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Course Materials
Lessons
Index Notation
- Video - Power and Indices (9:27)
- Video - Introduction to Index Notation (8:43)
- Video - Index Notation and Expanded Notation (1:28)
- Video - Writing Index Notation from Wording (1:33)
- Video - Index Form (6:45)
- Video - Index Notation using Negative Bases (7:27)
- Video - Equations involving Indices (1:45)
Division using Exponents
- Video - Simplification of Exponent in Fractions (2:24)
- Video - Index Law of Subtraction (5:51)
- Video - Simplification using Index Law of Subtraction (1:54)
- Video - Mixed Simplification using Index Law of Subtraction (4:58)
- Video - Evaluation using Index Law of Subtraction (4:14)
- Video - Substraction Law of Exponents (3:26)
- Video - Division using Indices (2:45)
Negative Exponents
- Video - Writing in Negative Exponents (7:40)
- Video - Equations involving Negative Exponents (2:03)
- Video - Writing in Positive Exponents (2:28)
- Video - Expressing in Positive Exponents (4:08)
- Video - Fractions to Index Form in Positive Exponents (2:27)
- Video - Simplifying Positive Exponents (4:05)
- Video - Mixed Simplification involving Negative Exponents (2:26)
- Video - Evaluating Negative Exponents (3:39)
- Video - Negative Bases in Index Form (3:49)
Complicated Exponent Laws
- Video - Algebraic Simplifications involving Negative Exponents (10:18)
- Video - Algebraic Simplifications involving Rational Exponents (3:55)
- Video - Algebraic Simplifications involving Fractions and Exponents (3:22)
- Video - Algebraic Simplifications involving Powers of Power (6:20)
- Video - Mixed Indices (3:34)
- Video - Evaluating Rational Expressions Given Index Values (3:29)
Algebraic Expansion with Exponents
- Video - Algebraic Expansions of Exponents (5:17)
- Video - Expanding Binomial Terms of Exponents (8:16)
- Topic - Algebraic Expansions with Exponents
- Topic - Algebraic Expansions with Exponents involving Binomial Terms
- Topic - Algebraic Expansions with Exponents involving Squaring Terms
- Topic - Algebraic Expansions with Exponents involving Difference of Squares
Algebraic Factorisation with Exponents
- Video - Simplification of Exponents in Rational Expressions (2:37)
- Video - Factorise by Common Factors (10:55)
- Video - Simplification of Exponents in Rational Expressions (2:37)
- Topic - Algebraic Factorise with Exponents
- Topic - Algebraic Factorise with Exponents involving Constants
- Topic - Algebraic Factorise with Exponents involving Common Exponents
- Topic - Algebraic Factorise with Exponents involving Difference of Squares
- Topic - Algebraic Factorise with Exponents involving Complete Squares
- Topic - Algebraic Factorise with Exponents involving Quadratic Trinomials
- Topic - Simplifying Algebraic Expressions involving Exponents
Exponential Equations
- Video - Basic Exponential Equations (2:03)
- Video - Exponential Equations involving Negative Exponents (1:40)
- Video - Exponential Equations involving Rational Exponents (3:35)
- Video - Exponential Equations by Changing the Bases (2:25)
- Video - Exponential Equations involving Surds (7:09)
- Video - Indicial Equations by Changing the Base (7:19)
- Video - Solving from Definition (2:43)
- Video - Solving by Factorise (5:15)
- Video - Inverse of Exponential Functions (5:47)
- Video - Exponential Literal Equations (3:54)
- Video - Index Equations Involving Linear Equations (1:11)
Exponential Graphs
- Video - Understanding Exponential Graphs (5:05)
- Video - Basic Exponential Graphs (5:18)
- Video - Transformation of Exponential Graphs (4:57)
- Video - Exponential Graphs Dilation from the x-axis (3:07)
- Video - Exponential Graphs Dilation from the y-axis (2:40)
- Video - Exponential Graphs Dilation from the base (1:44)
- Video - Translation of Exponential Graphs (2:40)
- Video - Reflection of Exponential Graphs (1:58)
- Video - Graphs of Exponential Curves (6:20)
- Video - Transformation of Exponential Curves x-axis and y-axis (1:23)
- Video - Translating Graphs of Exponential Functions (3:05)
Natural Exponential Graphs
- Video - Graphs of Natural Exponential Functions (2:12)
- Video - Transformation of Natural Exponential Graphs (3:06)
- Video - Coefficients of Natural Exponential Graphs (1:37)
