Questions and Answers
What are perfect squares?
What are rational numbers?
A real number that can be expressed as a ratio of two integers and has a terminating or repeating decimal.
Define natural numbers.
The counting numbers, all positive, not including 0.
What are whole numbers?
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Describe integers.
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What is an irrational number?
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What are real numbers?
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Define inequality.
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What is the distributive property?
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Define a constant in mathematics.
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What is a coefficient?
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Define a term in algebra.
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What are like terms?
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What are unlike terms?
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What is a solution to an equation with one variable?
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Define a solution of an equation with two variables.
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What is the radical in mathematics?
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Describe prime numbers.
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What is a factor tree?
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What is the order of operations?
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Define an exponent.
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What is scientific notation?
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What are parallel lines?
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Define perpendicular lines.
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What is slope?
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What is Point Slope Form of a linear equation?
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Describe Slope Intercept Form of a linear equation.
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What is the Standard Form of a linear equation?
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What is a system of linear equations?
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List three common methods for solving a system of linear equations.
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What is the process of using substitution to solve a system of linear equations?
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Describe the process of using elimination to solve a system of linear equations.
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What are linear inequalities?
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What happens when multiplying factors with the same base in exponents?
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What happens when dividing factors with the same base in exponents?
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What occurs when raising a power to a power in exponents?
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What is the value of any number raised to the power of zero?
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How do you add or subtract two terms with variables containing exponents?
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What is a negative exponent?
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What is a negative fractional exponent?
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What is the difference between $(-2)^4$ and $-2^4$?
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What is the rule when exponents appear on terms within parentheses?
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What is a quotient?
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Define a composite number.
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What is a difference?
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What is the greatest common factor (GCF)?
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What is exponential growth?
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What is exponential decay?
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Define polynomial.
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What is the degree of a polynomial?
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What does it mean to factor a polynomial?
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What is a perfect square trinomial?
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What is the difference of two squares?
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How do you factor a four-term polynomial by grouping?
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What is a quadratic function?
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Define the standard form of a quadratic function.
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What is a parabola?
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What is the vertex of a parabola?
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How many answers can there be when solving a quadratic equation?
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What are the methods to solve a quadratic equation?
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How do you factor a quadratic equation?
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Describe the process of extracting square roots when solving a polynomial.
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What does completing the square involve when solving a polynomial?
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What is the quadratic formula?
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Study Notes
Number Types
- Perfect squares: Numbers with integer square roots.
- Rational numbers: Can be expressed as a fraction of two integers; in decimal form, they are either terminating or repeating.
- Natural numbers: The set of counting numbers, excluding zero.
- Whole numbers: Non-negative integers, including zero.
- Integers: Whole numbers that include negative values.
- Irrational numbers: Cannot be expressed as a ratio of integers; their decimal representation is nonterminating and nonrepeating.
- Real numbers: Comprised of both rational and irrational numbers.
Algebraic Concepts
- Inequality: Compares two expressions with inequality symbols; graphically represented by open or closed circles.
- Distributive property: Describes how to remove parentheses in expressions: a(b + c) = ab + ac.
- Constant: A term without a variable factor.
- Coefficient: The numerical factor in a term with a variable.
- Term: May be a number, variable, or a combination of both.
- Like terms: Terms with the same variable and exponent, which can be combined.
- Unlike terms: Terms with different variables or exponents that cannot be combined.
Solutions in Equations
- Solution of an equation (one variable): Values that satisfy the equation.
- Solution of an equation (two variables): Ordered pairs that make the equation true.
- Radical: Another term for square root.
Geometry
- Parallel lines: Lines that never intersect and remain equidistant.
- Perpendicular lines: Lines that intersect at a 90-degree angle.
- Slope: The rate of change of a line; calculated as (y2 - y1) / (x2 - x1).
Equation Forms
- Point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point.
- Slope-intercept form: y = mx + b, with m as the slope and b as the y-intercept.
- Standard form: Ax + By = C; useful for finding intercepts.
Systems of Equations
- System of linear equations: Two or more equations combined, with potential solutions as intersections of their graphs.
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Common methods to solve:
- Graphing: Plot the equations to find can intersect points.
- Substitution: Solve one equation for a variable and substitute into the other.
- Elimination: Manipulate equations to eliminate one variable.
Exponents
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Exponent basics: Notation indicating repeated multiplication; rules for multiplying, dividing, and raising powers summarized:
- Multiplying: Add exponents.
- Dividing: Subtract exponents.
- Raising a power to a power: Multiply exponents.
- An exponent of zero equals one, regardless of the base.
Factoring and Polynomials
- Polynomial: An expression with one or more terms.
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Factoring techniques:
- Greatest common factor (GCF): Identifying and factoring out shared factors.
- Difference of squares: a² - b² = (a + b)(a - b).
- Factoring quadratics: Rewrite quadratic as (x - r)(x - s), finding roots.
Quadratic Functions
- Quadratic equation: y = ax² + bx + c; graphed as a parabola.
- Vertex: The highest or lowest point on the parabola, calculated as -(b/2a).
- Roots: Number of solutions varies: two roots for two intercepts, one for a single intercept, none for no intercepts.
Solving Quadratic Equations
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Methods:
- Graphing: Find x-intercepts where the graph crosses the x-axis.
- Factoring: Create two binomials and set each equal to zero.
- Completing the square: Transform the equation into a perfect square trinomial.
- Quadratic formula: Always applicable for finding solutions.
Additional Points
- Accounts for the behavior of exponents with positive/negative bases and the impact of zero and negative exponents.
- Proper notation involves using the "±" sign for roots when applicable.
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Test your understanding of key algebraic terms such as perfect squares, rational numbers, natural numbers, and whole numbers. This quiz will help solidify your knowledge essential for mastering Algebra 1 concepts. Perfect for students looking to enhance their math skills!