Achievement objective M8-2

Indicators

• Demonstrates understanding of inverse and/or reciprocal functions, including those of:
  • polynomial
  • exponential y = e^ax or y = b^x
  • logarithmic
  • rectangular hyperbola
  • trigonometric equations of the form y = Asin(Bx ) + C for sin, cos and tan functions with x in radians or degrees
  • f(x) = √ x
• Makes graphical and algebraic connections between a function and its inverse, including the consideration of restrictions on the domain of a function so that its inverse is also a function.
• Makes links with manipulate trigonometric expressions M8-6, solving equations M8-7 and identification of discontinuities M8-10.

Progression

M8-2 links from M7-2.

Possible context elaborations

• Given the graph of e^x, sketch its inverse function.
• Given a function algebraically, find the rule for its inverse.
• Explore the reciprocals and inverses of trigonometric functions.
• Investigate families of functions and their inverses making connections between transformations of a graph and changes to the equation of the graph.
• Use equations of functions to model situations such as temperature data, tides, ferris wheels, ski slopes, population growth.
• Activity: Big Bang Theory - Fractals and complex numbers
• Activity: Linking integration and differentiation

Assessment for qualifications

NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.

Learn more:

•   NZQA: Mathematics and statistics subject resources

Note: Aligned and registered level 3 achievement standards will not be on the NZQA website until December 2012.

• School planning draft level 3 achievement standards are on NCEA on TKI.
• Final draft level 3 achievement standards will be on  NCEA on TKI from end of September.
• Aligned level 3 achievement standards will be registered and published by NZQA for use in 2013 in December.

Full information on the level 3 draft standards and the alignment process can be found on NCEA on TKI.

The following achievement standard(s) could assess learning outcomes from this AO:

• There are currently no achievement standards that could assess learning outcomes from this AO.

Refer to the draft standards matrix.

Last updated September 26, 2012

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