"KhanAcademy" 修訂間的差異
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* Graphing two-variable inequalities | * Graphing two-variable inequalities | ||
* Modeling with linear inequalities | * Modeling with linear inequalities | ||
| − | ==== | + | ====Absolute value & piecewise functions==== |
| + | * Graphs of absolute value functions | ||
| + | * Piecewise functions | ||
| + | ====Rational exponents & radicals==== | ||
| + | * Exponent properties review | ||
| + | * Radicals | ||
| + | * Rational exponents intro | ||
| + | * Properties of exponents (rational exponents) | ||
| + | * Advanced exponent & radical evaluation | ||
| + | * Simplifying square roots | ||
| + | * Simplifying radicals (higher-index roots) | ||
| + | ====Exponential growth & decay==== | ||
| + | * Exponential vs. linear growth | ||
| + | * Exponential expressions | ||
| + | * Graphs of exponential growth | ||
| + | * Exponential vs. linear growth over time | ||
| + | * Exponential decay | ||
| + | * Exponential functions from tables & graphs | ||
| + | |||
| + | ====Polynomials==== | ||
| + | * Intro to polynomials | ||
| + | * Adding & subtracting polynomials | ||
| + | * Adding and subtracting polynomials: two variables | ||
| + | * Multiplying monomials | ||
| + | * Multiplying monomials by polynomials | ||
| + | * Multiplying binomials | ||
| + | * Multiplying binomials by polynomials | ||
| + | * Special products of binomials | ||
| + | * Polynomials word problems | ||
| + | ====Factorization==== | ||
| + | * Introduction to factorization | ||
| + | * Factoring monomials | ||
| + | * Factoring polynomials by taking common factors | ||
| + | * Evaluating expressions with unknown variables | ||
| + | * Factoring quadratics intro | ||
| + | * Factoring quadratics by grouping | ||
| + | * Factoring polynomials with quadratic forms | ||
| + | * Factoring quadratics: Difference of squares | ||
| + | * Factoring quadratics: Perfect squares | ||
| + | * Strategy in factoring quadratics | ||
| + | * Factoring polynomials with special product | ||
| + | ====Quadratics==== | ||
| + | * Parabolas intro | ||
| + | * Quadratic factored form | ||
| + | * Solving quadratics by taking square roots | ||
| + | * Quadratic vertex form | ||
| + | * Solving quadratics by factoring | ||
| + | * Completing the square | ||
| + | * The quadratic formula | ||
| + | * Quadratic standard form | ||
| + | * Features & forms of quadratic functions | ||
| + | * Transforming parabolas | ||
| + | ====Irrational numbers==== | ||
| + | * Irrational numbers | ||
| + | * Sums and products of rational and irrational numbers | ||
| + | * Proofs concerning irrational numbers | ||
===Geometry=== | ===Geometry=== | ||
| + | ====Geometry foundations==== | ||
| + | * Intro to Euclidean geometry | ||
| + | * Angles | ||
| + | * Polygons | ||
| + | ====Transformations==== | ||
| + | * Introduction to rigid transformations | ||
| + | * Translations | ||
| + | * Rotations | ||
| + | * Reflections | ||
| + | * Rigid transformations overview | ||
| + | * Dilations | ||
| + | * Properties & definitions of transformations | ||
| + | * Symmetry | ||
| + | ====Congruence==== | ||
| + | * Transformations & congruence | ||
| + | * Triangle congruence | ||
| + | * Theorems concerning triangle properties | ||
| + | * Working with triangles | ||
| + | * Theorems concerning quadrilateral properties | ||
| + | * Proofs of general theorems that use triangle congruence | ||
| + | * Constructing bisectors of lines & angles | ||
| + | ====Similarity==== | ||
| + | * Definitions of similarity | ||
| + | * Introduction to triangle similarity | ||
| + | * Solving similar triangles | ||
| + | * Angle bisector theorem | ||
| + | * Solving problems with similar & congruent triangles | ||
| + | * Solving modeling problems with similar & cong | ||
| + | ====Right triangles & trigonometry==== | ||
| + | * Pythagorean theorem | ||
| + | * Pythagorean theorem proofs | ||
| + | * Special right triangles | ||
| + | * Introduction to the trigonometric ratios | ||
| + | * Solving for a side in a right triangle using the trigonometric ratios | ||
| + | * Solving for an angle in a right triangle using the trigonometric ratios | ||
| + | * Modeling with right triangles | ||
