Past papers by chapter · Chapter 6
Application of Derivatives in past papers.
Every board and sample-paper question on Application of Derivatives, newest paper first. Each one opens with its full-marks exam answer.
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CBSE Board Examination 2026
- Board 2026 Q7Least value of on
Absolute minimum on a closed interval1 mark - Board 2026 Q22Rate at which the perfume level drops in an inverted cone
Rate of change: liquid level in an inverted cone2 marks - Board 2026 Q36Case study: subscription fee and maximum revenue
Revenue: maximum, increasing and decreasing4 marks
CBSE Board Examination 2025
- Board 2025 Q8Absolute maximum of on
Absolute maximum on a closed interval1 mark - Board 2025 Q24Where is increasing and decreasing
Increasing and decreasing functions2 marks - Board 2025 Q26Rate of increase of the area of an equilateral triangle of side 15 cm
Rate of change: area of an equilateral triangle3 marks - Board 2025 Q33Absolute maximum and minimum of on
Absolute maximum and minimum on a closed interval5 marks - Board 2025 Q36Case study: a solar panel with a partition and 300 m of boundary material
Case study: maximum area with a partition4 marks
CBSE Board Examination 2024
- Board 2024 Q4When is strictly increasing in ?
Increasing and decreasing functions1 mark - Board 2024 Q22Show that has neither maxima nor minima
Increasing function with no maxima or minima2 marks - Board 2024 Q36Case study: a speed camera and the rate of change of the angle of elevation
Rates of change: angle of elevation4 marks
CBSE Board Examination 2023
CBSE Sample Paper 2026-27
- Sample 2026-27 Q9Interval where decreases
Decreasing functions1 mark - Sample 2026-27 Q10Where the derivative of exceeds
Comparing a derivative with the function1 mark - Sample 2026-27 Q27Rate at which a surveillance drone rises
Rate of change: related rates3 marks - Sample 2026-27 Q37Case study: Yamuna water quality index and investment
Maximum value: second derivative test4 marks
CBSE Sample Paper 2025-26
- Sample 2025-26 Q9Interval where is increasing
Increasing and decreasing functions1 mark - Sample 2025-26 Q27A melting ball of ice: the radius decreases at a constant rate
Rate of change: a melting ball of ice3 marks - Sample 2025-26 Q37Case study: profit from energy-efficient LED bulbs
Maximum profit: second derivative test4 marks
CBSE Sample Paper 2024-25
- Sample 2024-25 Q3Where is strictly increasing
Increasing functions: the exponential function1 mark - Sample 2024-25 Q22Marginal cost when 150 items are produced
Rate of change: marginal cost2 marks - Sample 2024-25 Q26Rate at which a kite string is being released
Rate of change: kite string being released3 marks - Sample 2024-25 Q27Rate of increase of decreases with age
Rate of change: sign of the second derivative3 marks - Sample 2024-25 Q36Case study: container from a 25 cm by 40 cm sheet
Open box: maximum volume; point of inflection4 marks
CBSE Sample Paper 2023-24
- Sample 2023-24 Q19Minimum at when
First derivative test for a local minimum1 mark - Sample 2023-24 Q22Interval where is increasing
Increasing functions: sign of the derivative2 marks - Sample 2023-24 Q23Maximum value of , or the maximum profit
Maximum value of a function; maximum profit2 marks - Sample 2023-24 Q25Does have any critical points?
Critical points of a function2 marks - Sample 2023-24 Q38Case study: height of a plant and its rate of growth
Rate of change: growth of a plant4 marks
CBSE Sample Paper 2022-23
- Sample 2022-23 Q22A man walks away from a street light: rates of his shadow
Rate of change: a man's shadow from a street light2 marks - Sample 2022-23 Q36Case study: body temperature during an intestinal illness
Increasing/decreasing; local and absolute extrema4 marks - Sample 2022-23 Q37Case study: the largest rectangular soccer field in an elliptical sport field
Maximum area: rectangle inscribed in an ellipse4 marks
CBSE Sample Paper 2020-21
- Sample 2020-21 Q17Case study: a floor with semicircular ends and perimeter 200 m
Maxima: floor with semicircular ends4 marks - Sample 2020-21 Q22Normal to perpendicular to
Normal to a curve perpendicular to a given line2 marks - Sample 2020-21 Q32Where increases and decreases on
Intervals of increase and decrease3 marks