2025 NCEA Level 2 Algebra

2025 Algebra AS91261 worked answers

Guided, step-by-step worked solutions for Apply algebraic methods in solving problems.

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Paper overview

Work through the 2025 questions one step at a time

This page contains 15 independent worked question walkthroughs for NCEA Level 2 Algebra (AS91261). Each walkthrough offers hints, reveals the full working in a logical sequence, and focuses on the method described below.

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Worked question index

2025 Algebra questions

Choose a question part to open its guided worked solution.

Question 1

Question 1 walkthroughs

Question 1(a) worked solution Simplifying a radical expression. Question 1(b) worked solution Rearranging an equation to make x the subject. Question 1(c) worked solution Building a quadratic from a root and a point on the graph. Question 1(d) worked solution Using Pythagoras to write area in terms of the radius. Question 1(e) worked solution Solving an exponential equation with a substitution.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Identifying the missing term in a perfect square. Question 2(b) worked solution Factorising and simplifying an algebraic fraction. Question 2(c) worked solution Solving a quadratic and matching it to a surd form. Question 2(d) worked solution Combining logarithms and solving the resulting equation. Question 2(e) worked solution Using the discriminant in simultaneous equations.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Solving a logarithm with a variable base. Question 3(b) worked solution Forming a quadratic equation from its roots. Question 3(c) worked solution Rewriting a logarithm in terms of given values. Question 3(d) worked solution Using root relationships to rewrite an expression. Question 3(e) worked solution Modelling a golf shot with a quadratic and interpreting the result.

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