Course Materials
Lessons
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
Basic Differentiation Rules
- Video - Differentiation of Constant Terms (2:14)
- Video - Differentiation of Linear Functions (3:16)
- Video - Methods of Differentiation (5:01)
- Video - Differentiation of Negative Exponents (5:12)
- Video - Differentiation of Non-Monic Negative Exponents (8:13)
- Video - Simplifying Expressions before Differentiation (6:37)
- Video - Principle of Differentiation of Surds (5:02)
- Video - Principle of Differentiation of Surds: Square Roots (4:58)
- Video - Principle of Differentiation of Surds: Quad Roots (2:24)
- Video - Principle of Differentiation of Surds involving Fractions (6:35)
- Video - Differentiation of Polynomial Functions (3:48)
- Video - Differentiation of Functions in Terms of Specific Letters (2:43)
- Video - Differentiation of Functions in Terms of Specific Letters involving Additions (4:37)
- Video - Differentiation of Functions in Terms of Specific Letters involving Multiplications (6:20)
- Video - Equations involving Differentiation (1:51)
Chain Rule
- Video - Fundamental of Chain Rule (7:58)
- Video - Chain Rule involving Rational Functions (5:24)
- Video - Chain Rule involving Irrational Functions (6:06)
- Video - Derivative Value using Chain Rule involving Irrational Functions (1:46)
- Topic - Chain Rule: Power of Linear Expressions
- Topic - Chain Rule: Power of Quadratic Expressions
- Topic - Chain Rule: Surds 1/2 Power
- Topic - Chain Rule: Surds 3/2 Power
- Topic - Chain Rule: Surds 1/3 Power
- Topic - Chain Rule: Linear Rational Expressions
- Topic - Chain Rule: Quadratic Rational Expressions
- Topic - Chain Rule: Rational Expressions of Surds
- Topic - Chain Rule: Cubic Rational Expressions
Product Rule
- Video - Fundamental of Product Rule (7:49)
- Video - Product Rule and Chain Rule 1 (3:32)
- Video - Product Rule and Chain Rule 2 (4:12)
- Video - Derivative Value using Product Rule and Chain Rule (3:26)
- Topic - Product Rule: Linear Products
- Topic - Product Rule: Non-Monic Linear Products
- Topic - Product Rule: Quadratic Products
- Topic - Product Rule: Complete Square & Linear Products
- Topic - Product Rule: Complete Cubic and Quadratic Products
Quotient Rule
- Video - Fundamental of Quotient Rule (2:53)
- Video - Differentiations using Quotient Rule (7:53)
- Video - Finding Pronumerals involving Quotient Rule (2:42)
- Video - Derivative Value using Quotient Rule (1:37)
- Topic - Quotient Rule: Basic Rule
- Topic - Quotient Rule: Non-Monic Denominators
- Topic - Quotient Rule: Quadratic Numerators
- Topic - Quotient Rule: Quadratic Numerators and Denominators
Higher Derivatives
- Video - Fundamental of Higher Derivatives (5:34)
- Video - Higher Derivatives involving Chain Rule (4:59)
- Video - Higher Derivatives involving Surds (5:27)
- Video - Higher Derivatives involving Quotient Rule (2:40)
- Video - Higher Derivatives involving Product Rule (6:16)
- Topic - Higher Derivatives of Quadratic Polynomials
- Topic - Higher Derivatives of Cubic Polynomials
- Topic - Higher Derivatives using Chain Rule
Tangents
- Video - Gradient of Tangents (4:46)
- Video - Application of Gradient of Tangents (7:49)
- Video - Equation of Tangents (6:15)
- Video - Angle and Gradient of Tangents (3:39)
- Video - Gradient of Parallel and perpendicular Tangents (8:38)
- Video - Horizontal Tangents (2:39)
- Video - Tangents and Corresponding y-intercepts (2:07)
- Video - Tangents and Corresponding x-intercepts (4:33)
Normals
- Video - Equation of Normals (7:13)
- Video - Equation of Normals at Hyperbola (5:42)
- Video - Applications of Tangents and Normals of Cubic Polynomials (4:29)
- Video - Equation of Normals involving Surd Functions (3:33)
- Video - Normal of Parabola Cuts Parabola Again (4:52)
- Video - Equation of Tangents and Normals at Hyperbola (7:18)
Turning Points
- Video - Coordinates of Turning Points (7:30)
- Video - Identifying Nature of Turning Points from Derivative Curves (5:25)
- Video - Identifying Nature of Turning Points using Tables (5:08)
- Video - Identifying Stationary Points (8:17)
