Class 7 Important Questions for Maths - Algebraic Expressions ... - Free Printable
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Step-by-step solution for: Class 7 Important Questions for Maths - Algebraic Expressions ...
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Show Answer Key & Explanations
Step-by-step solution for: Class 7 Important Questions for Maths - Algebraic Expressions ...
Let’s go through each statement one by one and decide if it’s True or False, with simple explanations.
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33. 1 + x/2 + x³ is a polynomial.
✔ True — A polynomial can have variables raised to whole number powers (like 0, 1, 2, 3...). Here, x³ and x¹ (in x/2) are fine. Constants like 1 are also allowed. So yes, this is a polynomial.
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34. (3a – b + 3) – (a + b) is a binomial.
Let’s simplify:
(3a – b + 3) – a – b = 3a – a – b – b + 3 = 2a – 2b + 3 → That’s three terms: 2a, -2b, +3 → trinomial, not binomial.
✘ False
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35. A trinomial can be a polynomial.
✔ True — All trinomials are polynomials! “Polynomial” just means many terms (or even one). Trinomial = exactly 3 terms → still a polynomial.
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36. A polynomial with more than two terms is a trinomial.
✘ False — Trinomial means *exactly* three terms. If it has 4, 5, or more terms, it’s still a polynomial, but NOT a trinomial.
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37. Sum of x and y is x + y.
✔ True — That’s what “sum” means — add them together.
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38. Sum of 2 and p is 2p.
✘ False — Sum means addition: 2 + p. 2p means multiplication (2 times p).
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39. A binomial has more than two terms.
✘ False — Binomial means *exactly* two terms. Like x + y, or 3a – 5.
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40. A trinomial has exactly three terms.
✔ True — Yes! That’s the definition.
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41. In like terms, variables and their powers are the same.
✔ True — Like terms must have same variable(s) raised to same power(s). Example: 3x² and 5x² are like; 3x² and 3x are not.
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42. The expression x + y + 5x is a trinomial.
Wait — let’s combine like terms first: x + 5x = 6x → so expression becomes 6x + y → that’s two terms → binomial.
So originally it looked like 3 terms, but after simplifying, it’s only 2.
But the question says “the expression x + y + 5x” — without simplifying? Hmm… In math, we usually consider simplified form for classification.
Actually, even before simplifying, it’s written as 3 terms — but technically, since x and 5x are like terms, they should be combined.
Most textbooks say: classify after combining like terms. So 6x + y → binomial.
✘ False — It’s not a trinomial after simplification.
*(Note: Some might argue based on unsimplified form, but standard practice is to simplify first.)*
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43. 4p is the numerical coefficient of q² in –4pq².
In –4pq², the term is –4 × p × q².
The coefficient of q² would include everything else multiplying it → which is –4p.
But the question says “numerical coefficient” — that usually means just the number part, not including variables.
So numerical coefficient of q² in –4pq² is –4, because p is a variable.
So saying “4p is the numerical coefficient” is wrong — 4p includes a variable.
✘ False
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44. 5a and 5b are unlike terms.
✔ True — Different variables → unlike terms. You can’t add them directly.
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45. Sum of x² + x and y + y² is 2x² + 2y².
Add them: (x² + x) + (y + y²) = x² + x + y + y² → no like terms to combine → stays as x² + x + y + y².
Not 2x² + 2y² — that would mean doubling each squared term, which isn’t correct.
✘ False
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46. Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.
✔ True — Additive inverse of a term is its negative. So subtracting 5 is same as adding –5. Always true.
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47. The total number of planets of Sun can be denoted by the variable n.
✔ True — We can use any letter to represent a quantity. Even though we know there are 8 planets, using ‘n’ as a variable is perfectly fine in algebra.
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48. In like terms, the numerical coefficients should also be the same.
✘ False — Coefficients can be different! Like 3x and 7x are like terms — same variable, same power, different coefficients. That’s okay.
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49. If we add a monomial and binomial, then answer can never be a monomial.
Monomial: 1 term. Binomial: 2 terms.
Example: Add 3x (monomial) and (–3x + 5) (binomial):
3x + (–3x + 5) = 0x + 5 = 5 → which is a monomial!
So YES, it CAN become a monomial.
Therefore, saying “can never be” is false.
✘ False
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50. If we subtract a monomial from a binomial, then answer is at least a binomial.
Binomial minus monomial.
Example: (x + y) – x = y → which is a monomial.
So answer can be monomial → not “at least binomial”.