- Video - Reflection of Exponential Graphs (1:58)
- Video - Stating the Transformations of Exponential Graphs to Base e (9:58)
- Video - Dilation of Exponential Graphs to base e (3:24)
- Video - Sketching Exponential Graphs to base e (3:15)
- Video - Reflection of Exponential Graphs to base e (1:59)
- Video - Absolute Values (3:01)
Exponential Growth
- Video - Exponential Growth (5:47)
- Video - Fundamental of Exponential Growth (4:37)
- Video - Two Events of Exponential Growth and Decay (4:53)
- Video - Exponential Growh for Finding Values (7:19)
- Video - Application of Exponential Growth to Base e (2:05)
- Video - Investments using Exponential Growth (1:47)
Logarithms in Base 10
- Video - Simplifying Logarithms in base 10 (4:43)
- Video - Finding Exponents using Logarithms in base 10 (5:26)
- Video - Equations involving Logarithms in base 10 (2:36)
- Topic - Logarithms Base 10
- Topic - Logarithms Base 10 involving Decimal Numbers
- Topic - Logarithms Base 10 involving Surds
- Topic - Logarithms Base 10 involving Surds and Rational Form
- Topic - Logarithms Base 10 involving Indices
- Topic - Logarithms Base 10 involving Equations
Logarithmic Laws
- Video - Addition of Logarithms (7:29)
- Video - Subtraction of Logarithms (3:51)
- Video - Evaluation of Logarithms using Logarithmic Laws (5:23)
- Video - Indices involving Logarithms (3:38)
- Video - Zero Value involving Logarithms (4:04)
- Video - Unity of Logarithms (8:20)
- Video - Evaluating Multiple Logarithms (3:35)
Logarithmic Equations
- Video - Logarithmic Equations with Same Bases (5:51)
- Video - Logarithmic Equations with Different Bases (5:41)
- Video - Equations involving Definition of Logarithm (5:01)
- Video - Variables in Logarithms (3:57)
- Video - Variables in Base (5:58)
- Video - Variables in Other Side (3:20)
- Video - Variables in Multiple Terms (7:03)
- Video - Converting to an Index Form (4:42)
- Video - Multiple Terms (4:27)
- Video - Inverse of Logarithmic Functions (6:21)
- Video - Logarithmic Literal Equations (5:58)
Exponential Equations using Logarithms
- Video - Index Equations involving Logarithms (4:28)
- Video - Equatoins involving Natural Logarithms (3:22)
- Video - Equations involving Logarithms (2:37)
- Topic - Indicial Equations using Logarithms: Bases Greater Than 1
- Topic - Indicial Equations using Logarithms: Bases Less Than 1
- Topic - Indicial Equations using Logarithms: Bases Greater Than 1 and Non-Monic Indices
- Topic - Indicial Equations using Logarithms: Bases Less Than 1 and Non-Monic Indices
- Topic - Indicial Equations using Logarithms: Two Indicial Expressions
Exponential Inequalities using Logarithms
- Video - Index Inequalities involving Logarithms (5:05)
- Video - Probability involving Inequality and Logarithm (3:07)
- Video - Finding Values involving Probability, Inequality and Logarithm (2:28)
- Video - Probability and Inequality (3:15)
- Video - Exponential Inequalities (1:46)
- Topic - Indicial Inequalities using Logarithms: Bases Greater Than 1
- Topic - Indicial Inequalities using Logarithms: Bases Less Than 1
Graphing Natural Logarithmic Functions
- Video - Exponential Inequalities (1:46)
- Video - Stating the Transformations of Logarithmic Graphs to base e (3:51)
- Video - Dilation of Logarithmic Graphs to base e (7:39)
- Video - Translation of Logarithmic Graphs to base e (3:51)
- Video - Reflection of Logarithmic Graphs to base e (4:46)
- Video - Finding Equations for Graphs of Logarithmic Functions (3:23)
Number Sequences
- Video - Number Sequences (2:23)
- Video - Describing Number Sequences (4:06)
- Topic - Descriptions of Number Sequences
- Topic - Writing Terms from Patterns
- Topic - Pattern of Number Sequences by Adding or Subtracting
- Topic - Pattern of Number Sequences by Multiplying or Dividing
- Topic - Pattern of Number Sequences involving Indices
Arithmetic Sequences
- Video - Identifying Arithmetic Sequences (2:40)
- Video - Finding the First Term and Common Difference (2:49)
- Video - Finding a Term from a Rule of Arithmetic Sequence (3:41)
- Video - Understanding Formula of Arithmetic Sequences (8:10)
- Video - Set up a Rule of Arithmetic Sequence (6:41)
- Video - Calculating Number of Terms of Arithmetic Sequence (2:29)
Geometric Sequences
- Video - Identifying Geometric Sequences (2:24)
