### Exponentials and logarithms

Generalising Numbers (part of module)

• Gradients of line graphs (including finding the gradient of a given line, and drawing a line given the gradient)
• Linear equations (including special lines, and what if two lines cross)
• Introduction to curve
• Parabolic equations (including the axis of symmetry)
• Exponential equations (including a special number)
• When two graphs meet

• Exponential functions (including the function and its graph, case studies, average rate of change and the inverse of the exponential function)
• Logarithmic functions (including the function and its graph, case studies, average rate of change and properties of logarithms)
• Putting it all together – solving equations and real world applications

Relations and functions (part of module)

• What are functions
• Function toolbox (including functional notation, zero conditions of a function, average rate of change of a function, continuity and the inverse of a function)
• Families of functions (including polynomial functions (which include the constant function, the linear function, the quadratic function, and other polynomial functions), exponential and logarithmic functions, rational functions and functions over an integral domain (including arithmetic and geometric sequences)

• Inequalities and the real number line (including operations on inequalities, and linear inequalities of two variables)
• Quadratic Equations and Completing the Square
• Functions (including polynomials, rational functions, other important non-linear functions, solving simultaneous equations algebraically and graphically inverse Functions and continuity)

#### Video based resources

• An introduction to logarithms (printable handout)
This 12 minute video shows an introduction to logarithms.  It has examples of using different bases and applying the different logarithms laws.
• Solving equations using logarithms (printable handout)
This 7 minute video works through some examples of using logarithms to solve equations.
• Introduction to exponential and their graphs (printable handout)
This 3 minute video shows examples of using exponential to solve equations and the interpretations of exponential growth and decay curve.