Number Systems
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Questions and Answers

What is the set of numbers that includes all whole numbers and their negatives?

  • Whole Numbers
  • Natural Numbers
  • Integers (correct)
  • Rational Numbers
  • What is the term for a statement with an equal sign?

  • Equation (correct)
  • Variable
  • Expression
  • Inequality
  • What is the name for a shape with three sides?

  • Ray
  • Line Segment
  • Angle
  • Triangle (correct)
  • What is the term for a value that a function approaches as the input gets arbitrarily close?

    <p>Limit</p> Signup and view all the answers

    What is an unknown value represented by a letter?

    <p>Variable</p> Signup and view all the answers

    What is the term for a set of points extending infinitely in two directions?

    <p>Line</p> Signup and view all the answers

    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, ... (all whole numbers and their negatives)
    • Rational Numbers: fractions (e.g. 1/2, 3/4) and decimals (e.g. 0.5, 0.75)
    • Irrational Numbers: non-repeating decimals (e.g. π, e)
    • Real Numbers: all rational and irrational numbers
    • Complex Numbers: numbers with real and imaginary parts (e.g. 3 + 4i)

    Algebra

    • Variables: unknown values represented by letters (e.g. x, y)
    • Constants: known values (e.g. 2, 5)
    • Expressions: combinations of variables and constants (e.g. 2x + 3)
    • Equations: statements with equal signs (e.g. 2x + 3 = 5)
    • Inequalities: statements with greater than, less than, or equal to signs (e.g. 2x + 3 > 5)

    Geometry

    • Points: locations in space (e.g. A, B, C)
    • Lines: sets of points extending infinitely in two directions
    • Line Segments: parts of lines with fixed endpoints (e.g. AB, CD)
    • Rays: lines extending from a point to infinity (e.g. →AB)
    • Angles: formed by two rays sharing a common endpoint (e.g. ∠AOB)
    • Triangles: three-sided shapes (e.g. ΔABC)

    Calculus

    • Limits: values that a function approaches as the input gets arbitrarily close
    • Derivatives: rates of change of functions (e.g. dy/dx)
    • Integrals: accumulation of quantities over a interval (e.g. ∫f(x)dx)

    Statistics and Probability

    • Mean: average value of a dataset
    • Median: middle value of a dataset when arranged in order
    • Mode: most frequently occurring value in a dataset
    • Probability: measure of the likelihood of an event occurring (e.g. 0 ≤ P(event) ≤ 1)

    Trigonometry

    • Angles: measures of rotation (e.g. 30°, 45°)
    • Triangles: right-angled triangles (e.g. ΔABC)
    • Sine (sin), Cosine (cos), and Tangent (tan) functions relate to triangle sides and angles

    Number Systems

    • Natural numbers are positive integers: 1, 2, 3, ...
    • Whole numbers include 0 and all positive integers: 0, 1, 2, 3, ...
    • Integers include all whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...
    • Rational numbers are fractions and decimals: 1/2, 3/4, 0.5, 0.75
    • Irrational numbers are non-repeating decimals: π, e
    • Real numbers include all rational and irrational numbers
    • Complex numbers have real and imaginary parts: 3 + 4i

    Algebra

    • Variables represent unknown values: x, y
    • Constants are known values: 2, 5
    • Expressions combine variables and constants: 2x + 3
    • Equations are statements with equal signs: 2x + 3 = 5
    • Inequalities have greater than, less than, or equal to signs: 2x + 3 > 5

    Geometry

    • Points are locations in space: A, B, C
    • Lines extend infinitely in two directions
    • Line segments have fixed endpoints: AB, CD
    • Rays extend from a point to infinity: →AB
    • Angles are formed by two rays sharing a common endpoint: ∠AOB
    • Triangles are three-sided shapes: ΔABC

    Calculus

    • Limits are values that a function approaches as the input gets arbitrarily close
    • Derivatives are rates of change of functions: dy/dx
    • Integrals are accumulation of quantities over an interval: ∫f(x)dx

    Statistics and Probability

    • Mean is the average value of a dataset
    • Median is the middle value of a dataset when arranged in order
    • Mode is the most frequently occurring value in a dataset
    • Probability measures the likelihood of an event occurring: 0 ≤ P(event) ≤ 1

    Trigonometry

    • Angles are measures of rotation: 30°, 45°
    • Right-angled triangles relate to sine, cosine, and tangent functions: ΔABC
    • Sine, cosine, and tangent functions relate to triangle sides and angles

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