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# Achievement standards with achievement objectives – Level 2

## Level 2 Achievement standards

• AS91256 Mathematics and statistics 2.1 Apply co-ordinate geometry methods in solving problems – 2 credits; Internal
• AS91257 Mathematics and statistics 2.2 Apply graphical methods in solving problems – 4 credits; Internal
• AS91258 Mathematics and statistics 2.3 Apply sequences and series in solving problems – 2 credits; Internal
• AS91259 Mathematics and statistics 2.4 Apply trigonometric relationships in solving problems – 3 credits; Internal
• AS91260 Mathematics and statistics 2.5 Apply network methods in solving problems – 2 credits; Internal
• AS91261 Mathematics and statistics 2.6 Apply algebraic methods in solving problems – 4 credits; External
• AS91262 Mathematics and statistics 2.7 Apply calculus methods in solving problems – 5 credits; External
• AS91263 Mathematics and statistics 2.8 Design a questionnaire – 3 credits; Internal
• AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference – 4 credits; Internal
• AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods – 3 credits; Internal
• AS91266 Mathematics and statistics 2.11 Evaluate a statistically based report – 2 credits; Internal
• AS91267 Mathematics and statistics 2.12 Apply probability methods in solving problems – 4 credits; External
• AS91268 Mathematics and statistics 2.13 Investigate a situation involving elements of chance using a simulation – 2 credits; Internal
• AS91269 Mathematics and statistics 2.14 Apply systems of equations in solving problems – 2 credits; Internal

## Level 2 Achievement standards with achievement objectives

### Mathematics

AS91256 Mathematics and statistics 2.1 Apply co-ordinate geometry methods in solving problems:

• Apply co-ordinate geometry techniques to points and lines.

AS91257 Mathematics and statistics 2.2 Apply graphical methods in solving problems:

• Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs.
• Form and use linear, quadratic, and simple trigonometric equations.

AS91258 Mathematics and statistics 2.3 Apply sequences and series in solving problems:

• Use arithmetic and geometric sequences and series.

AS91259 Mathematics and statistics 2.4 Apply trigonometric relationships in solving problems:

• Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.

AS91260 Mathematics and statistics 2.5 Apply network methods in solving problems:

• Choose appropriate networks to find optimal solutions.

AS91261 Mathematics and statistics 2.6 Apply algebraic methods in solving problems:

• Manipulate rational, exponential, and logarithmic algebraic expressions.
• Form and use linear and quadratic equations.

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

• Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.
• Apply differentiation and anti-differentiation techniques to polynomials in the mathematics strand of the mathematics and statistics learning area.

AS91269 Mathematics and statistics 2.14 Apply systems of equations in solving problems:

• Form and use linear and quadratic equations.
• Form and use pairs of simultaneous equations, one of which may be non-linear.

### Statistics

AS91263 Mathematics and statistics 2.8 Design a questionnaire:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• conducting surveys
• evaluating the choice of measures for variables and data collection methods used
• using relevant contextual knowledge.

AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• using existing data sets
• evaluating the choice of sampling and data collection methods used
• using relevant contextual knowledge, exploratory data analysis, and statistical inference.
• Make inferences from surveys:
• using sample statistics to make point estimates of population parameters
• recognising the effect of sample size on the variability of an estimate.

AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods:

• Carry out investigations of phenomena, using the statistical enquiry cycle:
• conducting experiments
• evaluating the choice of measures for variables and data collection methods used
• using relevant contextual knowledge, exploratory data analysis, and statistical inference.

AS91266 Mathematics and statistics 2.11 Evaluate a statistically based report:

• Evaluate statistically based reports:
• identifying sampling and possible non-sampling errors in surveys, including polls.

AS91267 Mathematics and statistics 2.12 Apply probability methods in solving problems:

• Evaluate statistically based reports:
• interpreting risk and relative risk.
• Investigate situations that involve elements of chance:
• comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
• calculating probabilities, using such tools such as two-way tables, tree diagrams.

AS91268 Mathematics and statistics 2.13 Investigate a situation involving elements of chance using a simulation:

• Investigate situations that involve elements of chance:
• calculating probabilities using such tools as simulations and technology.

Last updated September 14, 2018