Class 7 Important Questions for Maths - Algebraic Expressions ... - Free Printable
Educational worksheet: Class 7 Important Questions for Maths - Algebraic Expressions .... Download and print for classroom or home learning activities.
JPG
630×1375
208.1 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1473571
⭐
Show Answer Key & Explanations
Step-by-step solution for: Class 7 Important Questions for Maths - Algebraic Expressions ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Class 7 Important Questions for Maths - Algebraic Expressions ...
Let’s solve each question one by one with clear explanations.
---
1. An algebraic expression containing three terms is called a
(a) monomial (b) binomial (c) trinomial (d) All of these
✔ Answer: (c) trinomial
> Explanation:
> - Monomial = 1 term (e.g., 5x)
> - Binomial = 2 terms (e.g., 3x + 2)
> - Trinomial = 3 terms (e.g., x² + 2x + 1)
> So, an expression with three terms is called a trinomial.
---
2. Number of terms in the expression 3x²y – 2y²z – z²x + 5 is
(a) 2 (b) 3 (c) 4 (d) 5
✔ Answer: (c) 4
> Explanation:
> Terms are separated by + or – signs.
> Expression: `3x²y` – `2y²z` – `z²x` + `5` → that’s 4 terms.
---
3. The terms of expression 4x² – 3xy are:
(a) 4x² and –3xy (b) 4x² and 3xy (c) 4x² and –xy (d) x² and xy
✔ Answer: (a) 4x² and –3xy
> Explanation:
> The expression has two terms:
> - First term: `4x²`
> - Second term: `–3xy` (note the negative sign belongs to the term)
---
4. Factors of –5x² y² z are
(a) –5 × x × y × z (b) –5 × x² × y × z (c) –5 × x × x × y × y × z (d) –5 × x × y × z²
✔ Answer: (c) –5 × x × x × y × y × z
> Explanation:
> Factor means breaking into prime/multiplicative components.
> –5x²y²z = –5 × x × x × y × y × z
> So, (c) is correct.
---
5. Coefficient of x in –9x y² z is
(a) 9yz (b) –9yz (c) 9y²z (d) –9y²z
✔ Answer: (d) –9y²z
> Explanation:
> Coefficient of x means “what multiplies x”.
> In –9x y² z, x is multiplied by –9y²z.
> So coefficient of x is –9y²z.
---
6. Which of the following is a pair of like terms?
(a) –7xy²z, –7x²yz (b) –10xyz², 3xyz² (c) 3xyz, 3x²y²z² (d) 4xyz², 4x²yz
✔ Answer: (b) –10xyz², 3xyz²
> Explanation:
> Like terms have same variables with same exponents.
> - (a): xy²z vs x²yz → different powers → not like
> - (b): xyz² vs xyz² → same → like terms ✔
> - (c): xyz vs x²y²z² → different → not like
> - (d): xyz² vs x²yz → different → not like
---
7. Identify the binomial out of the following:
(a) 3xy² + 5y – x²y (b) x²y – 5y – x²y (c) xy + yz + zx (d) 3xy² + 5y – xy²
✔ Answer: (d) 3xy² + 5y – xy²
> Explanation:
> Binomial = exactly 2 terms.
> Let’s simplify each:
> (a) 3 terms → trinomial
> (b) x²y – 5y – x²y = –5y → monomial (after simplification)
> (c) 3 terms → trinomial
> (d) 3xy² – xy² + 5y = 2xy² + 5y → two terms → binomial ✔
---
8. The sum of x⁴ – xy + 2y² and –x⁴ + xy + 2y² is
(a) Monomial and polynomial in y (b) Binomial and Polynomial (c) Trinomial and polynomial (d) Monomial and polynomial in x
✔ Answer: (a) Monomial and polynomial in y
> Explanation:
> Add:
> (x⁴ – xy + 2y²) + (–x⁴ + xy + 2y²)
> = (x⁴ – x⁴) + (–xy + xy) + (2y² + 2y²)
> = 0 + 0 + 4y² = 4y²
> This is a monomial (one term), and it's a polynomial in y.
---
9. The subtraction of 5 times of y from x is
(a) 5x – y (b) y – 5x (c) x – 5y (d) 5y – x
✔ Answer: (c) x – 5y
> Explanation:
> “5 times of y” = 5y
> “Subtraction of 5y from x” = x – 5y
---
10. –b – 0 is equal to
(a) –1 × b (b) 1 – b – 0 (c) 0 – (–1) × b (d) –b – 0 – 1
✔ Answer: (a) –1 × b
> Explanation:
> –b – 0 = –b
> And –b = –1 × b → so (a) is correct.
