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# Achievement standards with achievement objectives – Level 3

## Level 3 Achievement standards

• AS91573 Mathematics and statistics 3.1 Apply the geometry of conic sections in solving problems – 3 credits; Internal
• AS91574 Mathematics and statistics 3.2 Apply linear programming methods in solving problems – 3 credits; Internal
• AS91575 Mathematics and statistics 3.3 Apply trigonometric methods in solving problems – 4 credits; Internal
• AS91576 Mathematics and statistics 3.4 Use critical path analysis in solving problems – 2 credits; Internal
• AS91577 Mathematics and statistics 3.5 Apply the algebra of complex numbers in solving problems – 5 credits; External
• AS91578 Mathematics and statistics 3.6 Apply differentiation methods in solving problems – 6 credits; External
• AS91579 Mathematics and statistics 3.7 Apply integration methods in solving problems – 6 credits; External
• AS91580 Mathematics and statistics 3.8 Investigate time series data – 4 credits; Internal
• AS91581 Mathematics and statistics 3.9 Investigate bivariate measurement data – 4 credits; Internal
• AS91582 Mathematics and statistics 3.10 Use statistical methods to make a formal inference – 4 credits; Internal
• AS91583 Mathematics and statistics 3.11 Conduct an experiment to investigate a situation using experimental design principles – 4 credits; Internal
• AS91584 Mathematics and statistics 3.12 Evaluate statistically based reports – 4 credits; External
• AS91585 Mathematics and statistics 3.13 Apply probability concepts in solving problems – 4 credits; External
• AS91586 Mathematics and statistics 3.14 Apply probability distributions in solving problems – 4 credits; External
• AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems – 3 credits; Internal

## Level 3 Achievement standards with achievement objectives

### Mathematics

AS91573 Mathematics and statistics 3.1 Apply the geometry of conic sections in solving problems:

• Apply the geometry of conic sections.

AS91574 Mathematics and statistics 3.2 Apply linear programming methods in solving problems:

• Use linear programming techniques.

AS91575 Mathematics and statistics 3.3 Apply trigonometric methods in solving problems:

• Manipulate trigonometric expressions.
• Form and use trigonometric equations.

AS91576 Mathematics and statistics 3.4 Use critical path analysis in solving problems:

• Develop network diagrams to find optimal solutions, including critical paths.

AS91577 Mathematics and statistics 3.5 Apply the algebra of complex numbers in solving problems:

• Manipulate complex numbers and present them graphically.
• Form and use polynomial, and other non-linear equations.

AS91578 Mathematics and statistics 3.6 Apply differentiation methods in solving problems:

• Identify discontinuities and limits of functions.
• Choose and apply a variety of differentiation techniques to functions and relations using analytical methods.

AS91579 Mathematics and statistics 3.7 Apply integration methods in solving problems:

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

### Statistics

AS91580 Mathematics and statistics 3.8 Investigate time series data:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• using existing data sets
• finding, using, and assessing appropriate models (including additive models for time-series data), seeking explanations, and making predictions
• using informed contextual knowledge
• communicating findings and evaluating all stages of the cycle.

AS91581 Mathematics and statistics 3.9 Investigate bivariate measurement data:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• using existing data sets
• finding, using, and assessing appropriate models (including linear regression for bivariate data), seeking explanations, and making predictions
• using informed contextual knowledge and statistical inference
• communicating findings and evaluating all stages of the cycle.

AS91582 Mathematics and statistics 3.10 Use statistical methods to make a formal inference:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• using existing data sets
• seeking explanations
• using informed contextual knowledge, exploratory data analysis, and statistical inference
• communicating findings and evaluating all stages of the cycle.
• Make inferences from surveys and experiments:
• determining estimates and confidence intervals for differences
• use methods such as resampling to assess the strength of the evidence.

AS91583 Mathematics and statistics 3.11 Conduct an experiment to investigate a situation using experimental design principles:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• conducting experiments using experimental design principles
• seeking explanations
• using informed contextual knowledge, exploratory data analysis, and statistical inference
• communicating findings and evaluating all stages of the cycle.
• Make inferences from surveys and experiments:
• using methods such as randomisation to assess the strength of the evidence.

AS91584 Mathematics and statistics 3.12 Evaluate statistically based reports:

• Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
• critiquing causal-relationship claims
• interpreting margins of error.

AS91585 Mathematics and statistics 3.13 Apply probability concepts in solving problems:

• Investigate situations that involve elements of chance:
• calculating probabilities of independent, combined, and conditional events.

AS91586 Mathematics and statistics 3.14 Apply probability distributions in solving problems:

• Investigate situations that involve elements of chance:
• calculating and interpreting expected values and standard deviations of discrete random variables
• applying distributions such as the Poisson, binomial, and normal.

AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems:

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

Last updated September 14, 2018