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NCEA Mathematics Level 3 - Algebra and Calculus
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- COUNTING TECHNIQUES
- Product Principle9 Topics
- Video - Arrangements with Repetitions: Numeric Passwords (4:53)
- Video - Arrangements with Repetitions: Fixed Spot Alphanumeric Passwords (2:07)
- Video - Arrangements with Repetitions: Floating Spot Alphanumeric Passwords (3:10)
- Video - Arrangements with Repetitions: Combination Locks (1:35)
- Video - Arrangements with Repetitions: Lights On/Off (1:54)
- Video - Arrangements with Repetitions: Binary Numbers (1:46)
- Video - Arrangements without Repetitions: Numeric Passwords (3:06)
- Video - Arrangements without Repetitions: Alphanumeric Passwords (2:14)
- Video - Arrangements without Repetitions: Combination Locks (1:25)
- Video - Arrangements with Repetitions: Numeric Passwords (4:53)
- Factorials12 Topics|3 Quizzes
- Video - Definition of Factorial (5:52)
- Video - Simplifying Expressions involving Factorials (4:22)
- Video - Equations involving Factorials (2:08)
- Video - Arrangements of 4 Cards (2:04)
- Video - Arrangements of 9 People Queuing Up a Line (5:18)
- Video - Arrangements of 6 Girls and 2 Boys (4:09)
- Video - Formula of Considering Duplicates (2:57)
- Video - Arrangements involving Duplicates (3:01)
- Video - Arrangements involving Duplicates in Groups (1:11)
- Topic - Calculating Factorials
- Topic - Calculating Factorials involving Fractions
- Topic - Factorials involving Multi Factorials & Fractions
- Video - Definition of Factorial (5:52)
- Permutations7 Topics
- Video - Ordered Selections (4:45)
- Video - Ordered Selections without or with Replacement (2:38)
- Video - Definition of Permutation (2:57)
- Video - Calculating Permutations (2:23)
- Video - Equations involving Permutation (1:20)
- Video - Introduction to Permutation (4:34)
- Video - Applying Permutations (2:49)
- Video - Ordered Selections (4:45)
- Permutations Involving Restrictions3 Topics
- Arrangements in a Circle5 Topics
- Combinations11 Topics
- Video - Counting Techniques without Replacements (2:28)
- Video - Unordered Selections: Choosing Letters (8:21)
- Video - Unordered Selections: Forming Groups (3:03)
- Video - Definition of Combination (3:59)
- Video - Simplifying Combinations (3:25)
- Video - Equations involving Combination (3:46)
- Video - Proofs involving Combination (3:30)
- Video - Understanding Combination (1:49)
- Video - Choosing Combinations from Two Groups (4:17)
- Video - Combinations involving At Least (2:26)
- Video - Combinations involving Duplicates (5:05)
- Video - Counting Techniques without Replacements (2:28)
- Applications of Counting Techniques4 Topics
- Pigeon-Hole Principle2 Topics
- Probabilities using Combinations4 Topics
- INEQUALITIES
- Linear Inequalities8 Topics
- Video - Inequalities in Number Lines (5:22)
- Video - Writing Inequalities from Number Lines (2:29)
- Video - Understanding Linear Inequalities (5:10)
- Video - Simple Inequalities (2:04)
- Video - Linear Inequalities Pronumerals on Both Sides (2:48)
- Video - Reversing Inequality Sign (4:46)
- Video - Two Inequality Signs in Inequalities (5:20)
- Video - Linear Inequalities (4:36)
- Video - Inequalities in Number Lines (5:22)
- Linear Inequalities involving Fractions4 Topics
- Regions of Linear Inequalities8 Topics
- Video - Understanding Sketching Regions (2:43)
- Video - Regions Bounded by Horizontal Lines (1:41)
- Video - Regions Bounded by Vertical Lines (1:28)
- Video - Regions Bounded by Straight Lines (5:24)
- Video - Regions Bounded by Straight Lines in General Form (6:16)
- Video - Writing Inequalities (5:20)
- Video - Vertical & Horizontal Regions (4:20)
- Video - Regions involving Linear Lines (3:53)
- Video - Understanding Sketching Regions (2:43)
