• Introductory Material (123 kb pdf file) - Properities of real numbers, inequalities, intervals, infinity, absolute value, distance/midpoint/slope formula, intercepts, symmetry
• Functions ( kb pdf file) - definitions, examples of domian/range, function notation, odd/even/periodic and composite functions, algebraic functions, transcendental functions, special functions
• Formulas (57.5 kb pdf file) - Areas, volumes and lateral surface areas of triangles, parallelograms, trapezoids, ellipses, circles, sectors, rings, cylinders, cones, spheres amd wedges.
• Trigonometry Formulas -Formulas and Identities
• Algebra Rules - Operations, radicals, exponents,factors, binomial theorem, logs and natural logs

Quizzes/Assignments/Labs

• Domain and Range Assignment (51 kb pdf file) - determining domain/range by graphing functions, reading graphs to determine domain/range, determining equations of functions given domain/range, Answer Key
• Functions Assignment (53 kb pdf file) - evaluating f(x), finding sums/products of f and g, composite functions, using graphs to explore concept of "close to"
• Functions Assignment 2 ( kb pdf file) - evaluating f(x), g(x) and composite function from a graph
• Lab #1 - Functions and Graphs ( kb pdf file) - with permission from author Gabriela R. Sanchis - Elizabethtown College
  • Short form Answer key
• Factoring Review - summary, various types of questions, Answer Key
• Transformations - quadratic a, quadratic b, cubic a, cubic b, algebriac a, algebriac b, log a, log b, trig a, trig b , Answer Key

• Function Limit Exam Example (59.6 kb pdf file)
• Function Limit Exam Example Answer Key (77.2 kb pdf file)

• Limits (html format)- tangent problem, formal definition, informal definition, animation
• Limits (977 kb pdf file)-- tangent problem, formal definition, informal definition

• Limits of a Function (45.9 kb pdf file)
• Limits of a Trig Function (40.7 kb pdf file), Answer key
• Limits at Infinity, Answer key
• Lab #2 - An Introduction to Limits (153 kb pdf file) - with permission from author Gabriela R. Sanchis - Elizabethtown College
  • Short form Answer key
• Lab #4 - Average and Instantaneous Velocity (152kb pdf file) - with permission from author Gabriela R. Sanchis - Elizabethtown College
  • Short form Answer key
• Application of Limits

• Limits Exam (65.8kb pdf file)
• Limits Exam Answer Key (html format)
• Limits Exam Answer Key ( 73.3kb pdf file)

• The Laws of Derivatives - the laws are provided, the development is shown, and examples are given
• Implicit Differentiation
• Formulas (41.9 kb pdf file)
• Matching the graph of a slope formula to the original function

• Introduction to Derivatives - determining the slope formula using the formal definition and sketching the graph of the slope formula (58 kb pdf file)
• Basic Differentiation Rules - best used with symbolic manipultor "Derive" or TI-93 calculator (1600 kb pdf file)
• Basic Differentiation (636 kb pdf file), Answer Key (748 kb pdf file)
• Derivative Worksheet Basic (436 kb pdf file), Answer Key (716 kb pdf file)
• Derivative Worksheet One (444 kb pdf file), Answer Key (724 kb pdf file) NEW
• Derivative Worksheet Two (700 kb pdf file), Answer Key (1 - 30) (532 kb pdf file), Answer Key (31 - 60) (500 kb pdf file) NEW
• Derivative Rules Quiz (6.7 kb pdf file), Answer Key (41.9 kb pdf file)
• Derivatives of Trig Functions (92 kb pdf file), Answer key (244 kb pdf file)
• Extra Derivative Questions (all categories) ( html file)
• Graphs of first and second derivatives given an orginal equation or determining the original and first equation given the graph of the second derivative. Answer key
• Higher Order Derivatives (392 kb pdf file), Answer Key (484 kb pdf file)
• Implicit Differentiation (244 kb pdf file), Answer Key (524 kb pdf file)

• Derivative Exam (47.6 kb pdf file), Answer Key (55.4 kb pdf file)
• Derivative Exam (Basic, Chain, Product, Quotient) (80 kb pdf file), Answer key (112 kb pdf file)
• High Implicit Curve Exam (50.2 kb pdf file), Answer Key (79 kb pdf file)
• Higher Order, Implicit Differentiation, Application (40 kb pdf file), Answer Key (56 kb pdf file)

Related Rates

Reference Material

• Related Rates - categories of problems are defined and a series of problems with solutions are provided

• Problem Defined	GIF File	Mov File	Problem Defined	GIF File	Mov File
  Airplane			Baseball
  Conical tank			Ellipse
  Ladder			Oil
  Paint			Sand Pile
  Search Light			Shadow
  Snow Ball			Tank

Quizzes/Assignments/Labs

• Instantaneous Rate of Change
• Applications of 1st and 2nd Derivatives - critical values, points of inflection, max/min
• Related Rate Problems, Answer Key
• Related Rate Problems 2, Answer Key
• Related Rate Problems 3

