Skip to main content
Super TutorResources
Chapter 12 of 13
Flashcards

Applications of Derivatives - I — Flashcards

ICSE · Class 12 · Mathematics

37 flashcards for Applications of Derivatives - I (ICSE Class 12 Mathematics) to test yourself on key terms and facts.

55 questions37 flashcards23 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Applications of Derivatives - I? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.

Try Super Tutor — Free

Free trial, no card needed.

A graph of a function y=f(x) with a tangent line at a point (x, y), illustrating dy/dx as the slope of the tangent.
Super Tutor

Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Applications of Derivatives - I.

37 Flashcards·
Rate of change
Card 1Rate of change

Solve: A side of a square sheet is increasing at 4 cm/min. Find the rate at which the area increases when the side is 5 cm.

Answer

Step 1: Let side = x cm and area = A cm². Step 2: A = x². Step 3: Differentiate w.r.t. time t: dA/dt = 2x · dx/dt. Step 4: Substitute x = 5 and dx/dt = 4. Step 5: dA/dt = 2 × 5 × 4 = 40 cm²/min. Answe…

Card 2Rate of change

Solve: A side of a square is increasing at 0.5 cm/s. Find the rate of increase of its perimeter.

Answer

Step 1: Let side = x cm and perimeter = P cm. Step 2: P = 4x. Step 3: Differentiate w.r.t. time t: dP/dt = 4 · dx/dt. Step 4: Substitute dx/dt = 0.5. Step 5: dP/dt = 4 × 0.5 = 2 cm/s. Answer: 2 cm/s.

Card 3Rate of change

Solve: If x and y are the sides of two squares and y = x - x², find dA₂/dA₁, where A₁ = x² and A₂ = y².

Answer

Step 1: A₁ = x², so dA₁/dx = 2x. Step 2: A₂ = y² = (x - x²)². Step 3: dA₂/dx = 2(x - x²)(1 - 2x). Step 4: dA₂/dA₁ = (dA₂/dx)/(dA₁/dx). Step 5: dA₂/dA₁ = [2(x - x²)(1 - 2x)]/(2x). Step 6: Simplify: (1 …

Card 4Rate of change

Solve: The length of a rectangle decreases at 5 cm/min and width increases at 4 cm/min. Find the rate of change of perimeter when x = 8 cm and y = 6 cm.

Answer

Step 1: Let length = x, width = y, perimeter = P. Step 2: P = 2(x + y). Step 3: Differentiate: dP/dt = 2(dx/dt + dy/dt). Step 4: Substitute dx/dt = -5 cm/min and dy/dt = 4 cm/min. Step 5: dP/dt = 2(-5…

Card 5Rate of change

Solve: The same rectangle has length decreasing at 5 cm/min and width increasing at 4 cm/min. Find the rate of change of area when x = 8 cm and y = 6 cm.

Answer

Step 1: Let area = A = xy. Step 2: Differentiate: dA/dt = x(dy/dt) + y(dx/dt). Step 3: Substitute x = 8, y = 6, dy/dt = 4, dx/dt = -5. Step 4: dA/dt = 8(4) + 6(-5) = 32 - 30 = 2 cm²/min. Answer: 2 cm²…

Card 6Rate of change

Solve: A stone is dropped into a quiet lake and waves move in a circle at 5 cm/s. Find the rate at which the enclosed area changes when radius is 8 cm.

Answer

Step 1: Let radius = R and area = A. Step 2: A = πR². Step 3: Differentiate: dA/dt = 2πR · dR/dt. Step 4: Substitute R = 8 cm and dR/dt = 5 cm/s. Step 5: dA/dt = 2π × 8 × 5 = 80π cm²/s. Answer: 80π cm…

Card 7Rate of change

Solve: Find dA/dr for a circle when r = 5 cm, where A = πr².

Answer

Step 1: A = πr². Step 2: Differentiate w.r.t. r: dA/dr = 2πr. Step 3: Put r = 5. Step 4: dA/dr = 2π(5) = 10π cm. Answer: 10π cm.

Card 8Rate of change

Solve: Find dA/dC for a circular disc when radius is 8 cm, where A = πR² and C = 2πR.

Answer

Step 1: A = πR² and C = 2πR. Step 2: Write A in terms of C: R = C/(2π), so A = C²/(4π). Step 3: Differentiate: dA/dC = 2C/(4π) = C/(2π). Step 4: Since C = 2πR, dA/dC = R. Step 5: For R = 8, dA/dC = 8 …

+29 more flashcards

Practise All

Frequently Asked Questions

What are the important topics in Applications of Derivatives - I for ICSE Class 12 Mathematics?
Key topics in Applications of Derivatives - I include Rate of Change and Differentials, Approximation by Differentials, Increasing and Decreasing Functions, Tangent and Normal to a Curve. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many flashcards are available for Applications of Derivatives - I?
There are 37 flashcards for Applications of Derivatives - I covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Applications of Derivatives - I for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 55 practice questions on Applications of Derivatives - I. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Applications of Derivatives - I

All ICSE Class 12 Mathematics Flashcards

For serious students

Get the full Applications of Derivatives - I chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free