Questions and Answers
What does the Commutative Property signify?
What does the Associative Property signify?
What does the Distributive Property entail?
What does the Identity Property of Addition state?
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What does the Identity Property of Multiplication state?
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What is the Zero Property?
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What does the Additive Inverse Property indicate?
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What does the Multiplicative Inverse Property entail?
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What is Absolute Value?
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When multiplying or dividing an inequality by a negative number, the inequality symbol flips.
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What is the definition of a Function?
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What is Domain in mathematics?
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What is Range in mathematics?
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What is the model equation for Direct Variation?
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What is the model equation for Inverse Variation?
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What is the equation format for linear functions?
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What does Slope represent in a linear equation?
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What is a System of Equations?
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What characterizes Systems of Inequalities?
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Define Quadratic Equations.
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What is the Zero Product Property?
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How do you factor a difference of perfect squares?
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What are synonyms for 'Solutions' in algebra?
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What is the rule for Exponents 'Side by Side' with the same base?
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What does 'Power to Power' rule for Exponents state?
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What does any term to the zero power equal?
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Study Notes
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.
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Description
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!