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Master Logarithmic Equations: Step-by-Step Solutions Guide

NZ Year 12 Maths: Master Key Concepts & Skills

Solving Linear Equations

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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

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Gradient equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Gradient intercept form: y = mx + b

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from gradient-intercept form y=mx+b

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Factorising

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: \(ax^2 + bx + c\)

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

Quadratic Equations and Inequalities

Solving quadratic equations by factorising

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

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

Simultaneous Equations (Advanced)

Solving 3 variable simultaneous equations by substitution

Solving 3 variable systems of equations by substitution

Solving 3 variable simultaneous equations by elimination

Solving 3 variable systems of equations by elimination

Word problems relating 3 variable simultaneous equations

Word problems relating 3 variable systems of equations

Solving 3 variable simultaneous equations with no or infinite solutions

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Simultaneous linear equations

System of linear equations

Simultaneous linear-quadratic equations

System of linear-quadratic equations

Simultaneous quadratic-quadratic equations

Inequalities in two variables (Advanced)

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

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing simultaneous quadratic inequalities

Graphing systems of quadratic inequalities

Graphing simultaneous linear inequalities

Graphing systems of linear inequalities

Applications of inequalities

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

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

Year 12 Maths

math

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