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0. Functions(0)

Introduction to Functions
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Piecewise Functions
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Properties of Functions
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Common Functions
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Transformations
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Combining Functions
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Exponent rules
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Exponential Functions
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Logarithmic Functions
(0)

Properties of Logarithms
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Exponential & Logarithmic Equations
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Introduction to Trigonometric Functions
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Graphs of Trigonometric Functions
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Trigonometric Identities
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Inverse Trigonometric Functions
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1. Limits and Continuity(0)

Introduction to Limits
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Finding Limits Algebraically
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Continuity
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2. Intro to Derivatives(0)

Tangent Lines and Derivatives
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Derivatives as Functions
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Basic Graphing of the Derivative
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Differentiability
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3. Techniques of Differentiation(0)

Basic Rules of Differentiation
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Higher Order Derivatives
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Product and Quotient Rules
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Derivatives of Trig Functions
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The Chain Rule
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4. Applications of Derivatives(0)

Motion Analysis
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Implicit Differentiation
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Related Rates
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Linearization
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Differentials
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5. Graphical Applications of Derivatives(0)

Intro to Extrema
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Finding Global Extrema
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The First Derivative Test
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Concavity
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The Second Derivative Test
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Curve Sketching
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Applied Optimization
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6. Derivatives of Inverse, Exponential, & Logarithmic Functions(0)

Derivatives of Exponential & Logarithmic Functions
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Logarithmic Differentiation
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Derivatives of Inverse Trigonometric Functions
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7. Antiderivatives & Indefinite Integrals(0)

Antiderivatives
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Indefinite Integrals
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Integrals of Trig Functions
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Initial Value Problems
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8. Definite Integrals(0)

Estimating Area with Finite Sums
(0)

Riemann Sums
(0)

Introduction to Definite Integrals
(0)

Fundamental Theorem of Calculus
(0)

Average Value of a Function
(0)

Substitution
(0)

9. Graphical Applications of Integrals(0)

Area Between Curves
(0)

Introduction to Volume & Disk Method
(0)

10. Physics Applications of Integrals (0)

Kinematics
(0)

Work
(0)

11. Integrals of Inverse, Exponential, & Logarithmic Functions(0)

Integrals of Exponential Functions
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Integrals Involving Logarithmic Functions
(0)

Integrals Involving Inverse Trigonometric Functions
(0)

12. Techniques of Integration(0)

Integration by Parts
(0)

Partial Fractions
(0)

Improper Integrals
(0)

13. Intro to Differential Equations(0)

Basics of Differential Equations
(0)

Slope Fields
(0)

Euler's Method
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Separable Differential Equations
(0)

14. Sequences & Series(0)

Sequences
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Review of Factorials
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Series
(0)

Convergence Tests
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15. Power Series(0)

Introduction to Power Series
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Taylor Series & Taylor Polynomials
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16. Parametric Equations & Polar Coordinates(0)

Parametric Equations
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Calculus with Parametric Curves
(0)

Polar Coordinates
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Calculus in Polar Coordinates
(0)

Conic Sections
(0)

Rational Functions(0)

Asymptotes
(0)

Describing Data with Tables and Graphs(0)

Histograms
(0)

Probability(0)

Basic Concepts of Probability
(0)

Complements
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Addition Rule
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Multiplication Rule: Independent Events
(0)

Introduction to Contingency Tables
(0)

Multiplication Rule: Dependent Events
(0)

Bayes' Theorem
(0)

Fundamental Counting Principle
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Counting
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Probability

Fundamental Counting Principle

Probability

Fundamental Counting Principle: Videos & Practice Problems

Video Lessons Practice Worksheet

17 problems

Problem 1Multiple Choice

Five-digit even numbers greater than 90000 can be formed by using the digits 2, 3, 4, 5, 6, and 9. State the number of such numbers.

Problem 2Multiple Choice

If you perform binomial expansion on the expression, (3d + 2e)⁸, what is the fifth term?

Problem 3Multiple Choice

Enumerate the first three terms of the resulting expression if you are to apply binomial expansion to the following. (h - 3w)¹²

Problem 4Multiple Choice

Find the difference quotient, [f(x + h) - f(x)]/h, of the function: f(x) = x⁵ - 2

Problem 5Multiple Choice

Use the Fundamental Counting Principle to solve the following problem.

A shop sells their shirt in three different sizes (small, medium, and large), four types (polo, sleeveless, crew neck, and v-neck), and five colors (gray, blue, black, red, and pink). Determine how many ways a shirt can be bought.

Problem 6Multiple Choice

Evaluate the following expression: (₆C₄ x ₉C₁)/₁₂C₄

Problem 7Multiple Choice

Perform binomial expansion and simplify the resulting expression for the following binomial.
(x² +6y)⁴

Problem 8Multiple Choice

A restaurant offers 3 types of salads and 5 types of main courses. How many different meal combinations can a customer choose if they want one salad and one main course?

Problem 9Multiple Choice

How many different ways can 4 books be arranged on a shelf?

Problem 10Multiple Choice

In how many different ways can 3 students be chosen and arranged in a line from a class of 10 students?

Problem 11Multiple Choice

How many ways can a team of 4 be selected from a group of 10 people?

Problem 12Multiple Choice

A pizza shop offers 10 different toppings. How many different 3-topping pizzas can be made if the order of toppings does not matter?

Problem 13Multiple Choice

How many different 5-letter codes can be formed using the letters A, B, C, D, and E if each letter can be used more than once?

Problem 14Multiple Choice

A company has 6 different projects and wants to assign 3 of them to a team. How many different ways can the projects be assigned if the order of assignment matters?

Problem 15Multiple Choice

A car manufacturer offers 4 models, each available in 3 colors. How many different car options are available?

Problem 16Multiple Choice

How many different ways can 5 people be seated in a row?

Problem 17Multiple Choice

In how many different ways can 2 students be chosen and arranged in a line from a class of 8 students?