✘ False
---
51. When we subtract a monomial from a trinomial, then answer can be a polynomial.
Trinomial: 3 terms. Subtract monomial: could cancel one term → left with 2 terms → still a polynomial (since all binomials/trinomials are polynomials).
Even if you get 1 term or 0 terms, those are still considered polynomials (constant or zero polynomial).
So yes — answer will always be a polynomial.
✔ True
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52. When we add a monomial and a trinomial, then answer can be a monomial.
Monomial + trinomial → normally 4 terms, unless some cancel.
Example: Add 2x (monomial) and (–2x + y + z) → result: y + z → binomial.
Can we get monomial? Try: 3x + (–3x – y – z) = –y – z → still binomial.
What if trinomial is (–3x + 0 + 0)? But that’s not really a trinomial — needs 3 non-zero terms.
Actually, suppose trinomial is (–x – y – z), and monomial is x → sum: –y – z → binomial.
Is there any way to get down to 1 term? Only if two terms cancel and third remains? No — monomial cancels one term, leaves two others.
Unless... what if the trinomial has terms that cancel with the monomial AND among themselves? Not possible — monomial is single term.
Wait — example: Monomial = 5, Trinomial = –5 + x – x → but again, –5 + x – x simplifies to –5 → which is monomial, not trinomial.
To be a trinomial, all three terms must be present and non-canceling initially.
So when you add monomial to trinomial, best case: one term cancels → left with 2 terms → binomial. Worst case: 4 terms.
You cannot reduce to 1 term unless two terms vanish — but monomial can only cancel one term.
So actually, it cannot become a monomial.
Thus, statement says “can be a monomial” → which is false.
✘ False
Wait — let me double-check. Suppose trinomial is: 2x + 3y – 2x → but again, that simplifies to 3y → not a trinomial.
A true trinomial must have three unlike terms that don’t cancel.
So adding a monomial can cancel at most one term → minimum 2 terms remain → binomial.
So answer cannot be monomial.
Therefore, statement 52 is ✘ False.
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Now, compiling final answers:
33. True
34. False
35. True
36. False
37. True
38. False
39. False
40. True
41. True
42. False
43. False
44. True
45. False
46. True
47. True
48. False
49. False
50. False
51. True
52. False
Final Answer:
33. True
34. False
35. True
36. False
37. True
38. False
39. False
40. True
41. True
42. False
43. False
44. True
45. False
46. True
47. True
48. False
49. False
50. False
51. True
52. False
---
33. 1 + x/2 + x³ is a polynomial.
✔ True — A polynomial can have variables raised to whole number powers (like 0, 1, 2, 3...). Here, x³ and x¹ (in x/2) are fine. Constants like 1 are also allowed. So yes, this is a polynomial.
---
34. (3a – b + 3) – (a + b) is a binomial.
Let’s simplify:
(3a – b + 3) – a – b = 3a – a – b – b + 3 = 2a – 2b + 3 → That’s three terms: 2a, -2b, +3 → trinomial, not binomial.
✘ False
---
35. A trinomial can be a polynomial.
✔ True — All trinomials are polynomials! “Polynomial” just means many terms (or even one). Trinomial = exactly 3 terms → still a polynomial.
---
36. A polynomial with more than two terms is a trinomial.
✘ False — Trinomial means *exactly* three terms. If it has 4, 5, or more terms, it’s still a polynomial, but NOT a trinomial.
---
37. Sum of x and y is x + y.
✔ True — That’s what “sum” means — add them together.
---
38. Sum of 2 and p is 2p.
✘ False — Sum means addition: 2 + p. 2p means multiplication (2 times p).
---
39. A binomial has more than two terms.
✘ False — Binomial means *exactly* two terms. Like x + y, or 3a – 5.
---
40. A trinomial has exactly three terms.
✔ True — Yes! That’s the definition.
---
41. In like terms, variables and their powers are the same.
✔ True — Like terms must have same variable(s) raised to same power(s). Example: 3x² and 5x² are like; 3x² and 3x are not.
---
42. The expression x + y + 5x is a trinomial.
Wait — let’s combine like terms first: x + 5x = 6x → so expression becomes 6x + y → that’s two terms → binomial.
So originally it looked like 3 terms, but after simplifying, it’s only 2.
But the question says “the expression x + y + 5x” — without simplifying? Hmm… In math, we usually consider simplified form for classification.
Actually, even before simplifying, it’s written as 3 terms — but technically, since x and 5x are like terms, they should be combined.
Most textbooks say: classify after combining like terms. So 6x + y → binomial.
