Mathematics I

loreang98, 2015. 9. 28.

차례

  1. Functions
    1. Introducing functions
    2. The domain and range of a relation on a Cartesian plane
    3. Function notation
    4. Composite functions
    5. Inverse functions
    6. Transforming functions
  2. Quadratic functions and equations
    1. Solving quadratic equations
    2. The quadratic formula
    3. Roots of quadratic equations
    4. Graphs of quadratic equations
    5. Applications of quadratics
  3. Probability
    1. Definitions
    2. Venn diagrams
    3. Sample space diagrams and the product rule
    4. Conditional probability
    5. Probability tree diagrams
  4. Exponential and logarithmic functions
    1. Exponents
    2. Solving exponential equations
    3. Exponential functions
    4. Properties of logarithms
    5. Logarithmic functions
    6. Laws of logarithms
    7. Exponential and logarithmic equations
    8. Applications of exponential and logarithmic functions
  5. Rational functions
    1. Reciprocals
    2. The reciprocal function
    3. Rational functions
  6. Patterns, sequences and series
    1. Patterns and sequences
    2. Arithmetic sequences
    3. Geometric sequences
    4. Sigma (Σ) notation and series
    5. Arithmetic series
    6. Geometric series
    7. Convergent series and sums to infinity
    8. Applications of geometric and arithmetic patterns
    9. Pascal's triangle and the binomial expansion
  7. Limits and derivates
    1. Limits and convergence
    2. The tangent line and derivative of x^n
    3. More rules for derivatives
    4. The chain rule and higher order derivatives
    5. Rates of change and motion in a line
    6. The derivative and graphing
    7. More on extrema and optimization problems
  8. Descriptive statistics
    1. Univariate analysis
    2. Presenting data
    3. Measures of central tendency
    4. Measures of dispersion
    5. Cumulative frequency
    6. Variance and standard deviation
  9. Integration
    1. Antiderivatives and the indefinite integral
    2. More on indefinite integrals
    3. Area and definite integrals
    4. Fundamental Theorem of Calculus
    5. Area between two curves
    6. Volume of revolution
    7. Definite integrals with linear motion and other problems
  10. Bivariate analysis
    1. Scatter diagrams
    2. The line of best fit
    3. Least squares regression
    4. Measuring correlation
  11. Trigonometry
    1. Right-angled triangle trigonometry
    2. Applications of right-angled triangle trigonometry
    3. Using the coordinate axes in trigonometry
    4. The sine rule
    5. The cosine rule
    6. Area of a triangle
    7. Radians, arcs and sectors
  12. Vectors
    1. Vectors: basic concepts
    2. Addition and subtraction of vectors
    3. Scalar product
    4. Vector equation of a line
    5. Application of vectors
  13. Circular functions
    1. Using the unit circle
    2. Solving equations using the unit circle
    3. Trigonometric identities
    4. Graphing circular functions
    5. Translations and stretches of trigonometric functions
    6. Combined transformations with sine and cosine functions
    7. Modeling with sine and cosine functions
  14. Calculus with trigonometric functions
    1. Derivatives of trigonometric functions
    2. More practice with derivatives
    3. Integral of sine and cosine
    4. Revisiting linear motion
  15. Probability distributions
    1. Random variables
    2. The binomial distribution
    3. The normal distribution

1.

Functions

  • 1. Introducing functions
  • 2. The domain and range of a relation on a Cartesian plane
  • 3. Function notation
  • 4. Composite functions
  • 5. Inverse functions
  • 6. Transforming functions

1.1.

–

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

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2.

Quadratic functions and equations

  • 1. Solving quadratic equations
  • 2. The quadratic formula
  • 3. Roots of quadratic equations
  • 4. Graphs of quadratic equations
  • 5. Applications of quadratics

2.1.

–

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Probability

  • 1. Definitions
  • 2. Venn diagrams
  • 3. Sample space diagrams and the product rule
  • 4. Conditional probability
  • 5. Probability tree diagrams

3.1.

–

3.2.

