#
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.

## What is new/changed?

- This does not include finding definite integrals or areas.

## 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:

- AS91262 Mathematics and statistics 2.7 Apply calculus methods in solving problems

Refer to the
mathematics and statistics matrix.

Last updated September 26, 2013

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