Math Academy Mathematical Foundations 1

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My notes Math Academy Mathematical Foundations 1
Author

Tyler Hillery

Published

April 21, 2026

Notes

Lesson: Points, Lines, Rays, and Segments

  • A line is a straight object that extends forever in both directions
  • Using diagrams a line is shown with arrows on both sides
  • We can represent a line passing through points \(S\) and \(T\) as \(\overleftrightarrow{ST}\)
  • A ray is similar to a line but has a staring point and extends infinitely in one direction only.
  • We can represent a ray starting at point \(P\) and passing through point \(Q\) as \(\overrightarrow{ST}\)
  • A segment is part of aline bounded by two points, called endpoints.
  • We can represent a segment with endpoints \(A\) and \(B\) as \(\overline{AB}\)

Lesson: Additive Inverses of Numbers

  • Given a number, its additive inverse is the number we need to add to get to zero.

Lesson: The Greatest Common Factor of Two Linear Expressions

  • The greatest common factor of two numbers is the largest expression that will divide both numbers with no remainder.

Lesson: Multiplying Mixed Numbers by Whole Numbers

  • No notes

Lesson: Understanding Volume Using Unit Cubes

  • Volume is the amount of space that an object takes up, measured in unit cubes.

Lesson: Ratio Tables

  • No notes

Lesson: Angles and Measures of Angles

  • An angle is formed whenever two rays meet at a point.
  • The common point shared by the rays is called the vertex, and the rays themselves are called sides of the angle
  • Consider the follow angle made of the following rays \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\), this can be expressed as \(\angle{CAB}\) or \(\angle{BAC}\) the vertex is always in the middle. It can also be expressed as \(\widehat{CAB}\)
  • The measure of angle is the amount of “turn” from one side of the angle to the other. Angles are measured in degrees \(^\circ\).

Lesson: Distance Between Two Points in a Coordinate Plane

  • No notes. I am curious though how to calculate the distance when both x,y are different. The problems given were just vertical and horizontal lines.

Lesson: Solving Problems Using Addition and Subtraction of Rational Numbers

  • No notes.

Lesson: Multiplying Mixed Numbers by Fractions

  • No notes.

Lesson: Sums of Angles

  • When two angles share a common side, they are called adjacent angles.
  • When two angles are adjacent we can add their meseasures to find the larger angle

\[ m\angle{PST} = m\angle{PSR} + m\angle{RST} \]

Lesson: Right, Straight, Full, and Null Angles

  • Right Angle = \(90^\circ\)
  • Straight Angle = \(180^\circ\)
  • Null Angle = \(0^\circ\)
  • Full Angle = \(360^\circ\)

Lesson: Decimal and Fraction Operations Applied to Commercial Settings

  • No Notes.

Lesson: Simplifying Linear Expressions When a Group of Terms Is Subtracted

  • No Notes.

Lesson: Splitting Rational Expressions Into Separate Terms

  • No Notes.

Lesson: Simplifying Linear Expressions Containing Fractions

  • No Notes.

Lesson: Multiplying Mixed Numbers

  • No Notes.

Lesson: Acute, Obtuse, and Reflex Angles

  • Acute angle has a measure between \(0^/circ\) and \(90^/circ\)
  • Obtuse angle has a measure between \(90^/circ\) and \(180^/circ\)
  • Reflex angle has a measure between \(180^/circ\) and \(360^/circ\)

Lesson: Graphing Ratios

  • No notes.

Lesson: Polygons

  • A chain of straight lines that form a loop is called a polygon
  • Line segments are the sides for the polygon and the endpoints of the sides are the vertices
Number of Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
  • Polygon is simply if boundary does not intersect otherwise it’s complex
  • Polygon is convex if it has no angles pointing inwards otherwise it’s concave