Embark on an 8-hour journey through essential mathematical concepts in this comprehensive tutorial series designed to prepare learners for calculus. Master a wide range of topics, including prime factorization, fractions, order of operations, interest calculations, sequences, decimals, combinatorics, logarithms, equations, polynomials, functions, geometry, trigonometry, and complex numbers. Progress from basic arithmetic to advanced algebraic and trigonometric concepts, solving various types of equations and word problems along the way. Gain a solid foundation in mathematical reasoning and problem-solving skills necessary for success in calculus and higher-level mathematics.
Overview
Syllabus
Prime Factorization with Factor Trees - Transitioning to Calculus.
Adding Fractions with Different Denominators - Transitioning to Calculus.
Arithmetic: Order of Operations - Transitioning to Calculus.
Simple & Compound Interest Calculations - Transitioning to Calculus.
Arithmetic Sequences - Transitioning to Calculus.
Writing a Repeating Decimal as a Fraction - Transitioning to Calculus.
Finding the Last Digit in a Power of Three - Transitioning to Calculus.
Multiplication Rule - Transitioning to Calculus.
Percentages - Transitioning to Calculus.
Counting Solutions to an Equation - Transitioning to Calculus.
Combinatorics Problem Involving Combinations - Transitioning to Calculus.
Counting Perfect Squares & Perfect Cubes - Transitioning to Calculus.
Counting Multiples - Transitioning to Calculus.
Number of trailing zeros in 1000! - Transitioning to Calculus.
Logarithms, Example 1 - Transitioning to Calculus.
Logarithms, Example 2 - Transitioning to Calculus.
Solving a Linear Equation - Transitioning to Calculus.
Solving an Exponential Equation - Transitioning to Calculus.
Solving an Equation Involving a Logarithm, Example 1 - Transitioning to Calculus.
Solving an Equation Involving a Logarithm, Example 2 - Transitioning to Calculus.
Solving an Equation Involving a Logarithm, Example 3 - Transitioning to Calculus.
Simplifying an Expression Involving a Logarithm - Transitioning to Calculus.
Using Factoring to Solve a Quadratic Equation - Transitioning to Calculus.
Completing the Square to Solve a Quadratic Equation - Transitioning to Calculus.
Solving a Quadratic Equation by the Quadratic Formula - Transitioning to Calculus.
Solving an Exponential Equation - Transitioning to Calculus.
Solving a Quadratic Inequality - Transitioning to Calculus.
Solving Two Equations in Two Unknowns - Transitioning to Calculus.
Solving an Equation Involving Logarithms - Transitioning to Calculus.
Simplification of Quotients of Polynomials (Rational Functions) - Transitioning to Calculus.
Solving an Exponential Equation - Transitioning to Calculus.
Solving Two Exponential Equations in Two Variables - Transitioning to Calculus.
Simplification of an Expression Involving a Logarithm - Transitioning to Calculus.
Solving an Exponential Equation - Transitioning to Calculus.
Word Problem: Compound Interest - Transitioning to Calculus.
Solving an Exponential Equation - Transitioning to Calculus.
Sort problem: Work Problem - Transitioning to Calculus.
Solving a Quadratic Equation - Transitioning to Calculus.
Word Problem / Material Requirements - Transitioning to Calculus.
Line Segments - Transitioning to Calculus.
Cubes / Spheres / Volumes - Transitioning to Calculus.
Area of a Circle - Transitioning to Calculus.
Triangles / Circles / Areas - Transitioning to Calculus.
Finding the Value of a Function - Transitioning to Calculus.
Computing the Cosecant - Transitioning to Calculus.
Finding the Value of the Zero of a Function - Transitioning to Calculus.
Finding the Domain of a Function - Transitioning to Calculus.
Finding the Equation of a Line through a Point Parallel to a Line - Transitioning to Calculus.
Inverse Functions - Transitioning to Calculus.
Finding an Inverse Function - Transitioning to Calculus.
Zeros of a Cubic Polynomial Function - Transitioning to Calculus.
Piecewise functions - Transitioning to Calculus.
Composition of functions - Transitioning to Calculus.
Word Problem / Circles & Squares - Transitioning to Calculus.
Relationships Between Functions: Shifting, Stretching, Shrinking - Transitioning to Calculus.
Factoring Polynomials - Transitioning to Calculus.
Graphing Equations / Quadrants - Transitioning to Calculus.
Finding the Range of a Function - Transitioning to Calculus.
Rational Functions - Transitioning to Calculus.
Polynomials functions - Transitioning to Calculus.
Interest Problem / Continuous Compounding - Transitioning to Calculus.
Finding the Equations of Asymptotes - Transitioning to Calculus.
Absolute Value Function / Composition of Functions - Transitioning to Calculus.
Equation of an Ellipse - Transitioning to Calculus.
Finding the Range of a Function - Transitioning to Calculus.
Find the Equation of a Quadratic Function Passing Through Three Points - Transitioning to Calculus.
Finding the Equation of All Points that are Equidistant Between Two Points - Calculus.
Word Problem / Maximizing Area - Transitioning to Calculus.
Functions: Composition, Range, Piecewise, One-to-One - Transitioning to Calculus.
Functions: Composition, Inverses, Domain, Rigid Transformations - Transitioning to Calculus.
Converting Radians to Degrees - Transitioning to Calculus.
Converting Degrees to Radians - Transitioning to Calculus.
Computing the Cosine - Transitioning to Calculus.
Computing the Sine - Transitioning to Calculus.
Computing the cosecant - Transitioning to Calculus.
Computing the Tangent - Transitioning to Calculus.
Computing the Secant - Transitioning to Calculus.
The Winding Function - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Computing the Amplitude of a Trigonometric Function - Transitioning to Calculus.
Computing the Range of a Trigonometric Function - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Simplifying a Trigonometric Expression - Transitioning to Calculus.
Computing the Cosine and Arctangent - Transitioning to Calculus.
Trigonometric Functions - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Range of a Trigonometric Function - Transitioning to Calculus.
Simplifying a Trigonometric Expression - Transitioning to Calculus.
Computing the Arccosine - Transitioning to Calculus.
Computing the Arctangent - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Finding a Trigonometric Function from a Graph - Transitioning to Calculus.
Computing the Cosine / Half-Angle Formulas - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Computing the Arcsine - Transitioning to Calculus.
Graphing a Trigonometric Function - Transitioning to Calculus.
Word Problem / Shadow Cast by a Building - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Proving a Trigonometric Identity - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Trigonometric Function Definitions - Transitioning to Calculus.
Solving a Trigonometric Equation - Transitioning to Calculus.
Polar Graphs - Transitioning to Calculus.
Adding Complex Numbers - Transitioning to Calculus.
Multiplying Complex Numbers - Transitioning to Calculus.
Dividing complex numbers - Transitioning to Calculus.
Finding complex zeros of a quadratic function - Transitioning to Calculus.
Finding complex zeros of a cubic function - Transitioning to Calculus.
Finding Complex Zeros of a Quartic Function - Transitioning to Calculus.
Cubic Functions and Zeros - Transitioning to Calculus.
Taught by
Lawrence Leemis
