HSC Practice Questions - Working with Functions

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Original HSC style questions for Australian Curriculum Year 11/Year 12
Mathematics Advanced topic Working with Functions (Algebraic Techniques sold as a separate file).

Solutions and Marking Criteria included in each set.

8 sets of 10 questions including a mixture of the following:

*Defining a function

• Using f(x) notation
• Defining the domain and range of f(x) for linear, quadratic, cubic, hyperbolic, exponential, circle, semicircle, absolute value and piecewise functions.
• Point-gradient formula
• Two-point formula
• Quadratics - find intercepts, axis of symmetry and vertex. Find the equation given the graph. Graph an equation.
• Cubics - determine the equation of the form kx^3 and k(x+a)(x+b)(x+c). Graphing cubics.
• Direct/Indirect variation
• Solve inequalities
• Circles - graphing, determine the equation (including completing the square to find centre and radius), identify and graph semicircles
• Determine even/odd algebraically
• Composite functions
• Interpreting and graphing piecewise functions
• Absolute value functions (graphing, solving equations)