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Revision as of 03:08, 30 January 2022
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
References
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