Relative Rate of Change & Elasticity of Demand Practice Exam Solutions

Business Calculus 1

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Functions & Graphs — Topic Review (⏱️ <96 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Functions (p. 3-5) (13:48)
Finding The Domain of a Function (p. 6) (6:03)
Graphs (p. 7-9) (9:54)
Graphing with a Calculator (p. 10) (6:21)
Average Rate of Change and Secant Line (p. 11) (2:54)
The Difference Quotient (p. 12) (6:23)
Thinking of Old Things in New Ways (p. 13-14) (9:17)
Important Types of (Parent) Functions (p. 15-16) (11:47)
Piecewise Functions (p. 17) (7:50)
Transforming a Function (p. 18-21) (20:51)

Functions & Graphs — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Quick Overview of Functions Practice Exam Solutions (5:16)
Finding The Domain of a Function Practice Exam Solutions (14:09)
Average Rate of Change and Secant Lines Practice Exam Solutions (9:10)
The Difference Quotient Practice Exam Solutions (24:38)
Graphs Practice Exam Solutions (8:27)
Piecewise Functions Practice Exam Solutions (12:40)
Transforming a Function Practice Exam Solutions (34:13)

Linear & Quadratic Functions — Topic Review (⏱️ <45 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Linear Functions (p. 3-4) (6:12)
Word Problems and Modeling with Linear Functions (p. 5) (5:21)
Quick Overview of Quadratic Functions (p. 6-8) (11:52)
Properties of Quadratics (p. 9-10) (5:43)
Graphing a Quadratic Using Its Vertex, Axis of Symmetry, and Intercepts (p. 11) (9:36)
Maximum/Minimum Value of a Quadratic (p. 12) (6:06)

Linear & Quadratic Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Overview of Linear Functions Practice Exam Solutions (6:31)
Word Problems with Linear Functions Practice Exam Solutions (10:27)
Overview of Quadratic Functions Practice Exam Solutions (10:36)
Graphing Quadratics Practice Exam Solutions (23:15)
Finding Maxima and Minima of Quadratic Functions Practice Exam Solutions (10:16)

Polynomial & Rational Functions — Topic Review (⏱️ <104 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Polynomial Functions (p. 3-4) (5:08)
End Behavior (p. 5) (5:19)
Graphing Using Zeros and Multiplicities (p. 6-7) (19:01)
Quick Overview of Rational Functions and Domain (p. 8) (4:38)
Vertical Asymptotes of Rational Functions (p. 9) (3:09)
Horizontal and Oblique Asymptotes of Rational Functions (p. 10-13) (19:50)
Holes of Rational Functions (p. 14) (2:27)
Graphing Rational Functions (p. 15-17) (23:17)
Applications with Rational Functions (p. 18) (5:24)
Inequalities with Rational Functions and Polynomials (p. 19-20) (14:49)

Polynomial & Rational Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Graphing Using Zeros and Multiplicities Practice Exam Solutions (23:12)
Graphing and Analyzing Rational Functions Practice Exam Solutions (8:31)
Inequalities with Rational Functions and Polynomials Practice Exam Solutions (14:44)

Exponential & Logarithmic Functions — Topic Review (⏱️ <151 min)

Study Guide (fill this in as you watch the videos!)
Exponential Functions (p. 3-5) (14:31)
The Number e (p. 6) (2:06)
Solving Exponential Equations (p. 7-8) (6:36)
Composite Functions (p. 9-10) (8:19)
One-to-One Functions and Inverses (p. 11-12) (8:53)
Log Functions (p. 13-14) (13:07)
Log Rules (p. 15-18) (15:49)
Solving Equations with Logs (p. 19-21) (16:22)
Solving Equations with Exponentials (p. 22-23) (11:52)
Summary of Log and Exponent Rules (p. 24) (3:53)
Finance Applications - Overview (p. 25-27) (15:31)
Effective Rate of Interest (p. 28) (6:20)
Present Value (p. 29) (5:40)
Exponential Growth and Decay (p. 30-32) (21:10)

