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Linear Programming: Optimize Solutions with Math Techniques

Year 11 Maths: Master Key Concepts for VCE Success

Introduction to Matrices

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Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Determinants and Inverses of Matrices

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using Cramer"s Rule

Cramer"s Rule with 2 x 2 matrices

Solving linear systems using 2 x 2 inverse matrices

Linear programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Bearings

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Linear Inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Quadratic Equations and Inequalities

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Solving quadratic equations using the quadratic formula

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Solving Simultaneous Equations

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving systems of linear equations by graphing

Solving simultaneous equations by elimination

Solving systems of linear equations by elimination

Solving simultaneous equations by substitution

Solving systems of linear equations by substitution

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Direct Variation

Writing and solving for proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Understanding graphs of proportional relationships

Linear relations

Graphing and writing equations of proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Imaginary and Complex Numbers

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Complex Conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Factorising Polynomial

Factoring difference of cubes

Factoring sum of cubes

Factorise by taking out the greatest common factor

Factor by taking out the greatest common factor

Factor by taking out GCF

Factorise by grouping

Factor by grouping

Factorising difference of squares: x^2 - y^2

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factorising trinomials

Factoring trinomials

Factoring Trinomials

Quadratic Functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

Polynomial Functions

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Polynomial long division

Polynomial synthetic division

What is a polynomial function?

Polynomial functions

Recognizing a Polynomial Function

Remainder theorem

Finding the Remainder Using Synthetic Division and the Remainder Theorem

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Rational zero theorem

Rational Zero Theorem

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials

Year 11 Maths

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