AdelaideX: MathTrackX: Special Functions

• Properties and graphing of trigonometric functions including sine, cosine and tangent

• Exponential and logarithmic functions

• Application of trigonometric, exponential and logarithmic functions.

Week 1: Exponential functions

• Establish and use the algebraic properties of exponential functions
• Recognise the qualitative features of the graph of exponentials including asymptotes
• Identify contexts suitable for modelling with exponential functions and use them to solve practical problems.

Week 2: Logarithmic functions

• Recognise and use the inverse relationship between logarithms and exponentials
• Establish and use algebraic properties of logarithms
• Interpret and use logarithmic scales
• Recognise qualitative features of the graph of y=a(x) (with a>1) including asymptotes, and more generally y=a(x+c)+b.
• Identify contexts suitable for modelling with logarithmic functions and use them to solve practical problems (algebraically, graphically, and with technology).

Week 3: Trigonometric functions

• Understand the unit circle definition of sin, cos and tan using radians and recognise the exact values at integer multiples of pi/6 and pi/4
• Recognise the graphs of y=cos(x), y=sin(x), y=tan(x) and identify key elements of their graphs
• Describe amplitude, period and phase changes of sin, cos and tan, and graphs of y=asin(bx+c)+d, y=acos(bx+c)+d, y=a tan(bx+c)+d
• Prove and apply common trigonometric identities including angle sum and angle difference identities
• Identify contexts suitable for modelling with trigonometric functions and use them to solve practical problems.

Week 4: Reciprocal and absolute value functions

• Recognise the shape of the graph of a reciprocal function
• Recognise the shape of the graph of an absolute value function
• Apply the properties of absolute values, and use them to solve equations.
• Describe the effect of performing the absolute value on an existing function

Week 5: Assessment

There is a timed exam.