# INTEGRATED MATH 3, PART 2

## Price: $125 | Credits: One Semester | Dept: Math | Course ID# 233-2

Integrated Math 3 is the third year of a three-year high school mathematics sequence. The program is designed to build upon each year, increasing in difficulty and application of patterns, modeling and conjectures to develop a student’s understanding and competency in mathematics. This is the second semester of Integrated Math 3, it is approved by the University of California A-G as mathematics (category C).

Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.

### LEARNING OBJECTIVES

In this course, students gain a comprehension of the following:

- The Pythagorean theorem.
- The six basic trigonometric functions.
- Use the law of sines and the law of cosines to find the lengths of sides of any triangle.
- Understand radians, a method for measuring angles, and the unit circle with a radius of one.
- Solve and graph trigonometric functions.
- How to find inverse functions.
- The relationship between a logarithmic and exponential function and properties of logarithmic functions.
- Solve and graph logarithmic equations.
- Recognize and predict terms for geometric sequences as well as calculate the sum of finite geometric series and convergent infinite series.
- Recognize equations for and graphs of conic sections, including those for circle, ellipses, hyperbolas, and parabolas.
- Decipher the center and radius of a circle, given its equations, as well as match graphs of circles to their equations.
- Analyze the elements and characteristics of hyperbolas and sketch their graphs, given an equation.
- Distinguish between circles, ellipses, hyperbolas, and parabolas, using only their equations.
- Use trigonometry to determine the rectangular coordinates of a corresponding point on a polar graph.
- The relationships between rectangular and polar coordinates to find equivalent equations.
- Determine the magnitude and direction of a vector using trigonometry.
- Add and subtract vectors both analytically and visually.
- Multiply vectors by a scalar and using the dot product.
- How to solve real-life problems involving permutations and combinations, with scenarios like how many ways a certain number of players can form a roster, or how many ways some friends can be arranged in a photo.
- How to assess whether a combination or a permutation is required to solve a particular problem, and how to perform the appropriate calculation. How to solve random chance probability problems and to solve both “replacement” and “without replacement” problems.
- How to use the binomial theorem to raise polynomials to large powers.
- How to organize and manipulate data, and compute measures of central tendency such as mean, median, and mode.
- How to create visuals for measures of central tendency such as bar graphs, box plots, and histographs.
- How to compute the standard deviation of large and small data sets.
- How to use statistic analysis to compare data sets.

### TOPICS COVERED

- Trigonometry Ratios
- Trigonometric Functions
- Exponential and Logarithmic Functions
- Conic Sections
- Polar Coordinates
- Vectors and Motion
- Probability
- Data and Statistics