Equations, Circles and Linear Relationships

Study sheet excerpt

Course Outline

  1. Solving Linear Equations
  2. Quadratics and Word Problems
  3. Circle Parts and Core Formulas
  4. Arcs, Sectors and Composite Shapes
  5. Coordinates and Number Patterns
  6. Straight Lines and Intersections

1. Solving Linear Equations

★ Must-know

📌 An equation is solved by isolating the variable while performing the same operation on both sides.

📌 Opposite operations undo one another: addition and subtraction are opposites, while multiplication and division are opposites.

  • To solve a two-step equation, undo the operations in reverse order.

📌 For variables on both sides, move all variable terms to one side and all numerical terms to the other side.

📌 The distributive law states a(b+c)=ab+aca(b+c)=ab+ac, so the factor outside brackets must multiply every term inside.

Further detail

  • The equation 3x+5=203x+5=20 gives 3x=153x=15 and then x=5x=5.

Memory Hook

Undo operations in reverse order: brackets, terms, coefficients.

2. Quadratics and Word Problems

📐 Formula — A simple quadratic equation can have the form ax2=cax^2=c; isolate x2x^2 and then take the square root of both sides, remembering the ± sign.

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Quiz preview

1. Which procedure preserves the equality of an equation while isolating its variable?

2. What is the primary goal when solving a linear equation?

3. What is the correct first strategy for solving a two-step equation?

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Flashcards preview

How is an equation solved?

By isolating the variable while performing the same operation on both sides.

Linear Equation Solve Tip

Isolate variable, undo operations in reverse order.

Which operations undo each other in solving equations?

Addition and subtraction, and multiplication and division are opposite operations.

Opposite Operations

Addition vs subtraction, multiplication vs division.

How do you solve a simple quadratic equation like ax² = c?

Isolate x² and take the square root of both sides with ±.

Two-step Equation

Undo operations in reverse order for both steps.

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Frequently asked questions

What does the study sheet on Equations, Circles and Linear Relationships cover?

The study sheet covers the essential concepts of Equations, Circles and Linear Relationships. It is organized by topic to facilitate learning and memorization, with key definitions, explanations and summaries.

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How many questions are in the Equations, Circles and Linear Relationships quiz?

The quiz contains 10 multiple-choice questions with detailed corrections and explanations for each answer. Ideal for testing your knowledge and identifying gaps.

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How to study Equations, Circles and Linear Relationships with flashcards?

Revizly offers 12 interactive flashcards on Equations, Circles and Linear Relationships. Each card presents a question on the front and the answer on the back, enabling active, effective studying based on spaced repetition.

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