1. Let's start with algebraic fraction addition and subtraction. The key formula is to find a common denominator: $$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$$. Always multiply numerator and denominator to get the same denominator before adding or subtracting. 2. For linear inequalities, the rule is similar to linear equations but remember: if you multiply or divide by a negative number, reverse the inequality sign. For example, $$ax + b > c$$ can be solved by isolating $x$. 3. Coordinates transformations involve shifting, reflecting, or rotating points. For example, translating a point $(x,y)$ by $(h,k)$ results in $(x+h, y+k)$. Slopes determine line relationships: parallel lines have equal slopes, perpendicular lines have slopes that are negative reciprocals. 4. Probability basics: the chance of an event is the number of favorable outcomes over total outcomes. Permutations ($nPr$) count ordered arrangements: $$nPr = \frac{n!}{(n-r)!}$$. Combinations ($nCr$) count unordered selections: $$nCr = \frac{n!}{r!(n-r)!}$$. 5. Variations refer to direct and inverse variations. For direct variation, $y = kx$; for inverse, $xy = k$ where $k$ is constant. 6. Polynomials: operations include addition, subtraction, multiplication, and factoring. For example, factoring $ax^2 + bx + c$ involves finding two numbers that multiply to $ac$ and add to $b$. Each topic can be expanded with examples if needed.