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Class 9 Maths Chapter 2: Introduction to Linear Polynomials — Important Questions & Sample Paper

CBSE· Ganita Manjari· 44+ original questions readyहिन्दी में देखें

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Reviewed by qpaper's CBSE curriculum team · Edited by Mohit · Updated June 2026

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Yes — this page has 44+ original Class 9 Mathematics Chapter 2 (“Introduction to Linear Polynomials”) important questions with answers (Multiple Choice (MCQ), Assertion–Reason, Short Answer, Short Answer, Long Answer, Case Study). Practise them free, or generate a full CBSE board-pattern sample paper (80 marks) and export it to PDF or Word — in English & Hindi, for 2026-27.

Chapter 2 of Class 9 Mathematics, 'Introduction to Linear Polynomials', takes students from basic algebra into the world of polynomial functions. The chapter focuses on linear polynomials, which are expressions of degree one. You will learn to recognise and work with the standard form \(ax + b\) (where \(a \neq 0\)), identify coefficients and constant terms, and evaluate polynomials for given values of \(x\). Key skills include finding the zero of a linear polynomial, converting real-life situations into linear expressions, and exploring patterns that follow a linear rule. Exam questions often ask you to evaluate a polynomial at a specific \(x\), determine the value of \(x\) that makes the polynomial equal to a given number, or form linear polynomials from word problems involving fixed charges and variable rates—like mobile bills, taxi fares, or book and pen costs. You will also see questions on arithmetic patterns where the general term is a linear polynomial. This chapter lays the foundation for understanding linear equations and more complex polynomials later, making it essential to grasp these fundamental ideas thoroughly.

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Mathematics — Introduction to Linear Polynomials

Class 9Time: 3 hrsMax Marks: 80

SECTION A

  1. 1.

    A taxi charges a fixed fare of ₹30 plus ₹12 per kilometre. If a passenger travels x km, which linear polynomial represents the total fare in rupees?

    (a) 12x + 30(b) 30x + 12(c) 42x(d) 12x - 30
    1
  2. 2.

    In a growing pattern of dots, the number of dots at stage n is given by the linear polynomial 5n - 2. What is the constant difference between the number of dots in consecutive stages?

    (a) -2(b) 5(c) 3(d) 7
    1
  3. 3.

    A book costs ₹10 more than twice the cost of a pen. Two such books and three pens together cost ₹230. If the cost of a pen is ₹x, which linear equation correctly models this situation?

    (a) 2(2x + 10) + 3x = 230(b) 2(x + 10) + 3x = 230(c) (2x + 10) + 3x = 230(d) 2(2x + 10) + 3 = 230
    1

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Marks distribution & blueprint

In a CBSE exam, this chapter typically contributes questions across the following types. The last column shows how many original questions of each type we have ready in our bank for this chapter:

Question typeMarks eachIn our bank
Multiple Choice (MCQ)1 mark13
Assertion–Reason1 mark6
Short Answer2 marks8
Short Answer3 marks6
Long Answer5 marks5
Case Study4 marks6

44 original, exam-style questions in our bank for this chapter — with answers.

Important & sample questions (with answers)

Real, exam-style questions to practise and revise — each with its answer. Generate a full paper for unlimited more.

  1. Q1. A taxi charges a fixed fare of ₹30 plus ₹12 per kilometre. If a passenger travels x km, which linear polynomial represents the total fare in rupees?

    1 mark
    Multiple Choice (MCQ)
    (A) 12x + 30(B) 30x + 12(C) 42x(D) 12x - 30
    ▸ Answer

    A) 12x + 30

  2. Q2. In a growing pattern of dots, the number of dots at stage n is given by the linear polynomial 5n - 2. What is the constant difference between the number of dots in consecutive stages?

    1 mark
    Multiple Choice (MCQ)
    (A) -2(B) 5(C) 3(D) 7
    ▸ Answer

    B) 5

  3. Q3. A book costs ₹10 more than twice the cost of a pen. Two such books and three pens together cost ₹230. If the cost of a pen is ₹x, which linear equation correctly models this situation?

    1 mark
    Multiple Choice (MCQ)
    (A) 2(2x + 10) + 3x = 230(B) 2(x + 10) + 3x = 230(C) (2x + 10) + 3x = 230(D) 2(2x + 10) + 3 = 230
    ▸ Answer

    A) 2(2x + 10) + 3x = 230

  4. Q4. A car rental company charges a fixed fee of ₹500, then ₹8 per km for the first 100 km and ₹6 per km for any distance beyond 100 km. For a journey of x km (x > 100), which linear polynomial gives the total charge in rupees?

