Mathematics and Statistics Curriculum Model: New Zealand

Maths: Years 11–13 (NCEA Levels 1–3)

Year 11 (Age 15–16) - NCEA Level 1

Topics: Number & algebra, linear & quadratic equations, coordinate geometry, trigonometry, chance & data, measurement & geometry.

Focus Areas: External: Algebra & Graphs; Internal: Statistical investigation, Number, Measurement.

Year 12 (Age 16–17) - NCEA Level 2

Topics: Sequences & series, non-linear graphs, networks, probability distributions, calculus (intro), matrices, trigonometry (unit circle).

Focus Areas: External: Algebra & Calculus; Internal: Probability, Statistics, Geometry.

Year 13 (Age 17–18) - NCEA Level 3

Topics: Differentiation & integration, complex numbers, statistical inference, linear programming, conic sections, advanced probability & statistical models.

Focus Areas: Options: Calculus, Statistics, Mathematics with Calculus, Mathematics with Statistics. University preparation.

NCEA Statistics Overview (Years 11–13)

Year 11 (NCEA Level 1 Statistics, Age 15–16)

Key Topics

  • Data collection & presentation

  • Statistical investigations (PPDAC cycle: Problem, Plan, Data, Analysis, Conclusion)

  • Graphical displays (dot plots, histograms, box plots)

  • Measures of centre & spread (mean, median, IQR, standard deviation)

  • Probability (simple events, tables, tree diagrams)

Year 12 (NCEA Level 2 Statistics, Age 16–17)

Key Topics

  • Probability methods (including conditional probability, independence, two-way tables, tree diagrams)

  • Probability distributions (binomial, normal, etc.)

  • Statistical experiments & simulations

  • Inference from data (sample vs population, margins of error, confidence)

  • Relationship between variables (correlation, regression, bivariate data)

Year 13 (NCEA Level 3 Statistics, Age 17–18)

Key Topics

  • Statistical inference (formal confidence intervals, hypothesis testing concepts)

  • Advanced probability (including conditional, random variables, expectation)

  • Probability distributions & models (binomial, normal, Poisson, continuous)

  • Time series analysis (trends, seasonal patterns, smoothing)

  • Multivariate data analysis (comparing groups, sampling distributions, bootstrapping, re-sampling methods)

  • Statistical reports (evaluating reliability, bias, context relevance)

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