Case Study on Chapter 2: ‘Introduction to Linear Polynomials’ for Class 9 Maths

Case Study set for Class 9 Maths Chapter 2: Introduction to Linear Polynomials presents short, focused problem scenarios with clear answers and step‑by‑step solutions to build exam‑ready skills. Covering topics such as identifying polynomials, degree and coefficients, forming linear polynomial expressions from word problems, verifying linearity, solving simple linear equations, and applying algebraic identities, these questions help students strengthen conceptual understanding, practise algebraic manipulation, and improve speed and accuracy for board exams. A free PDF is included for offline timed practice, classroom worksheets, and homework, making this guide ideal for quick revision and targeted skill building before tests.

Case Study on Chapter 2: Introduction to Linear Polynomials for Class 9 With Answers

CBSE's case-based questions usually give you a short passage describing a real situation, sometimes with a small figure, followed by 4–5 questions of increasing difficulty, a couple of MCQs to check basic understanding, a short-answer question that needs a calculation, and a longer question that asks you to interpret or justify your answer.

Case Study 1: The School Fete Stall

Aarav and his classmates run a stall at the school's annual fete. They sell handmade greeting cards for ₹15 each and friendship bracelets for ₹8 each. On top of whatever they sell, Aarav adds a flat ₹20 of his own pocket money to the charity box every single day. If ‘p’ cards and ‘q’ bracelets are sold on a given day, the day's total contribution to the charity box can be written as 15p + 8q + 20.

Questions:

(i) Write down the terms of the expression 15p + 8q + 20.

(ii) What are the coefficients of p and q?

(iii) What is the constant term here, and what does it represent in real life?

(iv) If 6 cards and 4 bracelets are sold on a particular day, find the total contribution to the charity box.

OR 

 Is 15p + 8q + 20 a linear polynomial in two variables? Give a reason for your answer.

Solution: 

(i) The terms are 15p, 8q and 20. 

(ii) Coefficient of p = 15; coefficient of q = 8.

(iii) The constant term is 20. It represents the flat ₹20 Aarav contributes every day regardless of how many cards or bracelets are sold.

(iv) Substituting p = 6, q = 4: 15(6) + 8(4) + 20 = 90 + 32 + 20 = ₹142.

OR: Yes, every term has degree at most 1 (no variable is raised above the power 1), so 15p + 8q + 20 is a linear polynomial in the two variables p and q.

Case Study 2: Karan's E-Scooter (Linear Decay)

Karan buys a second-hand e-scooter for ₹54,000. Because of regular usage and battery wear, its resale value falls by a constant ₹4,500 every year.

Questions:

(i)  Write a linear expression for the resale value V (in ₹) after n years.

(ii) Find the resale value after 3 years.

(iii) Why does this situation represent linear decay rather than linear growth?

(iv) After how many complete years will the resale value first drop below ₹18,000?

OR 

 Will the graph of V against n rise or fall, and why?

Solution:

(i) V = 54000 − 4500n

(ii) V(3) = 54000 − 4500(3) = 54000 − 13500 = ₹40,500.

(iii) The value decreases by a fixed amount every year, and the coefficient of n is negative (−4500); this is exactly what defines linear decay.

(iv) 54000 − 4500n < 18000 ⇒ 36000 < 4500n ⇒ n > 8. At n = 8 the value is exactly ₹18,000, so it first drops below ₹18,000 after 9 complete years.

 

OR:

The graph will fall (slope downward from left to right), because the coefficient of n is negative. A negative slope always produces a falling line.

Case Study 3: Reading a Graph of Three Lines

Three linear relationships, y = 3x, y = 3x + 5 and y = 3x − 5, are plotted on the same coordinate grid below.

Questions:

(i) Identify the y-intercept of each of the three lines.

(ii) What do you notice about the slope of all three lines? What does this tell you about how they're positioned relative to one another?

(iii) Which line crosses the y-axis at the highest point, and why?

(iv) If a fourth line, y = −3x + 5, were added to this graph, would it be parallel to the others? Justify.

OR

At what point does the line y = 3x cross the y-axis?

Solution: 

(i) Substituting x = 0 in each: y = 3x → 0; y = 3x + 5 → 5; y = 3x − 5 → −5.

The y-intercept of each of the three lines are 0,5 and -5 respectively.

(ii) All three lines have the same slope, a = 3. Equal slopes mean the lines are parallel. They're equally steep, just shifted up or down by different amounts.

(iii) y = 3x + 5 crosses highest, at (0, 5), because it has the largest value of b among the three.

(iv) No. Its slope is −3, which is different in sign from the slope 3 shared by the other three lines. Lines are parallel only when their slopes are exactly equal, same magnitude isn't enough if the sign differs.

OR: y = 3x crosses the y-axis at the origin, (0, 0), since its constant term b is 0.

 

Click below to download your free Case Study PDF with worked-out examples for Class 9 Chapter 2: Introduction to Linear Polynomials, perfect for last-minute CBSE exam revision.

Class 9 Chapter 2: Introduction to Linear Polynomials Case Study PDF