| + | * Trigonometric ratios & similarity | ||
| + | * Sine & cosine of complementary angles | ||
| + | * Law of sines | ||
| + | * Law of cosines | ||
| + | * Solving general triangles | ||
| + | ====Solid geometry==== | ||
| + | * Solid geometry intro | ||
| + | * Density | ||
| + | * 2D vs. 3D objects | ||
| + | ====Analytic geometry==== | ||
| + | * Distance and midpoints | ||
| + | * Dividing line segments | ||
| + | * Problem solving with distance on the coordinate plane | ||
| + | * Parallel & perpendicular lines on the coordinate plane | ||
| + | * Equations of parallel & perpendicular lines | ||
| + | ====Circles==== | ||
| + | * Circle basics | ||
| + | * Arc measure | ||
| + | * Arc length (degrees) | ||
| + | * Introduction to radians | ||
| + | * Arc length (radians) | ||
| + | * Sectors | ||
| + | * Inscribed angles | ||
| + | * Inscribed shapes problem solving | ||
| + | * Properties of tangents | ||
| + | * Standard equation of a circle | ||
| + | * Expanded equation of a circle | ||
| + | * Constructing regular polygons inscribed in circles | ||
| + | * Constructing circumcircles & incircles | ||
| + | * Constructing a line tangent to a circle | ||
===Algebra 2=== | ===Algebra 2=== | ||
| + | |||
| + | ====Functions==== | ||
| + | * Combining functions | ||
| + | * Composing functions | ||
| + | * Modeling situations by combining and composing functions | ||
| + | * Shifting functions | ||
| + | * Stretching functions | ||
| + | * Introduction to inverses of functions | ||
| + | * Finding inverse functions | ||
| + | * Verifying that functions are inverses | ||
| + | * Determining whether a function is invertible | ||
| + | ====Complex numbers==== | ||
| + | * What are the imaginary numbers? | ||
| + | * What are the complex numbers? | ||
| + | * The complex plane | ||
| + | * Adding and subtracting complex numbers | ||
| + | * Multiplying complex numbers | ||
| + | ====Arithmetic with polynomials==== | ||
| + | * Adding and subtracting polynomials | ||
| + | * Multiplying polynomials | ||
| + | * Long division of polynomials | ||
| + | * Synthetic division of polynomials | ||
| + | * Practice dividing polynomials with remainders | ||
| + | * Polynomial Remainder Theorem | ||
| + | ====Polynomials==== | ||
| + | * The binomial theorem | ||
| + | * Understanding the binomial theorem | ||
| + | * Factoring polynomials - Quadratic forms | ||
| + | * Factoring polynomials - Special product forms | ||
| + | * Advanced polynomial factorization methods | ||
| + | * Proving polynomial identities | ||
| + | * Polynomial identities with complex numbers | ||
| + | * Quadratic equations with complex numbers | ||
| + | * The Fundamental Theorem of Algebra | ||
| + | * Finding zeros of polynomials | ||
| + | * Zeros of polynomials and their graphs | ||
| + | * End behavior of polynomial functions | ||
| + | * Graphs of polynomials | ||
| + | * Introduction to symmetry of functions | ||
| + | * Symmetry of polynomial functions | ||
| + | ====Radical relationships==== | ||
| + | * Solving square-root equations | ||
| + | * Extraneous solutions of radical equations | ||
| + | * Solving cube-root equations | ||
| + | * Domain of radical functions | ||
| + | * Graphs of radical functions | ||
| + | ====Rational relationships==== | ||
| + | * Simplifying rational expressions | ||
| + | * Multiplying & dividing rational expressions | ||
| + | * Adding & subtracting rational expressions | ||
| + | * Nested fractions | ||
| + | * Solving rational equations | ||
| + | * Direct and inverse variation | ||
| + | * End behavior of rational functions | ||
| + | * Discontinuities of rational functions | ||
| + | * Graphs of rational functions | ||
| + | * Modeling with rational functions | ||
| + | ====Exponential growth & decay==== | ||
| + | * Equivalent forms of exponential expressions | ||
| + | * Solving exponential equations using properties of exponents | ||
| + | * Interpreting the rate of change of exponential models | ||
| + | * Constructing exponential models according to rate of change | ||
| + | * Advanced interpretation of exponential models | ||
| + | * Distinguishing between linear and exponential growth | ||
| + | ====Exponentials & logarithms==== | ||
