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Class 9 Maths: Introduction to Linear Polynomials, 8 practice questions with answers

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These are 8 practice questions on Chapter 2, Introduction to Linear Polynomials, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). Each has a worked answer and the textbook page it comes from. They cover the degree and coefficients of a polynomial, finding the value of a linear polynomial, setting up and solving a linear equation, linear growth and decay, finding y = ax + b from two readings, and reading the slope and y-intercept of a line. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari: Mathematics, Textbook for Grade 9, Part I, Chapter 2, printed pages 16 to 40):

Degree and coefficients

Question 1. What is the degree of the polynomial 7x³ − 2x + 9, and what is this kind of polynomial called?

Answer: degree 3, a cubic polynomial. The highest power of x is 3, so the degree is 3, and a polynomial of degree 3 is called cubic. (Page 18.)

Question 2. In the polynomial 6y² − 4y + 11, what is the coefficient of y, and what is the constant term?

Answer: the coefficient of y is −4; the constant term is 11. The term with y is −4y, so its coefficient is −4 (the sign belongs to the coefficient). The term without y is 11. (Coefficients and the constant term, page 18.)

Values and equations

Question 3. Find the value of the linear polynomial 4x − 7 when x = 3.

Answer: 5. Put x = 3 in: 4 × 3 − 7 = 12 − 7 = 5. (A polynomial as an input-output process, page 20.)

Question 4. The sum of two numbers is 50, and one of them is 8 more than the other. Find the two numbers.

Answer: 21 and 29. Let the smaller number be x; the larger is x + 8. Then x + (x + 8) = 50, so 2x + 8 = 50, 2x = 42 and x = 21. The other number is 21 + 8 = 29. Check: 21 + 29 = 50. (Equating a linear polynomial to a constant gives a linear equation, page 20.)

Growth, decay and lines

Question 5. Ravi has ₹135 and spends ₹9 every day. After how many days will he have ₹45 left?

Answer: 10 days. After d days he has 135 − 9d rupees, a linear decay (the amount falls by ₹9 each day). Set 135 − 9d = 45: 9d = 90, so d = 10. (Linear decay, pages 24 and 25; the same kind of question is worked as a pattern on page 22.)

Question 6. A music class charges a fixed monthly fee plus a fixed amount for each class attended. In a month with 5 classes the bill is ₹405, and in a month with 9 classes it is ₹585. Write the bill y in the form y = ax + b, where x is the number of classes, and say what a and b mean.

Answer: y = 45x + 180. From the two months, 405 = 5a + b and 585 = 9a + b. Subtracting, 4a = 180, so a = 45; then b = 405 − 5 × 45 = 180. So y = 45x + 180: each class costs ₹45 (a) and the fixed monthly fee is ₹180 (b). Check: 9 × 45 + 180 = 585. (Finding a linear relationship from two pairs of values, page 26.)

Question 7. For the line y = −2x + 5, what are the slope and the y-intercept, and does the line show linear growth or linear decay?

Answer: slope −2, y-intercept 5 (the line cuts the y-axis at (0, 5)); linear decay. In y = ax + b, a = −2 is the slope and b = 5 is the y-intercept. The slope is negative, so y goes down as x goes up: linear decay. (Slope and y-intercept, pages 35 and 36; the sign of the slope, page 31.)

Question 8. Does the point (2, 9) lie on the line y = 4x + 1?

Answer: yes. Put x = 2 into the equation: y = 4 × 2 + 1 = 9, which is the point's y-coordinate. The coordinates satisfy the equation, so the point lies on the line. (Page 28.)

Practise more, and check your marks

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 15.

The definitions and methods are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.