    1 mark
    Multiple Choice (MCQ)
    (A) 6x + 700(B) 8x + 500(C) 6x + 500(D) 8x + 700
    ▸ Answer

    A) 6x + 700

  5. Q5. Assertion (A): The area of a rectangle formed by a 20 cm wire bent into a rectangle with length x cm is given by a linear polynomial in x. Reason (R): The expression for area is x(10 - x) = 10x - x^2, which is a quadratic polynomial.

    1 mark
    Assertion–Reason
    (A) Both A and R are true and R is the correct explanation of A.(B) Both A and R are true but R is not the correct explanation of A.(C) A is true but R is false.(D) A is false but R is true.
    ▸ Answer

    A is false but R is true.

  6. Q6. What is the coefficient of y in the linear polynomial 9y – 15?

    2 marks
    Short Answer
    ▸ Answer

    9

  7. Q7. Evaluate the linear polynomial 7x + 2 for x = –4.

    2 marks
    Short Answer
    ▸ Answer

    –26

  8. Q8. In a pattern of matchsticks, the number of matchsticks at stage \(n\) is given by \(5n + 2\). How many matchsticks are needed for stage 10? At what stage will 47 matchsticks be used?

    3 marks
    Short Answer
    ▸ Answer

    52 matchsticks; stage 9

  9. Q9. Find the value of the linear polynomial \(4x - 7\) when \(x = -3\).

    3 marks
    Short Answer
    ▸ Answer

    \(-19\)

  10. Q10. A pattern of figures is made using unit squares. The first figure contains 5 squares, the second 9 squares, the third 13 squares, and so on. (a) Write the number of squares in the next two figures. (b) Find the general term (nth term) of this pattern as a linear polynomial in n. (c) Which figure contains 61 squares? (d) Is it possible for a figure to have exactly 2026 squares? Justify your answer.

    5 marks
    Long Answer
    ▸ Answer

    (a) 17, 21. (b) 4n+1. (c) 15th figure. (d) No, because 4n+1=2026 gives n=2025/4 = 506.25, not an integer.

  11. Q11. A sequence is defined by the linear polynomial t_n = 2n + 1 for n = 1,2,3,… (i) Show that the difference between any two consecutive terms is constant. (ii) Prove that the sum of the first k terms is k(k+2). (iii) Hence, find the smallest k such that the sum of the first k terms exceeds 500. (iv) Check whether 2025 is a term of this sequence; if yes, state which term.

    5 marks
    Long Answer
    ▸ Answer

    (i) Difference = 2, constant. (ii) Proof by summation or pattern. (iii) k=22. (iv) Yes, 1012th term.

  12. Q12. A pattern is formed using dots. In the first figure, there are 5 dots; in the second, 8 dots; in the third, 11 dots; and so on, with each successive figure having 3 more dots than the previous one.

    4 marks
    Case Study
    1. (i) Write a linear expression for the number of dots in the nth figure.2 marks
    2. (ii) If a figure has 50 dots, find the value of n.2 marks
    ▸ Answer

    (i) 3n + 2; (ii) n = 16.

Frequently asked questions

What is a linear polynomial, and how does it appear in this chapter?

A linear polynomial is an algebraic expression of degree one, written in the standard form \(ax + b\) with \(a \neq 0\). In this chapter, you work with examples like \(4x - 7\), \(12 - 3x\), or expressions formed from real contexts, such as a fare that depends on distance. The focus is on identifying its coefficient and constant term, evaluating it, and finding its zero.

What is the zero of a linear polynomial, and how do we find it?

The zero of a linear polynomial \(p(x) = ax + b\) is the value of \(x\) for which \(p(x) = 0\). You find it by solving \(ax + b = 0\), which gives \(x = -b/a\). In exam questions, you may be asked to find the zero directly or to solve a problem like 'For what value of \(x\) does \(4x - 7 = 5\)?' which requires setting the polynomial equal to a number and solving for \(x\).

What kinds of word problems are typical for this chapter?

Common word problems ask you to translate a real-life situation into a linear polynomial. For example, a mobile plan with a fixed monthly fee plus a per-minute charge, a taxi fare with a base fare and a per-kilometre rate, or a cost relationship like 'a book costs ₹10 more than twice the cost of a pen'. You then use the expression to calculate a specific value or solve an equation.

How are linear polynomials related to patterns and sequences in this chapter?

Many questions involve patterns of figures or tiles that increase by a constant amount. You learn to express the number of elements in the nth figure as a linear polynomial, such as \(4n - 3\). This helps you find any term in the sequence, check if a given number belongs to the pattern, or justify why a particular total is or isn't possible.

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Class 9 Maths Ch2 — Important Questions & Sample Paper with Answers | Free PDF