–

3.3.

–

3.4.

–

3.5.

–

4.

Exponential and logarithmic functions

  • 1. Exponents
  • 2. Solving exponential equations
  • 3. Exponential functions
  • 4. Properties of logarithms
  • 5. Logarithmic functions
  • 6. Laws of logarithms
  • 7. Exponential and logarithmic equations
  • 8. Applications of exponential and logarithmic functions

4.1.

–

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

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4.8.

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5.

Rational functions

  • 1. Reciprocals
  • 2. The reciprocal function
  • 3. Rational functions

5.1.

–

5.2.

–

5.3.

–

6.

Patterns, sequences and series

  • 1. Patterns and sequences
  • 2. Arithmetic sequences
  • 3. Geometric sequences
  • 4. Sigma (Σ) notation and series
  • 5. Arithmetic series
  • 6. Geometric series
  • 7. Convergent series and sums to infinity
  • 8. Applications of geometric and arithmetic patterns
  • 9. Pascal's triangle and the binomial expansion

6.1.

–

6.2.

–

6.3.

–

6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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7.

Limits and derivates

  • 1. Limits and convergence
  • 2. The tangent line and derivative of x^n
  • 3. More rules for derivatives
  • 4. The chain rule and higher order derivatives
  • 5. Rates of change and motion in a line
  • 6. The derivative and graphing
  • 7. More on extrema and optimization problems

7.1.

–

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

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8.

Descriptive statistics

  • 1. Univariate analysis
  • 2. Presenting data
  • 3. Measures of central tendency
  • 4. Measures of dispersion
  • 5. Cumulative frequency
  • 6. Variance and standard deviation

8.1.

–

8.2.

–

8.3.

–

8.4.

–

8.5.

–

8.6.

–

9.

Integration

  • 1. Antiderivatives and the indefinite integral
  • 2. More on indefinite integrals
  • 3. Area and definite integrals
  • 4. Fundamental Theorem of Calculus
  • 5. Area between two curves
  • 6. Volume of revolution
  • 7. Definite integrals with linear motion and other problems

9.1.

–

9.2.

–

9.3.

–

9.4.

–

9.5.

–

9.6.

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9.7.

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10.

Bivariate analysis

  • 1. Scatter diagrams
  • 2. The line of best fit
  • 3. Least squares regression
  • 4. Measuring correlation

10.1.

–

10.2.

–

10.3.

–

10.4.

–

11.

Trigonometry

  • 1. Right-angled triangle trigonometry
  • 2. Applications of right-angled triangle trigonometry
  • 3. Using the coordinate axes in trigonometry
  • 4. The sine rule
  • 5. The cosine rule
  • 6. Area of a triangle
  • 7. Radians, arcs and sectors

11.1.

–

11.2.

–

11.3.

–

11.4.

–

11.5.

–

11.6.

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11.7.

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12.

Vectors

  • 1. Vectors: basic concepts
  • 2. Addition and subtraction of vectors
  • 3. Scalar product
  • 4. Vector equation of a line
  • 5. Application of vectors

12.1.

–

12.2.

–

12.3.

–

12.4.

–

12.5.

–

13.

Circular functions

  • 1. Using the unit circle
  • 2. Solving equations using the unit circle
  • 3. Trigonometric identities
  • 4. Graphing circular functions
  • 5. Translations and stretches of trigonometric functions
  • 6. Combined transformations with sine and cosine functions
  • 7. Modeling with sine and cosine functions

13.1.

–

13.2.

–

13.3.

–

13.4.

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13.5.

–

13.6.

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13.7.

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14.

Calculus with trigonometric functions

  • 1. Derivatives of trigonometric functions
  • 2. More practice with derivatives
  • 3. Integral of sine and cosine
  • 4. Revisiting linear motion

14.1.

–

14.2.

–

14.3.

–

14.4.

–

15.

Probability distributions

  • 1. Random variables
  • 2. The binomial distribution
  • 3. The normal distribution

15.1.

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15.2.

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15.3.

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정보