Class 9 CBSE Mathematics — Chapter 2: Introduction to Linear Polynomials MCQs with Answers
90 practice questions · 30 Easy · 30 Medium · 30 Hard
Practise the most important Class 9 CBSE Mathematics questions from Chapter 2, "Introduction to Linear Polynomials" — 9 separately timed quizzes built from 90 NCERT-aligned multiple-choice questions, with answers and explanations. The set is split into 30 Easy, 30 Medium and 30 Hard, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"Introduction to Linear Polynomials" is a chapter that rewards problem-solving speed, formula recall and step-by-step reasoning. Each MCQ on this chapter is timed and uses exam-grade marking (+4 correct, −1 wrong, 0 skipped), training the accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Introduction to Linear Polynomials, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below — answer and worked explanation — and signing in free opens all 90.
Key concepts: Introduction to Linear Polynomials (Class 9 Mathematics)
A polynomial is an algebraic expression built only from whole-number powers of a variable. This chapter classifies polynomials by degree and number of terms, finds their zeroes, reads them off a graph, and uses linear polynomials to model real situations such as cost, profit and break-even.
- Polynomial
- An expression of the form a₀ + a₁x + a₂x² + … in which every power of the variable is a whole number. Terms like 1/x or √x are therefore not allowed.
- Coefficient
- The number multiplying a power of the variable. In 7x − 4 the coefficient of x is 7, and −4 is the constant term (the coefficient of x⁰).
- Degree of a polynomial
- The highest power of the variable that appears with a non-zero coefficient. It fixes the polynomial's name and the maximum number of zeroes it can have.
- Linear polynomial
- A polynomial of degree 1, written ax + b with a ≠ 0. Its graph is always a straight line and it has exactly one zero.
Class 9 Mathematics Introduction to Linear Polynomials MCQs with answers
14 solved questions across the difficulty levels this chapter is graded on — answer and explanation shown for each. The remaining 76 are timed and scored when you sign in.
- Q1Easy
Which of the following is a polynomial?
A.√x + 1B.x² + 3x + 2✓ CorrectC.2/x + 5D.x⁻¹ + 4Answer: B. x² + 3x + 2
Explanation: A polynomial allows only whole-number, non-negative powers of the variable: x² + 3x + 2 has powers 2, 1, 0. √x is a power of ½, and 2/x, x⁻¹ carry negative powers, so none of those three qualify.
- Q2Easy
What is the coefficient of x in the polynomial 5x + 7?
A.7B.12C.1D.5✓ CorrectAnswer: D. 5
Explanation: The coefficient of x is the number multiplying it: in 5x + 7 that number is 5. Do not confuse it with the constant term 7, which has no x attached.
- Q3Easy
What is the constant term in the polynomial 3x + 8?
A.3B.8✓ CorrectC.0D.11Answer: B. 8
Explanation: The constant term is the piece with no variable attached: in 3x + 8, that is 8. Do not confuse it with the coefficient 3, which multiplies x instead of standing alone.
- Q4Easy
How many terms does the binomial 4x + 9 have?
A.1B.3C.4D.2✓ CorrectAnswer: D. 2
Explanation: A binomial by definition has exactly two terms, separated by + or −: here they are 4x and 9. Counting the coefficient 4 as a separate term would wrongly suggest more terms than there are.
- Q5Easy
Which of the following is a monomial?
A.7x✓ CorrectB.x + 1C.x² − 1D.3x + 2Answer: A. 7x
Explanation: A monomial has exactly one term: 7x is a single product of coefficient and variable, with no addition or subtraction joining it to anything else, unlike x + 1 or 3x + 2.
- Q6Easy
What is the coefficient of x² in 6x² − 4x + 1?
A.−4B.1C.6✓ CorrectD.2Answer: C. 6
Explanation: The coefficient of x² is the number multiplying x²: in 6x² − 4x + 1, that number is 6. The −4 multiplies x, not x², so it is not the answer here.
- Q7Medium
Which of the following is a binomial of degree 1?
A.2x + 5✓ CorrectB.5xC.x² + 3D.x² + x + 1Answer: A. 2x + 5
Explanation: A binomial of degree 1 needs exactly two terms and a highest power of 1: 2x + 5 fits both. 5x is a monomial (one term), and x² + 3 or x² + x + 1 have degree 2, not 1.
- Q8Medium
What is the coefficient of x in (3x + 2) + (5x − 7)?
A.−5B.2C.8✓ CorrectD.15Answer: C. 8
Explanation: Add the like x-terms and constants separately: (3x + 2) + (5x − 7) = (3 + 5)x + (2 − 7) = 8x − 5. The coefficient of x is 8, from 3 + 5, not the constant −5.
