Transitioning to Calculus
1. Arithmetic
Whole numbers
Number lines
Common mathematical symbols
Sets
The integers and some special subsets of the integers
Basic arithmetic operations
Multiples
Factors
Prime numbers
Factorial
Modulo
Fractions
Rational numbers, irrational numbers, and real numbers
Decimals
Rounding
Absolute value
Floor and ceiling functions
Percentages
Exponents
Radicals
Measurement systems
Order of operations
Scientific notation
Summation notation and formulas
Arithmetic sequences and series
Geometric sequences and series
Counting techniques
Digits
Number systems
Exercises
2. Algebra
Fundamental properties of addition
Fundamental properties of multiplication
Exponents
Radicals
Logarithms
Algebraic expressions
Simplifying algebraic expressions
Expanding algebraic expressions
Factoring algebraic expressions
Equations
Polynomials
Inequalities
Word problems
Exercises
3. Geometry
Points
Lines, line segments, and rays
Planes
Angles
Polygons
Circles
Perimeter and circumference
Area
Solid geometry
Exercises
4. Analytic Geometry
The Cartesian plane
Points
Midpoint and distance formulas
Graphs and symmetry
Intercepts
Functions
Transforming functions
Classifying functions
Combining functions
One-to-one functions
Inverse functions
Linear functions
Quadratic functions
Polynomial functions
Rational functions
Exponential functions
Logarithmic functions
Conic sections
Direct and indirect variation
Parametric equations
Exercises
5. Trigonometry
Angles
Trigonometric functions for a right triangle
Winding function
Powers of trigonometric functions
Trigonometric identities
Graphs of trigonometric functions
Modifying the graphs of the trigonometric functions
Inverse trigonometric functions
Equations involving trigonometric functions
Sum and difference formulas
Double-angle formulas
Half-angle formulas
The law of sines and the law of cosines
Polar coordinate system
Exercises
6. Complex Numbers
Imaginary numbers
Complex numbers
Quadratic equations
Graphs of quadratic functions
Polynomial functions
Exercises