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All questions of Framing Algebraic Expressions for Class 6 Exam
What is the total number of diagonals that can be drawn from one vertex of a polygon with 6 sides?- a)6
- b)3
- c)5
- d)4
Correct answer is option 'B'. Can you explain this answer?
What is the total number of diagonals that can be drawn from one vertex of a polygon with 6 sides?
a)
6
b)
3
c)
5
d)
4
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Get Idea answered |
The formula for the number of diagonals from one vertex of an n-sided polygon is (n - 3). For a hexagon (6 sides), the calculation is (6 - 3) = 3 diagonals.
What operation is equivalent to subtracting a term in algebra?- a)Multiplying by zero
- b)Adding its reciprocal
- c)Adding its inverse
- d)Dividing by the term
Correct answer is option 'C'. Can you explain this answer?
What operation is equivalent to subtracting a term in algebra?
a)
Multiplying by zero
b)
Adding its reciprocal
c)
Adding its inverse
d)
Dividing by the term
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EduRev Class 6 answered |
Subtracting a term is equivalent to adding its inverse. For example, subtracting 3 is the same as adding -3. This principle is foundational in algebraic manipulation.
In the context of algebra, what is a polynomial?- a)An expression with only constants
- b)A term with no variables
- c)A sum of like terms only
- d)An expression with whole number exponents
Correct answer is option 'D'. Can you explain this answer?
In the context of algebra, what is a polynomial?
a)
An expression with only constants
b)
A term with no variables
c)
A sum of like terms only
d)
An expression with whole number exponents
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Manoj Iyer answered |
Understanding Polynomials
A polynomial is a fundamental concept in algebra, and it can be defined by certain characteristics. Let's break down what makes an expression a polynomial.
Definition of a Polynomial
- A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative whole number exponents.
Key Characteristics of Polynomials
- Variables and Coefficients: Polynomials contain one or more variables (like x, y, etc.) multiplied by coefficients (numbers).
- Whole Number Exponents: Each variable in a polynomial can only have whole number exponents. This means that you cannot have negative exponents or fractional exponents in a polynomial.
- Sum of Terms: A polynomial is formed by adding or subtracting multiple terms, where each term is a product of a coefficient and a variable raised to a whole number exponent.
Examples of Polynomials
- 3x^2 + 2x - 5 is a polynomial because it contains whole number exponents (2 and 1).
- 4y^3 - 7y + 2 is also a polynomial for the same reason.
Non-Examples of Polynomials
- 2/x (this has a negative exponent), or 3y^(-1) (this also has a negative exponent) are not polynomials.
In summary, option 'D' is correct because a polynomial is defined by having whole number exponents. Understanding this definition helps in classifying different algebraic expressions accurately.
A polynomial is a fundamental concept in algebra, and it can be defined by certain characteristics. Let's break down what makes an expression a polynomial.
Definition of a Polynomial
- A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative whole number exponents.
Key Characteristics of Polynomials
- Variables and Coefficients: Polynomials contain one or more variables (like x, y, etc.) multiplied by coefficients (numbers).
- Whole Number Exponents: Each variable in a polynomial can only have whole number exponents. This means that you cannot have negative exponents or fractional exponents in a polynomial.
- Sum of Terms: A polynomial is formed by adding or subtracting multiple terms, where each term is a product of a coefficient and a variable raised to a whole number exponent.
Examples of Polynomials
- 3x^2 + 2x - 5 is a polynomial because it contains whole number exponents (2 and 1).
- 4y^3 - 7y + 2 is also a polynomial for the same reason.
Non-Examples of Polynomials
- 2/x (this has a negative exponent), or 3y^(-1) (this also has a negative exponent) are not polynomials.
In summary, option 'D' is correct because a polynomial is defined by having whole number exponents. Understanding this definition helps in classifying different algebraic expressions accurately.
For the sequence of square numbers (1, 4, 9, 16, ...), which of the following expressions denotes the nth term?- a)2n
- b)n^2
- c)n + 1
- d)n^2 + 1
Correct answer is option 'B'. Can you explain this answer?
For the sequence of square numbers (1, 4, 9, 16, ...), which of the following expressions denotes the nth term?
a)
2n
b)
n^2
c)
n + 1
d)
n^2 + 1
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Get Idea answered |
The nth term of the sequence of square numbers is represented by the expression n^2. This means that if n = 1, the term is 1^2 = 1, if n = 2, the term is 2^2 = 4, and so forth.
