AP Curriculum

AP Calculus AB Tutors Online


AP Calculus AB course is devoted to topics in differential and integral calculus. The AP course covers topics in these areas, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. This course teaches students concepts and problems when they are represented graphically, numerically, analytically and verbally, and to make connections amongst these representations. Review the course content in the next tab List of Topics.

Each student is assigned to an expert AP Calculus AB tutor to help them achieve success during their AP Calc AB course and master a high level of math at the college level. This course is a blend of one-on-one AP Calculus AB help with a designated tutor, and self-guided study. Students have up to two live sessions per week with their assigned AP Calc AB tutor at an agreed upon time that works best for the student. Between the live sessions, students seek AP Calculus AB help via lectures, online resources, AP Calc practice tests, and more. When students are on their own, they’ll be tasked with computer-based activities and assignments to help to reinforce concepts taught during the AP Calculus AB course. Students and parents can keep an eye on the student’s progress and access graded assessments online, which include chapter quiz, midterm exams, and a cumulative final.

  1. Functions and Graphs
    1. What is a Function?
    2. Graphs of Functions
    3. Domain, Range, and Zeros
    4. What is a Function?
  2. Basic Functions and Transformations
    1. Addition – Shifting functions up and left
    2. Subtraction – Shifting functions down or right
    3. Multiplication – Stretching or compressing functions
  3. Linear Functions and Mathematical Modeling
    1. Write the point-slope equation
    2. Mathematical models - regressions
  4. Exponential Functions
    1. Growth and decay functions
    2. Fitting an exponential model to data
    3. Modeling radioactive decay
  5. Compound Interest and the Number
    1. Compounding interest formula
    2. Continuous compounding formula
  6. Inverse Functions
    1. Horizontal and vertical Line tests
    2. One-To-One functions
  7. Logarithms
    1. Logarithmic functions
    2. Domain and range of logarithmic functions
    3. Properties of logarithms
    4. Changing the base for logarithmic functions
  8. Combining Functions: Polynomial and Rational Functions
    1. Evaluating functions/writing formulas for functions
    2. Polynomial functions/domain, range, zeros
    3. Graphing polynomial functions/odd and even functions
  9. Composition of Functions
    1. Composites – Inner/outer functions
    2. Composition of inverse functions
  10. Trigonometric Functions
    1. Graphs of sine/cosine, period, amplitude, shifts
    2. Unit circle and special triangles
    3. Tangent, cotangent, secant, cosecant (as ratios)
    4. Trigonometric identities
  • Chapter 1 – Limits and Continuity
  • Chapter 2 – The Derivative
  • Chapter 3 – Derivatives of Trigonometric Functions and Other Rules
  • Chapter 4 – Implicit Differentiation and Other Differentiation Rules
  • Chapter 5 – Graphs of Functions and Their Derivatives
  • Chapter 6 – Applications of the Derivative
  • Chapter 7 – The Integral
  • Chapter 8 – Methods of Integration
  • Chapter 9 – First Order Differential Equations
  • Chapter 10 – Applications of the Definite Integral

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