> Others don’t simplify to –b.
---
11. The side length of the top of square table is x. The expression for perimeter is:
(a) 4 + x (b) 2x (c) 4x (d) 8x
✔ Answer: (c) 4x
> Explanation:
> Perimeter of square = 4 × side = 4 × x = 4x
---
12. The number of scarfs of length half metre that can be made from y metres of cloth is:
(a) 2y (b) y/2 (c) y + 2 (d) y + ½
✔ Answer: (a) 2y
> Explanation:
> Each scarf = 0.5 m = ½ m
> Number of scarfs = total cloth ÷ length per scarf = y ÷ (½) = 2y
---
13. 123x⁶y – 138x⁶y is a like term of:
(a) 10xy (b) –15xy (c) –15xy² (d) 10x⁶y
✔ Answer: (d) 10x⁶y
> Explanation:
> First, simplify: 123x⁶y – 138x⁶y = –15x⁶y
> So, it’s a like term with any term having x⁶y, which is option (d).
---
14. The value of 3x² – 5x + 3 when x = 1 is
(a) 1 (b) 0 (c) –1 (d) 11
✔ Answer: (a) 1
> Explanation:
> Plug in x = 1:
> 3(1)² – 5(1) + 3 = 3 – 5 + 3 = 1
---
15. The expression for the number of diagonals that we can make from one vertex of a n sided polygon is:
(a) 2n + 1 (b) n – 2 (c) 5n + 2 (d) n – 3
✔ Answer: (d) n – 3
> Explanation:
> From one vertex, you cannot draw a diagonal to:
> - itself
> - the two adjacent vertices (they form sides, not diagonals)
> So, total possible diagonals from one vertex = n – 3
---
16. The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
(a) 2x + 16 (b) 6x + 9 (c) 8x + 3 (d) 8x + 12
✔ Answer: (d) 8x + 12
> Explanation:
> Perimeter = 4 × side = 4 × (2x + 3) = 8x + 12
---
## ✔ Final Answers:
1. (c)
2. (c)
3. (a)
4. (c)
5. (d)
6. (b)
7. (d)
8. (a)
9. (c)
10. (a)
11. (c)
12. (a)
13. (d)
14. (a)
15. (d)
16. (d)
Let me know if you’d like a summary sheet or printable version!
---
1. An algebraic expression containing three terms is called a
(a) monomial (b) binomial (c) trinomial (d) All of these
✔ Answer: (c) trinomial
> Explanation:
> - Monomial = 1 term (e.g., 5x)
> - Binomial = 2 terms (e.g., 3x + 2)
> - Trinomial = 3 terms (e.g., x² + 2x + 1)
> So, an expression with three terms is called a trinomial.
---
2. Number of terms in the expression 3x²y – 2y²z – z²x + 5 is
(a) 2 (b) 3 (c) 4 (d) 5
✔ Answer: (c) 4
> Explanation:
> Terms are separated by + or – signs.
> Expression: `3x²y` – `2y²z` – `z²x` + `5` → that’s 4 terms.
---
3. The terms of expression 4x² – 3xy are:
(a) 4x² and –3xy (b) 4x² and 3xy (c) 4x² and –xy (d) x² and xy
✔ Answer: (a) 4x² and –3xy
> Explanation:
> The expression has two terms:
> - First term: `4x²`
> - Second term: `–3xy` (note the negative sign belongs to the term)
---
4. Factors of –5x² y² z are
(a) –5 × x × y × z (b) –5 × x² × y × z (c) –5 × x × x × y × y × z (d) –5 × x × y × z²
✔ Answer: (c) –5 × x × x × y × y × z
> Explanation:
> Factor means breaking into prime/multiplicative components.
> –5x²y²z = –5 × x × x × y × y × z
> So, (c) is correct.
---
5. Coefficient of x in –9x y² z is
(a) 9yz (b) –9yz (c) 9y²z (d) –9y²z
✔ Answer: (d) –9y²z
> Explanation:
> Coefficient of x means “what multiplies x”.
> In –9x y² z, x is multiplied by –9y²z.
> So coefficient of x is –9y²z.
