Grade 9 Math Review Lecture Notes

Overview

• The lecture is a summary of Grade 9 Math, divided into three units: Algebra, Linear Relations, and Geometry.
• This video covers Algebra, including polynomials, like terms, distributive property, exponent laws, and solving equations.
• For in-depth explanations, refer to Jensen Math GA.

Algebra

Exponent Laws

• Definition of Power: e.g., 5² means 5 times 5.
• Components: Base (5), Exponent (2), Power (5²).
• Product of Powers Rule: xⁿ * xᵐ = xⁿ⁺ᵐ (same base required).
• Quotient of Powers Rule: xⁿ / xᵐ = xⁿ⁻ᵐ.
• Power of a Power Rule: (xⁿ)ᵐ = xⁿᵐ.
• Power of a Quotient: (a/b)ⁿ = aⁿ / bⁿ.
• Power of a Product: (ab)ⁿ = aⁿ * bⁿ.
• Zero Exponent Rule: x⁰ = 1.
• Negative Exponent Rule: x⁻ⁿ = 1/xⁿ.

Examples

• Combine like bases by adding or subtracting exponents.
• Evaluate powers after rewriting them.

Polynomials

• Definition of Term: Product of numbers and variables (e.g., 2x).
• Definition of Polynomial: Expression of terms connected by addition or subtraction.
• Classification:
  • Monomial: One term.
  • Binomial: Two terms.
  • Trinomial: Three terms.
• Degree of a Term: Sum of exponents in a term.
• Degree of a Polynomial: Highest degree of any term.

Collecting Like Terms

• Identify terms with the same variables and exponents.
• Collect by adding or subtracting coefficients.

Distributive Property

• Multiply each term inside the bracket by the term outside.
• Use to simplify expressions before solving.

Solving Equations

Basics

• Goal: Isolate the variable to find its value.
• Use balance method: Perform identical operations on both sides.

Types of Equations

• One-Step Equations: Simple addition/subtraction or multiplication/division.
• Two-Step Equations: Move terms and separate coefficients.
• Equations with Variables on Both Sides: Get all variable terms on one side.

Special Cases

• Fractions: Multiply both sides by the denominator to clear fractions.
• Fraction Equations: Use cross-multiplication if fraction equals fraction.

Worked Examples

• Practice through simplifying and solving various sample equations.

Word Problems

• Translate word problems into algebraic expressions.
• Solve using equations formed from expressions.

Conclusion

• For a full understanding, watch subsequent videos on Linear Relations and Geometry.
• Algebra is the most comprehensive section of the Grade 9 curriculum covered in this lecture.

These notes cover the essential points from the lecture, focusing on algebra. They are structured to assist in reviewing the key concepts of Grade 9 math, particularly for exam preparations.