- Video - Understanding Nature of Stationary Points (5:31)
- Video - No Stationary Points (1:50)
- Video - Condition of Being Stationary Points (2:51)
- Video - Maximum and Minimum Turning Points (6:49)
- Video - Stationary Points by their Shapes (7:34)
- Video - Maximum and Minimum Turning Points of Quartic Functions (7:54)
Curves of Rational Functions
- Video - Understanding Curve Sketching involving Asymptotes (5:00)
- Video - Finding Oblique Asymptotes Vertical Asymptotes (4:06)
- Video - Turning Points of Hyperbola (3:42)
- Video - Nature of Turning Points of Hyperbola (7:02)
- Video - Curve Sketching of Hyperbola involving Asymptotes (0:47)
- Video - Understanding Curve Sketching involving Symmetry (1:24)
- Video - Even Functions Odd Function (1:49)
- Video - Differentiation using Quotient Rule (2:29)
- Video - Turning Points of Rational Functions (1:17)
- Video - Nature of Turning Points of Rational Functions (3:03)
- Video - x-Intercepts of Rational Functions (0:58)
- Video - Vertical Asymptotes in Rational Functions (1:53)
- Video - Horizontal Asymptotes in Rational Functions (4:52)
- Video - Curve Sketching of Rational Functions involving Symmetry (1:53)
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)
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)
Optimisation
- Video - Maxima and Minima of Quadratic Functions (4:16)
- Video - Maxima and Minima of Cubic Functions 1 (8:47)
- Video - Maxima and Minima of Cubic Functions 2 (4:02)
- Video - Maxima and Minima in 2D Applications (4:23)
- Video - Maxima and Minima in 3D Applications 1 (6:09)
- Video - Maxima and Minima in 3D Applications 2 (3:53)
- Video - Absolute Maximum and Minimum (8:59)
- Video - Minimum Speed of the Motion (1:43)
- Video - Maximum Velocity Given Displacement (1:35)
Kinematics
- Video - Velocity and Speed using Exponential Functions (1:10)
- Video - Motion At Rest in Exponential Functions (1:38)
- Video - Motion Never At Rest (1:40)
- Video - Displacement-time Graphs (8:46)
- Video - Displacement-Velocity Graphs: Lines (7:12)
- Video - Displacement-Velocity Graphs: Curves (6:09)
- Video - Velocity-Time Graphs: Straight Lines (20:27)
- Video - Velocity-Time Graphs: Piecewise Graphs (17:12)
- Video - Velocity-Time Graphs: Curves (8:26)
- Video - Acceleration-Time Graphs: Concave Downwards (8:27)
- Video - Acceleration-Time Graphs: Concave Upwards (6:43)
Differentiation and Displacement, Velocity and Acceleration
- Video - Velocity and Speed (3:04)
- Video - Kinematics given Velocity (9:49)
- Video - Kinematics given Displacement (10:51)
- Topic - Working with Displacement
- Topic - Moving Forward or Backward
- Topic - Obtaining Velocity from Displacement
- Topic - Obtaining Acceleration from Velocity
- Topic - Obtaining Acceleration from Displacement
- Topic - Obtaining Displacement from Velocity
- Topic - Obtaining Displacement from Acceleration
- Topic - Understanding Velocity and Speed
- Topic - Total Distance Travelled of Linear Displacement
- Topic - Total Distance Travelled of Quadratic Displacement
- Topic - Total Distance Travelled of Cubic Displacement
Basic Integration Rules
- Video - Principles of Antidifferentiation (7:29)
- Video - Antidifferentiation and Differentiation (6:10)
- Video - Antidifferentiation of Polynomial Functions (3:51)
- Video - Integration of Fractions (7:09)
- Video - Integration for Surds (7:34)
- Video - Basic Integration Rules (7:18)
- Video - Integration of Multi Term Expressions (2:25)
- Video - Integration of Rational Exponents (9:38)
- Video - Simplifying before Integration (9:37)
- Video - Expanding before Integration (7:27)
- Video - Binomial Expansion before Integration (6:34)
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
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 of Power Functions (5:22)
- Video - Definite Integrals involving Simplifications (3:47)
- Video - Definite Integrals Backwards (1:58)
- Video - Definite Integrals of Odd Functions (2:59)
- Video - Definite Integrals of Even Functions (4:47)
- Video - Integration of Even & Odd Functions (1:14)
