In this course, students will develop the mathematical understanding and skills to solve problems relating to:

- Logarithmic Functions 2
- Further Differential and Applications 2
- Integrals

Logarithmic laws and definitions are developed and used. Logarithmic functions are explored graphically and algebraically. The calculus study continues with the derivatives of exponential, logarithmic and trigonometric functions and their applications, together with some differentiation techniques and applications to optimisation problems and graph sketching. Integration is introduced as a process that reverses differentiation and as a way of calculating areas and the fundamental theorem of calculus.

*Source – QCAA General Senior Syllabus 2019*

Lessons

#### Logarithmic Laws

- Video - Addition of Logarithms (7:29)
- Video - Subtraction of Logarithms (3:51)
- Video - Evaluation of Logarithms using Logarithmic Laws (7:04)
- Video - Simplifying Logarithms using Addition & Subtraction Laws (1:17)
- Video - Indices involving Logarithms (3:38)
- Video - Expressing Logarithms using Letters (2:28)
- Video - Zero Value involving Logarithms (4:04)
- Video - Unity of Logarithms (8:20)
- Video - Evaluating Multiple Logarithms (3:35)
- Video - Evaluating using Unity of Logarithms (5:20)
- Video - Interchangeable Logarithmic Forms (3:09)
- Video - Evaluation of Logarithmic Values (3:03)

#### Logarithmic Equations

- Video - Logarithmic Equations with Same Bases (5:51)
- Video - Logarithmic Equations with Different Bases (9:02)
- 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 Natural Logarithmic Functions (6:21)
- Video - Logarithmic Literal Equations (5:58)

#### Exponential Equations using Logarithms

- Video - Equations involving Natural Logarithms (3:22)
- Video - Index Equations involving Logarithms (5:05)
- Video - Equations involving Logarithms (2:37)
- Topic - Indicial Equations by Logarithms: Bases > 1
- Topic - Indicial Equations by Logarithms: Bases < 1
- Topic - Indicial Equations by Logarithms: Bases > 1 and Non-Monic Indices
- Topic - Indicial Equations by Logarithms: Bases < 1 and Non-Monic Indices
- Topic - Indicial Equations by Logarithms: Two Indicial Expressions

#### Limits at Constants

- Video - Understanding Limits at Constant Values (6:58)
- Topic - Limits at Constant Values
- Topic - Limits at Constant Values involving Common Factors
- Topic - Limits at Constant Values involving Differences of Squares
- Topic - Limits at Constant Values involving Factorise
- Topic - Limits at Constant Values involving Quadratic Factorise

#### Limits at Infinity

- Video - Understanding Limits at Infinity (6:20)
- Video - Calculating Limits at Infinity (7:51)
- Topic - Limits at Infinity
- Topic - Limits at Infinity involving Linear Fractions
- Topic - Limits at Infinity involving Quadratic Fractions
- Topic - Limits at Infinity involving Fractions Higher Degree Numerators

#### Evaluating Exponential Functions

- Video - Evaluating Exponential Functions (4:06)
- Topic - Evaluating Exponential Functions 1
- Topic - Evaluating Exponential Functions 2
- Topic - Evaluating Exponential Functions 3
- Topic - Evaluating Exponential Functions 4
- Topic - Evaluating Exponential Functions 5
- Topic - Evaluating Exponential Functions 6

#### Derivatives of Exponential Functions

- Video - Derivative of Exponential Functions (1:30)
- Video - Derivative of Exponential Functions using Chain Rule (6:29)
- Video - Derivative of Exponential Functions using Quotient Rule (7:20)
- Video - Derivative of Exponential Functions using Product Rule (6:12)
- Video - Second Derivative of Exponential Functions (6:10)
- Video - Equations of Tangent of Exponential Functions (4:46)
- Video - Stationary Point using Derivative of Exponential Functions (9:56)
- Video - Maximum Turning Point of Exponential Functions (7:18)

#### Derivatives of Logarithmic Functions

- Video - Fundamental of Derivative of Logarithmic Functions (2:41)
- Video - Derivative of Logarithmic Functions using Logarithm Law of Addition (4:06)
- Video - Derivative of Logarithmic Functions using Logarithm Law of Subtraction (1:47)
- Video - Derivative of Logarithmic Functions involving Indices (3:36)
- Video - Derivative of Mixed Logarithmic Functions (5:24)
- Video - Derivative of Non-Natural Logarithmic Functions (3:09)
- Video - Stationary Points using Derivative of Logarithmic Functions (5:32)
- Video - Derivative of Logarithmic Functions using Quotient Rule (4:40)
- Video - Tangents and Normals of Logarithmic Functions (2:15)

