Algebra 1 SOL Review Flashcards

Questions and Answers

What does the Commutative Property signify?

Changing groupings affects the result

Terms can be moved around without changing their signs (correct)

Any value added to itself equals zero

Changing the order of terms affects the result

What does the Associative Property signify?

Changing groupings does not affect the result (correct)

The product of any term by one equals itself

Any value added to itself equals zero

Changing the order of terms affects the result

What does the Distributive Property entail?

The product of any term by one equals itself

Multiplying a value by every term inside a group (correct)

Any value added to zero equals itself

Any term to the zero power equals itself

What does the Identity Property of Addition state?

Any value added to zero equals itself Signup and view all the answers

What does the Identity Property of Multiplication state?

Any value multiplied by one equals itself Signup and view all the answers

What is the Zero Property?

Any value multiplied by zero equals zero Signup and view all the answers

What does the Additive Inverse Property indicate?

Any value has an opposite value that adds to zero Signup and view all the answers

What does the Multiplicative Inverse Property entail?

Any value multiplied by its inverse fraction equals one Signup and view all the answers

What is Absolute Value?

The magnitude of a number disregarding its sign Signup and view all the answers

When multiplying or dividing an inequality by a negative number, the inequality symbol flips.

True Signup and view all the answers

What is the definition of a Function?

A relation with no shared x-values and passes the Vertical Line Test Signup and view all the answers

What is Domain in mathematics?

All possible x values. Signup and view all the answers

What is Range in mathematics?

All possible y values. Signup and view all the answers

What is the model equation for Direct Variation?

Y = KX Signup and view all the answers

What is the model equation for Inverse Variation?

Y = K / X or XY = K Signup and view all the answers

What is the equation format for linear functions?

Y = MX + B Signup and view all the answers

What does Slope represent in a linear equation?

Rate of change, represented by M in Y = MX + B Signup and view all the answers

What is a System of Equations?

A set of equations with multiple variables. Signup and view all the answers

What characterizes Systems of Inequalities?

They have shaded regions representing solutions. Signup and view all the answers

Define Quadratic Equations.

Any equation where x squared is the biggest exponent. Signup and view all the answers

What is the Zero Product Property?

If a product is zero, at least one of the factors must be zero. Signup and view all the answers

How do you factor a difference of perfect squares?

X^2 - 49 factors to (X + 7)(X - 7) Signup and view all the answers

What are synonyms for 'Solutions' in algebra?

X-intercepts, Roots, Zeros Signup and view all the answers

What is the rule for Exponents 'Side by Side' with the same base?

Add the exponents. Signup and view all the answers

What does 'Power to Power' rule for Exponents state?

Multiply the exponent outside the parentheses by every exponent inside. Signup and view all the answers

What does any term to the zero power equal?

One. Signup and view all the answers

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!