BJU Pre-Algebra Chapter 1 Flashcards

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Questions and Answers

What is the absolute value?

The product of a number with itself

The sum of two numbers

The distance of a number from zero on a number line (correct)

The opposite of a number

What is the additive inverse of a?

-a

What does cubed mean?

Any expression taken to the third power

What is an exponent?

A superscript that indicates how many times a base is used as a factor Signup and view all the answers

What are integers?

The set of whole numbers and their opposites Signup and view all the answers

What are opposites?

Two numbers an equal distance from zero on a number line but in opposite directions Signup and view all the answers

What is scientific notation?

The expression of a number as the product of a number from 1 to 10 and a power of ten Signup and view all the answers

What does squared mean?

A number or algebraic expression multiplied by itself Signup and view all the answers

What is subtraction?

Adding the opposite Signup and view all the answers

What is a variable?

A letter used to represent an unknown number Signup and view all the answers

What is zero power?

Any nonzero number to the zero power equals 1 Signup and view all the answers

What is an addend?

Any of the two or more numbers being added together Signup and view all the answers

What is a minuend?

A number in a subtraction problem from which another number is subtracted Signup and view all the answers

What is a subtrahend?

The number in a subtraction problem being subtracted Signup and view all the answers

What is a dividend?

The number in a division problem being divided into parts Signup and view all the answers

What is a divisor?

The number by which another number is divided Signup and view all the answers

What is a quotient?

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

What is the base in exponential notation?

The number used as a factor in exponential form Signup and view all the answers

What is a negative exponent?

For any nonzero real number x and any integer a, x^-a = 1/x^a Signup and view all the answers

What is one method for adding integers with like signs?

Add the absolute values of the addends and use the sign of the addends for the sum Signup and view all the answers

What is one method for adding integers with unlike signs?

Find the difference of the absolute values of the addends and use the sign of the addend with the greater absolute value for the sum Signup and view all the answers

What is the Multiplication Property of Exponents?

For any number x and integers a and b, x^a * x^b = x^(a+b) Signup and view all the answers

What is the Power Property of Exponents?

For any number x and integers a and b, (x^a)^b = x^(ab) Signup and view all the answers

What is the Division Property of Exponents?

For any number x and integers a and b, x^a / x^b = x^(a-b) Signup and view all the answers

What are the first two steps in the Order of Operations?

Evaluate expressions inside grouping symbols and evaluate all exponents Signup and view all the answers

Study Notes

Mathematical Concepts and Definitions

Absolute value: Measures the distance of a number from zero on a number line; always non-negative.
Additive inverse: For any number 'a', 'b' is its additive inverse if a + b = 0; represented as -a.
Cubed: Refers to raising any expression to the third power.
Exponent: A superscript showing how many times the base is multiplied by itself.
Integers: Include all whole numbers and their negatives; extend infinitely in both directions.
Opposites: Numbers located an equal distance from zero but in opposite directions; examples include 5 and -5.
Scientific notation: Format that expresses numbers as a product of a number between 1 and 10 and a power of ten.
Squared: Indicates a number or expression multiplied by itself, represented by an exponent of two.

Arithmetic Operations and Properties

Subtraction: Can be viewed as adding an opposite; for instance, a - b is equivalent to a + (-b).
Variable: A symbol (usually a letter) that represents an unknown quantity in expressions or equations.
Zero power: States that any non-zero number raised to the power of zero results in 1.
Addend: Any number involved in an addition operation; e.g., in 3 + 5, both 3 and 5 are addends.
Minuend: The number from which another is subtracted in a subtraction operation.
Subtrahend: The number being subtracted from the minuend in a subtraction operation.
Dividend: The quantity being divided in a division operation.
Divisor: The number by which another number (the dividend) is divided.
Quotient: The result of a division operation.

Exponents and Their Properties

Base: The number that is raised to a power in exponential form and also indicates place values in a numeral system.
Negative exponent: If 'x' is a non-zero number and 'a' is an integer, then x^-a = 1/x^a, reflecting division.

Operations with Integers

Adding integers with like signs: Sum the absolute values and apply the common sign for the result.
Adding integers with unlike signs: Compute the difference in absolute values and adopt the sign of the number with the larger absolute value.

Properties of Exponents

Multiplication Property of Exponents: States that when multiplying like bases, add their exponents: x^a * x^b = x^(a+b).
Power Property of Exponents: When raising a power to another power, multiply the exponents: (x^a)^b = x^(ab).
Division Property of Exponents: Describes how to handle division with exponents.

Order of Operations

Order of Operations: A set sequence to solve mathematical expressions:
- Evaluate grouping symbols first.
- Compute all exponents.
- Perform multiplication and division from left to right.
- Conduct addition and subtraction from left to right.

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Description

Test your understanding of key concepts from Chapter 1 of BJU Pre-Algebra. This quiz includes definitions for essential mathematical terms such as absolute value and additive inverse. Perfect for reinforcing your knowledge before exams!