NCEA Mathematics:
Level 2

Algebra and Measurement in NCEA Level 2 Mathematics covers the algebraic methods, sequences and series, and calculus skills assessed across Achievement Standards AS91261 (Apply algebraic methods in solving problems), AS91258 (Apply sequences and series in solving problems), and AS91262 (Apply calculus methods in solving problems) — including manipulating algebraic expressions, expanding and factorising including quadratics, solving quadratic equations by factorisation, completing the square, and the quadratic formula, simplifying rational expressions, solving inequalities, working with exponents and logarithms, arithmetic and geometric sequences and series including sigma notation and sum formulae, the sum to infinity of a convergent geometric series, differentiating polynomial, exponential, and trigonometric functions, finding gradients and equations of tangents and normals, identifying and classifying stationary points, applying differentiation to optimisation and rates of change, integrating polynomial functions, evaluating definite integrals, and finding areas under and between curves. Students are assessed at Achievement, Merit, and Excellence, with higher grades requiring relational thinking and multi-step reasoning across increasingly complex, unfamiliar situations.

Geometry and Trigonometry in NCEA Level 2 Mathematics covers the coordinate geometry, graphical methods, and trigonometric relationships assessed across Achievement Standards AS91256 (Apply co-ordinate geometry methods in solving problems), AS91257 (Apply graphical methods in solving problems), and AS91259 (Apply trigonometric relationships in solving problems) — including the distance formula, midpoint formula, gradient, equations of lines including parallel and perpendicular relationships, equations of circles, sketching and interpreting linear, quadratic, cubic, exponential, logarithmic, and rational function graphs, identifying key features including intercepts, turning points, and asymptotes, using graphs to solve equations, the unit circle and definitions of sine, cosine, and tangent for all angles, the sine rule and cosine rule for non-right-angled triangles, the area formula for triangles, radian measure, arc length and sector area, and graphing trigonometric functions including transformations of amplitude and period. Achievement requires the application of these skills in familiar contexts, Merit requires relational thinking connecting multiple concepts, and Excellence requires multi-step reasoning in extended, unfamiliar situations.

Statistics and Probability in NCEA Level 2 Mathematics covers the statistical inference, experimental investigation, and probability skills assessed across Achievement Standards AS91264 (Use statistical methods to make an inference), AS91265 (Conduct an experiment to investigate a situation using statistical methods), AS91267 (Apply probability methods in solving problems), and AS91268 (Investigate a situation involving elements of chance using a simulation) — including posing comparative investigative questions, selecting and using appropriate displays such as box plots, histograms, and dot plots, calculating and interpreting summary statistics, making informal inferences about populations from sample data using sampling variability, conducting statistical experiments and analysing results, writing clear statistical reports, theoretical and experimental probability, probability of combined events using two-way tables, Venn diagrams, and tree diagrams, conditional probability and independent events, the normal distribution and standardisation using z-scores, and designing and carrying out probability simulations to estimate the likelihood of outcomes. Excellence-level responses require students to demonstrate integrated statistical and probabilistic thinking in extended, unfamiliar contexts.