- Problem Solving with Regions of Linear Inequalities3 Topics
- Inequalities with Pronumerals in Denominators5 Topics
- Video - Inequality: Pronumerals in Denominators (7:37)
- Video - Inequality: Pronumerals in Denominators & Numerators (4:44)
- Video - Inequality: Pronumerals in Denominators & the Other Side (6:19)
- Video - Inequality: Pronumerals in Denominators in Multiple Fractions (4:17)
- Video – Pronumerals in Denominators in Multiple Fractions (4:32)
- Video - Inequality: Pronumerals in Denominators (7:37)
- SIMULTANEOUS EQUATIONS
- Linear Simultaneous Equations - Elimination Method13 Topics|3 Quizzes
- Video - Elimination Method for Simultaneous Equations (3:32)
- Video - Elimination Method for Simultaneous Equations by Subtraction (4:29)
- Video - Elimination Method for Simultaneous Equations by Addition (3:25)
- Video - Elimination Method by Manipulating One Pronumeral (6:40)
- Video - Elimination Method by Manipulating Two Pronumerals 1 (3:31)
- Video - Elimination Method by Manipulating Two Pronumerals 2 (1:49)
- Video - Elimination Method by Manipulating Two Pronumerals 3 (2:15)
- Video - Simultaneous Equations by Elimination Method (7:42)
- Video - Simultaneous Equations: Elimination Method (5:53)
- Topic - Elimination Method by Subtracting Equations
- Topic - Elimination Method by Adding Equations
- Topic - Elimination Method by Considering One Coefficient
- Topic - Elimination Method by Considering Two Coefficients
- Video - Elimination Method for Simultaneous Equations (3:32)
- Linear Simultaneous Equations - Substitution Method10 Topics|3 Quizzes
- Video - Equation Method for Simultaneous Equations (2:16)
- Video - Basic Substitution Method for Simultaneous Equations (6:43)
- Video - Substitution Method for Simultaneous Equations (7:48)
- Video - Simultaneous Equations by Substitution Method (5:26)
- Video - Simultaneous Equations: Substitution Method (3:00)
- Topic - Basic Substitution Method
- Topic - Substitution Method by Non-Monic Equations
- Topic - Substitution Method by Equating Equations
- Topic - Substitution Method by Rearranging Equations
- Topic - Substitution Method by Rearranging Non-Monic Equations
- Video - Equation Method for Simultaneous Equations (2:16)
- Numerical Application of Linear Simultaneous Equations5 Topics|2 Quizzes
- Video - Number Applications of Simultaneous Equations 1 (2:58)
- Video - Number Applications of Simultaneous Equations 2 (2:54)
- Video - Number Applications of Simultaneous Equations 3 (2:11)
- Video - Number Applications of Simultaneous Equations 4 (1:42)
- Video - Digit Applications of Simultaneous Equations (8:33)
- Video - Number Applications of Simultaneous Equations 1 (2:58)
- Practical Application of Linear Simultaneous Equations10 Topics|3 Quizzes
- Video - Coin Value Applications of Simultaneous Equations 1 (3:12)
- Video - Coin Value Applications of Simultaneous Equations 2 (2:52)
- Video - Age Applications of Simultaneous Equations 1 (2:04)
- Video - Age Applications of Simultaneous Equations 2 (3:51)
- Video - Geometry Applications of Simultaneous Equations 1 (3:14)
- Video - Geometry Applications of Simultaneous Equations 2 (3:13)
- Video - Cost Applications of Simultaneous Equations 1 (2:59)
- Video - Cost Applications of Simultaneous Equations 2 (2:01)
- Video - Measurement Applications of Simultaneous Equations (2:23)
- Video - Review Problem Solving of Simultaneous Equations (6:09)
- Video - Coin Value Applications of Simultaneous Equations 1 (3:12)
- Quadratic Simultaneous Equations8 Topics
- Video - Understanding Simultaneous Equations involving Quadratics (2:29)
- Video - Two Intersections of Quadratic Equations and Linear Equations (4:55)
- Video - One Intersection of Quadratic Equations and Linear Equations (1:35)
- Video - Intersections of Hyperbola and Linear Equations (4:01)
- Video - Quadratic and Linear Simultaneous Equations (3:08)
