Jacobs Elementary Algebra Flashcards

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Questions and Answers

What is the result of adding two numbers called?

Product

Sum (correct)

Quotient

Difference

What do you call the result of subtracting one number from another?

Difference

What is the product of two numbers?

The result of multiplying two numbers

What is the result of dividing one number by another called?

Quotient Signup and view all the answers

What does raising a number to a power involve?

Multipling the number by itself Signup and view all the answers

What are parentheses used for in mathematics?

Change the order of operations Signup and view all the answers

What does the Distributive Rule relate?

Addition to multiplication Signup and view all the answers

What is a function?

A pairing of two sets of numbers Signup and view all the answers

What are coordinate graphs used for?

Plotting points Signup and view all the answers

What is an example of direct variation?

y = ax Signup and view all the answers

What is a linear function?

A function that forms a straight line Signup and view all the answers

What is inverse variation?

y = a/x Signup and view all the answers

What are integers?

Positive integers, negative integers, and zero Signup and view all the answers

What are the characteristics of a coordinate graph?

Four quadrants and axes Signup and view all the answers

What happens when you add opposites?

Their sum is zero Signup and view all the answers

What is the method for subtraction in terms of addition?

Add the opposite Signup and view all the answers

What is the result when a positive number is multiplied by a negative number?

Always negative Signup and view all the answers

What does PEMDAS stand for in the order of operations?

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

What are rational numbers?

Numbers that can be expressed as a fraction of two integers Signup and view all the answers

What does absolute value represent?

The distance from zero Signup and view all the answers

What does the symbol ≈ indicate?

Approximation Signup and view all the answers

What defines an equation?

Two expressions representing the same number Signup and view all the answers

What are inverse operations?

Operations that undo each other Signup and view all the answers

How can an equation be transformed into an equivalent equation?

By adding, subtracting, multiplying or dividing each side by the same quantity Signup and view all the answers

What are equivalent expressions?

Expressions that are equal for all values of variables Signup and view all the answers

What is the perimeter of a rectangle?

Sum of the lengths of its sides Signup and view all the answers

What is the formula for distance, rate, and time?

d = rt Signup and view all the answers

How are solutions to equations in two variables represented?

As ordered pairs Signup and view all the answers

What are practical problems involving equations with multiple variables called?

Formulas Signup and view all the answers

What does the graph of an equation of the form ax + by = c look like?

A straight line Signup and view all the answers

What are intercepts in a graph?

Points where the line crosses the axes Signup and view all the answers

What is slope?

Rise over run Signup and view all the answers

What does slope-intercept form look like?

y = ax + b Signup and view all the answers

What are simultaneous equations?

Equations involving two or more unknowns Signup and view all the answers

How can simultaneous equations be solved?

By addition or subtraction Signup and view all the answers

What is the solution to simultaneous equations represented as?

The intersection point of their graphs Signup and view all the answers

What are inconsistent equations?

Equations with no common solution Signup and view all the answers

What characterizes equivalent equations?

Infinitely many solutions Signup and view all the answers

What is the process of solving by substitution?

Rearranging one equation to substitute into another Signup and view all the answers

What are mixture problems?

Problems involving combinations of two elements Signup and view all the answers

What is scientific notation?

A way of writing numbers as a decimal times a power of ten Signup and view all the answers

What form do exponential functions take?

y = a*b^x Signup and view all the answers

What is a monomial?

A single term in mathematics Signup and view all the answers

What is a coefficient?

A number in front of a variable Signup and view all the answers

What does the degree refer to in algebra?

The exponent Signup and view all the answers

Study Notes

Arithmetic Operations

Addition: The sum is the result of adding two numbers. Order does not affect the sum.
Subtraction: The difference is the result of subtracting one number from another.
Multiplication: The product results from multiplying two numbers, understood as repeated addition. Order does not affect the product.
Division: The quotient is the result of dividing one number by another.

Exponents and Order of Operations

Raising to a Power: Involves multiplying a number by itself a specified number of times indicated by the exponent.
Parentheses: Used to alter the order of operations, indicating that calculations inside them should be performed first.
Distributive Rule: Connects addition and multiplication, as shown by the equations a(b + c) = ab + ac and a(b - c) = ab - ac.

Functions and Graphs

Functions: Link two sets of numbers, with each number in the first set matched to exactly one number in the second set, represented in various forms.
Coordinate Graph: Plots points using pairs of numbers on two intersecting perpendicular lines, defining positions in four quadrants.
Direct Variation: A linear function in the form y = ax with a non-zero constant, graphing as a straight line through the origin.
Linear Function: Expressed as y = ax + b, with its graph forming a straight line.

Variations and Number Sets

Inverse Variation: Represented by y = a/x with a non-zero constant, resulting in a curved graph.
Integers: Include positive integers, zero, and negative integers, forming the set of whole numbers and their negatives.
Rational Numbers: Any number expressible as the quotient of two integers, encompassing all integers.

Algebraic Concepts

Absolute Value: Depicted as |x|, representing the distance from zero, where |x| = x for positive and |x| = -x for negative numbers.
Equation: A mathematical statement indicating equality between two expressions.
Inverse Operations: Actions that negate or reverse one another, such as addition and subtraction.

Equations and Their Solutions

Equivalent Equations: Can be transformed through addition, subtraction, multiplication, or division by the same non-zero quantity without changing their solutions.
Simultaneous Equations: Involve multiple variables with a shared solution point, solvable through various methods.
Graphing Simultaneous Equations: The intersection point of two equations' graphs represents their solution.
Inconsistent Equations: Have no solution, typically represented by parallel lines.

Practical Applications

Distance, Rate, and Time: d = rt expresses the relationship between distance traveled, rate of speed, and time.
Mixture Problems: Analyze mixtures using simultaneous equations to express relationships like weight, volume, or value.

Miscellaneous Concepts

Scientific Notation: Method for writing numbers with a decimal between 1 and 10 multiplied by a power of 10.
Exponential Functions: Expressed as y = a*b^x, where a, b > 0 and b ≠ 1.
Monomial: A single number, variable, or product of numbers and variables.
Coefficient: The numeric factor in front of a variable in an expression.
Degree: Refers to the exponent in polynomials.

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Description

Explore key concepts in elementary algebra with these flashcards. Each card presents important terms such as Addition, Subtraction, and Multiplication, along with their definitions. Perfect for quick reviews and enhancing your algebra skills.