High School Precalculus and Trigonometry

• Functions
  • Inverse functions
  • Domain, range and composite functions
  • Linear graphs
  • Slopes and intercepts
  • The equation of a straight line
  • Plotting and sketching graphs
  • Even, odd and periodic functions
  • Graphs of quadratic functions
  • Solving quadratic equations
  • Quadratic inequalities
  • Graphs of important non-linear functions
  • The equation of a circle
  • Operations with polynomials
  • Dividing polynomials
  • The Factor Theorem
  • Polynomials of degree 3 or more
  • Simplifying rational functions
  • Operations with algebraic fractions
  • Improper fractions
  • Partial fractions
  • Solving rational equations
  • Graphing rational functions
  • Absolute value functions
  • Piecewise-defined functions
  • Limits
  • Transforming functions part 1
  • Transforming functions part 2
  • Rate of change
• Trigonometry
  • The sine, cosine and tangent of any angle
  • Trigonometric graphs and exact values
  • Transforming trigonometric functions
  • The inverse trigonometric functions
  • Trigonometric equations
  • Trigonometric identities
  • Degrees and radians
  • Solving equations using radians
  • The reciprocal trigonometric functions
  • Trigonometric identities using reciprocal functions
  • The law of sines and the area of a triangle
  • The law of cosines
  • The addition formulas
  • The double angle formulas
  • Expressions of the form acos x + bsin x
  • 3-D trigonometry
  • Questions on trigonometry
• Exponentials and logarithms
  • Exponentials and logarithms
  • The laws of logarithms
  • Solving equations involving logarithms
  • Exponential growth and decay
  • Exponentials with bases other than e
  • Linear and exponential modeling
• Vector
  • Vectors in two and three dimensions
  • Adding and subtracting vectors
  • Position vectors and coordinate geometry
  • Using vectors
  • The magnitude of a vector
  • Vector arithmetic
  • The dot product
  • The vector equation of a line
  • Intersecting lines
  • The intersection of a line and a plane
  • Questions on vectors
• Sequences
  • Sequences
  • Arithmetic sequences
  • Geometric sequences
  • Quadratic sequences part 1
  • Quadratic sequences part 2
  • Other types of sequences
  • The sum of an arithmetic series
  • The sum of a geometric series
• Polar coordinates, parameterizations and conic sections
  • Parametric functions
  • Parametric equations of curves
  • Conic sections part 1
  • Conic sections part 2
  • Polar coordinates
• Skills
  • Using graphing calculators in applications