Achievement objective M7-10
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:
- apply differentiation and anti-differentiation techniques to polynomials.
Indicators
- Develops the rules for differentiation of polynomials using understanding of gradient function and technology (graphics calculator or computer).
- Solves differentiation problems involving:
- rates of change
- finding points where gradient has a particular value
- finding the equation of the tangent to a curve at a point
- finding local maxima/minima of a function
- kinematics.
- Develops rules for anti-differentiation of polynomials using understanding of gradient function and technology (graphics calculator or computer).
- Solves anti-differentation problems involving:
- finding a family of curves with a given gradient
- finding the constant of anti-differentiation
- simple polynomial differential equations (not including separation of variables).
- Make links with graphs
M7-9.
- See
key mathematical ideas on NZmaths.
Progression
M7-10 links from
NA6-4,
GM6-3 and to
M8-11,
M8-12.
Possible context elaborations
Assessment for qualifications
NCEA achievement standards at level 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 following achievement standard(s) could assess learning outcomes from this AO:
Last updated September 17, 2018
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and the curve passes through (1, 5), find the equation of the curve.