This course is designed to teach students the fundamentals of calculus. Students will begin the course by reviewing the concept of a function, then moving on to the ideas of limits and continuity, and finally will formally learn differentiation (they already learned about the general power rule last semester in their race car project) and how to apply it. This will set students up for next semester, when students will learn integration and how to apply it to area and volume problems. We will constantly be reviewing topics from last year’s pre-calculus course as needed to strengthen problem-solving, graphing, and algebra skills, all of which will be helpful in whichever math courses students wind up taking next year in college. One of the main goals for this course is to really prepare students for college-level math and give them the tools they need to succeed. Students will be assigned weekly problem sets, weekly quizzes, and will be administered midterms and finals, as will most likely be the case in college. The spring semester of this course will culminate in giving students the opportunity to take the Advanced Placement exam in Calculus AB, which is accepted as college credit in the vast majority of colleges.
Problem sets include examples require critical thinking and diligence. For example, curve sketching examples require an incredible amount of information gathering and application using graphing skills. Related rates problems entail the creation of diagrams and models, etc.
1&2. Reduce each fraction completely (3 pts ea):
1. EMBED Equation.3 2. EMBED Equation.3
3&4. Find the inverse functions (3 pts ea):
3. f(x) = EMBED Equation.3 4. g(x) = EMBED Equation.3
5-7. Find the domain of each of the following (2 pts for each):
5. a(x) = EMBED Equation.3 6. b(x) = EMBED Equation.3
7. c(x) = EMBED Equation.3
8&9. Find the zeroes of each of the functions (2 pts ea):
8. e(x) = EMBED Equation.3 9. f(x) = EMBED Equation.3
10-15. Based on the diagram below, find each of the following limits (1 pt ea):