Exponential & Logarithmic Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Solving Exponential Equations Practice Exam Solutions (7:16)
Log Rules Practice Exam Solutions (10:58)
Solving Equations with Logs Practice Exam Solutions (22:49)
Finance Applications Practice Exam Solutions (6:54)
Exponential Growth and Decay Practice Exam Solutions (7:10)

Limits & Continuity — Topic Review (⏱️ <103 min)

Study Guide (fill this in as you watch the videos!)
Limits - Overview (p. 3-6) (11:20)
Evaluating Limits - Overview (p. 7) (3:16)
Indeterminate Forms (p. 8) (2:42)
Evaluating Limits Algebraically - Piecewise Functions (p. 9) (5:26)
Evaluating Limits Algebraically - 0/0 Form (p. 10-13) (21:28)
Evaluating Infinite Limits - Number/0 Form (p. 14) (5:56)
Limits at Infinity and Horizontal Asymptotes (p. 15-21) (22:09)
Continuity (p. 22-24) (8:58)
Discontinuity (p. 25-28) (21:22)

Limits & Continuity — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Evaluating Limits from a Graph Practice Exam Solutions (4:30)
Evaluating Limits Algebraically Practice Exam Solutions (27:51)
Continuity Practice Exam Solutions (13:00)
Limits at Infinity Practice Exam Solutions (18:38)

The Definition of the Derivative & Basic Derivative Rules — Topic Review (⏱️ <83 min)

Study Guide (fill this in as you watch the videos!)
The Definition of the Derivative (p. 3-5) (21:39)
The Derivative as a Function (p. 6-7) (8:49)
Differentiability (p. 8-9) (10:55)
Power Rule & Derivatives of Polynomials (p. 10-12) (11:09)
Differentials & Error Measurement (p. 13-15) (11:37)
Marginal Analysis in Business & Economics (p. 16-19) (18:25)

The Definition of the Derivative & Basic Derivative Rules — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
The Definition of the Derivative Practice Exam Solutions (16:38)
The Derivative as a Function Practice Exam Solutions (14:15)
Differentiability Practice Exam Solutions (16:46)
Differentials Practice Exam Solutions (5:25)
Marginal Analysis Practice Exam Solutions (11:45)

Compound Interest & More Derivative Rules — Topic Review (⏱️ <39 min)

Study Guide (fill this in as you watch the videos!)
Compound Interest (p. 3) (3:34)
Derivatives of Exponential & Logarithmic Functions (p. 4) (3:13)
Product and Quotient Rules (p. 5-6) (12:35)
Finding Tangent and Normal Lines (p. 7-8) (7:31)
Horizontal and Vertical Tangent Lines (p. 9) (3:26)
The Chain Rule (p. 10-11) (8:14)

Compound Interest & More Derivative Rules — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Derivative Rules Practice Exam Solutions (6:05)
Product & Quotient Rules Practice Exam Solutions (16:47)
The Chain Rule Practice Exam Solutions (6:03)
Rate of Change Applications Practice Exam Solutions (10:59)

Implicit Differentiation, Related Rates, & Elasticity of Demand — Topic Review (⏱️ < min)

Study Guide (fill this in as you watch the videos!)
Implicit Differentiation (p. 3-4) (11:13)
Related Rates - Overview (p. 5-6) (8:11)
Related Rates - Harder Solved Examples (p. 7-8) (17:23)
Relative Rate of Change & Elasticity of Demand (p. 9-11) (10:32)

Implicit Differentiation, Related Rates, & Elasticity of Demand — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Implicit Differentiation Practice Exam Solutions (12:34)
Related Rates Practice Exam Solutions (14:23)
Relative Rate of Change & Elasticity of Demand Practice Exam Solutions (15:23)

First & Second Derivatives, Graphs, and Absolute Maxima & Minima — Topic Review (⏱️ <75 min

