Where are you on the Math roadmap?

This flowchart provides a clear overview of the progression and learning path of mathematical concepts.

1. Numbers and Operations

• Grade 7: Prime factorization → Integers and rational numbers → Greatest Common Divisor (GCD), Least Common Multiple (LCM)
• Grade 8: Rational numbers and repeating decimals → Square roots and real numbers
• Grade 9: Sets and propositions → Basics of sequences
• Grade 10: Limits of sequences → Exponent rules
• Grade 11: Logarithms → Algebra
• Grade 12: Complex numbers → Sums and general terms of sequences

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2. Change and Relationships

• Grade 7: Use of variables and expressions → Linear equations → Coordinate planes and graphs
• Grade 8: Systems of linear equations → Quadratic equations → Basics of functions
• Grade 9: Quadratic functions and graphs → Equations and inequalities
• Grade 10: Common Math (Function concepts, Limits, and Continuity)
• Grade 11: Trigonometric functions → Differentiation
• Grade 12: Integration → Applied problems (e.g., velocity, area calculation)

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3. Shapes and Measurements

• Grade 7: Basic shapes → Properties of plane shapes → Properties of solid shapes
• Grade 8: Properties of triangles and quadrilaterals → Circles and sectors → Congruence and similarity
• Grade 9: Solid figures → Solids of revolution → Vectors
• Grade 10: Geometry and coordinates → Conic sections
• Grade 11: Vectors → Spatial coordinates
• Grade 12: Advanced geometry → Geometric expansion problems

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4. Data and Probability

• Grade 7: Measures of central tendency → Frequency tables → Histograms
• Grade 8: Counting principles → Basic probability
• Grade 9: Scatter plots and correlations → Basic probability principles
• Grade 10: Probability and Statistics → Discrete probability distributions
• Grade 11: Continuous probability distributions → Normal distribution
• Grade 12: Statistical inference → Advanced probability problems

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This flowchart provides a clear overview of the progression and learning path of mathematical concepts.

Grade	Middle School 1st Year(7th)	Middle School 2nd Year(8th)	Middle School 2nd Year(9th)	High School 1st Year(10th)	High School 2st Year(11th)	High School 3st Year(12th)
Subjects	1st Semester : ①~⑤ 2nd Semester : ⑥~⑪	1st Semester : ①~⑥ 2nd Semester : ⑦~⑩	1st Semester : ①~④ 2nd Semester : ⑤~⑧	Common Math 1 : ①~④ Common Math 2 : ⑤~⑦	Algebra : ①~③ Calculus Ⅰ : ④~⑥ Probability and Statistics : ⑦~⑨	Calculus  Ⅱ : ①~③ Geometry : ④~⑥
Numbers and Operations	① Prime factorization	① Rational numbers and repeating decimals	① Square roots and real numbers	④ Matrices	③ Sequences	① Limits of sequences
	② Integers and rational numbers			⑥ Sets and propositions
Change and Relationships	③ Use of variables and expressions	② Operations with expressions	② Multiplication and factorization of polynomials	① Polynomials	① Exponential and logarithmic functions	② Differential calculus
	④ Linear equations	③ Linear inequalities	③ Quadratic equations	② Equations and inequalities	② Trigonometric functions	③ Integral calculus
	⑤ Coordinate planes and graphs	④ Systems of linear equations	④ Quadratic functions and graphs	⑦ Functions and graphs	④ Limits and continuity of functions
		⑤ Calculus			⑤ Linear functions and graphs
		⑥ Linear functions and linear equations			⑥ Integral calculus
Shapes and Measurements	⑥ Basic shapes	⑦ Properties of triangles and quadrilaterals	⑤ Trigonometric ratios	⑤ Equations of shapes		④ Conic sections
	⑦ Constructions and congruence	⑧ Similarity of shapes	⑥ Properties of circles			⑤ Solid shapes and spatial coordinates
	⑧ Properties of plane shapes	⑨ Pythagorean theorem				⑥ Vectors
	⑨ Properties of solid shapes
Data and Probability	⑩ Measures of central tendency	⑩ Counting principles and probability	⑦ Dispersion	⑩ Counting principles and probability	⑦ Counting principles
	⑪ Frequency tables and relative frequency		⑧ Box plots and scatter plots		⑧ Probability
					⑨ Statistics

