer: b) 5
8. In the equation y = ax2 + bx + c, which of the following options contain constants?
a) a, b, c
b) x2
c) y
d) x
Answer: a) a, b, c
9. Which of the following is a variable in the equation 2πr = 10?
a) π
b) r
c) 2
d) 10
Answer: b) r
10. In the expression 3x + 5 = 20, what does "x" represent?
a) A constant
b) A variable
c) An operation
d) A known value
Answer: b) A variable