| + | * Introduction to logarithms | ||
| + | * The constant e and the natural logarithm | ||
| + | * Properties of logarithms | ||
| + | * The change of base formula for logarithms | ||
| + | * Solving exponential equations with logarithms | ||
| + | * Solving exponential models | ||
| + | * Graphs of exponential functions | ||
| + | * Graphs of logarithmic functions | ||
| + | * Logarithmic scale (optional) | ||
| + | ====Trigonometry==== | ||
| + | * Introduction to radians | ||
| + | * The unit circle definition of sine, cosine, and tangent | ||
| + | * The graphs of sine, cosine, and tangent | ||
| + | * Basic trigonometric identities | ||
| + | * Trigonometric values of special angles | ||
| + | * The Pythagorean identity | ||
| + | * Introduction to amplitude, midline, and extrema of sinusoidal functions | ||
| + | * Finding amplitude and midline of sinusoidal functions from their formulas | ||
| + | * Period of sinusoidal functions | ||
| + | * Graphing sinusoidal functions | ||
| + | * Constructing sinusoidal functions | ||
| + | ====Advanced equations & functions==== | ||
| + | * Solving equations by graphing | ||
| + | * Systems of quadratic equations | ||
| + | * Interpreting the symmetry of algebraic models | ||
| + | * Interpreting the end behavior of algebraic models | ||
| + | * Interpreting the periodicity of algebraic models | ||
| + | * Comparing features of functions | ||
| + | |||
| + | ====Series==== | ||
| + | * Arithmetic sequences | ||
| + | * Basic sigma notation | ||
| + | * Finite arithmetic series | ||
| + | * Geometric sequences | ||
| + | * Finite geometric series | ||
| + | * Finite geometric series applications | ||
| + | |||
| + | ====Modeling==== | ||
| + | * Modeling with one-variable equations and inequalities | ||
| + | * Manipulating formulas | ||
| + | ====Conic sections==== | ||
| + | * Introduction to conic sections | ||
| + | * The features of a circle | ||
| + | * Standard equation of a circle | ||
| + | * Expanded equation of a circle | ||
| + | * Focus and directrix of a parabola | ||
===Trigonometry=== | ===Trigonometry=== | ||
| + | ====Trigonometry with right triangles==== | ||
| + | * Introduction to the trigonometric ratios | ||
| + | * Solving for a side in a right triangle using the trigonometric ratios | ||
| + | * Solving for an angle in a right triangle using the trigonometric ratios | ||
| + | * Modeling with right triangles | ||
| + | * Trigonometric ratios and similarity | ||
| + | * Sine and cosine of complementary angles | ||
| + | * Trigonometric ratios of special triangles | ||
| + | * Introduction to the Pythagorean trigonometric identity | ||
| + | * The reciprocal trigonometric ratios | ||
| + | ====Trigonometry with general triangles==== | ||
| + | * The law of sines | ||
| + | * The law of cosines | ||
| + | * Solving general triangles | ||
| + | ====The unit circle definition of sine, cosine, and tangent==== | ||
| + | * Introduction to radians | ||
| + | * The unit circle definition of sine, cosine, and tangent | ||
| + | * The graphs of sine, cosine, and tangent | ||
| + | * Basic trigonometric identities | ||
| + | * Trigonometric values of special angles | ||
| + | * The Pythagorean identity | ||
| + | * Long live Tau | ||
| + | ====Graphs of trigonometric functions==== | ||
| + | * The graphs of sine, cosine, and tangent | ||
| + | * Introduction to amplitude, midline, and extrema of sinusoidal functions | ||
| + | * Finding amplitude and midline of sinusoidal functions from their formulas | ||
| + | * Period of sinusoidal functions | ||
| + | * Graphing sinusoidal functions | ||
| + | * Constructing sinusoidal functions | ||
| + | ====Trigonometric equations and identities==== | ||
| + | * The inverse trigonometric functions | ||
| + | * Solving basic sinusoidal equations | ||
| + | * Solving advanced sinusoidal equations | ||
| + | * Solving sinusoidal models | ||
| + | * Introduction to the trigonometric angle addition identities | ||
| + | * Using trigonometric identities to solve problems | ||
| + | * Challenging trigonometry problems | ||
===Precalculus=== | ===Precalculus=== | ||
| + | ====Trigonometry==== | ||
| + | * The inverse trigonometric functions | ||