- Q9Medium
Simplify 2(x + 3) + 3(x − 1). What is the coefficient of x?
A.2B.6C.3D.5✓ CorrectAnswer: D. 5
Explanation: Distribute first, then collect like terms: 2(x + 3) + 3(x − 1) = 2x + 6 + 3x − 3 = 5x + 3. The coefficient of x is 5, the sum of 2 and 3 — not the constant term 3.
- Q10Medium
Which of the following is a polynomial in one variable?
A.x² + √2·x + 1✓ CorrectB.√x + 1C.x + 1/xD.2ˣ + 3Answer: A. x² + √2·x + 1
Explanation: A polynomial in one variable allows real coefficients, even irrational ones like √2, as long as every power of the variable is a whole number: x² + √2·x + 1 fits. √x has a fractional power, and 1/x, 2ˣ are not polynomial terms.
- Q11Medium
Simplify (x² + 2x) − (4x² − x). What is the coefficient of x²?
A.3B.−5C.−3✓ CorrectD.5Answer: C. −3
Explanation: Distribute the minus sign before combining like terms: (x² + 2x) − (4x² − x) = x² + 2x − 4x² + x = −3x² + 3x. The coefficient of x² is −3, from 1 − 4, not the coefficient of x, 3.
- Q12Hard
For p(x) = ax + b, p(1) = 5 and p(−1) = 1. What is the value of a?
A.2✓ CorrectB.3C.1D.4Answer: A. 2
Explanation: Set up two equations from the given values: a + b = 5 and −a + b = 1. Subtracting the second from the first eliminates b and gives 2a = 4, so a = 2.
- Q13Hard
The sum of all the coefficients of p(x) = 3x + 7 equals p(1). What is this sum?
A.3B.7C.10✓ CorrectD.4Answer: C. 10
Explanation: The sum of a polynomial's coefficients equals its value at x = 1, since every power of 1 is just 1: p(1) = 3(1) + 7 = 3 + 7 = 10. Reporting only one coefficient, like 3 or 7, misses that both must be added.
- Q14Hard
For (k − 2)x + 5 to be a linear polynomial (degree exactly 1), what must be true?
A.k = 2B.k ≠ 2✓ CorrectC.k = 0D.k ≠ 5Answer: B. k ≠ 2
Explanation: For (k − 2)x + 5 to stay degree exactly 1, the coefficient of x must not vanish, so k − 2 ≠ 0, meaning k ≠ 2. Setting k = 2 is exactly the value that destroys the x term, leaving only the constant 5.
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Start this chapter free →Introduction to Linear Polynomials — FAQs
What are the key concepts in Class 9 Mathematics Introduction to Linear Polynomials?+
A polynomial is an algebraic expression built only from whole-number powers of a variable. This chapter classifies polynomials by degree and number of terms, finds their zeroes, reads them off a graph, and uses linear polynomials to model real situations such as cost, profit and break-even. Key ideas include Polynomial, Coefficient, Degree of a polynomial, Linear polynomial.
What does Class 9 Mathematics Chapter 2 (Introduction to Linear Polynomials) cover on XamBaaz?+
It covers 90 NCERT-aligned MCQs on "Introduction to Linear Polynomials" — 30 Easy, 30 Medium and 30 Hard — making 9 separately timed quizzes you can sit without ever repeating the same set, each with an instant explanation, suitable for CBSE Board exams and the JEE & NEET foundation years.
Are these "Introduction to Linear Polynomials" questions free to practise?+
Yes — sign in with Google to practise "Introduction to Linear Polynomials" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Introduction to Linear Polynomials" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. There are 9 separately timed quizzes on this chapter, so you can come back and get a fresh set rather than re-sitting one you have seen. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Are these "Introduction to Linear Polynomials" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to practise all 90 questions with instant scoring.
Is there negative marking in the "Introduction to Linear Polynomials" quizzes?+
Yes — the timed quizzes use exam-grade marking: +4 for a correct answer, −1 for a wrong one and 0 for a skipped question. Note that MHT-CET and the CBSE board papers themselves carry no negative marking — our mocks for those are scored their way, not this way.
Are these important questions for Introduction to Linear Polynomials?+
The set is curated to the NCERT syllabus and weighted toward the question patterns that actually appear in CBSE Board exams and the JEE & NEET foundation years, across Easy, Medium and Hard — so it doubles as an "important questions" revision list for "Introduction to Linear Polynomials".