✘ False — It’s not a trinomial after simplification.
*(Note: Some might argue based on unsimplified form, but standard practice is to simplify first.)*
---
43. 4p is the numerical coefficient of q² in –4pq².
In –4pq², the term is –4 × p × q².
The coefficient of q² would include everything else multiplying it → which is –4p.
But the question says “numerical coefficient” — that usually means just the number part, not including variables.
So numerical coefficient of q² in –4pq² is –4, because p is a variable.
So saying “4p is the numerical coefficient” is wrong — 4p includes a variable.
✘ False
---
44. 5a and 5b are unlike terms.
✔ True — Different variables → unlike terms. You can’t add them directly.
---
45. Sum of x² + x and y + y² is 2x² + 2y².
Add them: (x² + x) + (y + y²) = x² + x + y + y² → no like terms to combine → stays as x² + x + y + y².
Not 2x² + 2y² — that would mean doubling each squared term, which isn’t correct.
✘ False
---
46. Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.
✔ True — Additive inverse of a term is its negative. So subtracting 5 is same as adding –5. Always true.
---
47. The total number of planets of Sun can be denoted by the variable n.
✔ True — We can use any letter to represent a quantity. Even though we know there are 8 planets, using ‘n’ as a variable is perfectly fine in algebra.
---
48. In like terms, the numerical coefficients should also be the same.
✘ False — Coefficients can be different! Like 3x and 7x are like terms — same variable, same power, different coefficients. That’s okay.
---
49. If we add a monomial and binomial, then answer can never be a monomial.
Monomial: 1 term. Binomial: 2 terms.
Example: Add 3x (monomial) and (–3x + 5) (binomial):
3x + (–3x + 5) = 0x + 5 = 5 → which is a monomial!
So YES, it CAN become a monomial.
Therefore, saying “can never be” is false.
✘ False
---
50. If we subtract a monomial from a binomial, then answer is at least a binomial.
Binomial minus monomial.
Example: (x + y) – x = y → which is a monomial.
So answer can be monomial → not “at least binomial”.
✘ False
---
51. When we subtract a monomial from a trinomial, then answer can be a polynomial.
Trinomial: 3 terms. Subtract monomial: could cancel one term → left with 2 terms → still a polynomial (since all binomials/trinomials are polynomials).
Even if you get 1 term or 0 terms, those are still considered polynomials (constant or zero polynomial).
So yes — answer will always be a polynomial.
✔ True
---
52. When we add a monomial and a trinomial, then answer can be a monomial.
Monomial + trinomial → normally 4 terms, unless some cancel.
Example: Add 2x (monomial) and (–2x + y + z) → result: y + z → binomial.
Can we get monomial? Try: 3x + (–3x – y – z) = –y – z → still binomial.
What if trinomial is (–3x + 0 + 0)? But that’s not really a trinomial — needs 3 non-zero terms.
Actually, suppose trinomial is (–x – y – z), and monomial is x → sum: –y – z → binomial.
Is there any way to get down to 1 term? Only if two terms cancel and third remains? No — monomial cancels one term, leaves two others.
Unless... what if the trinomial has terms that cancel with the monomial AND among themselves? Not possible — monomial is single term.
Wait — example: Monomial = 5, Trinomial = –5 + x – x → but again, –5 + x – x simplifies to –5 → which is monomial, not trinomial.
To be a trinomial, all three terms must be present and non-canceling initially.
So when you add monomial to trinomial, best case: one term cancels → left with 2 terms → binomial. Worst case: 4 terms.
You cannot reduce to 1 term unless two terms vanish — but monomial can only cancel one term.
So actually, it cannot become a monomial.
Thus, statement says “can be a monomial” → which is false.
✘ False
Wait — let me double-check. Suppose trinomial is: 2x + 3y – 2x → but again, that simplifies to 3y → not a trinomial.
A true trinomial must have three unlike terms that don’t cancel.
So adding a monomial can cancel at most one term → minimum 2 terms remain → binomial.
So answer cannot be monomial.
Therefore, statement 52 is ✘ False.
---
Now, compiling final answers:
33. True
34. False
35. True
36. False
37. True
38. False
39. False
40. True
41. True
42. False
43. False
44. True
45. False
46. True
47. True
48. False
49. False
50. False
51. True
52. False
Final Answer:
33. True
34. False
35. True
36. False
37. True
38. False
39. False
40. True
41. True
42. False
43. False
44. True
45. False
46. True
47. True
48. False
49. False
50. False
51. True
52. False
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions questions.