| + | * Solving basic sinusoidal equations | ||
| + | * Solving advanced sinusoidal equations | ||
| + | * Solving sinusoidal models | ||
| + | * Introduction to the trigonometric angle addition identities | ||
| + | * Using trigonometric identities to solve problems | ||
| + | ====Conic sections==== | ||
| + | * Introduction to conic sections | ||
| + | * The features of a circle | ||
| + | * Standard equation of a circle | ||
| + | * Expanded equation of a circle | ||
| + | * Center and radii of an ellipse | ||
| + | * Foci of an ellipse | ||
| + | * Focus and directrix of a parabola | ||
| + | * Introduction to hyperbolas | ||
| + | * Foci of a hyperbola | ||
| + | * Hyperbolas not centered at the origin | ||
| + | * Identifying conic sections from their expanded equations | ||
| + | * Challenging conic section problems (IIT JEE) | ||
| + | ====////==== | ||
| + | |||
===Statistics and probability=== | ===Statistics and probability=== | ||
===AP Calculus AB=== | ===AP Calculus AB=== | ||
於 2018年9月5日 (三) 07:52 的最新修訂
- 本站提供一些英文輔助教材，主要是單字練習和單句練習，幫助台灣的小學4,5,6年級的學生更有效地使用英文版的 KhanAcademy 數學內容，作為學習英文的另一種途徑。本站用 Quizlet 幫助學生自主學習英文單字和單句，並且用 Kahoot 的趣味競賽或合作方式幫助學生共學英文單字和單句。
- 小學4,5,6年級的學生，用英文版的 KhanAcademy 幼教和小學低年級的數學內容來學習英文時，不會有數學及英文的雙重困難；因為那些數學觀念在學校的小學低年級的數學課中早已熟悉，或中高年級正在學習，且幾乎天天在數學學習的環境中不斷使用。
- 這些簡單又每天都繼續在學習中使用的數學觀念，成為英文初學者入門學習英文的大好基礎和機會。
- 當學生日復一日地熟悉本站所提供的輔助教材時，就可以漸近地理解英文版 KhanAcademy 的教學影片所要教導的數學觀念的英文表達方式。
- 接下來，學生從做英文版的 KhanAcademy 練習題的解題過程中，反覆應用所學到的英文來回答類似題型的許多題目，並且即時獲得電腦的回饋，立刻得知自己是否能够用英文來理解題意。
- 這樣，讓學生能體驗到剛剛所學到的英文單字可以立刻學以致用解決問題，以利觸發並支持學習英文的動機和興趣。
- 此外，藉著不斷的在解題中應用所學到的英文，在來達到深刻理解英文和長期記憶的效果。
目錄
- 1 Khan Academy 的數學內容的結構和結構的名稱
- 2 單字的課程目錄
- 2.1 Kindergarten
- 2.2 Arithmetic
- 2.3 Pre-algebra
- 2.3.1 Arithmetic properties
- 2.3.2 Factors and multiples
- 2.3.3 Reading and interpreting data
- 2.3.4 Measurement
- 2.3.5 Fractions
- 2.3.6 Decimals
- 2.3.7 Negative numbers and coordinate plane
- 2.3.8 Ratios, rates, proportions
- 2.3.9 Equations, expressions, and inequalities
- 2.3.10 Exponents, radicals, and scientific notation
- 2.4 Algebra 1
- 2.4.1 Algebra foundations
- 2.4.2 Solving equations
- 2.4.3 Solving inequalities
- 2.4.4 Working with units
- 2.4.5 Linear equations & graphs
- 2.4.6 Functions
- 2.4.7 Linear word problems
- 2.4.8 Sequences
- 2.4.9 Systems of equations
- 2.4.10 Inequalities (systems & graphs)
- 2.4.11 Absolute value & piecewise functions
- 2.4.12 Rational exponents & radicals
- 2.4.13 Exponential growth & decay
- 2.4.14 Polynomials
- 2.4.15 Factorization
- 2.4.16 Quadratics
- 2.4.17 Irrational numbers
- 2.5 Geometry
- 2.6 Algebra 2
- 2.6.1 Functions
- 2.6.2 Complex numbers
- 2.6.3 Arithmetic with polynomials
- 2.6.4 Polynomials
- 2.6.5 Radical relationships
- 2.6.6 Rational relationships
- 2.6.7 Exponential growth & decay
- 2.6.8 Exponentials & logarithms
- 2.6.9 Trigonometry
- 2.6.10 Advanced equations & functions
- 2.6.11 Series
- 2.6.12 Modeling
- 2.6.13 Conic sections
- 2.7 Trigonometry
- 2.8 Precalculus
- 2.9 Statistics and probability
- 2.10 AP Calculus AB
- 2.11 AP Calculus BC
- 2.12 Multivariable calculus
- 2.13 Differential equations
- 2.14 Linear Algebra
- 3 小學雙語數學
Khan Academy 的數學內容的結構和結構的名稱
- 主題(subject)：例如： Trigonometry
- 1-8年級(grade)：例如：
- 條目：例如：
- 單元：例如：
- 影片/文件：例如：
- 測驗：例如：
- 單元：例如：
- 條目：例如：
- 9-12年級(High School)：High school math
- 主題(subject)：例如： Trigonometry
單字的課程目錄
Kindergarten
Counting and place value
Counting small numbers
- Learn
- Counting with small numbers
- Counting in order
- Practice
- Count with small numbers
- Count in order
- Find 1 more or 1 less than a number
Numbers 0 to 100
- Learn
- Number grid
- Missing numbers between 0 and 120
- Practice
- Missing numbers
- Numbers to 100
- Count tens
Counting objects
- Learn
- Counting in pictures
- Counting objects 1
- Counting objects 2
- Practice
- Count in pictures
- Count objects 1
- Count objects 2
Quiz 1
Comparing small numbers
- Learn
- Comparing numbers of objects
- Comparing numbers on the number line
- Counting by category
- Practice
- Compare numbers of objects 1
- Comparing numbers to 10
- Compare numbers of objects 2
Quiz 2
Teens
- Learn
- Teens as sums with 10
- Teen numbers: monkeys
- Practice
- Teen numbers
Unit test
Addition and subtraction
What is addition? What is subtraction?
