Class 9 Maths Question Paper 2026-27 | Linear Polynomials

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PRACTICE PAPER 04 (2026-27)

CHAPTER 02 – INTRODUCTION TO LINEAR POLYNOMIALS

SUBJECT: MATHEMATICS	MAX. MARKS: 40
CLASS: IX	DURATION: 1½ hrs

General Instructions:

All questions are compulsory.
This question paper contains 20 questions divided into five Sections A, B, C, D and E.
Section A comprises 10 MCQs of 1 mark each. Section B comprises 4 questions of 2 marks each. Section C comprises 3 questions of 3 marks each. Section D comprises 1 question of 5 marks. Section E comprises 2 Case Study Based Questions of 4 marks each.
There is no overall choice.
Use of calculators is not permitted.

SECTION – A

Questions 1 to 10 carry 1 mark each.

A catering company charges a fixed setup cost of ₹8,000 and ₹250 for every plate served. If x plates are served, the total cost is:
(a) 8000x + 250 (b) 250x + 8000 (c) 8250x (d) 8000 + 250
The graph of a linear polynomial passes through (0, 9) and (4, 29). The slope of the graph is:
(a) 3 (b) 4 (c) 5 (d) 6
A mobile plan charges a fixed rental of ₹149 and ₹2 for every extra minute. The bill for x extra minutes is:
(a) 149x + 2 (b) 2x + 149 (c) 151x (d) 149 + 2
The constant term of 17x − 34 is:
(a) 17 (b) −17 (c) 34 (d) −34
A library has 22,000 books. Every year, 800 new books are added. The total number of books after t years is:
(a) 22000 + 800t (b) 800 + 22000t (c) 22000 − 800t (d) 22800t
If p(x) = 6x − 11, then p(4) =
(a) 11 (b) 13 (c) 15 (d) 17
Which of the following equations represents a line passing through the origin?
(a) y = 7x + 2 (b) y = 7x − 3 (c) y = 7x (d) y = 7 − x
A water tank initially contains 5,000 litres and gains 60 litres every hour. The amount of water after h hours is:
(a) 5000 + 60h (b) 5000 − 60h (c) 60h − 5000 (d) 5060h
Assertion (A): The graph of y = −3x + 12 cuts the y-axis at (0, 12).
Reason (R): For a linear polynomial y = ax + b, the y-intercept is equal to b.
(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.
Assertion (A): The lines y = 5x + 4 and y = 5x − 7 are parallel.
Reason (R): Parallel lines have equal slopes.
(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.

SECTION – B

Questions 11 to 14 carry 2 marks each.

A tour company represents its transportation cost by T = 150x + 4000, where x is the number of students participating.
Find: (i) The transportation cost for 30 students.
(ii) The transportation cost for 50 students.
(iii) By how much does the transportation cost increase when the number of students increases from 30 to 50?
A coaching institute charges a fixed admission fee and ₹500 per month. A student pays ₹4,500 for 8 months.
Find: (i) The admission fee.
(ii) The total fee for 12 months.
The nth term of a number pattern is 15n − 8.
Find: (i) The 10th term.
(ii) The 20th term.
(iii) The difference between these two terms.
The equation of a straight road is y = 9x − 6.
Find: (i) Its slope.
(ii) Its y-intercept.
(iii) Explain whether the road rises or falls as x increases.

SECTION – C

Questions 15 to 17 carry 3 marks each.

A parking garage charges a fixed entry fee and ₹20 per hour. A customer parks for 6 hours and pays ₹170.
Find: (i) The fixed entry fee.
(ii) The linear equation representing the total parking charge.
(iii) The parking charge for 10 hours.
(iv) The additional amount required when the parking duration increases from 6 hours to 10 hours.
A graph passes through the points (3, 11) and (7, 27).
Find: (i) The slope of the graph.
(ii) The equation of the graph.
(iii) The value of y when x = 15.
(iv) The value of x when y = 79.
Draw the graph of the linear equation 4x − 5y = 20. Check whether (10, 4) is a solution of the given equation or not.

Fig. 1 – Graph of 4x − 5y = 20

SECTION – D

Question 18 carries 5 marks.

A digital library charges a one-time registration fee and ₹200 per month as subscription charges. A student pays ₹3,800 for 15 months.
Find: (i) The registration fee.
(ii) The linear equation representing the total payment.
(iii) The payment for 20 months.
(iv) The number of months corresponding to a payment of ₹5,000.
(v) If another platform charges ₹280 per month with no registration fee, determine which platform is cheaper for 20 months.

SECTION – E (Case Study Based Questions)

Questions 19 to 20 carry 4 marks each.

19. Case Study 1 – Solar Farm Operating Cost

A renewable energy company operates a solar farm. The operating expenditure includes a fixed maintenance cost of ₹40,000 per month plus ₹1,800 for every additional solar panel-array brought online during the month. Engineers use a linear polynomial to model the monthly operating cost C(n) in terms of the number of arrays n operated, so that planners can forecast expenses as the farm is expanded.

Fig. 2 – Monthly operating cost C(n) = 1800n + 40000

Answer the following questions:

Write the linear equation representing the monthly operating cost. (1)
Calculate the operating cost for 25 arrays. (1)
Find the number of arrays corresponding to a monthly expenditure of ₹1,03,000. (1)
State the slope of the equation and explain its practical significance. (1)

20. Case Study 2 – Lake Fish Population Study

Environmental researchers are studying a lake that currently holds 30,000 fish. Due to declining water quality, the fish population is falling by a constant 500 fish every year. Students use a linear polynomial to model the fish population P(t) after t years, in order to evaluate how urgently conservation measures are needed.

Fig. 3 – Fish population P(t) = 30000 − 500t