* * * Updated for 20202021 school year * * *
Course Syllabus and Standards
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Gateway Exams 




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Course Schedules 




Gateway Exams 




Note: Topics that are BConly are highlighted in yellow.
Summer Homework 
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Sol 




Summer Homework (Letter and Instructions) 






Prerequisite Content (Problems and Solutions) 






Precalculus Review (Problems and Solutions) 






Chapter 1: Limits and Their Properties 
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§1.2 Finding Limits Graphically and Numerically 






§1.3 Evaluating Limits Analytically 






§1.4 Continuity and OneSided Limits 






§1.5 Infinite Limits 






§1.6 Limits at Infinity 






Chapter 2: Differentiation 
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§2.1 The Derivative and the Tangent Line Problem 






§2.2 Basic Differentiation Rules and Rates of Change 






§2.3 Product and Quotient Rules and HigherOrder Derivatives 






§2.4a The Chain Rule 






§2.4b The Chain Rule 






§2.5 Implicit Differentiation 






§2.6 Derivatives of Inverse Functions 






§2.7 Related Rates 






Chapter 3: Applications of Differentiation 
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§3.1 Extrema on an Interval 






§3.2 Rolle's Theorem and the Mean Value Theorem 






§3.3a Increasing and Decreasing Functions 






§3.3b The First Derivative Test 






§3.4a Concavity 






§3.4b The Second Derivative Test 






§3.5 A Summary of Curve Sketching 






§3.6 Optimization Problems 






Chapter 4: Integration 
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§4.1 Antiderivatives and Indefinite Integration 






§4.3a Riemann Sums and Trapezoidal Approximations 






§4.3b Properties of Definite Integrals 






§4.4a The First Fundamental Theorem of Calculus 






§4.4b The Second Fundamental Theorem of Calculus 






§4.4c The Net Change Theorem 






§4.5 Integration by Substitution 






§4.6 The Natural Logarithmic Function: Integration 






§4.7 Inverse Trigonometric Functions: Integration 






Chapter 5: Differential Equations 
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§5.1a Slope Fields 






§5.1b Euler's Method 






§5.3 Separation of Variables 






§5.4 The Logistic Equation 






Chapter 6: Applications of Integration 
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§6.1 Area of a Region Between Two Curves 






§6.2a Volume: The Disk and Washer Methods 






§6.2b Volume: Solids with Known Cross Sections 






§6.4 Arc Length 






Chapter 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals 
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§7.1 Basic Integration Rules 






§7.2 Integration by Parts 






§7.5 Partial Fractions 






§7.7 Indeterminate Forms and L'Hôpital's Rule 






§7.8 Improper Integrals 






Chapter 8: Taylor Polynomials and Infinite Series 
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§8.1 Review of Sequences and Series 






§8.2 An Introduction to Taylor Polynomials 






§8.3 A Systematic Approach to Taylor Polynomials 






§8.4 Lagrange Remainder 






§8.6 Power Series and the Ratio Test 






§8.7a The Integral Test and pSeries 






§8.7b The Direct and Limit Comparison Tests 






§8.8a Alternating Series 






§8.8b VaryingSign Series 






§8.10a Taylor Series 






§8.10b Manipulation of Known Taylor Series 






Chapter Text and Solutions by B. Goldstein 






Chapter 9a: Polar Coordinates 
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§9.4a Polar Coordinates and Polar Graphs 






§9.4b Polar Coordinates and Differentiation 






§9.5 Area in Polar Coordinates 






Chapter 9b: Parametric Equations and Vectors 
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§9.2 Plane Curves and Parametric Equations 






§9.3 Parametric Equations and Calculus 






§9.7 VectorValued Functions 






§9.8 Velocity and Acceleration 






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