Number Version Page 1 of 2
Subject Reference Mathematics and Statistics 3.6
Title Apply differentiation methods in solving problems
Level 3 Credits 6 Assessment External
Status Status date
Planned review date Date version published
This achievement standard involves applying differentiation methods in solving problems.
Achievement Achievement with Merit Achievement with Excellence
Apply differentiation Apply differentiation Apply differentiation methods,
methods in solving methods, using relational using extended abstract
problems. thinking, in solving thinking, in solving problems.
1 This achievement standard is derived from Level 8 of The New Zealand Curriculum,
Learning Media, Ministry of Education, 2007; and is related to the achievement
Identify discontinuities and limits of functions
Choose and apply a variety of differentiation techniques to functions and relations
using analytical methods
in the Mathematics strand of the Mathematics and Statistics Learning Area. It is also
related to the material in the Teaching and Learning Guide for Mathematics and
Statistics, Ministry of Education, 2010 at http://seniorsecondary.tki.org.nz.
2 Apply differentiation methods in solving problems involves:
selecting and using methods
demonstrating knowledge of concepts and terms
communicating using representations.
Relational thinking involves one or more of:
selecting and carrying out a logical sequence of steps
connecting different concepts or representations
demonstrating understanding of concepts
Number Version Page 2 of 2
forming and using a model
and also relating findings to a context, or communicating thinking using appropriate
Extended abstract thinking involves one or more of:
devising a strategy to investigate or solve a problem
identifying relevant concepts in context
developing a chain of logical reasoning, or proof
forming a generalisation
and also using correct mathematical statements, or communicating mathematical
3 Problems are situations that provide opportunities to apply knowledge or
understanding of mathematical concepts and methods. Situations will be set in real-
life or mathematical contexts.
4 Methods include a selection from those related to:
derivatives of power, exponential, and logarithmic (base e only) functions
derivatives of trigonometric (including reciprocal) functions
equations of normals
maxima and minima and points of inflection
related rates of change
derivatives of parametric functions
chain, product, and quotient rules
properties of graphs (limits, differentiability, continuity, concavity).
5 Assessment Specifications for this achievement standard can be accessed through
the Mathematics and Statistics Resources page found at www.nzqa.govt.nz/maths.
1 Providers and Industry Training Organisations must have been granted consent to
assess by NZQA before they can register credits from assessment against
2 Organisations with consent to assess and Industry Training Organisations assessing
against achievement standards must engage with the moderation system that applies
to those achievement standards.
Consent and Moderation Requirements (CMR) reference 0233