Algebra 1 SOL Review Flashcards

Properties of Operations

• Commutative Property: Order of terms can change without affecting the sum or product.
• Associative Property: Changing groupings of terms (e.g., parentheses) does not affect the sum or product.
• Distributive Property: A value multiplied by every term inside a group; think of distributing across parentheses.

Identity and Zero Properties

• Identity Property of Addition: Any number added to zero is itself.
• Identity Property of Multiplication: Any number multiplied or divided by one remains unchanged.
• Zero Property: Any number multiplied by zero results in zero.

Inverses and Absolute Value

• Additive Inverse Property: A number plus its negative equals zero.
• Multiplicative Inverse Property: A number multiplied by its reciprocal equals one.
• Absolute Value: The value of a number disregarding its sign; |x| = x if x is positive, or -x if x is negative.

Inequalities and Intercepts

• Multiplying/Dividing Inequalities by Negative Numbers: Flip the inequality symbol.
• Intercepts: Points where graphs intersect axes; X-intercept crosses the X-axis, Y-intercept crosses the Y-axis.

Functions

• Function Definition: A relation with no shared X-values; passes the Vertical Line Test.
• Domain: All possible X-values (inputs).
• Range: All possible Y-values (outputs).

Variations and Linear Functions

• Direct Variation: Model expressed as Y = KX; graph is a straight line through the origin (0,0).
• Inverse Variation: Model forms of Y = K/X or XY = K; graph resembles a hyperbola.

Linear Equations and Slope

• Linear Function Model: Y = MX + B; defines a straight line.
• Slope (M): Represents rate of change; calculated as (change in Y)/(change in X); simplified fractions preferred.

Systems of Equations and Inequalities

• Systems of Equations: Comprising two equations; determine intersection points using calculator function.
• Systems of Inequalities: Similar to equations but results in shaded solution regions; darkest regions indicate solution points.

Quadratic Equations and Factorization

• Quadratic Equations: Any equation with X squared as the highest exponent; graph forms a parabola.
• Zero Product Property: When a quadratic is factored, set each factor (e.g., (x - n)(x + n)) to zero to find solutions.
• Subtraction of Perfect Squares: Follows a factorization pattern, e.g., X² - 49 factors to (X + 7)(X - 7).

Roots and Exponents

• Terms for Solutions: X-intercepts, roots, zeros; refer to points where the graph crosses the X-axis.
• Exponents with Same Base: When multiplied, add the exponents (e.g., X⁴ * X⁷ = X¹¹).
• Power to Power: Distribute the exponent across all terms inside parentheses; (2X³)⁴ = 16X¹².

Special Exponent Cases

• Exponent Zero: Any non-zero term raised to the zero power equals one.

This quiz focuses on key properties of operations in Algebra 1, including the Commutative, Associative, and Distributive Properties. Each card provides a simple definition and a mnemonic to help students remember these important concepts. Perfect for SOL exam preparation!