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ALGEBRAIC FRACTIONS

Home > My Courses > HSC Year 11 Mathematics Advanced – Functions > ALGEBRAIC FRACTIONS
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HSC Year 11 Mathematics Advanced - Functions

EXPONENTS
Powers and Bases
  • Topic – Powers & Bases
  • Topic – Factor Form
  • Topic – Multiple Index Form
  • Topic – Writing Index Form from Normal Numerals
  • Topic – Writing Index by Factorising Normal Numerals in Two bases
  • Topic – Writing Index by Factorising Normal Numerals in Three Bases
Multiplication using Exponents
  • Video – Index Law of Addition (6:17)
  • Video – Index Equations using Index Law of Addition (3:17)
  • Video – Evaluation using Index Law of Addition (5:12)
  • Video – Simplification using Index Law of Addition (3:32)
  • Video – Addition Law of Exponents (4:12)
  • Video – Multiplication using Indices (3:32)
  • Topic – Equations by Adding Indices
  • Topic – Simplifying by Adding Indices
  • Topic – Evaluation by Adding Indices
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 – Subtraction Law of Exponents (3:26)
  • Video – Division using Indices (5:20)
  • Topic – Simplifying by Subtracting Indices
  • Topic – Simplifying by Adding and Subtracting Indices
  • Topic – Evaluation by Subtracting Indices
Zero Index
  • Video – Index Law of Zero Power (5:52)
  • Video – Further Index Law of Zero Power (3:58)
  • Video – Zero Exponents (2:26)
  • Video – Index Equations Involving Zero Indices (1:45)
  • Topic – Zero Indices
Raising a Power to Another Power
  • Video – Index Law of Powers (4:35)
  • Video – Simplification using Index Law of Powers (6:53)
  • Video – Evaluation using Index Law of Powers (6:37)
  • Video – Index Law of Raising a Power to Another Power (4:19)
  • Video – Raising a Power to Another Base (5:27)
  • Video – Raising a Power to Another Indices (5:56)
  • Topic – Equations involving Power of Power
  • Topic – Simplifying by Power of Power
  • Topic – Evaluation by Power of Power
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 – Quadratic Equations involving Negative Indices (1:05)
  • Topic – Rational Fractions and Negative Indices
  • Topic – Handling Negative Indices
  • Topic – Expressing with Negative Indices
Negative Bases
  • Video – Negative Bases in Index Form (3:49)
  • Topic – Odd Power and Even Power of Negative Bases
  • Topic – Negative Bases in Brackets
Rational Exponents
  • Video – Rational Exponents using Index Law of Addition (4:50)
  • Video – Rational Exponents using Index Law of Subtraction (2:38)
  • Video – Rational Exponents using Index Law of Powers (3:10)
  • Video – Rational Exponents using Surds (4:00)
  • Video – Index Form in Rational Indices (5:42)
  • Video – Index Form in Negative Indices (4:46)
  • Video – Evaluating Rational Indices using Calculators (2:34)
  • Video – Equations involving Rational Indices (2:03)
Complicated Exponent Laws
  • Video – Mixed Indices (3:34)
  • Video – Evaluating Rational Expressions Given Index Values (3:29)
SURDS
Surd Definition
  • Video – Introduction to Surds (3:09)
  • Video – Introduction to Rational & Irrational Numbers (2:17)
  • Topic – Drag to arrange the numbers in ascending order
Simplifying Surds
  • Video – Simplifying Square Roots (5:22)
  • Video – Simplifying Cube Roots (4:39)
  • Video – Simplifying Quad Roots (2:11)
  • Video – Simplifying Cube Roots and Quad Roots (4:19)
  • Video – Simplifying Square Roots using Tree Diagrams (6:01)
  • Video – Simple Equations involving Surds (1:32)
  • Video – Completing the Surds (1:36)
  • Video – Simple Equations involving Higher Order Surds (3:13)
  • Video – Completing the Higher Order Surds (5:27)
Addition and Subtraction of Surds
  • Video – Simplifying Simple Surds (2:32)
  • Video – Simplifying by Completing Surds (4:16)
  • Video – Simplifying by Completing Surds in Multiple Like Terms (3:47)
  • Video – Basic Rules of Surds: Addition & Subtraction (3:14)
Multiplication of Surds
