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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

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

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

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)

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)

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

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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