- Learn
- Intro to addition
- Intro to subtraction
- Practice
- Add within 5
- Subtract within 5
Making 10
- Learn
- Getting to 10 by filling boxes
- Adding to 10
- Practice
- Make 10 (grids and number bonds)
- Make 10
Making small numbers
- Learn
- Making 5
- Practice
- Making 5
- Making small numbers in different ways
Quiz 1
Put together, take apart
- Learn
- Add and subtract: pieces of fruit
- Addition and subtraction within 10
- Practice
- Add within 10
- Subtract within 10
Addition and subtraction word problems
- Learn
- Addition word problems within 10
- Subtraction word problems within 10
- Practice
- Addition word problems within 10
- Subtraction word problems within 10
Quiz 2
Unit test
Measurement and geometry
Comparing size: Measurement and geometry
- Learn
- No videos or articles available in this lesson
- Practice
- Compare size
Basic shapes: Measurement and geometry
- Learn
- Cousin Fal's shape collection
- Recognizing shapes
- Practice
- Name shapes 1
- Name shapes 2
Quiz 1
Comparing shapes: Measurement and geometry
- Learn
- No videos or articles available in this lesson
- Practice
- Relative position
- Practice
- Compare shapes
Composing shapes
- Learn
- Composing shapes
- Practice
- Compose shapes
Quiz 2
Unit test
Arithmetic
Addition and subtraction
- Basic addition and subtraction
- Addition and subtraction within 20
- Strategies for adding and subtracting within 100
- Addition within 100
- Subtraction within 100
- Word problems within 100
- Multi-digit addition with regrouping
- Multi-digit subtraction with regrouping
Multiplication and division
- Multiplication intro
- Multiplication by 10s, 100s, and 1000s
- Multiplication: place value and area models
- Multi-digit multiplication
- Division intro
- Division: place value and area
- Multi-digit division (no remainders)
- Remainders
- Multi-digit division (remainders)
- Multiplication and division word problems
Negative numbers
- Intro to negative numbers
- Order negative numbers
- Number opposites
- Absolute value
- Intro to adding negative numbers
- Intro to subtracting negative numbers
- Adding & subtracting negative numbers
- Multiplying & dividing negative numbers
Fractions
- Fractions intro
- Fractions on the number line
- Equivalent fractions
- Comparing fractions
- Common denominators
- Decomposing fractions
- Adding and subtracting fractions with like denominators
- Mixed numbers
- Adding and subtracting fractions with unlike denominators
- Adding and subtracting mixed number with unlike denominators
- Adding and subtracting fractions word problems
- Multiplying whole numbers and fractions
- Multiplication as scaling
- Multiplying fractions
- Multiplying mixed numbers
- Multiplying fractions word problems
- Fractions as division
- Dividing unit fractions and whole numbers
- Dividing fractions by fractions
- Dividing fractions word problems
Decimals
- Intro to decimals
- Decimals on the number line
- Rounding decimals
- Comparing decimals
- Rewriting decimals as fractions
- Adding decimals
- Subtracting decimals
- Adding and subtracting decimals word problems
- Multiplying decimals
- Dividing decimals
Pre-algebra
Arithmetic properties
- Place value: Arithmetic properties
- Rounding whole numbers: Arithmetic properties
- Regrouping whole numbers: Arithmetic properties
- Order of operations: Arithmetic properties
- Arithmetic properties: Arithmetic properties
- Distributive property: Arithmetic properties
- Rational and irrational numbers
Factors and multiples
- Divisibility tests: Factors and multiples
- Factors and multiples: Factors and multiples
- Prime numbers: Factors and multiples
- Prime factorization: Factors and multiples
- Least common multiple: Factors and multiples
- Greatest common factor
Reading and interpreting data
- Representing data: Reading and interpreting data
- Stem and leaf plots: Reading and interpreting data
- Picture graphs, bar graphs, and histograms: Reading and interpreting data
- Frequency tables and dot plots: Reading and interpreting data
- Number patterns
Measurement
- Area of rectangles: Measurement
- Perimeter: Measurement
- Volume of a rectangular prism
Fractions
- Fractions intro: Fractions
- Fractions on the number line: Fractions
- Equivalent fractions: Fractions
- Comparing fractions: Fractions
- Common denominators: Fractions
- Decomposing fractions: Fractions
- Adding and subtracting fractions with like denominators: Fractions
- Mixed numbers: Fractions
- Adding and subtracting fractions with unlike denominators: Fractions
