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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

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## 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.

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### 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

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