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Unit 2: Algebraic Foundations: Unveiling Patterns & Relationships

The chapter provides a comprehensive overview of algebraic foundations, emphasizing the importance of expressions, equations, and their simplification. Key operations such as collecting like terms, expanding brackets, and factoring are illustrated with clear examples. The chapter also involves solving linear equations and inequalities, identifying patterns in sequences, and graphing linear relationships, providing students with essential tools to analyze and communicate mathematical concepts effectively.

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Sections

  • 1

    Unit 2: Algebraic Foundations: Unveiling Patterns & Relationships

    This section introduces fundamental concepts of algebraic expressions, including simplifying them and recognizing patterns through various operations.

    Learning Practice

  • 2

    Chapter 1: Simplifying Algebraic Expressions

    This section introduces algebraic expressions, focusing on the techniques of simplifying them through collecting like terms and expanding brackets.

    Learning Practice

  • 2.1

    Collecting Like Terms

    This section teaches students how to combine like terms in algebraic expressions for simplification.

    Learning Practice

  • 2.2

    Expanding Single Brackets

    Expanding single brackets involves using the distributive property to multiply a term outside the bracket by each term inside the bracket.

    Learning Practice

  • 2.3

    Expanding Double Brackets

    This section teaches students how to expand double brackets using the FOIL method and collect like terms.

    Learning Practice

  • 3

    Chapter 2: Factoring Basic Expressions

    Learning

  • 3.1

    Factoring Out Common Factors

    Factoring involves pulling out the greatest common factor from an expression, rewriting it as a product of its factors.

    Learning Practice

  • 4

    Chapter 3: Solving Linear Equations

    This section covers methods for solving linear equations, including one-step, two-step, and multi-step equations, as well as equations with variables on both sides.

    Learning Practice

  • 4.1

    One-Step Linear Equations

    One-step linear equations are mathematical expressions that can be solved by performing a single operation to isolate the variable.

    Learning Practice

  • 4.2

    Two-Step Linear Equations

    This section focuses on solving two-step linear equations, emphasizing the process of isolating the variable through inverse operations.

    Learning Practice

  • 4.3

    Multi-Step Linear Equations (With Brackets)

    This section focuses on solving multi-step linear equations involving brackets by expanding them and combining like terms.

    Learning Practice

  • 4.4

    Linear Equations With Variables On Both Sides

    This section discusses solving linear equations that have variables on both sides, explaining how to isolate variables and find their values.

    Learning Practice

  • 5

    Chapter 4: Solving Linear Inequalities

    Learning

  • 5.1

    Solving Basic Linear Inequalities

    This section explores the methods for solving basic linear inequalities and how to represent their solutions.

    Learning Practice

  • 5.2

    Representing Solutions On A Number Line

    This section discusses how to represent solutions to inequalities on a number line using open and closed circles.

    Learning Practice

  • 6

    Chapter 5: Introduction To Sequences

    Learning

  • 6.1

    Identifying Arithmetic And Simple Geometric Patterns

    This section focuses on identifying arithmetic and geometric sequences, helping students recognize patterns in numbers.

    Learning Practice

  • 6.2

    Finding The Nth Term Of An Arithmetic Sequence

    This section introduces how to identify the nth term of an arithmetic sequence using a formula involving the first term and the common difference.

    Learning Practice

  • 7

    Chapter 6: Linear Relationships (Graphing)

    This section introduces linear relationships in algebra, explaining how to graph these relationships on a coordinate plane using various methods.

    Learning Practice

  • 7.1

    Plotting Points On The Coordinate Plane

    This section introduces the coordinate plane and the process of plotting points using ordered pairs.

    Learning Practice

  • 7.2

    Graphing Linear Equations (Y = Mx + C)

    This section introduces graphing linear equations and the significance of the linear equation format y = mx + c, including understanding the components such as slope and y-intercept.

    Learning Practice

  • 7.3

    Understanding Gradient (M)

    This section focuses on gradient (or slope) in linear equations, describing its significance and how to calculate it using two points.

    Learning Practice

  • 7.4

    Understanding Y-Intercept (C)

    The y-intercept is the point where a linear equation intersects the y-axis, and it plays a crucial role in understanding linear relationships.

    Learning Practice

References

Untitled document (10).pdf

Class Notes

Memorization

What we have learnt

  • Algebra is a powerful tool ...
  • Simplifying expressions inv...
  • Factoring reveals the struc...

Final Test

Revision Tests

Chapter FAQs