#### Derivative of Sine Functions

- Video - Differentiation of Sine Function: Chain Rule 1 (3:21)
- Video - Differentiation of Sine Function: Chain Rule 2 (2:01)
- Video - Differentiation of Sine Function: Chain Rule 3 (2:33)
- Video - Differentiation of Sine Function: Chain Rule 4 (5:02)
- Video - Differentiation of Sine Function: Product Rule 1 (4:54)
- Video - Differentiation of Sine Function: Product Rule 2 (4:16)
- Video - Differentiation of Sine Function: Product Rule 3 (3:06)
- Video - Differentiation of Sine Function: Quotient Rule 1 (3:17)
- Video - Differentiation of Sine Function: Quotient Rule 2 (2:39)
- Video - Differentiation of Sine in Degrees (7:16)
- Video - Derivative Value of Sine Functions (1:33)

#### Derivatives of Cosine Functions

- Video - Differentiation of Cosine Function: Chain Rule 1 (3:17)
- Video - Differentiation of Cosine Function: Chain Rule 2 (5:10)
- Video - Differentiation of Cosine Function: Chain Rule 3 (4:10)
- Video - Differentiation of Cosine Function: Chain Rule 4 (3:02)
- Video - Differentiation of Cosine Function: Product Rule 1 (2:25)
- Video - Differentiation of Cosine Function: Product Rule 2 (2:58)
- Video - Differentiation of Cosine Function: Product Rule 3 (3:16)
- Video - Differentiation of Cosine Function: Quotient Rule (6:30)
- Video - Differentiation of Cosine in Degrees (2:55)
- Video - Stationary Points involving Cosine Functions (4:05)

#### Integrating Trigonometric Functions by Recognition

- Video - Definite Integral of Trigonometric Functions using Reverse Chain Rule (7:20)
- Topic - Integration by Recognition Basic
- Topic - Integration by Recognition involving Chain Rule 1
- Topic - Integration by Recognition involving Chain Rule 2
- Topic - Integration by Recognition involving Chain Rule 3
- Topic - Integration by Recognition involving Chain Rule 4
- Topic - Integration by Recognition involving Product Rule 1
- Topic - Integration by Recognition involving Product Rule 2
- Topic - Integration by Recognition involving Quotient Rule

#### Integration of Power Functions

- Video - Principle of Integration of Power Function (2:49)
- Video - Integration of Power Functions (1:56)
- Video - Integration of Power Functions involving Fractions (2:23)
- Video - Integration of Power Functions Surds (1:06)
- Video - Integration of Power Functions (5:32)
- Video - Integration of Reciprocal Functions (1:35)
- Video - Integration of Irrational Functions (4:32)
- Video - Integration of Reciprocal Irrational Functions (4:41)

#### Particular Values

- Video - Finding Integral Constants (7:27)
- Video - Finding Integral Constants involving Point of Inflections (4:45)
- Video - Finding Integral Constants involving Second Derivatives (2:33)
- Topic - Finding Integral Constants from Linear Expressions
- Topic - Integral Constants by Non-Monic Expressions from Linearity
- Topic - Finding Integral Constants from Quadratics
- Topic - Integral Constants using Non-Monic Expressions from Quadratics
- Topic - Finding Two Integral Constants from Linear Expressions

#### Indefinite Integration by Recognition

- Video - Reverse Chain Rule (7:06)
- Video - Integration by Recognition: Using Derivative of Exponential Functions (3:45)
- Video - Integration by Recognition using Derivative of Sine Function (3:32)
- Video - Integration by Recognition using Derivative of Cosine Function (4:20)
- Video - Integration by Recognition using Derivative of Tangent Function (4:16)
- Video - Integration by Recognition: Using Derivative of Logarithmic Functions (4:10)
- Video - Integration by Recognition using Product Rule (6:16)
- Video - Integration by Recognition using Long Division (7:22)
- Video - Integration of cosec x by Recognition involving Log TAN (4:18)
- Video - Integration of sec x by Recognition (4:52)

#### Definite Integrals

- Video - Theory of Definite Integrals (5:46)
- Video - Evaluating Plain Definite Integrals (4:56)
- Video - Evaluating Definite Integrals of Higher Orders (8:05)
- Video - Differentiating Definite Integrals (4:38)
- Video - Finding Unknown Limits of Definite Integrals (5:00)
- Video - Finding Unknowns of Expressions involving Definite Integrals (4:54)
- Video - Definite Integrals involving Simplifications (3:47)
- Video - Definite Integrals Backwards (1:58)

#### Definite Integration of Power Functions

- Video - Definite Integrals of Power Functions (5:22)
- Topic – Definite integral of Power Functions in Positive Coefficients
- Topic – Definite integral of Power Functions in Negative Coefficients
- Topic – Definite integral of Power Functions in Rational Expressions
- Topic - Definite integral of Power Functions involving Surds