Integration by Substitution
- Video - Integration using Substitutions 1 (3:45)
- Video - Integration using Substitutions 2 (3:05)
- Video - Integration using Substitutions 3 (2:06)
- Video - Removal of Pronumerals 1 (4:39)
- Video - Removal of Pronumerals 2 (2:28)
- Video - Removal of Pronumerals 3 (2:43)
- Topic - Integration by Substitution: Basic
- Topic - Integration by Substitution: Surds
- Topic - Integration by Substitution: Rational Expressions
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
Sine and Cosine Integration by Substitution
- Video - Integrating Trigonometric Functions by Substituting Cosine (2:45)
- Video - Integrating Trigonometric Functions by Substituting Sine (2:30)
- Video - Definite Integration of Trigonometric Functions by Substitutions (5:58)
- Video - Integration of Sine using Substitution (6:20)
- Video - Integration of Cosine using Substitution (4:30)
- Video - Definite Integral of Trigonometric Functions by Substituting Sine (3:09)
- Video - Definite Integral of Trigonometric Functions using Cosine Double Angle Formula (4:06)
- Video - Integration of Product of Sine and Cosine using Substitution (3:50)
Integrations involving Tangent
- Video - Indefinite Integration of Secant Square (1:20)
- Video - Definite Integration of Secant Square (2:42)
- Video - Indefinite and Definite Integration of Tangent Square (3:10)
- Video - Integration of tan x (6:22)
- Video - Integration of Tangent Square (1:10)
- Video - Integration of Even Powers of tan x (4:05)
- Video - Integration of Odd Powers of tan x (5:30)
Area Under a Curve
- Video - Theory of Area under Curves (4:17)
- Video - Area under Curves given Domains (6:09)
- Video - Area between Curves and Axes (5:01)
- Video - Signed Area (5:47)
- Video - Combined Positive and Negative Areas (5:09)
- Video - Positive and Negative Areas by Sketching Curves (4:00)
- Video - Theory of Area under Trigonometric Curves (2:58)
- Video - Finding the Area under Sine Curves (5:28)
- Video - Finding the Area under Cosine Curves (3:12)
Area between Two Functions
- Video - Area between Two Curves 1 (3:56)
- Video - Area between Two Curves 2 (6:24)
- Video - Area between Two Curves 3 (3:09)
- Video - Signed Area between Two Curves (4:39)
- Video - Combined Signed Areas between Two Curves 1 (6:43)
- Video - Combined Signed Areas between Two Curves 2 (8:49)
- Video - Finding Area between Sine Curve & a Straight Line (10:44)
- Video - Finding the Area between Sine and Cosine Curves (7:15)
Kinematics using Integration
- Video - Expression of the Distance using Integration (2:23)
- Video - Working with Velocity in Trigonometric Functions (3:11)
- Video - Working with Acceleration in Natural Exponential Functions (5:12)
- Video - Maximum Speed using Acceleration 1 (5:38)
- Video - Maximum Speed using Acceleration 2 (2:54)
- Video - Changes in Displacement and Velocity (2:57)
Volumes using Integration
- Video - Volumes Rotated about x-axis 1 (4:43)
- Video - Volumes Rotated about the y-axis (5:58)
- Video - Volumes Rotated about x-axis and y-axis (5:48)
- Video - Finding the Volume involving Trigonometric Functions (4:13)
- Topic - Volume of Revolution bounded by Straight Lines & x-axis
- Topic - Volume of Revolution bounded by Semi-Circles & x-axis
- Topic - Volume of Revolution bounded by Surd Graphs & y-axis
- Topic - Volume of Revolution bounded by Parabolas & x-axis
- Topic - Volume of Revolution bounded by Parabolas & y-axis
- Topic - True/False of Expression of Volumes Rotating the X-axis
- Topic - True/False of Expression of Volumes Rotating the Y-axis
Volumes for Two Functions
- Video - Volumes Rotated about x-axis 2 (5:44)
- Video - Volumes between Two Curves (5:13)
- Topic - Volume of Revolution between Horizontal Lines & Parabolas
- Topic - Volume of Revolution between Straight Lines & Parabolas
- Topic - Volume of Revolution between Straight Lines & Surd Graphs
- Topic - Volume of Revolution about y-axis between Parabolas & Surd Graphs
- Topic - Half Volume of Revolution between Parabolas & Surd Cubic Graphs
- Topic - Volume of Revolution between Parabolas