The detailed content for each grade is as follows:

Grade: Middle School 1st Year (7th Grade)

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Subjects:

• 1st Semester: ①~⑤
• 2nd Semester: ⑥~⑪

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Categories and Content:

1. Numbers and Operations

① Prime Factorization

• Greatest Common Divisor (GCD), Least Common Multiple (LCM)

② Integers and Rational Numbers

• Comparison of magnitudes, Four basic arithmetic operations

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2. Change and Relationships

③ Use of Variables and Expressions

• Expressions with variables

④ Linear Equations

⑤ Coordinate Planes and Graphs

• Ordered pairs, Direct proportionality, Inverse proportionality

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3. Shapes and Measurements

⑥ Basic Shapes

• Points, Lines, Planes, Angles, Parallel lines, Corresponding angles, Alternate angles

⑦ Constructions and Congruence

• Opposite sides, Opposite angles, Intersection points, Intersecting lines

⑧ Properties of Plane Shapes

• Polygons, Sectors, Frustums, Chords, Arcs

⑨ Properties of Solid Shapes

• Regular polyhedra, Frustums of pyramids, Pyramids, Prisms
• Surface area, Volume, Foot of a perpendicular, Solids of revolution

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4. Data and Probability

⑩ Measures of Central Tendency

• Variables, Mean, Median, Mode

⑪ Frequency Tables and Relative Frequency

• Stem-and-leaf plots, Histograms
• Classes, Class intervals

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Grade: Middle School 2nd Year (8th Grade)

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Subjects:

• 1st Semester: ①~⑥
• 2nd Semester: ⑦~⑩

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Categories and Content:

1. Numbers and Operations

① Rational Numbers and Repeating Decimals

• Conversion of repeating decimals to fractions

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2. Change and Relationships

② Operations with Expressions

• Exponents, Multiplication/Division of monomials
• Addition/Subtraction of polynomials

③ Linear Inequalities

④ Systems of Linear Equations

• Systems with two variables

⑤ Linear Functions and Graphs

• Function values

⑥ Linear Functions and Linear Equations

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3. Shapes and Measurements

⑦ Properties of Triangles and Quadrilaterals

• Isosceles triangles, Circumcenter, Incenter

⑧ Similarity of Shapes

• Ratio of similarity, Distance between parallel lines

⑨ Pythagorean Theorem

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4. Data and Probability

⑩ Counting Principles and Probability

• Permutations, Combinations, Probability

Grade: Middle School 3rd Year (9th Grade)

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Subjects:

• 1st Semester: ①~④
• 2nd Semester: ⑤~⑧

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Categories and Content:

1. Numbers and Operations

① Square Roots and Real Numbers

• Irrational numbers, Arithmetic operations, Comparison of magnitudes
• Square roots, Applications of the Pythagorean Theorem

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2. Change and Relationships

② Multiplication and Factorization of Polynomials

• Polynomial multiplication and division

③ Quadratic Equations

• Quadratic formula, Double roots

④ Quadratic Functions and Graphs

• Parabolas, Axis of symmetry, Vertex, Maximum and minimum values

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3. Shapes and Measurements

⑤ Trigonometric Ratios

⑥ Properties of Circles

• Tangents, Radian measure

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4. Data and Probability

⑦ Dispersion

• Variance, Standard deviation, Distribution of data

⑧ Box Plots and Scatter Plots

• Correlation, Quartiles

Grade: High School 1st Year (10th Grade)

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Subjects:

• Common Math 1: ①~④
• Common Math 2: ⑤~⑦

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Categories and Content:

