Algebra Class: Variables, Equations, and Functions

Algebra

• Variables and Expressions:
  • Variables: letters or symbols that represent unknown values
  • Expressions: combinations of variables, constants, and mathematical operations
• Equations and Inequalities:
  • Equations: statements that express the equality of two mathematical expressions
  • Inequalities: statements that compare two mathematical expressions using greater than, less than, or equal to
• Functions:
  • Domain: set of input values for a function
  • Range: set of output values for a function
  • Composition of functions: combining two or more functions to create a new function

Trigonometry

• Angles and Triangles:
  • Angles: measurements of rotation in degrees or radians
  • Triangles: three-sided shapes with angles and side lengths
• Trigonometric Ratios:
  • Sine (sin): opposite side / hypotenuse
  • Cosine (cos): adjacent side / hypotenuse
  • Tangent (tan): opposite side / adjacent side
• Identities and Formulas:
  • Pythagorean Identity: sin^2(A) + cos^2(A) = 1
  • Sum and Difference Formulas for sine, cosine, and tangent

Geometry

• Points, Lines, and Planes:
  • Points: locations in space defined by coordinates
  • Lines: sets of points extending infinitely in two directions
  • Planes: flat surfaces that extend infinitely in all directions
• Properties of Shapes:
  • Congruent shapes: identical in size and shape
  • Similar shapes: same shape but different size
  • Perimeter: distance around a shape
  • Area: measure of the amount of space inside a shape
• Measurement and Calculation:
  • Perimeter and area formulas for various shapes (e.g. triangles, quadrilaterals, circles)
  • Volume formulas for various three-dimensional shapes (e.g. rectangular prisms, spheres)

Algebra

• Variables represent unknown values and are often represented by letters or symbols.
• Expressions are combinations of variables, constants, and mathematical operations.
• Equations are statements that express the equality of two mathematical expressions.
• Inequalities compare two mathematical expressions using greater than, less than, or equal to.

Functions

• The domain of a function is the set of input values.
• The range of a function is the set of output values.
• Functions can be combined through composition to create a new function.

Trigonometry

Angles and Measurement

• Angles are measured in degrees or radians.
• Triangles have angles and side lengths.

Trigonometric Ratios

• Sine (sin) is the ratio of the opposite side to the hypotenuse.
• Cosine (cos) is the ratio of the adjacent side to the hypotenuse.
• Tangent (tan) is the ratio of the opposite side to the adjacent side.

Identities and Formulas

• The Pythagorean Identity is sin^2(A) + cos^2(A) = 1.
• Sum and Difference Formulas exist for sine, cosine, and tangent.

Geometry

Points, Lines, and Planes

• Points are locations in space defined by coordinates.
• Lines are sets of points extending infinitely in two directions.
• Planes are flat surfaces that extend infinitely in all directions.

Properties of Shapes

• Congruent shapes are identical in size and shape.
• Similar shapes have the same shape but are different in size.
• Perimeter is the distance around a shape.
• Area is the measure of the amount of space inside a shape.

Measurement and Calculation

• Formulas exist for calculating the perimeter and area of various shapes, such as triangles, quadrilaterals, and circles.
• Formulas also exist for calculating the volume of various three-dimensional shapes, such as rectangular prisms and spheres.