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Questions and Answers
What is the name of the set of numbers that includes all whole numbers and their negatives?
What is the name of the set of numbers that includes all whole numbers and their negatives?
What is a combination of variables, constants, and mathematical operations?
What is a combination of variables, constants, and mathematical operations?
What is the name of the ratio of the opposite side to the hypotenuse?
What is the name of the ratio of the opposite side to the hypotenuse?
What is the name of the set of numbers that can be expressed as a finite decimal?
What is the name of the set of numbers that can be expressed as a finite decimal?
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What is a location in space represented by coordinates (x, y)?
What is a location in space represented by coordinates (x, y)?
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What is an angle that is exactly 90°?
What is an angle that is exactly 90°?
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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, ... (all whole numbers and their negatives)
- 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: 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 mathematical operations
- Equations: statements asserting the equality of two expressions, e.g., 2x + 3 = 5
Geometry
- Points: locations in space, represented by coordinates (x, y)
- Lines: sets of points extending infinitely in two directions
- Rays: lines extending from a single point (endpoint) to infinity
- Angles: formed by two rays sharing a common endpoint (vertex)
Trigonometry
- Triangles: three-sided shapes with three vertices and three sides
-
Angles in Triangles:
- Acute: less than 90°
- Right: exactly 90°
- Obtuse: greater than 90°
- Straight: exactly 180°
-
Trigonometric Ratios:
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
Numbers
- Natural Numbers are positive integers, starting from 1.
- Whole Numbers are non-negative integers, including 0.
- Integers include all whole numbers and their negatives.
- Rational Numbers are fractions that can be expressed as a finite decimal.
- Irrational Numbers cannot be expressed as a finite decimal, such as π and e.
- Real Numbers encompass all rational and irrational numbers.
Algebra
- Variables are letters or symbols representing unknown values.
- Constants are numbers, such as 2, 5, or 10.
- Expressions are combinations of variables, constants, and mathematical operations.
- Equations are statements asserting the equality of two expressions, such as 2x + 3 = 5.
Geometry
- Points are locations in space, represented by coordinates (x, y).
- Lines are sets of points extending infinitely in two directions.
- Rays are lines extending from a single point (endpoint) to infinity.
- Angles are formed by two rays sharing a common endpoint (vertex).
Trigonometry
- Triangles are three-sided shapes with three vertices and three sides.
- Angles in Triangles can be:
- Acute: less than 90°
- Right: exactly 90°
- Obtuse: greater than 90°
- Straight: exactly 180°
- Trigonometric Ratios are:
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
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Description
Learn the basics of numbers and algebra, including types of numbers, integers, and more.
