Level 3 Maths

3.3 Trigonometry

Apply trigonometric methods in solving problems

AS91575, version 2 (2019), internal, 4 credits

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Student resources

• Formulae and tables booklet

In-class activities

• Unit circle GeoGebra illustrations: sine graph, cosine graph, and tangent graph, resources by Anthony C.M. OR
• GeoGebra - Transformations of trigonometric graphs

Standard information

• Standard (v2, 2019)
• Standard clarifications (September 2015)

Assessment information

• Conditions of assessment (2017)
• Exemplars
• Sample internal 1
• Sample internal 2

Curriculum links

This standard is linked to level 8 of the New Zealand Curriculum. It links to the achievement objectives:

• M8-6 Manipulate trigonometric expressions
• M8-7 Form and use trigonometric equations

3.6 Differentiation

Apply differentiation methods in solving problems

AS91578, version 2 (2019), external, 6 credits

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Student resources

• Formulae and tables booklet
• Differentiation from First Principles illustration

Past exams

2023	exam+answers
2022	exam+answers
2021	exam+answers
2020	exam+answers
2019	exam+answers
2018	exam+answers
2017	exam+answers
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2008	exam+answers
2007	exam+answers
2006	exam+answers
2005	exam+answers

Standard information

• Standard (v2, 2019)

Assessment information

• Assessment specifications (2021)

Curriculum links

This standard is linked to level 8 of the New Zealand Curriculum. It links to the achievement objectives:

• M8-10 Identify discontinuities and limits of functions
• M8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods

3.7 Integration

Apply integration methods in solving problems

AS91579, version 2 (2019), external, 6 credits

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Student resources

• Formulae and tables booklet

Past exams

2023	exam+answers
2022	exam+answers
2021	exam+answers
2020	exam+answers
2019	exam+answers
2018	exam+answers
2017	exam+answers
2016	exam+answers
2015	exam+answers
2014	exam+answers
2013	exam+answers
2012	exam+answers
2011	exam+answers
2010	exam+answers
2009	exam+answers
2008	exam+answers
2007	exam+answers
2006	exam+answers
2005	exam+answers
2004	exam+answers

Standard information

• Standard (v2, 2019)

Assessment information

• Assessment specifications (2021)

Curriculum links

This standard is linked to level 8 of the New Zealand Curriculum. It links to the achievement objectives:

• M8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods
• M8-12 Form differential equations and interpret the solutions

3.15 Systems of Equations

Apply systems of simultaneous equations in solving problems

AS91587, version 2 (2019), internal, 3 credits

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Standard information

• Standard (v2, 2019)
• Standard clarifications (September 2015)

Assessment information

• Conditions of assessment (2017)
• Exemplars
• Sample internal 1
• Sample internal 2

Curriculum links

This standard is linked to level 8 of the New Zealand Curriculum. It links to the achievement objective:

• M8-8 Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context