Gasing Math

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Gasing Math

Quadratic Equations

Linear Equation

Concrete Concepts - Abstract

Forms

“X+3=5” Form

“X-3=5” Form

“7-X=5” Form

“2X”=4 Form

“2/3X=4” Form

“2X+1=5” Form

Preparation to Quadratic Equation

Simple Quadratic Equation : X^2+1=5 form

2X^2+1=5 form

2X^2+1=5+x^2 form

Distributive: Concrete Concepts - Abstract

Distributive: 2(a+b)+3(2a+2b) form

Distributive: 3(X+1)=6 form

Associative: 3(x+1)+4(x+1) form

Associative: 3(x+1)+4(x+1)=20 form

Quadratic Equation

Find quadratic equation using distributive

Factorization of quadratic equation

Root square of quadratic equation : Calculate root square

Root square of quadratic equation :Perfect quadratic equation

Root square of quadratic equation : Solve equation with perfect quadratic equation

Root square of quadratic equation : ABC Formula

Variation of Quadratic Equation

Addition and multiplication of quadratic equation : addition & multiplication of root square

Addition and multiplication of quadratic equation : Several Important Equation Forms

Unique forms:

Rootsquare

Fraction rationalization

unique rootsquare forms (double square root)

Fraction Forms:Fractions

Find distinct root (2 real roots)

Multiple Roots

Relations and Straight Lines

Functions

Relation between groups

Arrow Diagram

Cartesian Diagram

Definition of Function

Function Formula

Definition of Terms

Domain

Co-Domain

Range

Function Graph

f(x)=x+2 form

f(x)=x^2 form

Straight Lines

Straight line through (0,0) (through the origin)

not through (0,0) (not through origin)

passing through two points : gradients of two points

passing through two points : perpendicular gradient

Variation of problems

Additive Materials: Elimination methods

Drawing Straight line and cutting point of two lines

Writing Math Sentence

Additive Material:

Mapping and Function

Definition of types of functions

Inequality

Inequality Forms

Inequality x≥0 form

Inequality x>0 form

Inequality x>-2 form

Inequality x<0 form

Inequality x-6<2 form

Inequality 6-x < 2 form

Inequality 6-1/2x<2 form

Determine Feasible Area

x>0 and x>3 form

x>0 and x<3 form

x> 3 ang x<0 form

x≥ -3 and x ≤ 3 form

-3 ≤ x ≤ 3 form

(x-4)(x+1) that are positive

(x-4)(x+1) that are negative

(x-4)(x-3) that are positive

(x-4)(x-3) that are negative

Solution of two inequalities (using graph)

Fraction Inequality

Absolute value Inequality

Inequality applications

Linear Program

Two Variables Inequality

Determine feasible area for inequality (forms as previous chapter)

Determine inequality

Determine inequality two inequalities

Determine Extreme Value

Linear Program

Various Problems

Quadratic equation and inversion

Quadratic Function

Curve of Various Function

symmetry point, extreme point

Curve drawing and determination of equation

Additive Materials: Solutions of three equations

Function Operation and Inverse Function

Function Operation

Introduction to Function Inverse

Quadratic Function Inverse

Fraction Function Inverse

Composition Function

Inverse and Composition

Exponents 1

Exponent Definition

Writing exponents

Negative muliplication

Exponent Division

Multiple Exponent

Exponent Equation

Root Square Exponent

Exponent Inequality

Logrithm

Definition of Logarithm

Logarithm equation

Logarithm properties

Various Problems

Story Problems

Logarithm inequalities

Polynomial

Definition of Polymomial

Polynomial operation

Binomial

Polynomial Factorization

Simplifying Fraction

Polynomial coefficient value

Determination of function value

Polynomial division

Remainer Theorem

Various Problems

Vieta Theorem

Circle

Circle

Definition of Circle

Parts of Circle

Center point

Radiant

Circle equation (naming of circle in graph) : x^2+y^2=r^2 form

Circle equation (naming of circle in graph) : (x-a)^2+y^2=r^2 form

Circle equation (naming of circle in graph) : x^2+(y-b)^2=r^2 form

Circle equation (naming of circle in graph) : (x-a)^2+(y-b)^2=r^2 form

Circle drawing and determination of central point from equation

Line and Circle

Cutting between line and circle

y=x line and x^2+y^2=r^2

y=x+a line and x^2+y^2=r^2

y=ax+b line and x^2+y^2=r^2

Equation of Tangent

Sequence and Series

Arithmetic Series

Definition of Arithmetic Series

Various forms of arithmetic series

Un= a + (n-1) b form

Arithmetic series Lvl 2 : Un=An^2+Bn+C form

Arithmetic series Lvl 3 Un = An^3+ Bn^2+Cn+D form

Geometric Series

Intro to Geometric Series

Ratio

Amount of Geometric Series

Application of Geometric series

Matrix

Intro to Matrix

Equal Matrix/Similar Matrix

Matrix Operation

Identity Matrix

Convert Equation to Matrix

Solving Linear Equation using Matrices

Matrix 3x3

Determinant

Cofactor Transpose

Matrix Inverse

Trigonometry

Trigonometry I

Introduction

Concept of Tangent

Concept of Sinus

Sin, Cos, Tan, an Gradient

Sin, Cos, Tan line inclication

30,45, 60, 90 deg.

120, 135 …

Relation of two angles

Trignometry II

Sinus Identities

Cosinus Identities

Trigonometric equation

Quadratic trigonometric equation

Simplifying Equation

Applications

Min and Max Value

Etc.

Inequalities

Logic

Statement

Negation

Compound Sentence

Conjunction

Disjunction

Implications

Converse, Inverse, contrapositive

Relation between negation, implication, converse, inverse, contra

Modus Ponens and Modus Ponens

Syllogism

Statistics

Data

Data Presentation

Data Sorting

Range and Quantities

Mean, Variance, and Standard Deviation

Frequency & Distribution

Central Tendency

Median of Grouped Data

Quartile of Grouped Data

Decil and Percentile of Grouped Data

Probability

Relative Frequency & Probability

Sample Space and Events

Probability of an Event

Probability Limit and Expected Frequency

Permutation value n from r

Circular Permutation

Value n from r in indistinguishable permutation

Combination

Binomial Theorem

Problems

Vector

Vector Operation

Addition

Subtraction

Unit Vector

Application of Unit Vector

Determination of angle for two vectors

Dot Product

Vector Projection

Parallelogram

Area

Volume

Prism

Additive Material

Multiplication of dot product

Cross

Position Vector

Types of Vectors

Motion Vector

Velocity Vector

Force Vector

Definition of Vector

Limit

Definition of Limit

Problem Solve

Limit Theorem

Factorization

Squeeze Theorem

Limit of Trigonometry function

Euler number

Differential

Pre-calculus

Review binomial theorem

Trigonometry

Introduction to differential

various forms

Composite function differential

Differential of multiplication of two functions

Differential of division of two functions

Differential of trigonometric functions

Differential of logarithmic function

Higher order differential

Stationary point

Maximum

Minimum

Applications and Problems

Integral

Anti-derivative

Linear function integral

Trigonometri function integral

Trigonometric function with linear part integral

Exponential function integral

Integration by parts

Definite integral

Application of definite integral

curve area

volume by rotation

Problems

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