  • Video – Multiplication of Surds (2:00)
  • Video – Simplifying after Multiplication of Surds (2:35)
  • Video – Multiplying Surds (5:26)
  • Video – Multiplying Surds Resulting Integers (2:34)
  • Video – Basic Rules of Surds: Multiplication (6:02)
Division of Surds
  • Video – Division of Surds (1:01)
  • Video – Simplifying after Division of Surds (1:41)
  • Video – Dividing Surds (5:01)
  • Video – Dividing Surds Resulting Rational Numbers (1:37)
  • Video – Basic Rules of Surds: Division (0:36)
Distributive Law of Surds
  • Video – Expansion of Surds 1 (3:20)
  • Video – Expansion of Surds 2 (3:57)
  • Video – Binomial Products of Two Surds (3:13)
  • Video – Binomial Products of Three Surds (1:11)
  • Video – Binomial Products of Four Surds 1 (1:59)
  • Video – Binomial Products of Four Surds 2 (2:16)
  • Video – Binomial Products of Four Surds 3 (1:21)
  • Video – Binomial Products of Four Surds 4 (2:37)
  • Video – Expansion & Simplify of Surds 2 by 3 (6:26)
  • Video – Expansion & Further Simplify of Surds 2 by 3 (5:30)
  • Video – Difference of Squares with Surds (4:45)
  • Video – Difference of Squares with Surds of Surds (2:13)
  • Video – Basic Rules of Surds: Expanding Binomial Terms (3:53)
Square of Binomial Expansions involving Surds
  • Video – Square of Binomial Expansion involving Surds (4:07)
  • Video – Square of Binomial Expansion involving Surds with Coefficients (6:55)
  • Video – Finding Unknowns using Square of Binomials with Surds (3:46)
Cube of Binomial Expansions involving Surds
  • Video – Cube of Binomial Expansion involving Surds (2:33)
  • Video – Finding Unknowns using Cube of Binomials with Surds (4:02)
Rationalising Denominators
  • Video – Rationalise Denominators in Single Term Denominators (5:37)
  • Video – Rationalise Denominators in Single Term Denominators & Simplifying (2:49)
  • Topic – Rationalising Denominators: Basic 1
  • Topic – Rationalising Denominators: Basic 2
  • Topic – Rationalising Denominators: Simplifying Surds
  • Topic – Rationalising Denominators: Simplifying Fractions
Rationalising Denominators using Conjugate Pairs
  • Video – Rationalise Denominators using Conjugate Pairs (5:31)
  • Video – Rationalise Denominators using Conjugate Pairs & Simplifying (4:01)
  • Video – Rationalise Denominators using Conjugate Pairs & Binomial Numerators (6:38)
  • Video – Pronumerals using Rationalise Denominators (7:49)
  • Video – Simplify Fractions using Rationalise Denominators & Multiplications (5:17)
  • Video – Simplify Fractions using Rationalise Denominators & Additions 1 (6:09)
  • Video – Simplify Fractions using Rationalise Denominators & Additions 2 (4:45)
  • Video – Simplify Fractions using Rationalise Denominators & Additions 3 (3:57)
  • Video – Simplify Fractions using Rationalise Denominators & Additions 4 (3:00)
  • Video – Simplify Fractions using Rationalise Denominators & Additions 5 (3:10)
Equality of Surds
  • Topic – Equality of Surds: Basic Comparison
  • Topic – Equality of Surds: Single Term Comparison
  • Topic – Equality of Surds by Simplification
  • Topic – Equality of surds involving Simultaneous Equations 1
  • Topic – Equality of surds involving Simultaneous Equations 2
  • Topic – Equality of surds involving Simultaneous Equations 3
  • Topic – Equality of surds involving Simultaneous Equations 4
  • Topic – Equality of surds involving Simultaneous Equations 5
Equations involving Surds
  • Video – Equations involving Square Roots (6:19)
  • Video – Equations involving Cube Roots (1:05)
  • Video – Quadratic Equations using Substitutions involving Surds (1:30)
  • Video – Quadratic Equations involving Surds Solving by Quadratic Equations (4:58)
  • Video – Quadratic Equations from Surds (6:59)
  • Video – Quadratic Equations from Surds & Fractions (2:49)
  • Video – Equations involving Nested Surds (2:23)
  • Video – Equations involving Surds (7:18)
  • Video – Linear Equations involving Surds (1:41)
QUADRATIC EQUATIONS
What are Quadratic Equations?