- Adding and subtracting mixed number with unlike denominators: Fractions
- Adding and subtracting fractions word problems: Fractions
- Multiplying whole numbers and fractions: Fractions
- Multiplication as scaling: Fractions
- Multiplying fractions: Fractions
- Multiplying mixed numbers: Fractions
- Multiplying fractions word problems: Fractions
- Fractions as division: Fractions
- Dividing unit fractions and whole numbers: Fractions
- Dividing fractions by fractions: Fractions
- Dividing fractions word problems
Decimals
- Intro to decimals
- Decimals on the number line
- Rounding decimals
- Comparing decimals
- Rewriting decimals as fractions
- Adding decimals
- Subtracting decimal
- Adding and subtracting decimals word problems
- Multiplying decimals
- Dividing decimals
Negative numbers and coordinate plane
- Intro to negative numbers
- Order negative numbers
- Number opposites
- Absolute value
- Intro to adding negative numbers
- Intro to subtracting negative numbers
- Adding & subtracting negative numbers
- Multiplying & dividing negative numbers
- Coordinate plane
Ratios, rates, proportions
- Intro to ratios
- Visualize ratios
- Ratio application
- Intro to rates
- Intro to percents
- Percent, fraction, decimal conversions
- Percent problems
- Percent word problems
- Constant of proportionality
- Identifying proportional relationships
- Writing & solving proportions
Equations, expressions, and inequalities
- Intro to variables
- Substitution & evaluating expressions
- Expression value intuition
- Constructing numeric expressions
- Evaluating expressions word problems
- Writing algebraic expressions introduction
- Writing basic algebraic expressions word problems
- Algebraic equations basics
- One-step equations intuition
- One-step addition & subtraction equations
- One-step multiplication and division equations
- One-step equation word problems
- Inequalities: Greater than and less than basics
- Two-step equations intro
- Dependent and independent variables
Exponents, radicals, and scientific notation
- Exponents
- Square roots
- Cube roots
- Exponent properties
- Negative exponents
- Scientific notation
- Orders of magnitude
- Computing with scientific notation
Algebra 1
Algebra foundations
- Overview and history of algebra
- Introduction to variables
- Substitution and evaluating expressions
- Evaluating expressions word problems
- Writing algebraic expressions introduction
- Dependent & independent variables
- Combining like terms
- Introduction to equivalent algebraic expressions
- Interpreting linear expressions
- Division by zero
Solving equations
- Algebraic equations basics
- Why we do the same thing to both sides of an equation
- One-step addition & subtraction equations
- One-step multiplication & division equations
- Two-steps equations intro
- Two-step equation word problems
- Linear equations with variables on both sides
- Linear equations with parentheses
- Analyzing the number of solutions to linear equations
- Linear equations word problems
- Linear equations with unknown coefficients
Solving inequalities
- Introduction to inequalities with variables
- One-step inequalities
- Two-step inequalities
- Multi-step inequalities
- Compound inequalities
Working with units
- Rate conversion
- Appropriate units
- Word problems with multiple units
Linear equations & graphs
- Two-variable linear equations intro
- x-intercepts and y-intercepts
- Slope
- Horizontal & vertical lines
- Intro to slope-intercept form
- Graphing slope-intercept equations
- Writing slope-intercept equations
- Point-slope form
- Standard form
- Summary: Forms of two-variable linear equations
Functions
- Evaluating functions
- Inputs and outputs of a function
- Functions and equations
- Interpreting function notation
- Introduction to the domain and range of a function
- Determining the domain of a function
- Recognizing functions
- Maximum and minimum points
- Intervals where a function is positive, negative, increasing, or decreasing
- Interpreting features of graphs
- Average rate of change
- Average rate of change word problems
Linear word problems
- Interpreting linear functions and equations
- Comparing linear functions
- Constructing linear models for real-world relationships
- Linear models word problems
Sequences
- Introduction to arithmetic sequences
- Constructing arithmetic sequences
- Introduction to geometric sequences
- Constructing geometric sequences
- Modeling with sequences
- General sequences
Systems of equations
- Introduction to systems of equations