- Video - Simultaneous Equations in Quadratics & Straight Lines (3:27)
- Video - Simultaneous Equations in Quadratics with No Solutions (2:30)
- Video - Simultaneous Equations in Two Quadratics (3:24)
- Video - Understanding Simultaneous Equations involving Quadratics (2:29)
- Quadratic Simultaneous Equations involving Hyperbolae3 Topics
- Undefined or All Real Values of Simultaneous Equations9 Topics|3 Quizzes
- Video - No Points of Intersection of Two Straight Lines (2:16)
- Video - Simultaneous Equations by Substitution Method & Graphs (4:55)
- Video - Simultaneous Equations in No Solutions & Graphs (3:40)
- Video - Theory of Undefined Solutions in Simultaneous Equations (2:56)
- Video - Simultaneous Equations in Undefined Solutions (2:49)
- Video - Simultaneous Equations in All Real Value Solutions (2:20)
- Video - Simultaneous Equations: No Solutions (1:39)
- Video - Simultaneous Equations: All Real values (2:23)
- Video - Intersections of Hyperbola and Linear Equations: Undefined (2:23)
- Video - No Points of Intersection of Two Straight Lines (2:16)
- RELATED RATES OF CHANGE
- Constant Rates8 Topics
- Video - Definition of Rates of Change (4:55)
- Topic - Choosing Constant Rates
- Topic - Graphs of Constant Rates
- Topic - Constant Rates of Change: Positive, Negative or Zero
- Topic - Constant Rates of Change: Behaviours
- Topic - Calculating Constant Rates of Change
- Topic - Constant Rates of Change: Rules
- Topic - Constant Rates of Change: Empty Swimming Pool
- Video - Definition of Rates of Change (4:55)
- Average Rates of Change5 Topics|3 Quizzes
- DIFFERENTIATION
- Basic Differentiation Rules11 Topics|3 Quizzes
- 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 - 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)
- Video - Differentiation of Constant Terms (2:14)
- Differentiation of Surds4 Topics
- Chain Rule13 Topics|3 Quizzes
- 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
- Video - Fundamental of Chain Rule (7:58)
- Product Rule9 Topics|3 Quizzes
- 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
- Video - Fundamental of Product Rule (7:49)
- Quotient Rule8 Topics|3 Quizzes
- 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
- Video - Fundamental of Quotient Rule (2:53)
- Higher Derivatives8 Topics|3 Quizzes
- 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
- Video - Fundamental of Higher Derivatives (5:34)
- APPLICATION OF DIFFERENTIATION
- Tangents8 Topics|3 Quizzes
- 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)
- Video - Gradient of Tangents (4:46)
- Normals6 Topics|3 Quizzes
- 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)
- Video - Equation of Normals (7:13)
- Increasing and Decreasing Functions6 Topics|3 Quizzes
- Turning Points10 Topics|3 Quizzes
- 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)
- Video - Coordinates of Turning Points (7:30)
- Points of Inflection and Concavity6 Topics|3 Quizzes
- Curves of Rational Functions in Quadratics by Linear Form5 Topics
- Sketching Graphs Containing Stationary Points4 Topics
- Curves of Rational Functions in Quadratics by Quadratic Form9 Topics
- Video - Understanding Curve Sketching involving Symmetry (1:24)
- Video - Even Functions Odd Functions (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)
- Video - Understanding Curve Sketching involving Symmetry (1:24)
- Gradient Functions11 Topics
- Video - Principle of Graphing Gradient Functions (5:08)
- Video - Gradient Function Graphs of Straight Lines (5:23)
- Video - Gradient Function Graphs of Parabola (8:13)
- Video - Gradient Function Graphs of Cubic Functions (10:46)
- Video - Gradient Function Graphs of Hyperbola (13:22)
- Video - Gradient Function Graphs of Surds (12:19)
- Video - Gradient Function Graphs of Periodic Functions (8:15)
- Video - Gradient Function Graphs of Quartic Functions (8:25)
