NCEA Pāngarau Co-requisite (NZQA Standard 32412) study plan

Solve 30 operations with whole numbers, integers, and decimals without a calculator, applying correct order of operations (whakaarohia te raupapa mahi) and checking each answer by estimation.

Convert fluently between fractions, decimals, and percentages for 25 values, including recurring decimals such as 0.333... and 2/3, and rank a mixed list from smallest to largest.

Calculate fractions and percentages of amounts in 15 word problems drawn from pay, discounts, and GST-style contexts, showing each step of working.

Explain in writing why a common error (for example adding denominators when adding fractions) is wrong, using a counter-example with numbers.

Apply ratio and proportion to scale recipes, mix ratios, and map scales, solving 12 problems and stating the unit of every answer.

Compute rates (speed, wage per hour, cost per unit) from given data and rearrange the relationship to find an unknown, across 10 problems.

Solve 10 percentage-change problems involving increases, decreases, and finding the original amount after a change, showing the multiplier used.

Identify and correct three of your own recurring arithmetic slips by writing a personal checklist of checking strategies.

Simplify and evaluate 20 algebraic expressions by substituting values, including negative numbers and simple powers.

Solve 15 linear equations and rearrange 10 formulas to make a specified variable the subject, checking each solution by substitution.

Construct and use 8 linear patterns or tables of values, describing the rule in words and as an equation, and predicting the 20th term.

Sketch the graph of a linear relationship from an equation and read off the gradient and intercept in context (for example cost versus hours).

Convert confidently between metric units of length, mass, capacity, and area/volume (for example cm² to m²), completing 20 conversions with correct unit labels.

Calculate perimeter and area of rectangles, triangles, circles, and composite shapes in 12 problems, selecting the correct formula and rounding sensibly.

Calculate volume and surface area of prisms and cylinders in 8 problems drawn from packaging and container contexts.

Use Pythagoras' theorem to find an unknown side in 8 right-angled triangle problems, identifying when the converse applies.

Measure and construct angles to the nearest degree using a protractor, and calculate unknown angles in triangles, quadrilaterals, and parallel-line configurations across 15 diagrams you draw yourself.

Apply bearings and scale drawings to solve 5 navigation-style problems, stating direction and distance in correct notation.

Read and interpret 6 statistical graphs (bar, line, pie, histogram, scatter) and describe the trend or comparison each one shows in two sentences.

Classify 20 data variables as categorical or numerical, and discrete or continuous, giving a reason for each classification.

Calculate mean, median, mode, and range for 8 data sets, including one with an outlier, and explain in writing how the outlier changes each measure.

Construct and interpret a box-and-whisker plot and a histogram from raw data, commenting on shape, centre, and spread.

Calculate experimental and theoretical probabilities for 10 simple and combined events (two-step, with and without replacement), using lists or tables of outcomes.

Critically evaluate 3 media or report claims involving statistics, identifying at least one misleading feature in each.

Decompose 6 multi-step real-world problems into sub-tasks, choosing and justifying the operation or formula at each stage before calculating.

Write full solutions to 8 contextual problems (budgeting, travel, recipes, trades) that show working, units, and a sentence interpreting the answer in context.

Check the reasonableness of every answer by estimation and identify deliberately planted errors in 5 worked solutions.

Communicate reasoning clearly by writing two solutions that a non-mathematical reader could follow, defining any symbols used.

Complete two full-length practice papers under timed conditions, allocating time across number, measurement, statistics, and reasoning sections.

Mark both papers against the given answers, log every error by domain, and rework each incorrect question to a fully correct solution.

Revisit the three weakest topics identified in the error log and solve 10 fresh questions on each.

Write a one-page exam-day strategy covering time allocation, showing working, unit checks, and how to attempt unfamiliar context questions.