Credits: 5
Assessment: External
Course will expire on:
Dec 30, 2026
📘 Course Overview
AS91261:Apply the Algebraic Methods in Solving Problems
Master the essential concepts of the Algebra.
This course provides a comprehensive and academically rigorous treatment of NCEA Level 2 Algebra, designed to support strong performance in the external assessment. Content is carefully structured to develop algebraic fluency, logical reasoning, and mathematical accuracy across all required topics. Major areas of study include algebraic expansion and factorisation, linear and quadratic equations, quadratic inequalities, exponents, logarithms, and the equation of a parabola, presented through a progressive sequence of increasingly demanding problems.
A strong emphasis is placed on quadratic algebra, including solving equations and inequalities, analysing the nature of roots, forming equations from given roots or conditions, and applying relationships such as the sum and product of roots. Algebraic methods are further extended through perfect square polynomials, parameter-based problems, and multi-step reasoning tasks that require clear justification and structured working. Graphical interpretation is incorporated where appropriate, particularly in quadratic inequalities and parabola-based problems, to support deeper understanding and accurate interpretation of results.
The course also develops robust skills in exponential and logarithmic algebra, beginning with foundational laws and conditions and progressing to equation solving, contextual word problems, and applications involving growth, decay, and interest. Throughout the course, problems are deliberately sequenced to move from foundational skills to Merit- and Excellence-level challenges, requiring precise mathematical communication, logical organisation of working, and accurate interpretation of answers. This course is designed to provide thorough preparation for the NCEA Level 2 external examination, building confidence in applying algebraic methods under exam conditions.
Who This Course is For?
- Students sitting NCEA Level 2 External examination
- Students needing a structured, concept-focused approach to algebra
Student Outcomes
Students who complete this course typically:
- Develop strong algebraic problem-solving skills
- Gain confidence in equations, inequalities, and logarithm
- Present work clearly to achieve Merit/Excellence criteria
- Build a strong foundation for Level 3 Calculus
Course Currilcum
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- Algebraic Expansion – Basics Unlimited
- Formula-Based Expansion Unlimited
- Expansion – Applied Problems of Merit level (Part-1) Unlimited
- Expansion – Applied Problems of Merit level (Part-2) Unlimited
- Algebraic Expressions Involving x + and (Pages 21–24) Unlimited
- Linear Equations in One Variable Unlimited
- Linear Equations with Fractions Unlimited
- Factorisation of Quadratic Trinomials – Using Simple, Structured Rules Unlimited
- Simplification of Algebraic Expressions – Step-by-Step Process (Part-1) Unlimited
- Simplification of Algebraic Expressions – Step-by-Step Process (Part-2) Unlimited
- Simplification of Rational Expressions Using Factorisation Unlimited
- Solving Quadratic Equations Using the Quadratic Formula (Part-1) Unlimited
- Solving Quadratic Equations Using the Quadratic Formula (Part-2) Unlimited
- Quadratic Equations with Parameters – Discriminant and Inequalities (Merit Focused) Unlimited
- Solving Quadratic Inequalities with Graphical Interpretation Unlimited
- Discriminant and Nature of Roots: Merit level questions (Part-1) Unlimited
- Discriminant and Nature of Roots: Merit level questions (Part-2) Unlimited
- Quadratic Equations Involving Parameters – Quadratic within a Quadratic (Merit Focus) Unlimited
- Obtain a Quadratic Equation from Given Roots Unlimited
- Sum and Product of Roots of Quadratic Equations (Basics) Unlimited
- Sum and Product of Roots of a Quadratic Equation (Merit Focus) Unlimited
- Solving Rational Equations Unlimited
- Laws of Exponents (Part-1) Unlimited
- Laws of Exponents (Part-2) Unlimited
- Exponents-Higher-Order Problems Unlimited
- Exponents – Higher-Order Problems Unlimited
- Logarithms-Introduction, Conditions, and Laws Unlimited
- Logarithms – Basic Level Questions and Application of Laws Unlimited
- Logarithms – Strengthening Foundations and Mixed Basic Problems Unlimited
- Logarithms – Consolidation of Laws and Expression Simplification Unlimited
- Solving Logarithmic Equations: HOQ Unlimited
- Logarithmic Equations-Extended Practice and Increasing Difficulty: HOQ Unlimited
- Logarithms – Word Problems (High Difficulty, Merit–Excellence Focus) Unlimited
- Logarithms – Word Problems Involving Natural Logarithms (Merit Focus) Unlimited
- Logarithms – Rate of Interest Problems Unlimited
- Logarithms – Rate of Interest and Equation Formation Unlimited
- Logarithms – Rate of Growth and Decay (Merit Focus) Unlimited
- Logarithms – Rate of Growth and Decay (Extended Problems) Unlimited
- Logarithms – Algebraic Higher-Order Questions Unlimited
- Logarithms-Algebraic Manipulation and Equation Solving: HOQ Unlimited
- Perfect Square Polynomials – Identification and Algebraic Structure Unlimited
- Perfect Square Polynomials-Higher-Order and Parameter-Based Problems: HOQ Unlimited
- Perfect Square Polynomials-Advanced Reasoning and Final Applications:HOQ Unlimited
- Equation of a Parabola – Forms, Features, and Interpretation Unlimited
- Equation of a Parabola Through Three Given Points Unlimited
- Parabola Word Problems Unlimited
- Parabola Word Problems-Modelling and Interpretation:HOQ Unlimited
- Tangents to Quadratic Curves: HOQ Unlimited
- Intersection of Curves – Algebraic Substitution and Higher-Order Equations Unlimited