- Video - Gradient Function Graphs of Semicircle (2:24)
- Video - Gradient Function Graphs of Exponential Functions (2:11)
- Video - Gradient Function Graphs of Logarithmic Functions (1:47)
- Video - Principle of Graphing Gradient Functions (5:08)
- Sketching Curves from Derivatives5 Topics
- Video - Introduction to Sketching Curves from Derivatives (7:49)
- Video - Sketching Curves from Derivatives involving Concave Down (3:35)
- Video - Sketching Curves from Derivatives involving Point of Inflection (2:39)
- Video - Sketching Curves from Graphs of Derivatives 1 (4:33)
- Video - Sketching Curves from Graphs of Derivatives 2 (8:23)
- Video - Introduction to Sketching Curves from Derivatives (7:49)
- Optimisation9 Topics|3 Quizzes
- 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)
- Video - Maxima and Minima of Quadratic Functions (4:16)
- EXPONENTIAL FUNCTIONS
- Derivative of Exponential Functions8 Topics|3 Quizzes
- 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)
- Video - Derivative of Exponential Functions (1:30)
- Integration of Exponential Functions4 Topics|3 Quizzes
- Definite Integral of Exponential Functions6 Topics|3 Quizzes
- Video - Definite Integration of Exponential Functions (6:47)
- Video - Volume of Region bounded by Exponential Graphs (1:57)
- Topic - Definite Integral of Exponential Functions
- Topic - Definite Integral of Exponential Functions involving Reciprocals
- Topic - Definite Integral of Exponential Functions involving Expansions
- Topic - Definite Integral of Exponential Functions involving Surds
- Video - Definite Integration of Exponential Functions (6:47)
- Exponential Growth4 Topics|3 Quizzes
- Exponential Decay4 Topics|3 Quizzes
- Derivative of Logarithmic Functions9 Topics|3 Quizzes
- 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)
- Video - Fundamental of Derivative of Logarithmic Functions (2:41)
- HYPERBOLA
- Definition of Hyperbola5 Topics
- Hyperbola12 Topics
- Video - Plotting Hyperbola From Tables (3:50)
- Video - Graphs of Hyperbola (2:14)
- Video - Hyperbola: Basics (3:27)
- Video - Hyperbola: Transform involving Steepness (1:37)
- Video - Hyperbola: Shift Upwards (1:00)
- Video - Hyperbola: Transform Symmetrically & Shift Downwards (2:29)
- Video - Hyperbola: Shift to the Left (1:32)
- Video - Hyperbola: Transform Symmetrically & Shift to the Right (2:09)
- Video - Vertical Asymptotes & Horizontal Asymptotes (4:02)
- Video - Transformation of Hyperbola by Partial Fractions 1 (3:26)
- Video - Transformation of Hyperbola by Partial Fractions 2 (2:43)
- Video - Transformation of Hyperbola by Reformatting (2:22)
- Video - Plotting Hyperbola From Tables (3:50)
- Equations of Hyperbola8 Topics
- Video - Rules of Transformation of Hyperbola (1:35)
- Video - Transformation of Hyperbola (5:57)
- Video - Transformation of Hyperbola by Completing the Square (5:14)
- Video - Finding Equations of Hyperbola (5:53)
- Video - Parametric Equations of Hyperbola (3:01)
- Video - Constant Distance between Foci from Points on Hyperbola (3:50)
- Video - Same Focus between Hyperbolas (2:47)
- Video - Determination Being Hyperbola (1:51)
- Video - Rules of Transformation of Hyperbola (1:35)
- Inequalities involving Hyperbola1 Topic
- Sketching Rectangular Hyperbola6 Topics
- Video - Rotation of Rectangular Hyperbola (7:00)
- Video - Sketching Rectangular Hyperbola (2:23)
- Video - Directrices of Rectangular Hyperbola (3:42)
- Video - Sketching Rectangular Hyperbola with Directrices (2:18)
- Video - Foci of Rectangular Hyperbola (4:43)
- Video - Sketching Rectangular Hyperbola with Directrices & Foci (3:21)
- Video - Rotation of Rectangular Hyperbola (7:00)
- Parametric Equations of Rectangular Hyperbola3 Topics
- Tangents and Normals of Rectangular Hyperbola4 Topics
- PARAMETERS
- Parametric Equations5 Topics