Exams

• Combined exam - Curve Sketching, Related Rates, Optimization Problems (114 kb pdf file), Answer Key - Part 1( 308 kb pdf file) and part 2 (80 kb pdf file)

Curve Sketching

Reference Material

• Curve Sketching - Concepts of intercetps, symmetry, domain and range, continuity, vertical and horizontal asymptotes, differentiability, increasing and decreasing functions, maximum and minimum values, concavity, points of inflecton, and examples of polynomial, rational, radical and trig function

Quizzes/Assignments/Labs

Exams

• Combined exam - Curve Sketching, Related Rates, Optimization Problems (114 kb pdf file), Answer Key - Part 1( 308 kb pdf file) and part 2 (80 kb pdf file)

Optimization Problems

Reference Material

• Optimization Problems - derivative tests, rules for solving problems, and a series of problems involving maximum and minimum values

• Problem Defined	Gif File	Mov File	Problem Defined	Gif File	Mov File
  Max Volume Cardboard Box			Max Volume of a Cone
  Minimize Distance between a Curve and a Point			Max Area of an Enclosure
  Maximum Volume Inscribed Cylinder			Max Area of an Inscribed Rectangle under a Curve.
  Max Area of an Inscribed Rectangle in an Isoceles Triangle.			Max Area of Printable Surface
  Walk and Row shortest possible Time			Max Viewing Angle
  Max Enclosed Area

Quizzes/Assignments/Labs

• Optimization Problems (148 kb pdf file), Answer Key (1000 kb pdf file)

Exams

• Combined exam - Curve Sketching, Related Rates, Optimization Problems (114 kb pdf file), Answer Key - Part 1( 308 kb pdf file) and part 2 (80 kb pdf file)

Definite Integral

Reference Material

• Definite Integral - Reimann Sums, rules for definite integrals, Fundamental Theorem of Calculus, evaluating integrals, Mean Value Theorem

Quizzes/Assignments/Labs

• Definite Integrals (296 kb pdf file), Answer Key ( 304kb pdf file)

Exams

Integration

Reference Material

• Integration Formula Sheet (520 kb pdf file)
• Basic Integration
• Integration by Substitution
• Integration By Parts
  • By Parts Hints (216 kb pdf file)
• Integration using Partial Fractions

Quizzes/Assignments/Labs

• Integration Basic (408 kb pdf file), Answer Key (432 kb pdf file)
• Integration - Regular and Substitution (410 kb pdf file), Answer Key (620 kb pdf file)
• Extra Practice Basic Integration and Substitution (380 kb pdf file), Answer Key (572 kb pdf file)
• Integration By Parts (556 kb pdf file),
  • Questions 1 - 6 Answer Key (160 kb pdf file), Questions 7 - 12 Answer Key (168 kb pdf file),
  • Questions 13 - 18 Answer Key (160 kb pdf file), Questions 19 - 26 Answer Key (220 kb pdf file),
  • Questions 27 - 32 Answer Key (156 kb pdf file)
• Integration - Partial Fractions (336 kb pdf file), Answer Key (336 kb pdf file)

Exams

• Exam - Basic Integration, Related Rates amd Max Min Problems (563 kb pdf file), Answer Key (2200 kb pdf file)
• Integration - Basic, Substitution, Parts. Partial fractions, Definite (256 kb pdf file), Answer Key (992 kb pdf file)

Exams

Applications of Integration

Reference Material

• Disk Method		Wire		Slice		Washer Region		Shell Region
  f(x) = x^2		Pyramid		Pyramid		x = 0, y = x, y = (x - 1)^2 + 1		y = 0, x = 0, y = 1, y = x^2 + 1
  f(x) = sqrtx		Semicircular		Semicircular		y = 1, y = (x - 1)^2 + 1, x = 1		y = 0, y = sinx, x = 0, x = pi
  f(x) = sinx		Square Cross		Square Cross		y = (x - 1)^2, y = 1, x = 1		y = 0, y = -12+8x-x^2, x = 2, x = 6
  Polynomial		Equilateral Cross		Equilateral Cross		y = 1,x = 0, y = x^2		y = 0, x = 0, y = -2x+3
  f(x) = x^2sinx		Isosceles Cross		Isosceles Cross		x = y^2, y = x^2		y = =, y = sinx, x = pi/2. x = pi
  						y = sinx, y = 0		y = sqrtx, y = x^2
  						x = 0, y = 0, x = 1, y = x^2 + 1		y = 1/2 x, y = (x - 1)^2
  						x = y^2, y = x^2

Quizzes/Assignments/Labs

• Area between the Curves (36kb pdf file), Answer key (356kb pdf file)

Exams

Review

Final Exam Review,(80kb pdf file), Answer key (108kb pdf file)