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Ordinary Level Mathematics Revision Notes

Topic 4.2: Solving Equations

These notes explain Solving Equations in simple English so students can understand the topic clearly, not just memorise rules. The Ordinary Level version keeps the focus on the core ideas without unnecessary higher-only pressure.

Curriculum Irish Leaving Certificate
Subject Mathematics
Level Ordinary Level
Premium feature Teacher-style explanations and cleaner study flow
Focus
Understanding before memorising
Interactive
Study tools and guided structure
Question Style
Explained examples and exam practice
Format
Website reading and printable notes

Subtopics Covered

  • Linear & Quadratic Equations
  • Simultaneous Equations
  • 📝 Exam Style Questions

What Makes This Version Better

  • Cleaner Ordinary Level focus with no unnecessary higher-only material
  • Simple teacher-style explanations before each method
  • Worked examples in clear stages
  • Cleaner page flow for student understanding
  • SEO-friendly website naming and branding
Disclaimer This publication is an independent educational resource developed by ExamsLogic and compiled by experienced educators. It is based on publicly available official curricula, including Cambridge, Pearson Edexcel, IB, and the Irish Leaving Certificate. This product is not endorsed by, affiliated with, or sponsored by any examination board or governing authority. All registered trademarks remain the property of their respective owners.
Start Reading Open Study Tools

Learning Objectives

What You Should Be Able To Do

    Interactive Study Tools

    These tools are here to help students slow down and think about the method before rushing to an answer.

    Tool 1

    Study Planner

    Use this to break a topic into small study sessions.

    Plan: A clear breakdown will appear here.
    Tool 2

    Method Reminder

    This quick guide reminds students what to do when they feel stuck.

    • Read the story: what is the question really asking?
    • Choose the method: identify the correct idea before calculating.
    • Show the reason: do not skip the logic.
    • Check the answer: make sure it fits the situation.

    1. Linear & Quadratic Equations

    Simple explanation: This section is about solving for unknown values step by step without losing the logic.

    Solving for variables is fundamental.

    • Linear: Move variables to one side, constants to the other.
    • Quadratic (ax² + bx + c = 0): Use factorisation or the Quadratic Formula:
    x = [-b ± √(b² - 4ac)] / 2a
    Examiner Tip
    💡 Examiner Tip: Always set your quadratic equation to equal 0 before trying to factorise or use the formula. If it equals 5, subtract 5 from both sides first!

    2. Simultaneous Equations

    Simple explanation: This section is about solving for unknown values step by step without losing the logic.

    When you have two variables, you need two equations. Use the Elimination or Substitution method to reduce the system to one variable.

    Common Mistake
    ❌ Common Mistake: When using the elimination method, forgetting to multiply the *entire* equation by the constant required to match coefficients.

    📝 Exam Style Questions

    Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

    Easy Q1: Solve 3x + 5 = 14.

    Medium Q2: Solve x² - 5x + 6 = 0.

    A1: 3x = 9, so x = 3.

    A2: (x-2)(x-3) = 0, so x = 2 or x = 3.