- Tangents and Normals3 Topics
- Parametric Equations of Parabolas4 Topics
- Parametric Equations of Circles5 Topics
- Parametric Equations of Ellipses3 Topics
- Parametric Equations of Hyperbolas2 Topics
- INTEGRATION
- Basic Integration Rules5 Topics|3 Quizzes
- Integration of Power Functions8 Topics|3 Quizzes
- 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)
- Video - Principle of Integration of Power Function (2:49)
- Particular Values8 Topics|3 Quizzes
- 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
- Video - Finding Integral Constants (7:27)
- Indefinite Integration by Recognition10 Topics
- 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)
- Video - Reverse Chain Rule (7:06)
- Graphs of Antiderivatives of Functions3 Topics
- Basic Integration Rules involving Algebra6 Topics
- Upper and Lower Rectangles4 Topics|3 Quizzes
- Definite Integrals8 Topics|3 Quizzes
- 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)
- Video - Theory of Definite Integrals (5:46)
- Definite Integration of Power Functions5 Topics|3 Quizzes
- 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
- Video - Definite Integrals of Power Functions (5:22)
- Proofs involving Definite Integrals4 Topics
- Definite Integrals of Even and Odd Functions4 Topics
- APPLICATION OF INTEGRATION
- Area Under a Curve3 Topics|3 Quizzes
- Integration and Displacement Velocity and Acceleration2 Topics
- Area between Two Functions3 Topics|3 Quizzes
- Kinematics using Integration6 Topics|3 Quizzes
- 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)
- Video - Expression of the Distance using Integration (2:23)
- Area Between Y-axis3 Topics
- Signed Areas3 Topics
- Area between Two Functions involving Signed Areas3 Topics
- ELLIPSE
- Definition of Ellipse6 Topics
- Tangents and Ellipse10 Topics
- Video - Equation of Tangents of Ellipse using Implicit Differentiation (3:13)
- Video - Tangents of Ellipse with Latus Rectum by Implicit Differentiation (6:42)
- Video - Equation of Tangents of Ellipse that are Perpendicular (2:32)
- Video - Tangent from External Point of Ellipse by Discriminant (6:42)
- Video - Tangent of Ellipse given Gradient using Discriminant (2:13)
- Video - Locus of Perpendicular Tangents of Ellipse using Discriminant (4:04)
- Video - Gradient of Tangent to Ellipse with Parametric Equations (3:02)
- Video - Tangents to Ellipse & Circle with Parametric Equations (9:20)
- Video - Tangents & Normals to Ellipse (11:19)
- Video - Tangents & Normals to Ellipse with Perpendicular Distances (4:31)
- Video - Equation of Tangents of Ellipse using Implicit Differentiation (3:13)
- Equations of Ellipse5 Topics
- PARABOLA
- Transformation of a Parabola10 Topics
- Video - Introduction to Transformation of Parabola Parallel to y-axis (4:59)
- Video - Transformation of Parabola Parallel to y-axis: Shift Right (4:03)
- Video - Transformation of Parabola Parallel to y-axis: Shift Left & Move Up (5:13)
- Video - Equation of Parabola Parallel to y-axis using Vertex and Focus (4:09)
- Video - Equation of Parabola using Vertex & Directrix (3:38)
- Video - Introduction to Transformation of Parabola Parallel to x-axis (3:36)
- Video - Transformation of Parabola Parallel to x-axis (5:00)
- Video - Transformation of Parabola Parallel to x-axis by Completing the Square (7:34)
- Video - Equation of Parabola using Focus & Directrix (2:54)
- Video - Equation of Parabola Parallel to x-axis using Vertex & Focus (2:48)
- Video - Introduction to Transformation of Parabola Parallel to y-axis (4:59)
- Tangents and Normals of Parabola4 Topics
- Chords of Contact5 Topics
- Components of a Parabola8 Topics
- Video - Introduction to Parabola (5:21)
- Video - Parabola Symmetric to y-axis: Concave Up (4:11)
- Video - Parabola Symmetric to y-axis: Concave Down (4:30)
- Video - Finding Equation using Focus & Directrix (1:59)
