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## Senior Secondary navigation

Achievement objectives

What has changed:

# Achievement objectives by level

For convenience, all achievement objectives have been given a three-part code consisting of:

1. the strand (NA for number and algebra, GM for geometry and measurement, S for statistics, and M for mathematics)
2. the curriculum level
3. the ordinal position of the achievement objective (1st, 2nd, 3rd, and so on) as listed in the Curriculum.

Download this document to view the achievement objectives as a table.

### Level 6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

#### Number and algebra

• NA 6-1 Apply direct and inverse relationships with linear proportions
• NA 6-2 Extend powers to include integers and fractions
• NA 6-3 Apply everyday compounding rates
• NA 6-4 Find optimal solutions, using numerical approaches
• NA 6-5 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns
• NA 6-6 Generalise the properties of operations with rational numbers, including the properties of exponents
• NA 6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns
• NA 6-8 Relate rate of change to the gradient of a graph

#### Geometry and measurement

• GM 6-1 Measure at a level of precision appropriate to the task
• GM 6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures
• GM 6-3 Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae
• GM 6-4 Deduce and apply the angle properties related to circles
• GM 6-5 Recognise when shapes are similar and use proportional reasoning to find an unknown length
• GM 6-6 Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions
• GM 6-7 Use a co-ordinate plane or map to show points in common and areas contained by two or more loci
• GM 6-8 Compare and apply single and multiple transformations
• GM 6-9 Analyse symmetrical patterns by the transformations used to create them

#### Statistics

• S 6-1 Plan and conduct investigations using the statistical inquiry cycle:
• A – justifying the variables and measures used
• B – managing sources of variation, including the use of random sampling
• C – identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
• D – making informal inferences about populations from sample data
• E – justifying findings, using displays and measures
• S 6-2 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made
• S 6-3 Investigate situations that involve elements of chance:
• A – comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
• B – calculating probabilities in discrete situations

### Level 7

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

#### Mathematics

• M 7-1 Apply co-ordinate geometry techniques to points and lines
• M 7-2 Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs
• M 7-3 Use arithmetic and geometric sequences and series
• M 7-4 Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions
• M 7-5 Choose appropriate networks to find optimal solutions
• M 7-6 Manipulate rational, exponential, and logarithmic algebraic expressions
• M 7-7 Form and use linear, quadratic, and simple trigonometric equations
• M 7-8 Form and use pairs of simultaneous equations, one of which may be non-linear
• M 7-9 Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs
• M 7-10 Apply differentiation and anti-differentiation techniques to polynomials

#### Statistics

• S 7-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets
• B – evaluating the choice of measures for variables and the sampling and data collection methods used
• C – using relevant contextual knowledge, exploratory data analysis, and statistical inference
• S 7-2 Make inferences from surveys and experiments:
• A – making informal predictions, interpolations, and extrapolations
• B – using sample statistics to make point estimates of population parameters
• C – recognising the effect of sample size on the variability of an estimate
• S 7-3 Evaluate statistically based reports:
• A – interpreting risk and relative risk
• B – identifying sampling and possible non-sampling errors in surveys, including polls
• S 7-4 Investigate situations that involve elements of chance:
• A – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
• B – calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology

### Level 8

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

#### Mathematics

• M 8-1 Apply the geometry of conic sections
• M 8-2 Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions
• M 8-3 Use permutations and combinations
• M 8-4 Use curve fitting, log modelling, and linear programming techniques
• M 8-5 Develop network diagrams to find optimal solutions, including critical paths
• M 8-6 Manipulate trigonometric expressions
• M 8-7 Form and use trigonometric, polynomial, and other non-linear equations
• M 8-8 Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context
• M 8-9 Manipulate complex numbers and present them graphically
• M 8-10 Identify discontinuities and limits of functions
• M 8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods
• M 8-12 Form differential equations and interpret the solutions

#### Statistics

• S 8-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – conducting experiments using experimental design principles, conducting surveys, and using existing data sets
• B – finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions
• C – using informed contextual knowledge, exploratory data analysis, and statistical inference
• D – communicating findings and evaluating all stages of the cycle
• S 8-2 Make inferences from surveys and experiments:
• A – determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
• B – using methods such as resampling or randomisation to assess the strength of evidence
• S 8-3 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
• A – critiquing causal-relationship claims
• B – interpreting margins of error
• S 8-4 Investigate situations that involve elements of chance:
• A – calculating probabilities of independent, combined, and conditional events
• B – calculating and interpreting expected values and standard deviations of discrete random variables
• C – applying distributions such as the Poisson, binomial, and normal

Last updated September 15, 2018