Unit 6: Differentiation questions and answers

Differentiation: sample questions with answers

What unit 6 covers

Questions follow the book: Mathematics, Secondary, Form Four, Student Book.

1. Lesson 1: Derivatives

   • Gradient of a curve
   • Derivatives
   • Derivatives of kf(x) where k is a constant
   • Some more rules for differentiation

2. Lesson 2: The Product and Quotient Rule

   • The product rule
   • The quotient rule
   • The chain rule

3. Lesson 3: Second Derivative

   • Second derivative

4. Lesson 4: Differentiation of Trigonometric Functions

   • Differentiation of trigonometric functions
   • Derivatives of sin f(x) and cos f(x) by the chain rule

5. Lesson 5: Increasing and Decreasing Functions

   • Increasing and decreasing functions
   • The relationship between the sign of d^2y/dx^2 and concavity

6. Lesson 6: Stationary Point, Maximum Point and Minimum Point

   • Stationary points
   • Maximum or Minimum Points (Local Extremum Points)
   • First derivative test
   • Second Derivative test or Maximum and Minimum Points
   • Point of inflexion

7. Lesson 7: Rates of Change

   • Rates of change
   • Velocity and acceleration
   • Chapter Exercise