Welcome to On Ramps College Algebra

  • Here is the page for AP Calculus students. Students enrolled in AP courses will have the opportunity to earn credit for high school while being exposed to the rigors of a college level course. AP students have the opportunity to earn credit for college by taking and passing the AP exam for the course. AP Calculus requires thourough understanding of several of the major topics that are covered in Algebra classes. However, this course goes deeper into the content than previous classes did and (most significantly) strictly limits the use of a graphing calculator. AB and BC Calculus are very similar in their scope, however, BC covers content (mostly related to Precalculus) that AB students will not be exposed to. 

    College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses in 38 subjects, each culminating in a challenging exam, students learn to think critically, construct solid arguments, and see many sides of an issue—skills that prepare them for college and beyond. Taking AP courses demonstrates to college admission officers that students have sought the most challenging curriculum available to them, and research indicates that students who score a 3 or higher on an AP Exam typically experience greater academic success in college and are more likely to earn a college degree than non-AP students. Each AP teacher’s syllabus is evaluated and approved by faculty from some of the nation’s leading colleges and universities, and AP Exams are developed and scored by college faculty and experienced AP teachers. Most four-year colleges and universities in the United States grant credit, advanced placement, or both on the basis of successful AP Exam scores—more than 3,300 institutions worldwide annually receive AP scores.
     
    Enrolling Students:
     
    Equity and Access College Board strongly encourages educators to make equitable access a guiding principle for their AP programs by giving all willing and academically prepared students the opportunity to participate in AP. We encourage the elimination of barriers that restrict access to AP for students from ethnic, racial, and socioeconomic groups that have been traditionally underserved. College Board also believes that all students should have access to academically challenging coursework before they enroll in AP classes, which can prepare them for AP success. It is only through a commitment to equitable preparation and access that true equity and excellence can be achieved.
     
    Topics Covered in AP Calculus:
     
    Limits & Continuity
    Instantaneous Rates of Change
    Understanding Limits Graphically & Numerically
    Properties of limits
    Finding Limits Analytically
    Limits of Transcendental Functions
    Limits & Continuity
    Infinite Limits & Limits at Infinity
    Intermediate Value Theorem
     
    Differentiation & Basic Derivative Rules
    Rates of Change & Tangent Lines
    Tangent Lines and the Derivative
    Understanding the Derivative
    Differentiability & Continuity
    Basic Derivative Rules
    The Product & Quotient Rules
    Velocity and Other Rates of Change
     
    Derivatives of Composite, Implicit and Inverse Functions
    The Chain Rule
    Symbolic Differentiation
    Implicit Differentiation
    Inverse Derivatives
    Derivatives of Inverse Trig Functions
     
    Contextual Applications of Derivatives
    Interpretations of the Derivative
    Straight Line Motion
    Other Rates of Change
    Related Rates
    Linear Approximations
    L'Hopital's Rule
     
    Analytical Applications of Differentiation
    Mean Value Theorem
    Extrema on an Interval
    First & Second Derivative Test
    Curve Sketching
    Optimization
     
    Integration
    Riemann Sums
    Summation Notation
    Accumulation Functions
    Properties of Definite Integrals
    Antiderivatives and Indefinite Integrals
    Fundamental Theorem of Calculus
    U-Substitution
    Integration of Transcendental Functions
    Integration by Parts - BC ONLY
    Partial Fractions - BC ONLY
    Improper Integrals - BC ONLY
     
    Differential Equations
    Slope Fields
    Separation of Variables
    Growth & Decay
    Euler's Method - BC ONLY
    Logistic Growth - BC ONLY
     
    Applications of Integration
    Average Value for Integrals
    Particle Motion
    Accumulation Functions in Context
    Area Between Curves
    Volumes by Cross Section
    Volumes by Disk & Washer Method
    Volumes of Curves Around Other Axes
    Arc Length of a Plane Curve - BC ONLY
     
    Parametrics, Polars & Vectors - ALL BC ONLY
    Parametric Equations
    Vector Valued Functions
    Velocity & Acceleration of Vector Functions
    Polar Coordinates & Graphs
    Area & Arc Length in Polar Coordinates
     
    Infinite Series & Sequences - ALL BC ONLY
    Series & Convergence
    Integral Test & P-Series
    Comparison of Series
    Alternating Series
    Ratio & Root Tests
    Taylor & Maclaurin Polynomials
    Lagrange Error Bound
    Power Series
    Taylor & Maclaurin Series