- Video - Finding Equation using Vertex & Focal Length (3:06)
- Video - Parabola Symmetric to x-axis: Introduction (12:12)
- Video - Parabola Symmetric to x-axis: Concave Right (2:59)
- Video - Parabola Symmetric to x-axis: Concave Left (3:48)
- Video - Introduction to Parabola (5:21)
- CIRCLES
- Circles7 Topics
- Video - Graphs of Circles (2:47)
- Video - Graphs of Circles using Centre & Radius (6:39)
- Video - Sketching Circles (5:14)
- Video - Finding Equations of Circles from Graphs (3:54)
- Video - Theory of General Equation of a Circle (3:31)
- Video - General Equation of a Circle (4:59)
- Video - Equation of Circles (7:02)
- Video - Graphs of Circles (2:47)
- Circle Definitions1 Topic
- Circles with Completing Squares4 Topics
- Circles and Pythagoras' Theorem4 Topics
- Regions of Circles and Hyperbolas6 Topics
- Video - Graphing Regions of Circles: Basic Form (3:06)
- Video - Graphing Regions of Circles: Completed Square Form (3:01)
- Video - Graphing Regions of Circles: Reformat to Completed Square Form (3:04)
- Video - Graphing Regions of Circles: Conjunctions with Straight Lines (3:49)
- Video - Regions involving Circles (5:02)
- Video - Regions involving Hyperbola (1:20)
- Video - Graphing Regions of Circles: Basic Form (3:06)
- COMPLEX NUMBERS
- Negative Discriminant and Imaginary Numbers5 Topics
- Introduction to Complex Numbers3 Topics
- Operations with Complex Numbers4 Topics
- Equality of Complex Numbers5 Topics
- Complex Conjugates7 Topics
- Video - Conjugate Pairs of Complex Numbers (3:54)
- Topic - Writing Conjugate Pairs of Complex Numbers
- Topic - Writing Conjugate Pairs of Complex Numbers using Notation
- Topic - Proof using Conjugate Pairs 1
- Topic - Proof using Conjugate Pairs 2
- Topic - Quadratic Equations with Real Coefficients Having Complex Roots 1
- Topic - Quadratic Equations with Real Coefficients Having Complex Roots 2
- Video - Conjugate Pairs of Complex Numbers (3:54)
- Conjugates and Division of Complex Numbers7 Topics
- Video - Realising the Denominators using Conjugate Pairs (6:28)
- Video - Proof regarding Conjugate Pairs (4:13)
- Video - Proof regarding Conjugate Pairs & Realising Denominators (2:20)
- Topic - Division of Complex Numbers 1
- Topic - Division of Complex Numbers 2
- Topic - Multiplicative Inverse of Complex Numbers 1
- Topic - Multiplicative Inverse of Complex Numbers 2
- Video - Realising the Denominators using Conjugate Pairs (6:28)
- Properties of Conjugates4 Topics
- Square Roots of Complex Numbers5 Topics
- Video - Square Roots of Complex Numbers in Positive Real Parts (13:45)
- Video - Square Roots of Complex Numbers in Negative Real Parts (4:50)
- Video - Square Roots of Complex Numbers using Factorise Method 1 (7:03)
- Video - Square Roots of Complex Numbers using Factorise Method 2 (5:33)
- Video - Square Roots of Complex Numbers with Irrational Coefficients (2:43)
- Video - Square Roots of Complex Numbers in Positive Real Parts (13:45)
- 2-D Vectors5 Topics
- Modulus9 Topics
- Topic - Modulus of Complex Numbers
- Topic - Modulus of Purely Imaginary Complex Numbers
- Topic - Modulus of Purely Real Complex Numbers
- Topic - Modulus of Conjugate Pairs
- Topic - Modulus of Polar Form
- Topic - Proof Regarding Modulus
- Topic - Proof Regarding Modulus and Conjugate Pairs
- Topic - Modulus Squared and Multiple of Complex Number and its Conjugate
- Topic - Finding Modulus by Polar Form
- Topic - Modulus of Complex Numbers
- Complex Number Plane or Argand Diagram4 Topics
- Complex Factors of Polynomials15 Topics
- Topic - Factorise two-term quadratics over complex number field 1
- Topic - Factorise two-term quadratics over complex number field 2
- Topic - Factorise three-term quadratics over complex number field 1
- Topic - Factorise three-term quadratics over complex number field 2