  • Video – Simple Quadratic Equations (3:31)
  • Video – Basic Quadratic Equations (3:05)
  • Topic – What are Quadratic Equations?
  • Topic – Quadratic Equations in Standard Form 1
  • Topic – Quadratic Equations in Standard Form 2
  • Topic – Quadratic Equations in Standard Form 3
Finding Solutions by Inspecting Graphs
  • Topic – Number of Roots of Quadratic Equations by Inspecting Graphs
  • Topic – Roots of Quadratic Equations by Inspecting Graphs
Quadratic Equations in Factorised Form
  • Video – Solving Quadratic Equations by Factors (3:55)
  • Topic – Monic Times Monic
  • Topic – Non-Monic Expressions
  • Topic – Zeroes & Linear Factors
  • Topic – Non-Monic Zeroes & Linear Factors
  • Topic – Non-Monic Times Non-Monic
Quadratic Equations in Square Form
  • Video – Basic Quadratic Equations in Approximated Solutions (2:30)
  • Video – Quadratic Equations in Completing Square Form (4:38)
  • Video – Quadratic Equations with Square Roots (4:53)
  • Video – Quadratic Equations in Completing Square Form with Surds (6:45)
  • Topic – Quadratic Equations in Square Form: Basic
  • Topic – Quadratic Equations in Square Form: Non-Monic
  • Topic – Quadratic Equations in Square Form: Non-Monic & Moving Terms
  • Topic – Quadratic Equations in Square Form: No Solutions
  • Topic – Quadratic Equations in Square Form: Zeroes
  • Topic – Quadratic Equations in Square Form: Simplifying
  • Topic – Quadratic Equations in Square Form: Non-Monic Simplifying
  • Topic – Quadratic Equations in Square Form: Variables on Both Sides
  • Topic – Quadratic Equations in Square Form: Completed Square Form
  • Topic – Quadratic Equations in Square Form: Non-Monic Completed Square Form
  • Topic – Quadratic Equations in Square Form: Zeroes in Completed Square Form
Quadratic Identities
  • Video – Theory of Quadratic Identities (3:15)
  • Video – Quadratic Identities: Expanding & Comparing 1 (6:13)
  • Video – Quadratic Identities: Expanding & Comparing 2 (6:08)
  • Video – Quadratic Identities: Expanding & Comparing 3 (3:31)
  • Video – Quadratic Identities: Expressing in Quadratic Form (7:52)
  • Topic – Quadratic Identities: Simple Comparison
  • Topic – Quadratic Identities: Expand and Comparison
  • Topic – Quadratic Identities: Substitution 1
  • Topic – Quadratic Identities: Substitution 2
Substitutions into Quadratics
  • Video – Finding y-values Given x-values from Quadratics (2:42)
  • Video – Quadratics: Substituting Points (1:51)
  • Video – Quadratics: Finding x given y (5:41)
  • Topic – Substitutions into Quadratics
  • Topic – Checking Quadratics
  • Topic – Substitution into Quadratic Function Values: Single Values
  • Topic – Substitution into Quadratic Function Values: Two Values 1
  • Topic – Substitution into Quadratic Function Values: Two Values 2
  • Topic – Substitution into Quadratic Function Values: Quadratic Formula
  • Topic – Substitution into Quadratic Function Values: No Values
Solving by Factorisation
  • Video – Solving Quadratic Equations by Factorise (6:04)
  • Video – Solving Quadratic Equations by Factorise involving Rearrangements (9:34)
  • Video – Quadratic Equations using Substitutions (9:04)
  • Video – Quadratic Equations using Indices (4:21)
  • Video – Equations Involving Higher Orders (5:38)
  • Video – Equations Involving Higher Orders with Undefined Solutions (1:35)
  • Video – Solving Quadratic Equations by Factorising Monic Quadratic Trinomials (2:22)
  • Video – Solving Non-Monic Quadratic Equations by Factorising (4:09)
  • Video – Solving Quadratic Equations by Rearranging and Factorising (1:26)
  • Video – Quadratic Equations by Factorise Difference of Squares (1:30)
Solving by Factorisation involving Fractions
  • Video – Quadratic Equations involving Fractions 1 (6:34)
  • Video – Quadratic Equations involving Fractions 2 (3:31)
  • Video – Quadratic Equations using Indices with Undefined Solutions (2:21)
