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Skills available for New Zealand year 13 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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New Zealand Curriculum: Level 7 New Zealand Curriculum: Level 7
New Zealand Curriculum: Level 8 New Zealand Curriculum: Level 8

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L7.1 Mathematics

L7.1.1 Patterns and relationships
L7.1.2 Equations and expressions
L7.1.3 Calculus
- L7.1.3.1 Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.
- L7.1.3.2 Apply differentiation and anti-differentiation techniques to polynomials.

L7.2 Statistics

L7.2.1 Statistical investigation
- L7.2.1.1 Carry out investigations of phenomena, using the statistical enquiry cycle:
  - L7.2.1.1.a conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets;
  - L7.2.1.1.b evaluating the choice of measures for variables and the sampling and data collection methods used;
  - L7.2.1.1.c using relevant contextual knowledge, exploratory data analysis, and statistical inference.
- L7.2.1.2 Make inferences from surveys and experiments:
  - L7.2.1.2.a making informal predictions, interpolations, and extrapolations;
  - L7.2.1.2.b using sample statistics to make point estimates of population parameters;
  - L7.2.1.2.c recognising the effect of sample size on the variability of an estimate.
L7.2.2 Statistical literacy
- L7.2.2.1 Evaluate statistically based reports:
  - L7.2.2.1.a interpreting risk and relative risk;
  - L7.2.2.1.b identifying sampling and possible non-sampling errors in surveys, including polls.
L7.2.3 Probability
- L7.2.3.1 Investigate situations that involve elements of chance:
  - L7.2.3.1.a comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions;
  - L7.2.3.1.b calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

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L7.1 Mathematics

L7.1.1 Patterns and relationships

L7.1.1.1 Apply co-ordinate geometry techniques to points and lines.

L7.1.1.2 Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs.

L7.1.1.3 Use arithmetic and geometric sequences and series.

L7.1.1.4 Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.

L7.1.1.5 Choose appropriate networks to find optimal solutions.

L7.1.2 Equations and expressions

L7.1.2.1 Manipulate rational, exponential, and logarithmic algebraic expressions.

L7.1.2.2 Form and use linear, quadratic, and simple trigonometric equations.

L7.1.2.3 Form and use pairs of simultaneous equations, one of which may be nonlinear.

L7.1.3 Calculus

L7.1.3.1 Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.

L7.1.3.2 Apply differentiation and anti-differentiation techniques to polynomials.

L7.2 Statistics

L7.2.1 Statistical investigation

L7.2.1.1 Carry out investigations of phenomena, using the statistical enquiry cycle:

L7.2.1.1.a conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets;

L7.2.1.1.b evaluating the choice of measures for variables and the sampling and data collection methods used;

L7.2.1.1.c using relevant contextual knowledge, exploratory data analysis, and statistical inference.

L7.2.1.2 Make inferences from surveys and experiments:

L7.2.1.2.a making informal predictions, interpolations, and extrapolations;

L7.2.1.2.b using sample statistics to make point estimates of population parameters;

L7.2.1.2.c recognising the effect of sample size on the variability of an estimate.

L7.2.2 Statistical literacy

L7.2.2.1 Evaluate statistically based reports:

L7.2.2.1.a interpreting risk and relative risk;

L7.2.2.1.b identifying sampling and possible non-sampling errors in surveys, including polls.

L7.2.3 Probability

L7.2.3.1 Investigate situations that involve elements of chance:

L7.2.3.1.a comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions;

L7.2.3.1.b calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.