Algebra Flashcards for Unit 1: Foundations of Algebra

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Questions and Answers

What is a quantity?

An expression that has a square root
How much there is of something (correct)
A well-defined collection of objects
A fixed value

What represents one or more values of a quantity that changes?

variable

What is an algebraic expression?

Mathematical phrase that includes one or more variables

What defines a numerical expression?

Mathematical phrase which has numbers and operation symbols, but no variables Signup and view all the answers

What is a power in mathematics?

A number that can be expressed using a base and an exponent Signup and view all the answers

What does an exponent signify?

A quantity representing the power to which a given number or expression is to be raised Signup and view all the answers

What is the base in an expression?

The number that is going to be raised to a power Signup and view all the answers

What does it mean to simplify something in mathematics?

To make something easier to work with by putting it in simplest form Signup and view all the answers

What does it mean to evaluate an expression?

Find the value of a numerical or algebraic expression Signup and view all the answers

What is a square root?

A value that, when multiplied by itself, gives the original number Signup and view all the answers

What is a radicand?

The value inside the radical symbol Signup and view all the answers

What is a radical expression?

An expression that has a square root, cube root, etc. Signup and view all the answers

What defines a perfect square?

A number that has a whole number square root Signup and view all the answers

What is a set in mathematics?

A well-defined collection of objects Signup and view all the answers

What is an element of a set?

An object in a set Signup and view all the answers

What is a subset?

Only certain elements from a given set Signup and view all the answers

What are rational numbers?

Any number that can be written in the form a/b (as a fraction) Signup and view all the answers

What constitutes natural numbers?

Whole numbers starting from 1 upwards Signup and view all the answers

What are whole numbers?

Numbers 0, 1, 2, 3, and so on Signup and view all the answers

What are integers?

Includes whole numbers and their negatives Signup and view all the answers

What are irrational numbers?

Any number that cannot be written as a fraction Signup and view all the answers

What are real numbers?

Natural, whole, integers, rational, and irrational numbers Signup and view all the answers

What is an inequality?

Shows two values are not equal Signup and view all the answers

What is absolute value?

The distance a number is from 0 on the number line Signup and view all the answers

What are opposites in terms of integers?

Two integers that are equidistant from zero on opposite sides of the number line Signup and view all the answers

What are additive inverses?

Numbers that are opposite each other and sum to 0 Signup and view all the answers

What is a multiplicative inverse?

The reciprocal of a number Signup and view all the answers

What are reciprocal numbers?

Two numbers whose product is 1 Signup and view all the answers

What does the Distributive Property state?

Multiplying a number by a group of numbers added together is the same as doing each multiplication separately Signup and view all the answers

What is a term in algebra?

A number, a variable, or the product of a number and one or more variables Signup and view all the answers

What is a constant?

A fixed value Signup and view all the answers

What is a coefficient?

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term Signup and view all the answers

What are like terms?

Terms whose variables (and their exponents) are the same Signup and view all the answers

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Study Notes

Algebra Foundations

Quantity: Represents the amount of something.
Variable: A letter symbolizing one or more changing values of a quantity.
Algebraic Expression: A mathematical phrase that consists of one or more variables.
Numerical Expression: A mathematical phrase containing only numbers and operation symbols, devoid of variables.
Power: Represents a number expressed with a base and an exponent.
Exponent: Indicates the power to which a number is raised, shown as a superscript.
Base: The number that is raised to a power in an exponentiation.
Simplify: The process of putting expressions into their simplest form for easier manipulation.
Evaluate: Determining the numerical value of an expression.
Square Root: A value that, when multiplied by itself, yields the original number (e.g., √16 = 4).
Radicand: The value under a radical symbol that is being evaluated.
Radical: An expression that involves roots, such as square roots or cube roots.
Perfect Square: A number with an integer as its square root (e.g., 25 has a square root of 5).
Set: A defined collection of distinct objects.
Element of a Set: An individual object or item contained within a set.
Subset: A set containing some or all elements from another set.
Rational Numbers: Numbers that can be expressed as a fraction (a/b) where both a and b are integers, and b is not zero.
Natural Numbers: Whole numbers starting from 1, including no fractions or negatives.
Whole Numbers: The set of numbers starting from 0 and including positive integers with no fractions or decimals.
Integers: A set that includes whole numbers and their negative counterparts.
Irrational Numbers: Numbers that cannot be expressed as fractions.
Real Numbers: The complete set including natural numbers, whole numbers, integers, rational, and irrational numbers.
Inequality: A mathematical statement indicating that two values are not equal.
Absolute Value: The distance of a number from zero on the number line.
Opposites: Integers that are equidistant from zero but located on opposite sides of the number line.
Additive Inverses: A pair of numbers that are opposites and together total to zero.
Multiplicative Inverse: The reciprocal of a number.
Reciprocal: The result of flipping the numerator and denominator of a fraction, resulting in a product of 1.
Distributive Property: States that multiplying a number by an addition of numbers is equivalent to multiplying separately and then adding (e.g., a(b + c) = ab + ac).
Term: Can be a number, variable, or the product of a number and one or more variables.
Constant: A value that remains fixed.
Coefficient: A numerical factor that multiplies a variable in an algebraic term.
Like Terms: Terms that have the same variable parts (including exponents), allowing them to be combined.