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Questions and Answers
What is the set of numbers that includes all rational and irrational numbers?
What is the term for a statement that two expressions are equal?
What is the measure of how functions change as their input changes?
What is the middle value of a dataset when arranged in order?
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What is a three-sided polygon with three vertices and three sides?
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What is a set of points extending infinitely in two directions?
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What is a measure of the spread of a dataset?
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What is a non-repeating decimal number?
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What is the value a function approaches as the input gets arbitrarily close to a certain point?
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What is a letter or symbol representing an unknown value?
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Study Notes
Number Systems
- 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: non-repeating decimals, e.g. π, e (cannot be expressed as a finite decimal)
- Real Numbers: all rational and irrational numbers
Algebra
- Variables: letters or symbols representing unknown values
- Constants: numbers, e.g. 2, 5, 10
- Expressions: combinations of variables, constants, and operations, e.g. 2x + 5
- Equations: statements that two expressions are equal, e.g. 2x + 5 = 11
- Inequalities: statements that one expression is greater than, less than, or equal to another, e.g. 2x + 5 > 11
Geometry
- Points: locations in space, represented by coordinates (x, y)
- Lines: sets of points extending infinitely in two directions
- Angles: formed by two lines or rays sharing a common endpoint
- Triangles: three-sided polygons with three vertices and three sides
- Quadrilaterals: four-sided polygons with four vertices and four sides
Calculus
- Limits: the value 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 accumulation of quantities
Statistics
- Mean: the average value of a dataset
- Median: the middle value of a dataset when arranged in order
- Mode: the most frequent value in a dataset
- Range: the difference between the largest and smallest values in a dataset
- Standard Deviation: a measure of the spread of a dataset
Number Systems
- Natural numbers are positive integers, starting from 1.
- Whole numbers include 0 and all positive integers.
- Integers consist of all whole numbers and their negatives.
- Rational numbers are fractions that can be expressed as finite decimals.
- Irrational numbers are non-repeating decimals that cannot be expressed as finite decimals.
- Real numbers encompass all rational and irrational numbers.
Algebra
- Variables are letters or symbols that represent unknown values.
- Constants are numbers that do not change value.
- Algebraic expressions combine variables, constants, and operations.
- Equations state that two expressions are equal and can be solved for variables.
- Inequalities compare two expressions using greater than, less than, or equal to.
Geometry
- Points are locations in space represented by coordinates (x, y).
- Lines extend infinitely in two directions and can be defined by two points.
- Angles are formed by two lines or rays sharing a common endpoint.
- Triangles are three-sided polygons with three vertices and three sides.
- Quadrilaterals are four-sided polygons with four vertices and four sides.
Calculus
- Limits describe the value 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 measure the area under curves or the accumulation of quantities.
Statistics
- Mean is the average value of a dataset, calculated by summing values and dividing by the count.
- Median is the middle value of a dataset when arranged in order, which separates the higher and lower halves.
- Mode is the most frequent value in a dataset.
- Range is the difference between the largest and smallest values in a dataset.
- Standard deviation measures the spread of a dataset, calculating how much individual values deviate from the mean.
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Description
Test your understanding of different number systems, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers, as well as the basics of algebra. Learn about variables and more.
