Pre-Calculus Part 2 begins with trigonometry topics such as identities, trigonometric equation solving, half-angle and double-angle formulas, the law of sines, and the law of cosines. Students solve linear equalities and inequalities in two and three variables using graphing and algebraic techniques (i.e. substitution, row-echelon, and Gaussian elimination). Infinite series, partial sums of series, and geometric series are introduced and limits are studied. Statistical concepts include probability, the counting principle, and the Binomial Theorem. The course concludes with an in-depth study of conics (i.e. parabolas, hyperbolas, and ellipses).
It is recommended that students successfully complete Pre-Calculus Part 1 or equivalent course work before enrolling in this course.
Course Objectives
Unit 1: Essential Content and Skills
- Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions.
- Use standard algebraic techniques to solve trigonometric equations.
- Use sum and difference formulas, multiple-angle formulas, power-reducing formulas, half-angle formulas, and product-sum formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations.
- Use the Law of Sines to solve oblique triangles and real-life problems.
- Use the Law of Cosines to solve oblique triangles and real-life problems.
Unit 2: Essential Content and Skills
- Solve systems of equations and inequalities in two variables graphically and analytically.
- Use back-substitution to solve linear systems in row-echelon form.
- Use Gaussian elimination to solve systems of linear equations.
- Use summation notation to write sums.
- Find the sum of an infinite series and the partial sum of an arithmetic sequence.
- Recognize, write, and find the sums of geometric sequences.
Unit 3: Essential Content and Skills
- Use mathematical induction.
- Find the sums of powers of integers.
- Use finite differences to help write formulas or equations.
- Use the Binomial Theorem to expand binomial expression.
- Solve counting problems and find the probabilities of events.
- Chart vectors and find the component forms.
- Find the magnitude, the direction angles, and the dot product of vectors.
Unit 4: Essential Content and Skills
- Find the angle between two lines and the distance between a point and a line.
- Write the standard form of the equation of a parabola, an ellipse, and a hyperbola.
- Identify the graphical characteristics of a parabola, an ellipse, and a hyperbola.
- Classify conics by its graph, its equation, and the value of its discriminant.
- Chart conics with a graphing utility.
Course Materials
- Pre-Calculus (textbook)
- Pre-Calculus Study And Solutions Guide
- Pre-Calculus (program DVD)
**NCAA approved