What is the definition of a term in an algebraic expression?- a)A part of an expression separated by + and - signs
- b)A product of constants only
- c)A combination of variables only
- d)A fixed numerical value
Correct answer is option 'A'. Can you explain this answer?
What is the definition of a term in an algebraic expression?
a)
A part of an expression separated by + and - signs
b)
A product of constants only
c)
A combination of variables only
d)
A fixed numerical value
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A term in an algebraic expression is defined as a part of the expression that is separated by + and - signs. Each term typically consists of constants and variables multiplied together. For example, in the term -3xy, -3, x, and y are all factors of that term.
Which statement is true regarding adding or subtracting unlike terms?- a)They can be simplified easily
- b)They can be combined directly
- c)They must be kept separate
- d)They result in a like term
Correct answer is option 'C'. Can you explain this answer?
Which statement is true regarding adding or subtracting unlike terms?
a)
They can be simplified easily
b)
They can be combined directly
c)
They must be kept separate
d)
They result in a like term
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EduRev Class 6 answered |
Unlike terms cannot be combined directly. They must be kept separate because they represent different variables or different powers of the same variable, which means they cannot be simplified into a single term.
What is the first step in simplifying an algebraic expression?- a)Gather all like terms
- b)Add constants only
- c)Ignore all variables
- d)Combine unlike terms
Correct answer is option 'A'. Can you explain this answer?
What is the first step in simplifying an algebraic expression?
a)
Gather all like terms
b)
Add constants only
c)
Ignore all variables
d)
Combine unlike terms
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EduRev Class 6 answered |
The first step in simplifying an algebraic expression is to gather all like terms together. This allows for easier addition or subtraction of terms that share the same variable and power.
What does the term 'constant term' refer to in an expression?- a)A term that has coefficients only
- b)A term with a fixed numerical value
- c)A term that can change
- d)A term that contains variables
Correct answer is option 'B'. Can you explain this answer?
What does the term 'constant term' refer to in an expression?
a)
A term that has coefficients only
b)
A term with a fixed numerical value
c)
A term that can change
d)
A term that contains variables
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EduRev Class 6 answered |
A constant term refers to a term that has no variable factor. It is simply a fixed numerical value within an expression, such as the number 5 in the expression 2x + 5.
How can the area of a rectangle be expressed?- a)A = 2(l + b)
- b)A = l + b
- c)A = l × b
- d)A = l^2
Correct answer is option 'C'. Can you explain this answer?
How can the area of a rectangle be expressed?
a)
A = 2(l + b)
b)
A = l + b
c)
A = l × b
d)
A = l^2
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EduRev Class 6 answered |
The area of a rectangle is calculated as A = l × b, where l is the length and b is the breadth. This formula allows one to find the total space within the rectangle.
Identify the coefficient in the term -7xy.- a)x
- b)-xy
- c)-7
- d)y
Correct answer is option 'C'. Can you explain this answer?
Identify the coefficient in the term -7xy.
a)
x
b)
-xy
c)
-7
d)
y
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EduRev Class 6 answered |
The coefficient of a term is the numerical factor in that term. In -7xy, -7 is the coefficient because it is the number multiplying the variables x and y.
How do you find the value of an algebraic expression?- a)Add all constants only
- b)Only consider the coefficients
- c)Substitute the values of the variables and simplify
- d)Ignore the variables
Correct answer is option 'C'. Can you explain this answer?
How do you find the value of an algebraic expression?
a)
Add all constants only
b)
Only consider the coefficients
c)
Substitute the values of the variables and simplify
d)
Ignore the variables
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EduRev Class 6 answered |
To find the value of an algebraic expression, you need to substitute the values of the variables into the expression and then simplify it. This process allows you to evaluate the expression based on the given variable values.
Which of the following is an example of unlike terms?- a)7z and 8z
- b)2x and 3x
- c)4y^2 and 5y^2
- d)6a^3b and 2ab^2
Correct answer is option 'D'. Can you explain this answer?
Which of the following is an example of unlike terms?
a)
7z and 8z
b)
2x and 3x
c)
4y^2 and 5y^2
d)
6a^3b and 2ab^2
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EduRev Class 6 answered |
Unlike terms are those that have different variables or powers. In this case, 6a^3b and 2ab^2 have different powers of a and b, making them unlike terms, while the other options contain like terms.
