Podcast
Questions and Answers
What is the result of adding two numbers called?
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?
What do you call the result of subtracting one number from another?
Difference
What is the product of two numbers?
What is the product of two numbers?
The result of multiplying two numbers
What is the result of dividing one number by another called?
What is the result of dividing one number by another called?
What does raising a number to a power involve?
What does raising a number to a power involve?
What are parentheses used for in mathematics?
What are parentheses used for in mathematics?
What does the Distributive Rule relate?
What does the Distributive Rule relate?
What is a function?
What is a function?
What are coordinate graphs used for?
What are coordinate graphs used for?
What is an example of direct variation?
What is an example of direct variation?
What is a linear function?
What is a linear function?
What is inverse variation?
What is inverse variation?
What are integers?
What are integers?
What are the characteristics of a coordinate graph?
What are the characteristics of a coordinate graph?
What happens when you add opposites?
What happens when you add opposites?
What is the method for subtraction in terms of addition?
What is the method for subtraction in terms of addition?
What is the result when a positive number is multiplied by a negative number?
What is the result when a positive number is multiplied by a negative number?
What does PEMDAS stand for in the order of operations?
What does PEMDAS stand for in the order of operations?
What are rational numbers?
What are rational numbers?
What does absolute value represent?
What does absolute value represent?
What does the symbol ≈ indicate?
What does the symbol ≈ indicate?
What defines an equation?
What defines an equation?
What are inverse operations?
What are inverse operations?
How can an equation be transformed into an equivalent equation?
How can an equation be transformed into an equivalent equation?
What are equivalent expressions?
What are equivalent expressions?
What is the perimeter of a rectangle?
What is the perimeter of a rectangle?
What is the formula for distance, rate, and time?
What is the formula for distance, rate, and time?
How are solutions to equations in two variables represented?
How are solutions to equations in two variables represented?
What are practical problems involving equations with multiple variables called?
What are practical problems involving equations with multiple variables called?
What does the graph of an equation of the form ax + by = c look like?
What does the graph of an equation of the form ax + by = c look like?
What are intercepts in a graph?
What are intercepts in a graph?
What is slope?
What is slope?
What does slope-intercept form look like?
What does slope-intercept form look like?
What are simultaneous equations?
What are simultaneous equations?
How can simultaneous equations be solved?
How can simultaneous equations be solved?
What is the solution to simultaneous equations represented as?
What is the solution to simultaneous equations represented as?
What are inconsistent equations?
What are inconsistent equations?
What characterizes equivalent equations?
What characterizes equivalent equations?
What is the process of solving by substitution?
What is the process of solving by substitution?
What are mixture problems?
What are mixture problems?
What is scientific notation?
What is scientific notation?
What form do exponential functions take?
What form do exponential functions take?
What is a monomial?
What is a monomial?
What is a coefficient?
What is a coefficient?
What does the degree refer to in algebra?
What does the degree refer to in algebra?
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.
Studying That Suits You
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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.
