Collier County Public Schools Calculus Correlations with FDOE

Collier County Public Schools Calculus Correlations with FDOE

Course Descriptions and Standards

2007-2008 School Year

AP Calculus AB / AP CalculusBC pairing

Text: Houghton Mifflin Calculus of a Single Variable

FDOE Topic or Standard / Location in CCPS Curriculum Guide
Advanced Placement CalculusAB
1. Identify and apply properties of algebraic, trigonometric, exponential and logarithmic functions / Weeks 1, 2, 3; Supplementary Material
2. Apply the concept of limits to functions / Weeks 1, 2, 7; Chapters 1.2-1.5 and 3.5
3. Determine derivatives of algebraic, trigonometric, exponential and logarithmic functions / Weeks 12 and 14; Chapters 5.1-5.2 and 5.4-5.5
4. Determine derivatives of the inverse of a function / Week 13; Chapter 5.3
5. Determine the relation between differentiability and continuity / Week 3; Chapter 2.1
6. Demonstrate an understanding of the application of the derivative to problem situations / Week 5; Chapter 2.6
7. Identify increasing and decreasing functions, relative and absolute maximum and minimum points, concavity, and points of inflection / Week 6 and Week 8;
Chapters 3.1-3.4 and 3.7
8. Determine antiderivatives of algebraic, trigonometric, exponential and logarithmic functions / Weeks 9 and 10;
Chapters 4.1, 4.2, 4.4
9. Apply antiderivatives to solve problems / Weeks 4 and 5; Chapters 5.6, 5.7 and appendix 3
10. Use techniques of integration / Week 11; Chapter 4.5
11. Determine the approximations of definite integrals using rectangles or trapezoids / Weeks 10 and 11;
Chapters 4,3, 4.6
12. Apply knowledge of integral calculus to find the area between curves and the volume of a solid of revolution / Week 17;
Chapters 6.1-6.2
AP Calculus BC
1. Identify and apply properties of algebraic, trigonometric,. exponential and logarithmic functions / Throughout course; Supplementary material and Algebra review
2. Apply the concept of limit to functions / Weeks 27 and 33; Chapters 1.2-1.5 and 3.5
3. Determine derivatives of algebraic, trigonometric, exponential and logarithmic functions / Weeks 28, 29, 30, 31;
Chapters 2.1-2.6, 5.1-5.2, 5.4-5.5
4. Determine the derivatives of the inverse of a function / Week 30;
Chapter 5.3
5. Determine the relation between differentiability and continuity / Week 28; Chapter 2.1
6. Demonstrate and understanding of the application of the derivative in problem situations / Week 29;
Chapter 2.6
7. Identify increasing and decreasing functions, relative and absolute maximum and minimum points, concavity, and points of inflection / Weeks 33 and 34;
Chapters 3.1-3.4 and 3.7
8. Determine antiderivatives of algebraic, trigonometric, exponential and logarithmic functions / Week 35; Chapters 4.1, 4.2, 4.4
9. Apply antiderivatives to solve problems / Week 31;
Chapters 5.6, 5.7 and Appendix 3
10. Use the techniques of integration / Week 36
Chapter 4.5
11. Determine approximations of definite integrals using rectangles or trapezoids / Weeks 35, 36;
Chapters 4.3, 4.6
12. Apply knowledge of integral calculus to find the area between curves, the volume of a solid of revolution, and other practical applications / Week 19;
Chapters 6.1-6.2
13. Apply the concepts involving sequences and series of real numbers and convergence / Weeks 22 – 24
Chapters 8.1 – 8.10
14. Determine solutions to elementary differential equations / Week 31;
Chapter 5.7