Algebra questions are provided here, with answers, for students based on Class 6 and 7 syllabi. The questions are prepared as per NCERT (CBSE) guidelines. Solving these questions will help students understand the concept very well in an easy way. Learn expressions and equations of algebra here.
Algebra Questions for Class 6
Basic algebra deals with finding the unknown value using variables.
1. Soldiers are marching in a parade. There are 10 soldiers in a row. What is the rule which gives the number of soldiers, given the number of rows?
Solution: Let n be the number of rows
Number of soldiers in a row = 10
Total number of soldiers = number of soldiers in a row × number of rows
= 10n
2. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Write Leela’s age with respect to Radha’s age. Take Radha’s age to be x years.
Solution: Let Radha’s age be x years
Leela’s age = 4 years younger than Radha
= (x – 4) years
3. If a is the side-length of the equilateral triangle, then the perimeter of the triangle will be?
Solution: Side of equilateral triangle = a
The perimeter of triangle = sum of all its three sides
Since we know that an equilateral triangle has all its sides equal.
Therefore,
Perimeter of equilateral triangle = a+a+a = 3a
4. Give expressions for:
(i) p multiplied by 7
(ii) p divided by 7
Solution:
(i) p multiplied by 7
P×7 = 7p
(ii) p divided by 7
P÷7 = p/7
5. If Sam age is x years. Then, what is the age of Sam after 7 years?
Solution: Sam’s present age = x
After 7 years,
Sam’s age = x+7 years
Also, read: Algebra For Class 6
Algebra Questions for Class 7
Terms and Coefficient
If ax^{2}+bx+c is an algebraic expression, then: ax^{2}, bx and c are the terms a, b and c are the coefficients |
1. Express when x and y are both squared and added.
Solution: x^{2} + y^{2}
2. Identify the terms in 1 + x + x^{2}
Solution: Given, 1 + x + x^{2}
Terms: 1, x, x^{2}
3. Write the coefficients of terms y and y^{2} in the given expression 13 – y + 5y^{2}.
Solution: The coefficient of y = -1 and of y^{2} = 5
Like terms: When the terms have the same algebraic factors. (Ex: 2x, 3x, 4x)
Unlike terms: When the terms have different algebraic factors (Ex: 2x, 3x^{2}, 4y) Monomial: An algebraic expression having only one term. (Ex: 2x) Binomial: An algebraic expression having only two terms. (Ex: 2x+1) Trinomial: An algebraic expression having only three terms. (Ex: x^{2}+x+1) Polynomials: An algebraic expression having one or more than one term. *Note: Monomial, binomial and trinomial are all polynomials. |
4. Find which are the like and unlike terms.
(i) 12x, 7x
(ii) 3xy, 3y
Solution:
(i) 12x and 7x both have the same algebraic factors, i.e. x.
Hence, both are like terms.
(ii) 3xy have factors 3,x and y
Whereas 3y have factors 3 and y.
Hence, both have different algebraic factors, thus are unlike terms.
5. Classify into monomials, binomials and trinomials.
(i) 3x – 5y
(ii) 100z^{2}
(iii) x^{2}-2x+3
(iv) 32
Solution:
(i) 3x-5y is a binomial because it consists of two terms (i.e.) 3x and 5y.
(ii) 100z^{2} is monomial since there is only one term.
(iii) x^{2}-2x+3 is trinomial, since x^{2}, -2x and 3 are three different terms.
(iv) 32 is a monomial since it represents only a single term.
Also, read: Algebra Problems
Addition and Subtraction of Algebraic Expression
6. Collect like terms and simplify the expression:
12m^{2} – 9m + 5m – 4m^{2} – 7m + 10
Solution: Rearranging terms, we have:
12m^{2} – 4m^{2} + 5m – 9m – 7m + 10
= (12 – 4) m^{2} + (5 – 9 – 7) m + 10
= 8m^{2} + (– 4 – 7) m + 10
= 8m^{2} + (–11) m + 10
= 8m^{2} –11 m + 10
7. Subtract 24ab – 10b – 18a from 30ab + 12b + 14a.
Solution: 30ab + 12b + 14a – (24ab – 10b – 18a)
= 30ab + 12b + 14a – 24ab + 10b + 18a
= 30ab – 24ab + 12b + 10b + 14a + 18a
= 6ab + 22b + 32a
8. Find the value of x^{2}-5x+8, for x = 2.
Solution: Given: x^{2}-5x+8
By putting x =2, we get;
= (2)^{2} – 5(2) + 8
= 4 – 10 + 8
= 12 -10
= 2.
Practice Questions
Solve the following problems:
- Find the coefficients of x and x^{2 }and the terms for the polynomial x^{2}+4x-12.
- Classify the following polynomials:
- 5x+2
- 3x^{2}
- 2x^{2}+xy-4
- Solve: 2x^{2}-4x-2 = 0
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