1. Numbers and Operations

④ Matrices

• Matrix multiplication, Inverse matrices, Identity matrices

⑥ Sets and Propositions

• Necessary and sufficient conditions, Contrapositives, Inverses
• Venn diagrams, Proof by contradiction

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2. Change and Relationships

① Polynomials

• Factorization, Polynomial identities, Remainder theorem
• Synthetic division

② Equations and Inequalities

• Real roots, Imaginary roots, Complex numbers, Relationships between roots and coefficients
• Basic cubic and quartic equations
• Systems of quadratic equations, Systems of linear inequalities

⑦ Functions and Graphs

• Domain, Range, Codomain, Correspondence
• Rational functions, Radical functions
• Identity functions, Polynomial functions, One-to-one functions
• Composite functions, Inverse functions

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3. Shapes and Measurements

⑤ Equations of Shapes

• Internal division, Distance between points and lines
• Equation of a circle
• Symmetry transformations, Translations
• (Excluding external division)

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4. Data and Probability

③ Counting Principles

• Addition rule, Multiplication rule
• Permutations (nPk), Factorials (n!), Combinations (nCk), Tree diagrams

Grade: High School 2nd Year (11th Grade)

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Subjects:

• Algebra: ①~③
• Calculus I: ④~⑥
• Probability and Statistics: ⑦~⑨

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Categories and Content:

1. Numbers and Operations

③ Sequences

• Arithmetic sequences: Common difference, Arithmetic mean
• Geometric sequences: Common ratio, Geometric mean
• Sum of sequences (Sigma notation), Mathematical induction

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2. Change and Relationships

① Exponential and Logarithmic Functions

• Exponents, Common logarithms, Inverse functions

② Trigonometric Functions

• Sine, Cosine, Tangent functions
• Sine rule, Cosine rule
• Radian measure, Graphs, Real-world applications

④ Limits and Continuity of Functions

• Limits, Continuity, Discontinuity, Divergence, Infinity
• Extreme Value Theorem, Intermediate Value Theorem

⑤ Differentiation

• Instantaneous rate of change, Derivative, Differentiability
• Derivative functions, Rolle's Theorem, Tangent equations

⑥ Integration

• Indefinite integrals, Integration constants, Definite integrals
• Applications in velocity and acceleration

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3. Shapes and Measurements

No specific content listed for this grade level.

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4. Data and Probability

⑦ Counting Principles

• Permutations with repetition, Combinations with repetition, Binomial theorem
• Pascal's Triangle, $nΠr$, $nHr$

⑧ Probability

• Addition rule, Conditional probability, Statistical probability
• Complementary events, Mutually exclusive events, Dependent and independent events

⑨ Statistics

• Discrete and continuous random variables, Sampling
• Binomial distribution, Normal distribution, Samples, Confidence level

Grade: High School 3rd Year (12th Grade)

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Subjects:

• Calculus II: ①~③
• Geometry: ④~⑥

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Categories and Content:

1. Numbers and Operations

① Limits of Sequences

• Convergence, Divergence, Series, Geometric series

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2. Change and Relationships

② Differentiation

• Exponential functions, Logarithmic functions, Trigonometric functions
• Addition formulas for trigonometric functions, Quotient rule
• Composite functions, Implicit functions, Inverse functions
• Parametric equations, Second derivatives, Inflection points

③ Integration

• Exponential functions, Trigonometric functions
• Substitution integration, Integration by parts
• Definite integrals and sums of series
• Area of figures, Volume of solids

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3. Shapes and Measurements

④ Conic Sections

• Parabolas, Ellipses, Hyperbolas
• Focus, Vertex, Center, Major axis, Asymptotes

⑤ Spatial Geometry and Coordinates

• Spatial coordinates, Points of division, Positional relationships
• Simson’s line theorem, Projections, Spheres

⑥ Vectors

• Initial and terminal points, Dot product, Normal vectors
• Equations of planes, Equations of spheres

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4. Data and Probability

No specific content listed for this grade level.