Solving by Completing the Square
  • Video – Quadratic Equations given Perfect Square (4:01)
  • Video – Quadratic Equations given Perfect Square involving Irrationals (2:09)
  • Video – Evaluation of the Solutions to Decimal Numbers (2:55)
  • Video – Theory of Completing Square for Solving Quadratic Equations (6:44)
  • Video – Non-Monic Completing the Square by Filling Blanks (6:36)
  • Video – Non-Monic Completing the Square (5:33)
  • Video – Solving Monic Quadratic Equations by Completing the Square (8:06)
  • Video – Solving Non-Monic Quadratic Equations by Completing the Square (9:01)
  • Video – Basics of Completing the Square (6:14)
  • Video – Completing the Square with Rational Numbers (4:48)
  • Video – Solving by Completing the Square (3:12)
  • Video – Solving by Completing the Square of Non-Monic Quadratic Equations (3:41)
  • Video – Solving Quadratic Equations by Completing the Square (2:49)
Quadratic Formula
  • Video – Deriving Quadratic Formula (4:50)
  • Video – Solving Quadratic Equations using Quadratic Formula 1 (9:00)
  • Video – Solving Quadratic Equations using Quadratic Formula 2 (6:50)
  • Video – Forming Quadratic Equations using Quadratic Formula (2:45)
  • Video – Quadratic Equations using Quadratic Formula Approximated Roots (6:18)
  • Video – Quadratic Equations using Quadratic Formula Undefined Solutions (2:23)
  • Video – Quadratic Equations using Substitutions involving Quadratic Formula (4:50)
  • Topic – Quadratic Formula: Monic Quadratic Equations
  • Topic – Quadratic Formula: Non-Monic Quadratic Equations
  • Topic – Quadratic Formula: Monic Equations
  • Topic – Quadratic Formula: Non-Monic Equations
  • Topic – Quadratic Formula: Undefined
Problem Solving with Quadratics
  • Video – Product of Two Consecutive Numbers by Quadratic Equations (5:31)
  • Video – Product of Two Consecutive Odd Numbers by Quadratic Equations (2:44)
  • Video – Sum of Squares of Numbers by Quadratic Equations (4:20)
  • Video – Sum of Number and Its Reciprocal by Quadratic Equations (3:49)
  • Video – Checking the Solutions of Quadratic Equations (8:51)
  • Video – Application of Quadratic Equations: Finding Numbers (2:10)
  • Video – Application of Quadratic Equations: Sum of N Positive Integers (3:08)
  • Video – Applications of Quadratic Functions (3:16)
Problem Solving with Quadratics involving Geometry
  • Video – Right-Angled Triangle by Quadratic Equations (2:39)
  • Video – Area of Composite Shapes by Quadratic Equations (5:28)
  • Video – Similar Triangles by Quadratic Equations (3:43)
  • Video – Intersections of Quadratic Parabola and Straight Line (3:29)
  • Video – Application of Quadratic Equations: Area of Rectangular Shapes (2:34)
  • Video – Application of Quadratic Equations: Border of Rectangular Fields (7:44)
  • Video – Quadratic Equations using Pythagoras Theorem (3:04)
ALGEBRAIC FRACTIONS
Adding and Subtracting Algebraic Fractions
  • Video – Simplifying Fractions with Same Denominators (4:10)
  • Video – Simplifying Fractions with Different Denominators (5:18)
  • Video – Adding Algebraic Fractions (0:48)
  • Video – Subtracting Algebraic Fractions (3:22)
  • Video – Adding Algebraic Fractions involving Expansions (4:35)
  • Video – Subtracting Algebraic Fractions involving Expansions (3:23)
  • Topic – Algebraic Fractions: Addition and Subtraction
  • Topic – Algebraic Fractions: Simplify by Denominators
  • Topic – Algebraic Fractions: Simplify by More Denominators
Multiplying and Dividing Algebraic Fractions
  • Video – Multiplying Algebraic Fractions (2:16)
  • Video – Dividing Algebraic Fractions (5:35)
  • Topic – Multiplying Algebraic Fractions 1
  • Topic – Multiplying Algebraic Fractions 2
  • Topic – Multiplying Algebraic Fractions 3
  • Topic – Multiplying Algebraic Fractions 4
  • Topic – Multiplying Algebraic Fractions 5
  • Topic – Dividing Algebraic Fractions 1
  • Topic – Dividing Algebraic Fractions 2
