NCEA Level 2 Mathematics and Statistics study plan

Diagnose algebra baseline by completing 20 mixed questions on fractions, exponents, and formula rearrangement, then record each error by type.

Rearrange linear and quadratic formulae, solve linear equations and inequalities, and verify answers by substitution.

Expand and factorise quadratic expressions, solve quadratic equations by factorising and by formula, and check the discriminant.

Set up and solve systems of two linear equations both graphically and algebraically, interpreting the intersection point.

Sketch and interpret linear, quadratic, and exponential graphs by identifying intercepts, turning points, and asymptotes.

Apply exponent and logarithm laws to solve equations, showing each inverse operation clearly.

Generate arithmetic and geometric sequences, calculate nth terms and sums, and use them to answer context questions.

Translate short word problems into equations, solve them, and state the solution with correct units and context.

Apply Pythagoras and trigonometric ratios to right-angled triangles, including bearings and angles of elevation or depression.

Use the sine rule, cosine rule, and area formula for non-right-angled triangles in multi-step problems.

Calculate perimeter, area, surface area, and volume of composite 2D and 3D shapes, converting units correctly.

Use coordinate geometry to find distance, midpoint, gradient, and equations of lines, including parallel and perpendicular cases.

Solve coordinate geometry problems involving line intersections, parallel lines, and perpendicular lines.

Apply trigonometric relationships to combined right-triangle and coordinate problems, checking reasonableness of answers.

Use network diagrams to identify vertices, edges, paths, and traversability, and solve a simple shortest-path problem.

Interpret scale drawings or maps, convert between units, and justify the scale factor used.

Classify data types and sampling methods, then identify bias and sources of error in short scenarios.

Construct and interpret dot plots, histograms, and box plots, and calculate mean, median, range, IQR, and standard deviation.

Evaluate a report-style data summary by checking sample size, graph scale, claims, and correlation versus causation.

Design a simple questionnaire or experiment with clear variables, sampling method, and ethical considerations.

Apply probability rules using complements, addition, multiplication, two-way tables, and tree diagrams.

Use simulations to estimate probabilities and compare simulated results with theoretical probabilities.

Make an inference from sample data by calculating a sample statistic and stating a claim with appropriate uncertainty.

Solve chance problems involving combined events and justify whether events are independent or mutually exclusive.

Solve mixed algebra and geometry problems that require setting up equations before calculating lengths, areas, or coordinates.

Apply trigonometric and algebraic methods together in coordinate geometry contexts, checking each answer by an alternative method.

Review the weeks 1-6 error log and correct recurring mistakes in three targeted practice blocks.

Complete a timed mixed paper under exam conditions without notes, then classify every error by cause.

Complete a full mixed paper covering Number and Algebra, Geometry and Measurement, and Statistics and Probability under timed conditions.

Audit the final error log and retest the five most frequent errors until each is answered correctly twice.

Write a concise summary of formula selection, unit checks, and statistical claim checks to use during revision.

Set a final 20-question speed drill across all three domains and review timing and accuracy.