This Algebra 1 reference sheet provides a concise overview of key concepts and formulas, serving as a valuable resource for students throughout their learning journey. We'll cover essential topics, offering clear explanations and examples to reinforce understanding.
I. Real Numbers and Operations
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Real Numbers: The set of all rational (fractions, integers, whole numbers, natural numbers) and irrational (non-repeating, non-terminating decimals like π) numbers.
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Number Line: A visual representation of real numbers, ordered from least to greatest.
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Absolute Value: The distance of a number from zero on the number line (always non-negative). |x| = x if x ≥ 0; |x| = -x if x < 0. Example: |5| = 5; |-3| = 3
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Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
II. Variables and Expressions
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Variable: A letter representing an unknown quantity.
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Algebraic Expression: A combination of variables, constants, and operations. Example: 3x + 5y - 7
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Constant: A fixed numerical value.
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Coefficient: The numerical factor of a variable term. In 5x, 5 is the coefficient.
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Term: A single number, variable, or product of numbers and variables.
III. Equations and Inequalities
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Equation: A mathematical statement indicating that two expressions are equal (=).
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Solving Equations: The process of finding the value(s) of the variable that make the equation true. This often involves using inverse operations (addition/subtraction, multiplication/division).
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Inequality: A mathematical statement comparing two expressions using inequality symbols (<, >, ≤, ≥).
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Solving Inequalities: Similar to solving equations, but remember to reverse the inequality symbol when multiplying or dividing by a negative number.
IV. Linear Equations and Graphs
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Linear Equation: An equation whose graph is a straight line. Often written in slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept.
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Slope: The steepness of a line, calculated as the change in y divided by the change in x (rise over run).
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Y-intercept: The point where the line crosses the y-axis (x = 0).
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Graphing Linear Equations: Plot points that satisfy the equation and connect them to form a line.
V. Systems of Linear Equations
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System of Linear Equations: Two or more linear equations considered together.
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Solving Systems of Equations: Finding the values of the variables that satisfy all equations in the system. Methods include graphing, substitution, and elimination.
VI. Polynomials
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Polynomial: An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
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Degree of a Polynomial: The highest power of the variable in the polynomial.
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Adding and Subtracting Polynomials: Combine like terms.
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Multiplying Polynomials: Use the distributive property (FOIL method for binomials).
VII. Factoring
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Factoring: Rewriting an expression as a product of simpler expressions.
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Greatest Common Factor (GCF): The largest factor that divides evenly into all terms of an expression.
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Factoring Trinomials: Finding two binomials whose product is the given trinomial.
VIII. Quadratic Equations
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Quadratic Equation: An equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
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Solving Quadratic Equations: Methods include factoring, the quadratic formula, and completing the square.
IX. Radicals and Exponents
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Radicals (Roots): The inverse operation of exponentiation. √x represents the principal square root of x.
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Exponents: Indicate repeated multiplication. xⁿ means x multiplied by itself n times.
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Rules of Exponents: Learn and apply the rules for simplifying expressions with exponents (e.g., xᵐ * xⁿ = xᵐ⁺ⁿ).
This reference sheet provides a foundational overview. Each topic listed above warrants further exploration and practice for mastery in Algebra 1. Remember to consult your textbook, class notes, and teacher for more detailed explanations and examples. Consistent practice is key to success in Algebra 1.