If the expression is 3x + 4y - 2x + 5, what is the coefficient of x after simplification?- a)1
- b)3
- c)5
- d)2
Correct answer is option 'A'. Can you explain this answer?
If the expression is 3x + 4y - 2x + 5, what is the coefficient of x after simplification?
a)
1
b)
3
c)
5
d)
2
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EduRev Class 6 answered |
To simplify the expression, combine like terms: 3x - 2x = 1x. Thus, the coefficient of x after simplification is 1.
What is the perimeter of a regular pentagon if the length of one side is 7 cm?- a)35 cm
- b)28 cm
- c)21 cm
- d)14 cm
Correct answer is option 'A'. Can you explain this answer?
What is the perimeter of a regular pentagon if the length of one side is 7 cm?
a)
35 cm
b)
28 cm
c)
21 cm
d)
14 cm
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Get Idea answered |
The perimeter of a regular pentagon is calculated using the formula P = 5l, where l is the length of a side. For a side length of 7 cm, the perimeter is P = 5 × 7 = 35 cm.
Which of the following represents like terms?- a)4y and 7z
- b)3a and -8b
- c)3 and 5x
- d)2x^2 and 5x^2
Correct answer is option 'D'. Can you explain this answer?
Which of the following represents like terms?
a)
4y and 7z
b)
3a and -8b
c)
3 and 5x
d)
2x^2 and 5x^2
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EduRev Class 6 answered |
Like terms are those that have the same variable and the same power. Here, 2x^2 and 5x^2 both contain the variable x raised to the same power (2), making them like terms.
What is the successor of a natural number n?- a)n + 1
- b)n + 2
- c)2n
- d)n - 1
Correct answer is option 'A'. Can you explain this answer?
What is the successor of a natural number n?
a)
n + 1
b)
n + 2
c)
2n
d)
n - 1
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Get Idea answered |
The successor of a natural number n is defined as n + 1. This means that if you take any natural number and add one to it, you will get the next natural number in the sequence.
In the term 4x^3y^2, what is the degree of the term?- a)2
- b)6
- c)3
- d)5
Correct answer is option 'D'. Can you explain this answer?
In the term 4x^3y^2, what is the degree of the term?
a)
2
b)
6
c)
3
d)
5
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Get Idea answered |
The degree of a term is the sum of the exponents of all variables in that term. For 4x^3y^2, the degree is 3 (from x) + 2 (from y) = 5.
Which of the following formulas represents the area of a triangle?- a)A = l × b
- b)A = 2l
- c)A = l^2
- d)A = (b × h) / 2
Correct answer is option 'D'. Can you explain this answer?
Which of the following formulas represents the area of a triangle?
a)
A = l × b
b)
A = 2l
c)
A = l^2
d)
A = (b × h) / 2
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Get Idea answered |
The area of a triangle is given by the formula A = (b × h) / 2, where b is the base and h is the height of the triangle. This formula accounts for the triangular shape by halving the area of a rectangle.
What is the perimeter of a square with a side length of 5 cm?- a)10 cm
- b)20 cm
- c)15 cm
- d)25 cm
Correct answer is option 'B'. Can you explain this answer?
What is the perimeter of a square with a side length of 5 cm?
a)
10 cm
b)
20 cm
c)
15 cm
d)
25 cm
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Get Idea answered |
The perimeter of a square is calculated using the formula P = 4l, where l is the length of a side. For a side length of 5 cm, the perimeter would be P = 4 × 5 = 20 cm.
Which of the following is considered a constant in algebra?- a)y^2
- b)5
- c)2a
- d)x
Correct answer is option 'B'. Can you explain this answer?
Which of the following is considered a constant in algebra?
a)
y^2
b)
5
c)
2a
d)
x
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EduRev Class 6 answered |
A constant is a symbol that has a fixed numerical value. In this case, 5 is a constant, while x and y are variables that can take on various values, and 2a is a term that includes a variable.
Chapter doubts & questions for Framing Algebraic Expressions - Mathematics Class 6 ICSE 2025 is part of Class 6 exam preparation. The chapters have been prepared according to the Class 6 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 6 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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Mathematics Class 6 ICSE
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