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# Achievement standards with achievement objectives – Level 1

## Level 1 Achievement standards

• AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
• AS91027 Mathematics and statistics 1.2 Apply algebraic procedures in solving problems – 4 credits; External (CAT)
• AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs – 4 credits; External
• AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems – 3 credits; Internal
• AS91030 Mathematics and statistics 1.5 Apply measurement in solving problems – 3 credits; Internal
• AS91031 Mathematics and statistics 1.6 Apply geometric reasoning in solving problems – 4 credits; External
• AS91032 Mathematics and statistics 1.7 Apply right-angled triangles in solving measurement problems – 3 credits; Internal
• AS91033 Mathematics and statistics 1.8 Apply knowledge of geometric representations in solving problems – 3 credits; Internal
• AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems – 2 credits; Internal
• AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
• AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle – 3 credits; Internal
• AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data – 4 credits; External
• AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance – 3 credits; Internal

## Level 1 Achievement standards with achievement objectives

### Number and algebra

AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problem:

• Reason with linear proportions.
• Use prime numbers, common factors and multiples, and powers (including square roots).
• Understand operations on fractions, decimals, percentages, and integers.
• Use rates and ratios.
• Know commonly used fraction, decimal, and percentage conversions.
• Know and apply standard form, significant figures, rounding, and decimal place value.
• Apply direct and inverse relationships with linear proportion.
• Extend powers to include integers and fractions.
• Apply everyday compounding rates.

AS91027 Mathematics and statistics 1.2 Apply algebraic procedures in solving problems:

• Generalise the properties of operations with fractional numbers and integers.
• Generalise the properties of operations with rational numbers including the properties of exponents.
• Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs:

• Find optimal solutions, using numerical approaches.
• Solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
• Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
• Relate rate of change to the gradient of a graph.

AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems:

• Form and solve linear equations.
• Solve linear equations and inequations and simultaneous equations with two unknowns.
• Relate graphs, tables, and equations to linear relationships.
• Relate rate of change to the gradient of a graph.

### Geometry and measurement

AS91030 Mathematics and statistics 1.5 Apply measurement in solving problem:

• Convert between metric units, using decimals.
• Deduce and use formulae to find the perimeters and areas of polygons, and volumes of prisms.
• Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
• Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
• Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

AS91031 Mathematics and statistics 1.6 Apply geometric reasoning in solving problems:

• Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
• Recognise when shapes are similar and use proportional reasoning to find an unknown length.
• Use trigonometric ratios and Pythagoras’ Theorem in two dimensions.
• Deduce and apply the angle properties related to circles.

AS91032 Mathematics and statistics 1.7 Apply right angled triangles in solving measurement problems:

• Use trigonometric ratios and Pythagoras’ Theorem in two and three dimensions.
• Recognise when shapes are similar and use proportional reasoning to find an unknown length.
• Select and use appropriate metric units for length and area.
• Measure at a level of precision appropriate to the task.

AS91033 Mathematics and statistics 1.8 Apply knowledge of geometric representations in solving problems:

• Construct and describe simple loci.
• Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
• Create accurate nets for simple polyhedra and connect three dimensional solids with different two dimensional representations.
• Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.

AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems:

• Define and use transformations and describe invariant properties of figures and objects under these transformations.
• Compare and apply single and multiple transformations.
• Analyse symmetrical patterns by the transformations used to create them.

### Statistics

AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle:

• Plan and conduct surveys and experiments using the statistical enquiry cycle:
• determining appropriate variables
• cleaning data
• using multiple displays, and re-categorising data to find patterns, variations, in multivariate data sets
• comparing sample distributions visually, using measures of centre, spread, and proportion
• presenting a report of findings.
• Plan and conduct investigations using the statistical enquiry cycle:
• justifying the variables used
• identifying and communicating features in context (differences within and between distributions), using multiple displays
• making informal inferences about populations from sample data
• justifying findings, using displays and measures.

AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle:

• Plan and conduct surveys and experiments using the statistical enquiry cycle:
• determining appropriate variables and measures
• considering sources of variation
• gathering and cleaning data
• using multiple displays, and re-categorising data to find patterns and relationships, in multivariate data sets
• presenting a report of findings.
• Plan and conduct investigations using the statistical enquiry cycle:
• justifying the variables and measures used
• managing sources of variation including through the use of random sampling
• identifying and communicating features in context (relationships between variables), using multiple displays
• justifying findings, using displays and measures.

AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data:

• Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
• Calculate probabilities, using fractions, percentages, and ratios.
• Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.
• Investigate situations that involve elements of chance: calculating probabilities in discrete situations.

AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance:

• Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.
• Investigate situations that involve elements of chance:
• comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
• calculating probabilities in discrete situations.

Last updated September 14, 2018