• 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