NCEA maths skill practice

Algebraic Methods NCEA practice questions

Practise algebraic methods using the existing NCEA question bank.

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Skill overview

What these questions practise

Choose a question, attempt it independently, then compare the reasoning and restrictions in its walkthrough.

Relevant standards: NCEA Level 2 Algebra — AS91261

This collection contains 15 matching walkthroughs across 1 examination years.

The grouping is based on the method recorded for each walkthrough. Use the linked NZQA standard and paper material for authoritative wording, diagrams, and assessment information.

Before you start

Common mistakes in these methods

Related practice

Algebraic Methods questions from different years

Open a question for hints and a progressive worked solution, or use the standard and paper links to return to its assessment context.

NCEA Level 2 · AS91261 2025 Algebra 15 questions

Open a question or return to its assessment context.

Standard overview 2025 paper
Question 1(a) — Radicals and Surds Simplifying a radical expression. Question 1(b) — Rearranging Formulae Rearranging an equation to make x the subject. Question 1(c) — Quadratic Algebra Building a quadratic from a root and a point on the graph. Question 1(d) — Pythagoras and Area Using Pythagoras to write area in terms of the radius. Question 1(e) — Algebraic Substitution Solving an exponential equation with a substitution. Question 2(a) — Perfect Squares Identifying the missing term in a perfect square. Question 2(b) — Polynomial Algebra Factorising and simplifying an algebraic fraction. Question 2(c) — Quadratic Algebra Solving a quadratic and matching it to a surd form. Question 2(d) — Logarithms Combining logarithms and solving the resulting equation. Question 2(e) — Discriminants and Simultaneous Equations Using the discriminant in simultaneous equations. Question 3(a) — Logarithms Solving a logarithm with a variable base. Question 3(b) — Quadratic Algebra Forming a quadratic equation from its roots. Question 3(c) — Logarithms Rewriting a logarithm in terms of given values. Question 3(d) — Root Relationships Using root relationships to rewrite an expression. Question 3(e) — Quadratic Algebra Modelling a golf shot with a quadratic and interpreting the result.

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