Preparing for your Class 9 Maths exam? This collection of 25 most important questions on Linear Polynomials is designed to help students strengthen their concepts and prepare effectively for school examinations and CBSE-style assessments.
These Class 9 Linear Polynomials questions cover important concepts such as degree of a polynomial, coefficients, constant terms, finding the value of a polynomial, linear expressions, word problems, linear growth and decay, real-life applications, and graphs of linear polynomials. The questions range from basic concept-based problems to application-based questions that encourage students to think and apply their mathematical skills.
This Class 9 Maths Linear Polynomials practice set is useful for exam preparation, revision, homework, classroom practice, and self-study. Students can use these questions to identify important concepts, improve problem-solving skills, and build confidence before their exams.
Whether you are preparing for a CBSE Class 9 Maths exam, school test, periodic assessment, or revision, practising these important Linear Polynomials questions can help you prepare in a structured way.
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Grade 9 – Linear Polynomials
25 Most Important Questions
Q1. Find the degrees of the following polynomials:
(i) 2x2 − 5x + 3
(ii) y3 + 2y − 1
(iii) −9
(iv) 4z − 3
Q2. Write one polynomial each of degree 1, degree 2 and degree 3 in a single variable of your choice.
Q3. What are the coefficients of x2 and x3 in the polynomial x4 − 3x3 + 6x2 − 2x + 7?
Q4. What is the coefficient of z in the polynomial 4z3 + 5z2 − 11?
Q5. What is the constant term of the polynomial 9x3 + 5x2 − 8x − 10?
Q6. Find the value of the linear polynomial 5x − 3 if:
(i) x = 0
(ii) x = −1
(iii) x = 2
Q7. Find the value of the quadratic polynomial 7s2 − 4s + 6 if:
(i) s = 0
(ii) s = −3
(iii) s = 4
Q8. The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.
Q9. The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.
Q10. Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total of Rs.88, how many coins does she have of each type?
Q11. A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?
Q12. If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?
Q13. In the growing pattern of square tiles where the number of squares at Stage n is given by 2n − 1, find the number of tiles at Stage 15 and Stage 26. Also find which stage contains 21 tiles and which contains 47 tiles.
Q14. Bela has Rs.100 for pocket money and spends Rs.5 every day, so the amount left on the nth day is Rs.(100 − 5n). What amount will be left on the 15th day? After how many days will the entire amount be spent?
Q15. An auto-rickshaw fare for a distance of n km (n ≥ 2) is given by 15n − 5 (in rupees). For how many km will the fare be Rs.130?
Q16. The cost of a journey is given by the linear function C(d) = 100 + 60d, where C is the cost in rupees and d is the distance in km. What is the cost for travelling 15 km? For how many km will the cost be Rs.700?
Q17. The height of water in a cylindrical tank, h(t) = 3 − 0.5t (in metres), depends on the number of months t. What will be the height of the water at the end of 5 months?
Q18. A plant has a height of 1.75 feet and grows by 0.5 feet each month. Find its height after 7 months, and write the linear expression relating height h and time t (in months). Explain why it represents linear growth.
Q19. A mobile phone is bought for Rs.10,000 and its value decreases by Rs.800 every year. Find its value after 3 years, and write the linear expression relating value v and time t (in years). Explain why it represents linear decay.
Q20. The initial population of a village is 750, and every year 50 people move into the village from a nearby city. Find the population after 6 years, using a suitable linear expression.
Q21. A telecom company charges Rs.600 for a recharge scheme, and the prepaid balance is reduced by Rs.15 each day after recharge. After how many days will the balance run out?
Q22. A learning platform charges a fixed monthly fee plus an additional cost per module accessed. A student who accessed 10 modules was billed Rs.400, and one who accessed 14 modules was billed Rs.500. If the bill y depends on the number of modules x according to y = ax + b, find a and b.
Q23. A gym charges a fixed monthly fee plus an additional cost per hour for using its badminton court. A student who used the court for 10 hours was billed Rs.800, and one who used it for 15 hours was billed Rs.1100. If the bill y depends on the hours x according to y = ax + b, find a and b.
Q24. The relationship between temperature in degrees Celsius (°C) and degrees Fahrenheit (°F) is given by °C = a°F + b. Given that ice melts at 0°C (32°F) and water boils at 100°C (212°F), find the values of a and b.
Q25. The graph of a linear polynomial p(x) passes through the points (1, 5) and (3, 11). Find the polynomial p(x), and find the coordinates of the points where its graph cuts the x-axis and the y-axis.