- Equivalent systems of equations and the elimination method
- Solving systems of equations with substitution
- Manipulating expressions with unknown variables
- Number of solutions to systems of equations
- Solving any system of linear equations
- Systems of equations word problems
Inequalities (systems & graphs)
- Checking solutions of two-variable inequalities
- Graphing two-variable inequalities
- Modeling with linear inequalities
Absolute value & piecewise functions
- Graphs of absolute value functions
- Piecewise functions
Rational exponents & radicals
- Exponent properties review
- Radicals
- Rational exponents intro
- Properties of exponents (rational exponents)
- Advanced exponent & radical evaluation
- Simplifying square roots
- Simplifying radicals (higher-index roots)
Exponential growth & decay
- Exponential vs. linear growth
- Exponential expressions
- Graphs of exponential growth
- Exponential vs. linear growth over time
- Exponential decay
- Exponential functions from tables & graphs
Polynomials
- Intro to polynomials
- Adding & subtracting polynomials
- Adding and subtracting polynomials: two variables
- Multiplying monomials
- Multiplying monomials by polynomials
- Multiplying binomials
- Multiplying binomials by polynomials
- Special products of binomials
- Polynomials word problems
Factorization
- Introduction to factorization
- Factoring monomials
- Factoring polynomials by taking common factors
- Evaluating expressions with unknown variables
- Factoring quadratics intro
- Factoring quadratics by grouping
- Factoring polynomials with quadratic forms
- Factoring quadratics: Difference of squares
- Factoring quadratics: Perfect squares
- Strategy in factoring quadratics
- Factoring polynomials with special product
Quadratics
- Parabolas intro
- Quadratic factored form
- Solving quadratics by taking square roots
- Quadratic vertex form
- Solving quadratics by factoring
- Completing the square
- The quadratic formula
- Quadratic standard form
- Features & forms of quadratic functions
- Transforming parabolas
Irrational numbers
- Irrational numbers
- Sums and products of rational and irrational numbers
- Proofs concerning irrational numbers
Geometry
Geometry foundations
- Intro to Euclidean geometry
- Angles
- Polygons
Transformations
- Introduction to rigid transformations
- Translations
- Rotations
- Reflections
- Rigid transformations overview
- Dilations
- Properties & definitions of transformations
- Symmetry
Congruence
- Transformations & congruence
- Triangle congruence
- Theorems concerning triangle properties
- Working with triangles
- Theorems concerning quadrilateral properties
- Proofs of general theorems that use triangle congruence
- Constructing bisectors of lines & angles
Similarity
- Definitions of similarity
- Introduction to triangle similarity
- Solving similar triangles
- Angle bisector theorem
- Solving problems with similar & congruent triangles
- Solving modeling problems with similar & cong
Right triangles & trigonometry
- Pythagorean theorem
- Pythagorean theorem proofs
- Special right triangles
- Introduction to the trigonometric ratios
- Solving for a side in a right triangle using the trigonometric ratios
- Solving for an angle in a right triangle using the trigonometric ratios
- Modeling with right triangles
- Trigonometric ratios & similarity
- Sine & cosine of complementary angles
- Law of sines
- Law of cosines
- Solving general triangles
Solid geometry
- Solid geometry intro
- Density
- 2D vs. 3D objects
Analytic geometry
- Distance and midpoints
- Dividing line segments
- Problem solving with distance on the coordinate plane
- Parallel & perpendicular lines on the coordinate plane
- Equations of parallel & perpendicular lines
Circles
- Circle basics
- Arc measure
- Arc length (degrees)
- Introduction to radians
- Arc length (radians)
- Sectors
- Inscribed angles
- Inscribed shapes problem solving
- Properties of tangents
- Standard equation of a circle
- Expanded equation of a circle
- Constructing regular polygons inscribed in circles
- Constructing circumcircles & incircles
- Constructing a line tangent to a circle
Algebra 2
Functions
- Combining functions
- Composing functions
- Modeling situations by combining and composing functions
- Shifting functions
- Stretching functions
- Introduction to inverses of functions
- Finding inverse functions
- Verifying that functions are inverses
- Determining whether a function is invertible
Complex numbers
- What are the imaginary numbers?
- What are the complex numbers?