Study Guide (fill this in as you watch the videos!)
Maximum and Minimum Values - Overview (p. 3) (5:52)
Critical Numbers and the First Derivative Test (p. 4-7) (20:21)
Inflection Points and Concavity (p. 8-9) (10:26)
The Second Derivative Test (for Local Extrema) (p. 10-11) (6:16)
Graphing & Curve Sketching (p. 12-15) (22:47)
Finding Absolute Extrema (p. 16-17) (9:21)

First & Second Derivatives, Graphs, and Absolute Maxima & Minima — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Critical Numbers and Increasing/Decreasing Behavior Practice Exam Solutions (8:22)
Absolute Extrema Practice Exam Solutions (5:15)
Relative Extrema with the First Derivative Test Practice Exam Solutions (6:17)
Concavity Practice Exam Solutions (8:48)
The Second Derivative Test Practice Exam Solutions (8:16)
Graphing Practice Exam Solutions (15:51)

Optimization — Topic Review (⏱️ <21 min)

Study Guide (fill this in as you watch the videos!)
Optimization (p. 3-5) (20:24)

Optimization — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Optimization Practice Exam Solutions (70:49)

L'Hôpital's Rule — Topic Review (⏱️ <25 min)

Study Guide (fill this in as you watch the videos!)
Indeterminate Forms and L'Hôpital's Rule (p. 3-5) (15:02)
Growth Rates (How to Skip L'Hôpital's Rule) (p. 6) (4:51)
How to Do Nasty Limits and Skip the Algebra (p. 7) (4:10)

L'Hôpital's Rule — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
L’Hôpital’s Rule Practice Exam Solutions (13:01)

Antiderivatives & Indefinite Integrals — Topic Review (⏱️ <22 min)

Study Guide (fill this in as you watch the videos!)
Antiderivatives & Indefinite Integrals (p. 3-6) (10:05)
Initial Value Problems & Fixed Cost (p. 7-8) (11:45)

Antiderivatives & Indefinite Integrals — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Initial Value Problems Practice Exam Solutions (7:11)
Basic Antiderivatives/Indefinite Integrals Practice Exam Solutions (2:15)
Harder Antiderivatives/Indefinite Integrals Practice Exam Solutions (5:34)

Definite Integrals & The Fundamental Theorem of Calculus — Topic Review (⏱️ <45 min)

Study Guide (fill this in as you watch the videos!)
Approximating Area Under the Curve (p. 3-5) (12:03)
The Definite Integral (p. 6-9) (17:09)
Evaluating Definite Integrals Using Geometry (p. 10-12) (11:07)
The Average Value of a Function (p. 13) (4:32)

Definite Integrals & The Fundamental Theorem of Calculus — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Approximating Area Under the Curve Practice Exam Solutions (7:46)
Properties of Definite Integrals Practice Exam Solutions (7:37)
Evaluating Definite Integrals Using Geometry Practice Exam Solutions (4:35)
The Average Value of a Function Practice Exam Solutions (2:40)

Substitution — Topic Review (⏱️ <35 min)

Study Guide (fill this in as you watch the videos!)
Substitution (p. 3-5) (11:48)
My F-ing Variable Didn't Cancel (p. 6) (4:23)
Substitution with Definite Integrals (p. 7-8) (7:48)
Substitution vs Basic Integration (p. 9-10) (10:54)

Substitution — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Substitution Practice Exam Solutions (13:06)
Substitution with Definite Integrals Practice Exam Solutions (6:31)
Mixed Integration Practice (Substitution vs Basic Integral Rules) Practice Exam Solutions (13:19)

Area Between Curves & Integral Applications — Topic Review (⏱️ <75 min)

Study Guide (fill this in as you watch the videos!)
Area Between Curves (p. 3-4) (9:58)
Consumers' & Producers' Surplus (p. 5-9) (21:26)
Continuous Income Streams (p. 10-13) (15:08)
Annuities (p. 14-15) (10:32)
Probability (p. 16-19) (17:42)