- Topic - Factorise three-term quadratics over complex number field 3
- Topic - Factorise two-term quartics over complex number field
- Topic - Factorise three-term quartics over complex number field
- Topic - Find all factors of cubic polynomials over complex number field 1
- Topic - Find all factors of cubic polynomials over complex number field 2
- Topic - Find all factors of cubic polynomials over complex number field 3
- Topic - Find all factors of quartic polynomials over complex number field
- Topic - Complex roots and conjugate root theorem 1
- Topic - Complex roots and conjugate root theorem 2
- Topic - Complete Polynomials with Imaginary Coefficients using Factors 1
- Topic - Complete Polynomials with Imaginary Coefficients using Factors 2
- Topic - Factorise two-term quadratics over complex number field 1
- Equations over Complex Number Field5 Topics
- Video - Complex Roots of Quadratic Equations (4:06)
- Video - Complex Roots of Cubic Equations (2:35)
- Video - Complex Roots of Quadratic Equations using Quadratic Formula (4:19)
- Video - Quadratics in Complex Number Field using Quadratic Formula (2:41)
- Video - Quadratics in Complex Number Field using Completing Square (7:54)
- Video - Complex Roots of Quadratic Equations (4:06)
- Connection to Coordinate Geometry5 Topics
- Modulus-Argument (Polar) Form7 Topics
- Video - Understanding Modulus-Argument Form (8:13)
- Topic - Horizontal Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Vertical Complex Numbers to Modulus-Argument (Polar) Form
- Topic - First Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Second Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Third Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Fourth Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Video - Understanding Modulus-Argument Form (8:13)
- Properties of Argument4 Topics
- Conversion between Cartesian and Polar Forms9 Topics
- Video - Complex Numbers in 1st Quarter to Mod-Arg Form (4:26)
- Video - Complex Numbers in 2nd Quarter to Mod-Arg Form (2:33)
- Video - Complex Numbers in 4th Quarter to Mod-Arg Form (4:29)
- Video - Complex Numbers in Purely Real to Mod-Arg Form (2:23)
- Video - Complex Numbers in Purely Imaginary to Mod-Arg Form (1:47)
- Video - Modulus-Argument Form to Cartesian Form (5:38)
- Video - Mod-Arg Form to Cartesian Form in Pure Real or Imaginary (4:23)
- Video - Simplifying Complex Numbers using Mod-Arg Form (3:45)
- Video - Exact Values of Sine & Cosine using Mod-Arg Form (4:57)
- Video - Complex Numbers in 1st Quarter to Mod-Arg Form (4:26)
- De Moivre's Theorem10 Topics
- Video - Understanding De Moivre's Theorem (2:44)
- Video - Proof of De Moivre's Theorem Multiplication (3:42)
- Video - Proof of De Moivre's Theorem Division (2:20)
- Video - Proof of De Moivre's Theorem Subtraction (4:04)
- Video - Simplifying Complex Numbers using De Moivre's Theorem (7:42)
- Video - Purely Imaginary using De Moivre's Theorem (5:11)
- Video - Purely Real using De Moivre's Theorem (5:24)
- Video - Trigonometric Expression using De Moivre's Theorem (5:27)
- Video - De Moivre's Theorem involving Conjugate Pairs (6:58)
- Video - Trigonometric Properties & De Moivre's Theorem (6:04)
- Video - Understanding De Moivre's Theorem (2:44)
- Roots of Complex Numbers7 Topics
- Video - 4th Roots of 4 using Complex Numbers (2:32)
- Video - 5th Roots of -32 using Complex Numbers (2:45)
- Video - Cube Roots of i using Complex Numbers (2:19)
- Video - 4th Roots of -16i using Complex Numbers (1:42)
- Video - 5th Roots of 1+i using Complex Numbers (2:07)
- Video - Cube Roots of Irrational Real Part & i using Complex Numbers (1:30)
- Video - Exact Values of Trigonometric Ratios involving Fifth Roots (6:37)
- Video - 4th Roots of 4 using Complex Numbers (2:32)
- Factorising using Complex Numbers5 Topics
Lesson 81 of 124
In Progress
APPLICATION OF INTEGRATION
