1. Algebraic Fraction (Addition and Subtraction): - Problem: Simplify $\frac{a}{b} + \frac{c}{d}$ or $\frac{a}{b} - \frac{c}{d}$. - Formula: Find common denominator $bd$, then add/subtract numerators: $$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$$ - Important: Simplify the resulting fraction by factoring numerator and denominator and canceling common factors. 2. Linear Inequality: - Problem: Solve inequalities like $ax + b > c$. - Rule: Solve like equations but reverse inequality sign when multiplying/dividing by negative number. - Example: If $-2x > 6$, dividing by $-2$ gives $x < -3$. 3. Coordinates (Transformation of Points) and Slopes: - Transformations: Translation $(x,y) \to (x+h, y+k)$, Reflection, Rotation. - Slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ - Parallel lines have equal slopes: $m_1 = m_2$. - Perpendicular lines have slopes $m_1$ and $m_2$ such that $$m_1 \times m_2 = -1$$. - Collinear points lie on the same line; slopes between any two pairs are equal. 4. Probability + Permutation (nPr) + Combination (nCr): - Probability: $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$$ - Permutation (order matters): $$nPr = \frac{n!}{(n-r)!}$$ - Combination (order does not matter): $$nCr = \frac{n!}{r!(n-r)!}$$ 5. Variations: - Direct variation: $y = kx$, $y$ varies directly as $x$. - Inverse variation: $y = \frac{k}{x}$, $y$ varies inversely as $x$. - $k$ is the constant of variation. 6. More about Polynomials: - Polynomial: expression like $a_nx^n + a_{n-1}x^{n-1} + ... + a_0$. - Addition/Subtraction: combine like terms. - Multiplication: use distributive property. - Factorization: find common factors, use formulas like difference of squares $a^2 - b^2 = (a-b)(a+b)$. - Solve polynomial equations by factoring and setting each factor to zero. Master these concepts with practice to pass your quiz!