- The complex plane
- Adding and subtracting complex numbers
- Multiplying complex numbers
Arithmetic with polynomials
- Adding and subtracting polynomials
- Multiplying polynomials
- Long division of polynomials
- Synthetic division of polynomials
- Practice dividing polynomials with remainders
- Polynomial Remainder Theorem
Polynomials
- The binomial theorem
- Understanding the binomial theorem
- Factoring polynomials - Quadratic forms
- Factoring polynomials - Special product forms
- Advanced polynomial factorization methods
- Proving polynomial identities
- Polynomial identities with complex numbers
- Quadratic equations with complex numbers
- The Fundamental Theorem of Algebra
- Finding zeros of polynomials
- Zeros of polynomials and their graphs
- End behavior of polynomial functions
- Graphs of polynomials
- Introduction to symmetry of functions
- Symmetry of polynomial functions
Radical relationships
- Solving square-root equations
- Extraneous solutions of radical equations
- Solving cube-root equations
- Domain of radical functions
- Graphs of radical functions
Rational relationships
- Simplifying rational expressions
- Multiplying & dividing rational expressions
- Adding & subtracting rational expressions
- Nested fractions
- Solving rational equations
- Direct and inverse variation
- End behavior of rational functions
- Discontinuities of rational functions
- Graphs of rational functions
- Modeling with rational functions
Exponential growth & decay
- Equivalent forms of exponential expressions
- Solving exponential equations using properties of exponents
- Interpreting the rate of change of exponential models
- Constructing exponential models according to rate of change
- Advanced interpretation of exponential models
- Distinguishing between linear and exponential growth
Exponentials & logarithms
- Introduction to logarithms
- The constant e and the natural logarithm
- Properties of logarithms
- The change of base formula for logarithms
- Solving exponential equations with logarithms
- Solving exponential models
- Graphs of exponential functions
- Graphs of logarithmic functions
- Logarithmic scale (optional)
Trigonometry
- Introduction to radians
- The unit circle definition of sine, cosine, and tangent
- The graphs of sine, cosine, and tangent
- Basic trigonometric identities
- Trigonometric values of special angles
- The Pythagorean identity
- Introduction to amplitude, midline, and extrema of sinusoidal functions
- Finding amplitude and midline of sinusoidal functions from their formulas
- Period of sinusoidal functions
- Graphing sinusoidal functions
- Constructing sinusoidal functions
Advanced equations & functions
- Solving equations by graphing
- Systems of quadratic equations
- Interpreting the symmetry of algebraic models
- Interpreting the end behavior of algebraic models
- Interpreting the periodicity of algebraic models
- Comparing features of functions
Series
- Arithmetic sequences
- Basic sigma notation
- Finite arithmetic series
- Geometric sequences
- Finite geometric series
- Finite geometric series applications
Modeling
- Modeling with one-variable equations and inequalities
- Manipulating formulas
Conic sections
- Introduction to conic sections
- The features of a circle
- Standard equation of a circle
- Expanded equation of a circle
- Focus and directrix of a parabola
Trigonometry
Trigonometry with right triangles
- Introduction to the trigonometric ratios
- Solving for a side in a right triangle using the trigonometric ratios
- Solving for an angle in a right triangle using the trigonometric ratios
- Modeling with right triangles
- Trigonometric ratios and similarity
- Sine and cosine of complementary angles
- Trigonometric ratios of special triangles
- Introduction to the Pythagorean trigonometric identity
- The reciprocal trigonometric ratios
Trigonometry with general triangles
- The law of sines
- The law of cosines
- Solving general triangles
The unit circle definition of sine, cosine, and tangent
- Introduction to radians
- The unit circle definition of sine, cosine, and tangent
- The graphs of sine, cosine, and tangent
- Basic trigonometric identities
- Trigonometric values of special angles
- The Pythagorean identity
- Long live Tau
Graphs of trigonometric functions
- The graphs of sine, cosine, and tangent
- Introduction to amplitude, midline, and extrema of sinusoidal functions
- Finding amplitude and midline of sinusoidal functions from their formulas
- Period of sinusoidal functions
- Graphing sinusoidal functions
- Constructing sinusoidal functions
Trigonometric equations and identities
- The inverse trigonometric functions
- Solving basic sinusoidal equations
- Solving advanced sinusoidal equations
- Solving sinusoidal models
- Introduction to the trigonometric angle addition identities
- Using trigonometric identities to solve problems
- Challenging trigonometry problems
Precalculus
Trigonometry
- The inverse trigonometric functions
- Solving basic sinusoidal equations
- Solving advanced sinusoidal equations
- Solving sinusoidal models
- Introduction to the trigonometric angle addition identities
- Using trigonometric identities to solve problems
Conic sections
- Introduction to conic sections
- The features of a circle
- Standard equation of a circle
- Expanded equation of a circle
- Center and radii of an ellipse
- Foci of an ellipse
- Focus and directrix of a parabola
- Introduction to hyperbolas
- Foci of a hyperbola
- Hyperbolas not centered at the origin
- Identifying conic sections from their expanded equations
- Challenging conic section problems (IIT JEE)
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Statistics and probability
AP Calculus AB
AP Calculus BC
Multivariable calculus
Differential equations
Linear Algebra
小學雙語數學
- 和均一教育平台小學數學的內容和進度配合
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