NCEA Level 3 Maths, standard by standard
NCEA Level 3 Mathematics and Statistics, the university-entrance year, typically taken as Calculus (Algebra, Differentiation, Integration, Complex numbers) or Statistics (inference, time series, bivariate, probability). Credit values are the long-standing legacy values; confirm against NZQA.
Apply trigonometric methods in solving problems
- Trig equations and identities
- Radians, general solutions
- Compound and double-angle formulae
- Modelling periodic situations
Apply the algebra of complex numbers in solving problems
- Complex numbers, rectangular and polar form
- Operations and conjugates
- De Moivre's theorem
- Loci and manipulation of surds/indices
Apply differentiation methods in solving problems
- Product, quotient and chain rules
- Trig, exponential and log derivatives
- Rates of change and optimisation
- Curve features and kinematics
Apply integration methods in solving problems
- Anti-derivatives of standard functions
- Definite integrals and area
- Integration by substitution
- Differential equations and applications
Investigate time series data
- Trend, seasonality and moving averages
- Additive models and forecasting
- Interpreting a time series in context
- Statistical enquiry cycle
Investigate bivariate measurement data
- Scatter plots and correlation
- Fitting a linear model
- Using a model to predict
- Evaluating the relationship in context
Use statistical methods to make a formal inference
- Sampling variability and bootstrapping
- Formal confidence intervals
- Comparing populations
- Justifying an inference
Evaluate statistically based reports
- Margins of error and confidence intervals
- Experiments and observational studies
- Surveys, sampling and bias
- Judging claims in a report
Apply probability concepts in solving problems
- Conditional probability and independence
- Two-way tables and trees
- Risk and relative risk
- Probability distributions in context
Apply probability distributions in solving problems
- Normal distribution
- Binomial and Poisson distributions
- Uniform and triangular distributions
- Choosing and applying the right model
Apply systems of simultaneous equations in solving problems
- Systems in 3 unknowns
- Gaussian elimination
- Unique, infinite and no solutions
- Modelling with systems
NCEA Level 3 Maths, explained step by step
Free lessons built to the Level 3 standards. Each one works through its examples with a reason for every step, then ends on four questions to try and their answers. Videos open on YouTube, and nothing loads from YouTube until you click.
Watch the whole course in order. All 34 NCEA Level 3 lessons, about 3 hours 37 minutes, as one YouTube playlist.
Open the NCEA Level 3 playlistAS 91577 · Apply the algebra of complex numbers in solving problems
6 lessons, about 39 minutes.
AS 91578 · Apply differentiation methods in solving problems
7 lessons, about 44 minutes.
AS 91579 · Apply integration methods in solving problems
6 lessons, about 37 minutes.
AS 91584 · Evaluate statistically based reports
5 lessons, about 32 minutes.
AS 91585 · Apply probability concepts in solving problems
5 lessons, about 32 minutes.
AS 91586 · Apply probability distributions in solving problems
5 lessons, about 33 minutes.
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Book a free NCEA assessmentAchievement standard titles, codes and credit values are referenced from NZQA (nzqa.govt.nz) for course-information purposes; confirm current details on the NZQA website. Vertex Academy is an independent tutoring centre and is not affiliated with or endorsed by NZQA or the Ministry of Education. All practice materials are original.