---
6. Which of the following is a pair of like terms?
(a) –7xy²z, –7x²yz (b) –10xyz², 3xyz² (c) 3xyz, 3x²y²z² (d) 4xyz², 4x²yz
✔ Answer: (b) –10xyz², 3xyz²
> Explanation:
> Like terms have same variables with same exponents.
> - (a): xy²z vs x²yz → different powers → not like
> - (b): xyz² vs xyz² → same → like terms ✔
> - (c): xyz vs x²y²z² → different → not like
> - (d): xyz² vs x²yz → different → not like
---
7. Identify the binomial out of the following:
(a) 3xy² + 5y – x²y (b) x²y – 5y – x²y (c) xy + yz + zx (d) 3xy² + 5y – xy²
✔ Answer: (d) 3xy² + 5y – xy²
> Explanation:
> Binomial = exactly 2 terms.
> Let’s simplify each:
> (a) 3 terms → trinomial
> (b) x²y – 5y – x²y = –5y → monomial (after simplification)
> (c) 3 terms → trinomial
> (d) 3xy² – xy² + 5y = 2xy² + 5y → two terms → binomial ✔
---
8. The sum of x⁴ – xy + 2y² and –x⁴ + xy + 2y² is
(a) Monomial and polynomial in y (b) Binomial and Polynomial (c) Trinomial and polynomial (d) Monomial and polynomial in x
✔ Answer: (a) Monomial and polynomial in y
> Explanation:
> Add:
> (x⁴ – xy + 2y²) + (–x⁴ + xy + 2y²)
> = (x⁴ – x⁴) + (–xy + xy) + (2y² + 2y²)
> = 0 + 0 + 4y² = 4y²
> This is a monomial (one term), and it's a polynomial in y.
---
9. The subtraction of 5 times of y from x is
(a) 5x – y (b) y – 5x (c) x – 5y (d) 5y – x
✔ Answer: (c) x – 5y
> Explanation:
> “5 times of y” = 5y
> “Subtraction of 5y from x” = x – 5y
---
10. –b – 0 is equal to
(a) –1 × b (b) 1 – b – 0 (c) 0 – (–1) × b (d) –b – 0 – 1
✔ Answer: (a) –1 × b
> Explanation:
> –b – 0 = –b
> And –b = –1 × b → so (a) is correct.
> Others don’t simplify to –b.
---
11. The side length of the top of square table is x. The expression for perimeter is:
(a) 4 + x (b) 2x (c) 4x (d) 8x
✔ Answer: (c) 4x
> Explanation:
> Perimeter of square = 4 × side = 4 × x = 4x
---
12. The number of scarfs of length half metre that can be made from y metres of cloth is:
(a) 2y (b) y/2 (c) y + 2 (d) y + ½
✔ Answer: (a) 2y
> Explanation:
> Each scarf = 0.5 m = ½ m
> Number of scarfs = total cloth ÷ length per scarf = y ÷ (½) = 2y
---
13. 123x⁶y – 138x⁶y is a like term of:
(a) 10xy (b) –15xy (c) –15xy² (d) 10x⁶y
✔ Answer: (d) 10x⁶y
> Explanation:
> First, simplify: 123x⁶y – 138x⁶y = –15x⁶y
> So, it’s a like term with any term having x⁶y, which is option (d).
---
14. The value of 3x² – 5x + 3 when x = 1 is
(a) 1 (b) 0 (c) –1 (d) 11
✔ Answer: (a) 1
> Explanation:
> Plug in x = 1:
> 3(1)² – 5(1) + 3 = 3 – 5 + 3 = 1
---
15. The expression for the number of diagonals that we can make from one vertex of a n sided polygon is:
(a) 2n + 1 (b) n – 2 (c) 5n + 2 (d) n – 3
✔ Answer: (d) n – 3
> Explanation:
> From one vertex, you cannot draw a diagonal to:
> - itself
> - the two adjacent vertices (they form sides, not diagonals)
> So, total possible diagonals from one vertex = n – 3
---
16. The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
(a) 2x + 16 (b) 6x + 9 (c) 8x + 3 (d) 8x + 12
✔ Answer: (d) 8x + 12
> Explanation:
> Perimeter = 4 × side = 4 × (2x + 3) = 8x + 12
---
## ✔ Final Answers:
1. (c)
2. (c)
3. (a)
4. (c)
5. (d)
6. (b)
7. (d)
8. (a)
9. (c)
10. (a)
11. (c)
12. (a)
13. (d)
14. (a)
15. (d)
16. (d)
Let me know if you’d like a summary sheet or printable version!
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions questions.
