CBSE Class 10 · Section E · 2026-27

CBSE Class 10 Maths case study questions, chapter-wise

Case study (case-based) questions are Section E of the Class 10 Maths board paper: three questions of 4 marks, 12 of the 80 marks. Each starts with a real-life passage, then asks three parts worth 1, 1 and 2 marks, with a choice on the 2-mark part. Here are 28 free case studies, two for every chapter, and the 15 in our sample papers, all with worked answers.

28 chapter case studies
15 in our sample papers
12 of the 80 marks
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Start: Polynomials case studies

One worked in full: Polynomials

Try each part before you open its answer. The marks in brackets are what the part is worth.

Case study 1: Bakery profit (4 marks)

The owner of a home bakery models her weekly profit (in hundreds of rupees) from selling $x$ dozen cupcakes by the quadratic polynomial $P (x) = - x^{2} + 14 x - 40$ . The graph of $y = P (x)$ is a parabola opening downwards; she makes a profit only where the graph lies above the $x$ -axis.

(i) Find the zeroes of

P (x)

. [1 mark]

Show answer

Answer:

4

and

10

- x^{2} + 14 x - 40 = - (x - 4) (x - 10)

, so the zeroes are

4

and

10

. A1

(ii) Verify that the sum of the zeroes equals

- \frac{b}{a}

for

P (x)

. [1 mark]

Show answer

Answer:

4 + 10 = 14 = - \frac{14}{- 1}

Sum

= 4 + 10 = 14

and

- \frac{b}{a} = - \frac{14}{- 1} = 14

. A1

(iii) Find the profit when she sells

7

dozen cupcakes, and state for which whole numbers of dozens between the zeroes she makes a profit. [2 marks]

Show answer

Answer: ₹900;

x = 5, 6, 7, 8, 9

P (7) = - 49 + 98 - 40 = 9

, i.e. ₹

900

A1. The graph is above the

x

-axis between the zeroes, so

x = 5, 6, 7, 8, 9

. A1

OR Find a quadratic polynomial whose zeroes are each

2

more than the zeroes of

P (x)

. [2 marks]

Show answer

Answer:

x^{2} - 18 x + 72

New zeroes

6

and

12

M1: sum

18

, product

72

, so

x^{2} - 18 x + 72

. A1

How to answer a case study

Read the passage once and write down the numbers. Most of the 4 marks depend on setting the situation up correctly: name the quantity, the formula and the values before you start.
Parts (i) and (ii) are 1 mark each. They usually need one idea from the chapter. Give the answer with a line of working and move on; don't spend long here.
Part (iii) holds 2 marks, usually split between the working and the answer. Write the formula or equation you are using before any arithmetic, so a method mark is safe even if a number slips.
Pick the OR option you can finish. Read both versions of part (iii) and choose the one you can complete fully; both are worth the same.

More on reading real-life questions: competency-based questions in Class 10 Maths, and how step marks are given.

Case study questions by chapter

Two for every chapter, in NCERT order. A case study's title opens the chapter's free set, with the answers behind "Show answer"; the chapter name opens its notes.

Chapter	Case study 1	Case study 2
Ch 1: Real Numbers	Bus depot timetable HCF and LCM by prime factorisation	Stationery kits HCF and LCM by prime factorisation
Ch 2: Polynomials	Bakery profit Relationship between zeroes and coefficients	Kitchen garden Relationship between zeroes and coefficients
Ch 3: Pair of Linear Equations in Two Variables	School canteen Situational problems	Fencing a park Situational problems
Ch 4: Quadratic Equations	Cycling to the village Situational problems	Buying school bags Situational problems
Ch 5: Arithmetic Progressions	Weekly savings Situational problems	Stadium stand Situational problems
Ch 6: Triangles	Pinhole camera Criteria for similarity (AA, SSS, SAS)	Width of a river Criteria for similarity (AA, SSS, SAS)
Ch 7: Coordinate Geometry	Drone deliveries Distance formula	Park fountain Mid-point formula
Ch 8: Introduction to Trigonometry	Solar panel frame Trigonometric ratios	Geometry-box set squares Ratios of standard angles
Ch 9: Some Applications of Trigonometry	Lighthouse watch Angle of depression	Drone at the sports day Problems with two right triangles
Ch 10: Circles	Roundabout and roads Tangent perpendicular to the radius	Plate in a triangular tray Lengths of tangents from an external point
Ch 11: Areas Related to Circles	Lawn sprinkler Area and arc of a sector	Pendulum in a science lab Area of a segment
Ch 12: Surface Areas and Volumes	Rocket model Surface area of combinations of solids	Spinning top Surface area of combinations of solids
Ch 13: Statistics	Electricity use in a housing society Mode of grouped data	Unit-test marks Median of grouped data
Ch 14: Probability	Spin wheel at the school fete Classical probability	Class monitor by lottery Classical probability

Case studies in our sample papers

Questions 36 to 38 of each paper, to sit inside a full 3-hour paper once the chapters are done.

Paper 1, Q36: Daily savings (Arithmetic Progressions)
Paper 1, Q37: Village planning (Coordinate Geometry)
Paper 1, Q38: Watering the lawn (Areas Related to Circles)
Paper 2, Q36: Fire-rescue ladder (Some Applications of Trigonometry)
Paper 2, Q37: Park pathway (Quadratic Equations)
Paper 2, Q38: Mela dice game (Probability)
Paper 3, Q36: Delivery times (Statistics)
Paper 3, Q37: Drone delivery corridor (Coordinate Geometry)
Paper 3, Q38: Fitness challenge (Arithmetic Progressions)
Paper 4, Q36: Community hall (Surface Areas and Volumes)
Paper 4, Q37: Theatre pricing (Quadratic Equations)
Paper 4, Q38: Blood donation camp (Probability)
Paper 5, Q36: Kite festival (Some Applications of Trigonometry)
Paper 5, Q37: Three friends' homes (Coordinate Geometry)
Paper 5, Q38: Juice counter (Pair of Linear Equations in Two Variables)

Questions

How many case study questions are in the CBSE Class 10 Maths paper?

Three, in Section E. Each is worth 4 marks, so case studies carry 12 of the 80 marks. Each has a short real-life passage and three parts worth 1, 1 and 2 marks.

Is there a choice in the case study questions?

Yes, inside each one: the 2-mark part (iii) has an OR alternative, and you answer one of the two. There is no choice between the three case studies themselves.

How long should I spend on a case study?

About 9 minutes each. The paper is 180 minutes for 80 marks, a little over 2 minutes a mark, and a 4-mark case study is mostly reading plus one longer part.

Which chapters do case study questions come from?

Any chapter can be set as a case study, so practise all of them. In our 5 sample papers, Coordinate Geometry, Arithmetic Progressions, Some Applications of Trigonometry came up most often; CBSE does not publish which chapters it will use.

Are these official CBSE case study questions?

No. They are original questions written by CBSE Math Revision to the CBSE 2026-27 pattern, each checked twice. For CBSE's own, sit the official sample paper linked from our question papers page.

Original questions written by CBSE Math Revision; not taken from NCERT, NCERT Exemplar or CBSE papers. CBSE Math Revision is independent and not affiliated with CBSE or NCERT.