Algebra-1B Key Terms Quiz

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Questions and Answers

What are perfect squares?

Numbers whose square roots are integers (correct)

Numbers that cannot be divided

Any negative number

Any whole number

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?

The non-negative integers, including 0. Signup and view all the answers

Describe integers.

Whole numbers that include negative numbers. Signup and view all the answers

What is an irrational number?

A number that cannot be expressed as a ratio of two integers. Signup and view all the answers

What are real numbers?

Numbers that can be either rational or irrational. Signup and view all the answers

Define inequality.

A mathematical sentence comparing the values of two expressions using an inequality symbol. Signup and view all the answers

What is the distributive property?

Remove parentheses and simplify expressions involving multiplication. Signup and view all the answers

Define a constant in mathematics.

A term that has no variable factor. Signup and view all the answers

What is a coefficient?

The numerical factor in a term that contains a variable. Signup and view all the answers

Define a term in algebra.

A number, a variable, or a combination of a number and a variable. Signup and view all the answers

What are like terms?

Terms with the same variable and exponent, which can be combined. Signup and view all the answers

What are unlike terms?

Terms with different variables and/or exponents, which cannot be combined. Signup and view all the answers

What is a solution to an equation with one variable?

Any value that makes the equation true. Signup and view all the answers

Define a solution of an equation with two variables.

An ordered pair (x, y) that makes the equation true. Signup and view all the answers

What is the radical in mathematics?

Another name for a square root. Signup and view all the answers

Describe prime numbers.

Whole numbers greater than 1 that have exactly two positive factors: itself and 1. Signup and view all the answers

What is a factor tree?

A diagram showing the prime factorization of a number. Signup and view all the answers

What is the order of operations?

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Signup and view all the answers

Define an exponent.

A mathematical notation indicating how many times a number is multiplied by itself. Signup and view all the answers

What is scientific notation?

A method of writing numbers using powers of ten. Signup and view all the answers

What are parallel lines?

Lines that run side by side and never intersect. Signup and view all the answers

Define perpendicular lines.

Lines that intersect to form a 90-degree angle. Signup and view all the answers

What is slope?

The rate of change of a line, calculated as $(y2 - y1)/(x2 - x1)$. Signup and view all the answers

What is Point Slope Form of a linear equation?

The form $y - y1 = m(x - x1)$ where m is the slope. Signup and view all the answers

Describe Slope Intercept Form of a linear equation.

The form $y = mx + b$ where m is the slope and b is the y-intercept. Signup and view all the answers

What is the Standard Form of a linear equation?

The form $Ax + By = C$. Signup and view all the answers

What is a system of linear equations?

Two or more linear equations to be solved simultaneously. Signup and view all the answers

List three common methods for solving a system of linear equations.

Graphing, substitution, elimination. Signup and view all the answers

What is the process of using substitution to solve a system of linear equations?

Combine information from both equations to find the variable values. Signup and view all the answers

Describe the process of using elimination to solve a system of linear equations.

Adjust the equations to eliminate one variable by adding or subtracting. Signup and view all the answers

What are linear inequalities?

An inequality such as $y > -3x + 4$, defining a region of the coordinate plane. Signup and view all the answers

What happens when multiplying factors with the same base in exponents?

You add the exponents. Signup and view all the answers

What happens when dividing factors with the same base in exponents?

You subtract the exponents. Signup and view all the answers

What occurs when raising a power to a power in exponents?

You multiply the exponents. Signup and view all the answers

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?

The variable and the exponent must be the same to combine them. Signup and view all the answers

What is a negative exponent?

It indicates to change to positive exponent by changing the position in a fraction. Signup and view all the answers

What is a negative fractional exponent?

It indicates to change to positive exponent by changing the position in a fraction. Signup and view all the answers

What is the difference between $(-2)^4$ and $-2^4$?

The first has a negative base, and the second has a positive base. Signup and view all the answers

What is the rule when exponents appear on terms within parentheses?

You must distribute the exponent to every term inside the parentheses. Signup and view all the answers

What is a quotient?

The answer to a division problem. Signup and view all the answers

Define a composite number.

A number that is not prime. Signup and view all the answers

What is a difference?

The answer to a subtraction problem. Signup and view all the answers

What is the greatest common factor (GCF)?

The largest common factor of two or more given numbers. Signup and view all the answers

What is exponential growth?

When a graph is growing with a constant rate. Signup and view all the answers

What is exponential decay?

When a graph is reduced with a constant rate. Signup and view all the answers

Define polynomial.

An algebraic expression consisting of one or more terms. Signup and view all the answers

What is the degree of a polynomial?

The highest combined sum of exponents in the polynomial. Signup and view all the answers

What does it mean to factor a polynomial?

To reverse the multiplication process and express it as a product of factors. Signup and view all the answers

What is a perfect square trinomial?

An expression of the form $a^2 ± 2ab + b^2$ that factors to $(a ± b)^2$. Signup and view all the answers

What is the difference of two squares?

$a^2 - b^2 = (a + b)(a - b)$. Signup and view all the answers

How do you factor a four-term polynomial by grouping?

Group the first two and last two terms, and factor out the GCF. Signup and view all the answers

What is a quadratic function?

An equation of the form $y = ax^2 + bx + c$. Signup and view all the answers

Define the standard form of a quadratic function.

A quadratic function ordered by the exponents of the variables, greatest to least. Signup and view all the answers

What is a parabola?

The U-shaped graph of a quadratic equation. Signup and view all the answers

What is the vertex of a parabola?

The lowest or highest point on the parabola. Signup and view all the answers

How many answers can there be when solving a quadratic equation?

2 if there are two x-intercepts, 1 if there is one, and none if there are no x-intercepts. Signup and view all the answers

What are the methods to solve a quadratic equation?

Graphing, factoring, extracting square roots, completing the square, and the quadratic formula. Signup and view all the answers

How do you factor a quadratic equation?

Rewrite to standard form and set each factor equal to zero. Signup and view all the answers

Describe the process of extracting square roots when solving a polynomial.

Isolate $x^2$ and take the square root of both sides. Signup and view all the answers

What does completing the square involve when solving a polynomial?

Add or subtract a constant to form a perfect square trinomial. Signup and view all the answers

What is the quadratic formula?

A formula for finding the solutions of a quadratic equation using $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Signup and view all the answers

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.
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

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.
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

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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Description

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!