Area Between Curves & Integral Applications — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Area Between Curves Practice Exam Solutions (14:51)
Consumers' & Producers' Surplus Practice Exam Solutions (22:46)
Continuous Income Streams Practice Exam Solutions (21:54)
Annuities Practice Exam Solutions (9:21)
Probability Practice Exam Solutions (7:33)

[OPTIONAL] Sh*t You Forgot from Algebra 1

Study Guide (fill this in as you watch the videos!)
Algebraic Expressions (p. 3) (5:43)
Exponent Rules (p. 4-5) (8:08)
Square Roots (p. 6) (2:45)
Monomials and Polynomials (p. 7-8) (5:57)
Special Products and Factoring (p. 9-12) (19:55)
Lines (Quick Overview) (p. 13) (4:04)
Finding Equations and Graphing Lines (p. 14-17) (13:45)
General Form of a Line (p. 18) (3:06)
Vertical and Horizontal Lines (p. 19) (2:19)
Parallel and Perpendicular Lines (p. 20) (5:09)
Basics of Graphing - Plotting Points to Graph an Equation (p. 21-22) (5:40)
Basics of Graphing - Finding Intercepts from a Graph (p. 23) (1:33)
Basics of Graphing - Finding Intercepts from an Equation (p. 24) (4:13)
Solving Equations with Absolute Value (p. 25) (5:33)
Number Lines and Inequalities (p. 26) (5:05)
Solving Inequalities and Writing Intervals (p. 27-29) (12:44)
Solving Inequalities with Absolute Value (p. 30-31) (14:22)
Completing the Square (p. 32-35) (9:58)
Solving Quadratics by Factoring (p. 36) (5:35)
Solving Quadratics by Using Square Roots (p. 37) (2:39)
Solving Quadratics by Completing the Square (p. 38) (8:43)
Solving Quadratics by Using the Quadratic Formula (p. 39) (5:38)
Sets (p. 40-41) (8:47)

[OPTIONAL] Sh*t You Forgot from Algebra 2

Study Guide (fill this in as you watch the videos!)
Parent Graphs You Should Memorize (p. 3) (2:09)
Graphing Common Equations (p. 4) (2:36)
Symmetry of Graphs (p. 5) (8:22)
Solving Equations by Factoring (p. 6-7) (11:20)
Long Division with Numbers and Polynomials (p. 8-10) (14:18)
Synthetic Division (p. 11-13) (7:39)
Multiplying and Dividing Fractions (Rational Expressions) (p. 14-16) (10:16)
Adding and Subtracting Fractions (Rational Expressions) (p. 17-18) (16:24)
Simplifying Complex Fractions (Rational Expressions) (p. 19-20) (6:29)
Solving Systems of Linear Equations (p. 21-22) (10:04)
General Tips for Solving Word Problems (p. 23) (5:25)
Some Perfect Roots You Should Memorize (p. 25) (5:00)
Simple Interest Word Problems (p. 24) (3:47)
Radical Rules (p. 26) (4:28)
Combining Like Terms with Radicals (p. 27) (3:26)
Rationalizing a Denominator (p. 28) (5:43)
Fractional (Rational) Exponents (p. 29-31) (18:53)
Operations with Complex Numbers (p. 32-34) (11:41)
Patterns in the Powers of i (p. 35) (4:31)
Solving Quadratic Equations that Have Complex Solutions (p. 36) (8:19)

[OPTIONAL] Sh*t You Forgot from Geometry

Study Guide (fill this in as you watch the videos!)
The Pythagorean Theorem (p. 3) (5:10)
Common Geometry Formulas (p. 4-5) (3:19)
Congruent Triangles (p. 6-7) (4:08)
Similar Triangles (p. 8-10) (8:34)
Distance Formula (p. 11) (7:59)
Midpoint Formula (p. 12) (5:26)
Graphing Circles (p. 13-14) (7:32)
General Form of a Circle (p. 15-16) (11:09)

Relative Rate of Change & Elasticity of Demand Practice Exam Solutions

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