  • Topic – Algebraic Fractions: Multiplication
  • Topic – Algebraic Fractions: Division
  • Topic – Algebraic Fractions: Multiplication and Division
Simplifying Algebraic Expressions using Laws of Exponents
  • Video – Index Notation using Negative Bases (7:27)
  • Video – Algebraic Simplifications involving Zero Exponents (2:44)
FUNCTIONS
Relations and Functions
  • Video – Vertical Line Test (9:37)
  • Video – One-to-One Relations (2:02)
  • Video – One-to-Many Relations (1:56)
  • Video – Many-to-One Relations (1:50)
  • Video – Many-to-Many Relations (2:21)
  • Video – Functions and Vertical Line Test (3:13)
  • Video – Checking Functions using Ordered Pairs (3:31)
  • Video – Checking Functions using Graphs (9:43)
Function Notation
  • Video – Function Values using Function Notations (3:40)
  • Video – Linear Equations involving Functions (1:23)
  • Video – Quadratic Equations involving Functions (2:36)
  • Video – Finding Algebraic Expressions from Functions (3:20)
  • Video – Function Notation (7:32)
Domain and Range
  • Video – Definition of Domain and Range (4:11)
  • Video – Finding Domain and Range (9:02)
  • Video – Range of Squares (7:21)
  • Video – Domain and Range of Surds (7:03)
  • Video – Domain and Range of Logarithmic Graphs (1:16)
  • Video – Domain of Sum of Two Functions (3:41)
  • Video – Restricting the Domain of Cubic Polynomials (4:22)
  • Video – Range of Reciprocal of Quadratic Expressions (5:37)
Domain and Range by Graphs
  • Video – Domain and Range by Graphs (7:16)
  • Video – Domain and Range of Functions (6:53)
  • Video – Domain and Range of Functions involving Asymptotes (5:12)
Ranges of Linear Inequalities
  • Video – Regions Bounded by Horizontal & Vertical Lines (3:49)
  • Video – Regions Bounded by Horizontal, Vertical & Straight Lines (4:27)
  • Video – Regions Bounded between Straight Lines (4:00)
  • Video – Regions Bounded between Straight Lines in General Form (6:01)
  • Video – Regions involving Linear Inequalities: Greater Than (5:11)
  • Video – Regions involving Linear Inequalities: Less Than (0:55)
  • Video – Regions involving Linear Inequalities including Borders (1:44)
  • Video – Regions involving Linear Inequalities in General Form (2:55)
Composite Functions
  • Video – Combining Functions (5:25)
  • Video – Composite of Functions (4:39)
  • Topic – Composite of Linear Functions 1
  • Topic – Composite of Linear Functions 2
  • Topic – Nested Composite of Linear Functions 1
  • Topic – Nested Composite of Linear Functions 2
  • Topic – Composite of Quadratic Functions and Linear Functions 1
  • Topic – Composite of Quadratic Functions and Linear Functions 2
  • Topic – Nested Composite of Quadratic Functions 1
  • Topic – Nested Composite of Quadratic Functions 2
  • Topic – Composite Functions of Ordered Pairs 1
  • Topic – Composite Functions of Ordered Pairs 2
  • Topic – Composite Functions of Ordered Pairs 3
  • Topic – Composite Function Equations
  • Topic – Composite of Linear and Square Root Functions
Even Functions and Odd Functions
  • Video – Introduction to Even & Odd Functions (5:15)
  • Video – Determining Even & Odd Functions (6:37)
  • Video – Even Functions Odd Functions (1:49)
  • Topic – Determine Functions Even, Odd or Neither 1
  • Topic – Determine Functions Even, Odd or Neither 2
  • Topic – Determine Functions Even, Odd or Neither 3
STRAIGHT LINES
Gradient of Lines
  • Video – Understanding Gradient Formula (3:56)
  • Video – Finding Gradients of Straight Lines (2:56)
  • Video – Applications of Gradients (6:38)
  • Video – Gradient from Two Points (4:10)
  • Video – Gradient from an Angle (4:03)
  • Video – Finding the Positive Angle of x-axis (4:10)
  • Video – Finding Gradients (4:55)
  • Video – Gradient Undefined (1:21)
  • Video – Gradient Zero (1:32)
  • Video – Gradient from Rise and Run (4:48)
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