# AP Calculus AB/BC Primer

Intimidated by your upcoming AP Calculus (AB or BC) class? Let AJ Tutoring’s summer calculus primer build skills and confidence before it starts!

Locations: Online, Burlingame, Danville, Lafayette, Los Altos,  Los Gatos, Menlo Park, Mountain View, Palo Alto, San Carlos, San Jose, San Mateo, Saratoga, Woodside.

Cost: \$120/hr

Recommended hours: 9-12

Goals:

• Prepare students to succeed in their upcoming calculus courses
• Introduce the fundamental concepts of calculus
• Instill an understanding of calculus’s relevance to real-world applications

## Course Description:

This class is designed to get students ready to ace their upcoming calculus courses. It focuses on limits (including limits at a point, limits at infinity, limit properties, and more advanced applications); continuity (including open/closed intervals, polynomials and rational functions); and basic differentiation (including differentiation at a point, graphical interpretations of derivatives, differentiation on intervals, and properties of the derivative).

We will also emphasize the real-world applications of calculus, which are sometimes ignored in a fast-paced AP class. This course will introduce initially intimidating calculus ideas at a comfortable personalized pace.

## AP Calculus AB/BC Primer Topics:

We will select and teach the topics that will best match your student’s level and interest and build a personally tailored curriculum from these sample lessons.

#### Limits & Continuity

Convergence, examination of graphical/computational limits, Intermediate Value Theorem

#### Differentiability

Limit definition of a derivative, notation, derivative properties, instantaneous vs. average rates of change, tangent vs. secant lines

#### Differentiation Rules

Power rule, exponential functions, product/quotient rules, trig functions, L’Hopital’s Rule, chain rule, implicit differentiation

#### Derivative Theorems & Applications

Maxima/minima, Extreme Value Theorem, Fermat’s Theorem, Mean Value Theorem, particle motion, curve-sketching, optimization

#### Integration

Areas under a curve, definite integrals, Fundamental Theorem of Calculus, antiderivatives, indefinite integrals

#### Integration Applications

More particle motion! Area between curves, volumes, arclengths

## Make the Most of the Summer!

Students who stay actively engaged in the learning process during the summer perform better during the school year.