Pre-Calculus 12 is a course designed to equip students with the mathematical skills required for the further study of Calculus. Mathematics is one way of trying to understand, interpret, and describe our world. Components integral to the nature of mathematics include change, constancy, number sense, patterns, relationship, spatial sense, and uncertainty. These components are woven throughout this course.
1.1 Horizontal and Vertical Translations
1.2A Reflections
1.2B Stretching Graphs of Functions
1.3 Combining Transformations
1.4 Inverse of a Relation
2.1 Radical Function and Transformation
2.2 Square Root of a Function
2.3 Solving Radical Equations
Notes (*See Pre-Calculus 11 notes for more examples)
3.1 Characteristics of Polynomial Functions
3.2A Long Division of Polynomials
3.2B The Remainder Theorem
3.3A Factor Theorem
3.3B The Integral Zero Theorem
3.4A Graphs of Polynomial Functions
3.4B Equations of Polynomial Functions
4.1A Radian Measure
4.1B Coterminal Angles
4.2A The Unit Circle
4.2B The Unit Circle (Given the point, finding the angle)
4.3A The Trigonometric Ratio
4.3B Finding the Angle
4.4A Trigonometric Equations
4.4B Factoring to Solve Trigonometric Equations
5.1A Graphs of Sine and Cosine Functions (Properties and Amplitude)
5.1B Graphs of Sine and Cosine Functions (Period)
5.2A Transforming Sinusoidal Functions (Graphing)
5.2B Transforming Sinusoidal Functions (Writing Equations)
5.3 Graphing the Tangent Function
5.4A Solving Trigonometric Equations Graphically
5.4B Modeling Real Situations Using Trigonometric Functions
6.1 Reciprocal, Quotient, and Pythagorean Identities
6.2A Sum and Difference Identities
6.2B Double Angle Identities
6.3 Proving Trigonometric Identities
6.4 Solving Trigonometric Equations using Identities
7.1 Characteristics of Exponential Functions
7.2 Transformation of Exponential Functions
7.3 Solving Exponential Equations
8.1 Understanding Logarithms
8.2 Transformations of Logarithmic Functions
8.3 The Laws of Logarithms
8.4A Equations involving Logarithms
8.4B Exponential Equations
9.1A Rational Functions
9.1B Rational Functions (y=1/x^2)
9.2 Analyzing Rational Functions
9.3 Rational Equations
Notes (*See Pre-Calculus 11 notes for more examples)
10.1 Sums and Differences of Functions
10.2 Products and Quotients of Functions
10.3 Composite Functions
11.1 Geometric Sequences
11.2 Geometric Series
11.3 Infinite Geometric Series
11.4 Sigma Notation