GED Math Essential Guide and Core Skills Study Skills

Core Mathematical Operations and Conversions

• Fractions: Mastery of the four fundamental operations is required:     * Addition of fractions.     * Subtraction of fractions.     * Multiplication of fractions.     * Division of fractions.
• Decimals and Percents: Ability to perform fluid conversions between decimal forms and percentage forms (e.g., $0.75 \leftrightarrow 75\%$).
• Ratios and Proportions: Understanding the relationship between two quantities and solving for unknown values within proportional statements.
• Order of Operations (PEMDAS): Mathematical expressions must be solved according to the established hierarchy:     * P: Parentheses     * E: Exponents     * M/D: Multiplication and Division (from left to right)     * A/S: Addition and Subtraction (from left to right)
• Negative Numbers Rules: Application of specific rules for adding, subtracting, multiplying, and dividing positive and negative integers.

Exponents, Roots, and Perfect Squares

• Exponent Rules ($a^n$):     * Multiplication with the Same Base: When multiplying terms with the same base, add the exponents: $a^m \times a^n = a^{m+n}$.     * Division with the Same Base: When dividing terms with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.     * Negative Exponents: A negative exponent indicates a reciprocal: $a^{-n} = \frac{1}{a^n}$.
• Roots and Perfect Squares:     * Knowledge of perfect squares up to the value of $100$ (e.g., $1^2 = 1$, $2^2 = 4$, …, $10^2 = 100$).     * Calculation of square roots (e.g., $\sqrt{81}$).

Algebra Fundamentals

• Solving Equations:     * One-Step Equations: Solving for a variable in a single operation.     * Two-Step Equations: Solving for a variable using two operations (e.g., solving $3x + 5 = 20$).
• Combining Like Terms: Simplifying algebraic expressions by grouping terms with the same variables and exponents.
• Slope Calculation: The slope ($m$) between two points $(x_1, y_1)$ and $(x_2, y_2)$ is determined by the formula:     * $\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}$
• Linear Equations: Recognition and use of the slope-intercept form:     * $y = mx + b$     * Where $m$ is the slope and $b$ is the $y$-intercept.

Geometry Formulas

• Area Formulas:     * Rectangle: $\text{Area} = l \times w$ (Length multiplied by Width).     * Triangle: $\text{Area} = \frac{1}{2} \times b \times h$ (One-half base multiplied by height).     * Circle: $\text{Area} = \pi \times r^2$ (Pi multiplied by the radius squared).
• Volume Formula:     * Rectangular Solid/Prism: $\text{Volume} = l \times w \times h$ (Length multiplied by Width multiplied by Height).

Word Problem Strategy

To effectively solve mathematical word problems, follow this four-step procedural guide:

1. Identify what is asked: Determine exactly what the question is seeking to find.
2. Turn words into math: Translate the verbal descriptions and relationships into mathematical expressions or equations.
3. Solve step by step: Perform the necessary calculations in a logical sequence.
4. Check reasonableness: Evaluate the final answer to ensure it makes sense within the context of the original problem.

Practice Core Skills: Questions and Applications

• Question 1 (Algebra): Solve for $x$ in the equation $3x + 5 = 20$.     * Step 1: Subtract $5$ from both sides ($3x = 15$).     * Step 2: Divide by $3$ ($x = 5$).
• Question 2 (Percentages): Calculate $25\%$ of $80$.     * Calculation: $0.25 \times 80 = 20$.
• Question 3 (Exponents): Simplify the expression $2^3 \times 2^4$.     * Rule application: $2^{3+4} = 2^7$.
• Question 4 (Slope): Find the slope between the points $(2, 3)$ and $(6, 11)$.     * Calculation: $\text{Slope} = \frac{11 - 3}{6 - 2} = \frac{8}{4} = 2$.
• Question 5 (Geometry): Find the area of a rectangle with dimensions $8$ by $5$.     * Calculation: $8 \times 5 = 40$.
• Question 6 (Algebra): Solve for $x$ in the equation $\frac{x}{4} = 6$.     * Calculation: $x = 6 \times 4 = 24$.
• Question 7 (Conversions): Convert the decimal $0.75$ to a percent.     * Result: $75\%$.
• Question 8 (Roots): Evaluate $\sqrt{81}$.     * Result: $9$.
• Question 9 (Ratios): Simplify the ratio $12 : 18$.     * Simplification: Divide both numbers by the greatest common factor $(6)$ to get $2 : 3$.
• Question 10 (Algebra): Solve for $x$ in the equation $5x - 7 = 18$.     * Step 1: Add $7$ to both sides ($5x = 25$).     * Step 2: Divide by $5$ ($x = 5$).