Linear Inequalities
• Description: Solving for a variable (\bm{x} or \bm{y}) while maintaining the balance of an inequality. Key skills include flipping the sign when multiplying/dividing by a negative and representing the solution set on a number line.
• Concepts Covered: Greater than/less than symbols, number line graphing, and basic isolation of variables.
• Intensity: 6/10 (Moderate). The logic of the "flipped sign" is where most students make mistakes.
2. Algebraic Expansion & Products
• Description: Multiplying binomials and trinomials. This involves using the FOIL method or specific identities to "open" brackets.
• Concepts Covered: \bm{(a+b)^2}, \bm{(a-b)^2}, and \bm{(a+b)(a-b)}. Also includes basic monomial multiplication like \bm{(5x \times 6y)}.
• Intensity: 5/10 (Foundational). It’s mostly about following a formulaic pattern accurately.
3. Factorization (The "Inverse" of Expansion)
• Description: Taking a long expression and breaking it back down into its factors (brackets). This is the most diverse section in your notes.
• Concepts Covered: * Common Factors: Pulling out what is shared.
• Grouping: For expressions with 4 terms.
• Splitting the Middle Term: For quadratic trinomials (\bm{ax^2 + bx + c}).
• Difference of Two Squares: \bm{a^2 - b^2}.
• Intensity: 8/10 (High). This requires "pattern recognition"—you have to look at the problem and decide which of the four methods to use.
4. Simultaneous Equations
• Description: Solving two equations with two variables (\bm{x} and \bm{y}) at the same time to find the point where they meet.
• Concepts Covered: The Elimination Method (adding or subtracting equations to cancel out one variable).
• Intensity: 7/10 (Calculative). It requires several steps of neat algebra; one small plus/minus error at the start ruins the whole answer.
