• Chapter 6 – Differentiation

When students have completed this lesson they should be able to:

• Calculate and approximation to the gradient at a point on a curve, given its equation
• Calculate the exact gradient at a point on a quadratic curve and certain other curves
• Find the equations of the tangent and normal to a curve at a point

Chapter 7 – Applications of Differentiation

When students have completed this lesson they should be able to:

• Understand that the derivative of a function is itself a function
• Appreciate the significance of positive, negative and zero derivatives
• Locate maximum and minimum points on graphs
• Know that you can interpret a derivative as a rate of change of one variable with respect to another
• Be familiar with notation for a derivative
• Apply these techniques to solve real-world problems

Chapter 12 – Extending Differentiation

When students have completed this lesson they should be able to:

• Differentiate composite functions of the form f(F(x))
• Apply differentiation to rates of change, and related rates of change

Chapter 15 – Second Derivatives

When students have completed this lesson they should be able to:

• Understand the significance of the second derivative for the shape of graphs and in real-world applications
• Use second derivatives where appropriate to distinguish minimum and maximum points
• Understand that at a point of inflexion the second derivative is zero