Achievement objective M8-2
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
- display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.
- Demonstrates understanding of inverse and/or reciprocal functions, including those of:
- exponential y = eax or y = bx
- 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
M8-2 links from M7-2.
Possible context elaborations
- Given the graph of ex, 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
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.
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