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Questions and Answers
What is the set of numbers that includes positive and negative whole numbers?
What is the set of numbers that includes positive and negative whole numbers?
What is the term for a symbol that represents an unknown value?
What is the term for a symbol that represents an unknown value?
What is the term for a set of points that extends infinitely in two directions?
What is the term for a set of points that extends infinitely in two directions?
What is the term for the value that a function approaches as the input gets arbitrarily close to a certain point?
What is the term for the value that a function approaches as the input gets arbitrarily close to a certain point?
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What is the measure of the spread or dispersion of a dataset?
What is the measure of the spread or dispersion of a dataset?
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What is the term for a statement that two expressions are equal?
What is the term for a statement that two expressions are equal?
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What is the term for a part of a line that extends from a point to infinity in one direction?
What is the term for a part of a line that extends from a point to infinity in one direction?
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What is the term for the middle value of a dataset when arranged in order?
What is the term for the middle value of a dataset when arranged in order?
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Study Notes
Numbers
- Natural Numbers: 1, 2, 3, ... (positive integers)
- Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
- Rational Numbers: fractions, e.g. 3/4, 22/7 (can be expressed as a finite decimal)
- Irrational Numbers: cannot be expressed as a finite decimal, e.g. π, e
- Real Numbers: includes rational and irrational numbers
Algebra
- Variables: symbols that represent unknown values, e.g. x, y
- Constants: numbers, e.g. 2, 5
- Expressions: combinations of variables, constants, and mathematical operations
- Equations: statements that two expressions are equal, e.g. 2x + 3 = 5
- Inequalities: statements that one expression is greater than, less than, or equal to another
Geometry
- Points: locations in space, represented by coordinates (x, y)
- Lines: sets of points that extend infinitely in two directions
- Line Segments: parts of lines with a fixed length
- Rays: parts of lines that extend from a point to infinity in one direction
- Angles: formed by two rays sharing a common endpoint
Calculus
- Limits: the value that a function approaches as the input gets arbitrarily close to a certain point
- Derivatives: measures of how functions change as their input changes
- Integrals: measures of the area under curves or the accumulation of a quantity over an interval
Statistics
- Mean: average value of a dataset
- Median: middle value of a dataset when arranged in order
- Mode: most frequently occurring value in a dataset
- Range: difference between the largest and smallest values in a dataset
- Standard Deviation: measure of the spread or dispersion of a dataset
Numbers
- Natural numbers are positive integers, starting from 1 and going up to infinity.
- Whole numbers are non-negative integers, including 0 and all positive integers.
- Integers include both positive and negative whole numbers, as well as 0.
- Rational numbers are fractions that can be expressed as a finite decimal, such as 3/4 or 22/7.
- Irrational numbers cannot be expressed as a finite decimal, like π or e.
- Real numbers encompass both rational and irrational numbers.
Algebra
- Variables are symbols that represent unknown values, such as x or y.
- Constants are numbers, like 2 or 5, that remain unchanged.
- Expressions combine variables, constants, and mathematical operations.
- Equations assert that two expressions have equal values, like 2x + 3 = 5.
- Inequalities compare two expressions, indicating that one is greater than, less than, or equal to the other.
Geometry
- Points are locations in space, defined by their coordinates (x, y).
- Lines extend infinitely in two directions and consist of a set of points.
- Line segments are parts of lines with a fixed length.
- Rays are parts of lines that extend from a point to infinity in one direction.
- Angles are formed by two rays sharing a common endpoint.
Calculus
- Limits determine the value that a function approaches as the input gets arbitrarily close to a certain point.
- Derivatives measure the rate of change of a function as its input changes.
- Integrals calculate the area under curves or the accumulation of a quantity over an interval.
Statistics
- The mean is the average value of a dataset.
- The median is the middle value of a dataset when arranged in order.
- The mode is the most frequently occurring value in a dataset.
- The range is the difference between the largest and smallest values in a dataset.
- The standard deviation measures the spread or dispersion of a dataset.
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Description
Understand the basics of numbers and algebra, including types of numbers and variables. Learn about natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