- Video - Finding Sum of Geometric Sequences (5:17)
- Video - Finding the General Term of Geometric Sequence via Geometic Series (7:51)
- Video - Negative Common Ratio in Geometric Series (2:24)
- Video - Finding the Term of Geometric Series (2:55)
- Video - Finding the number of Terms of Geometric Sequences (2:39)
- Video - Finding the First Term and Common Ratio (3:14)
- Video - Finding a Term from a Rule of Geometric Sequence (4:16)
- Video - Set up a Rule of Geometric Sequences (3:56)
- Video - Finding the number of Terms of Geometric Sequences (2:39)
Compound Interest
- Video - Understanding Compound Interest (9:29)
- Video - Compound Interest Annually (0:44)
- Video - Compound Interest Quarterly (1:58)
- Video - Compound Interest Monthly (1:20)
- Video - Compound Interest Daily (1:41)
- Video - Application of Compound Interests (4:20)
- Video - Appreciation using Compound Interest (3:08)
- Video - Finding Unknown Values of Geometric Sequences (6:05)
Sigma Notation
- Video - Sigma Notation of Arithmetic Series (10:30)
- Video - Sigma Notation of Geometric Series (6:04)
- Video - Binomial Expansion: Sigma Notation (5:57)
- Topic - Matching Sigma Notations and Number Series
- Topic - Calculating Arithmetic Series in Sigma Notations
- Topic - Calculating Geometric Series in Sigma Notations
- Topic - Finding the Last Order of Sigma Notations
- Topic - Calculating Constant Series in Sigma Notations
Arithmetic Series
- Video - Sum of an Arithmetic Series (6:04)
- Video - Set up Sum Formula of Arithmetic Series (4:35)
- Video - Finding Sum using Formula of Arithmetic Series (4:18)
- Video - Finding Terms from Sum of Arithmetic Sequences (4:46)
- Video - Sum of Arithmetic Series using the First and Last Terms (4:32)
- Video - Sum of Arithmetic Series using the Formula (3:02)
- Video - Sum of Arithmetic Series using General Term (5:31)
- Video - Finding Common Difference from Sum of Arithmetic Series (5:07)
- Video - Number of Terms of Arithmetic Series (6:22)
Geometric Series
- Video - Set up a Sum Formula of Geometric Series (3:22)
- Video - Finding the Sum using a Formula of Geometric Series (4:43)
- Video - Finding Number of Terms of Geometric Series (3:50)
- Video - Finding the Number of Terms of Geometric Series (6:19)
- Video - Geometric Series using Formula (3:13)
- Video - Geometric Series involving Sums and Common Ratios (7:42)
- Video - Geometric Series using Logarithms (5:11)
- Video - Geometric Series Formula (3:34)
- Video - Geometric Series involving Tricky Common Ratios (6:02)
- Video - Inequalities involving Geometric Series (5:53)
Sum of an Infinite Geometric Series
- Video - Finding the Limiting Sum (6:39)
- Video - Finding the First Term and the Common Ratio (3:10)
- Video - Recurring Decimals (5:23)
- Video - Recurring Decimal with an Extra Value (3:38)
- Video - Sum to Infinity or Limiting Sum of Geometric Series (6:41)
- Video - No Existence of Limiting Sum (1:09)
- Video - Recurring Decimals involving Limiting Sum (5:56)
- Video - Application of Limiting Sum (5:12)
- Video - Limiting Sum involving Success or Failure (7:03)
- Video - Limiting Sum involving Success Failure or Draw (7:53)
Binomial Coefficient
- Video - Binomial Expansion using Combination Coefficients (13:29)
- Video - General Term of Binomial Expansions (6:19)
- Video - Binomial Expansion: Term Independent of x (5:52)
- Video - Binomial Expansion: Finding the Term (3:53)
- Video - Binomial Expansion: Finding the Coefficient (2:44)
- Video - Finding Coefficients of Binomial Expansions involving Rational Terms (2:50)
- Video - Finding Coefficients of Binomial Expansions with Two Pronumerals (2:05)
General Binomial Theorem
- Video - Binomial Expansion: Finding the Coefficients (7:14)
- Video - Binomial Expansion: Finding the Coefficients involving Fractions (6:20)
- Video - Proof involving Binomial Expansions (6:39)
- Video - Simplifying Binomial Series by Substituting Values (5:58)
- Video - Simplifying Binomial Series by Differentiations (4:00)
- Video - Simplifying Binomial Series by Integrations (7:30)
- Video - Binomial Expansion: Ratio of Consecutive Terms (13:56)
- Video - Binomial Expansion: The Greatest Coefficient (14:34)
- Video - Binomial Expansion: The Numerically Greatest Coefficient (10:53)