Integrated IV

 

Vergennes Union High School

Course Syllabus

Integrated IV

 

Sequences and Series: (Unit Four- Integrated 3- McDougal Littell)

 

  • Exploring Patterns: Graphing sequences and deciding if an infinite sequence appears to have a limit.
  • Sequences:  Finding and using formulas for sequences related to algebraic and geometric situations.
  • Recursive Formulas: Writing and applying formulas for sequences in which each term is found by using the preceding terms.
  • Arithmetic and Geometric Sequences: Writing and applying explicit and recursive formulas for sequences.  Finding geometric means.
  • Arithmetic Series and Sigma Notation: Finding the sum of a finite arithmetic series.  Representing and evaluating a series with sigma notation.
  • Geometric Series: Finding the sum of a finite geometric series.
  • Infinite Series: Recognizing when an infinite series has a sum.  Finding the sum of an infinite geometric series.

 

Exponential and Logarithmic Functions: (Unit Five- Integrated 3- McDougal Littell)

 

  • Exponential Growth and Decay: Using graphs and recursion with exponential growth and decay functions to model and solve real world problems.
  • Negative Exponents: Exploring Exponential Functions with negative exponents.
  • Fractional Exponents: Apply relationships between fractional exponents and radicals.
  • The Number e: Modeling real world situations using exponential functions with base e and with logistic growth functions.
  • Inverse Functions: Recognizing when a function has an inverse.  Finding and graphing the inverse.
  • Logarithmic Functions: Apply relationships between an exponential and logarithmic function.
  • Properties of Logarithms: Investigate properties of logarithms.  Use them to simplify and evaluation expression and equations.
  • Exponential and Logarithmic Equations: Solve exponential and logarithmic equations.

 

Polygons & Circles: (Unit Three- Integrated 3- McDougal Littell)

 

  • Angles in Polygons: Find the measure of exterior and interior angles of both regular and non-regular polygons. 
  • Inscribed Polygons: Explore polygons inscribed in a circle, central angles, arcs and perpendicular bisector of a chord in a circle.
  • Arcs and Angles: Apply relationships between inscribed angles and arcs of circles.
  • Circumscribed Polygons: Explore relationships between circumscribed polygons and inscribed circles.  Find the area of a circumscribed polygon.

 

Angles, Trigonometry, and Vectors: (Unit Eight- Integrated 3- McDougal Littell)

 

  • Polar Coordinates: Use polar coordinates to locate points in the plane.
  • Converting Coordinates: Convert polar coordinates to rectangular and vice versa.  Find the sine, cosine and tangent of any angle.
  • The Geometry of Vectors: Solve problems using graphic representations of vectors, sums of vectors, and scalar multiples of vectors.
  • Algebra of Vectors: Solve problems using vectors in rectangular form.
  • Parametric Equations: Solve problems by using pairs of equations that define x and y in terms of t.
  • Law of Cosines: Use the law of cosines to solve problems.
  • Law of Sines: Use the law of sines to solve problems.

 

Modeling and Analyzing Data: (Unit Six & Nine- Integrated 3- McDougal Littell)

 

  • Distributions of Data: Analyzing types of frequency distributions.  Drawing and interpreting histograms and relative frequency histograms.
  • Standard Deviation: Use technology to compute the mean and standard deviation of a data set.
  • Normal Distributions: Explore and apply properties of normal distributions.
  • Adding a Constant to Data: Explore the effect of adding a constant to a set of data.
  • Multiplying Data by a constant: Explore the effect of multiplying a constant to a set of data.

 

Transformations of Graphs: (Unit Nine- Integrated 3- McDougal Littell)

 

  • Translating Graphs: Explore and apply relationships between the graph of a parent function y = f(x) and the graph y-k=f(x-h).
  • Stretching Graphs: Exploring and applying relationships between the graph of a parent function y=f(x) and the graphs of f(x/a) and y/b=f(x).
  • Multiple Transformations: Recognizing the effects of multiple transformations on data and graphs of functions.
  • Reflecting Graphs: Exploring and applying the relationship between the graphs of y=f(x), y=-f(x), and y=f(-x).  Combining translations, dilations, and reflections to produce new functions.

 

Periodic Models: (Unit Ten- Integrated 3- McDougal Littell)

 

  • Describing the Behavior of Functions: Comparing rates of growth and decay of functions.
  • Periodic Functions: Exploring periodic functions related to real-world situations.
  • Graphs of Sine and Cosine: Investigating and applying the characteristics of the graphs of sine and cosine functions.
  • Transforming Sine and Cosine Graphs: Exploring and applying properties of graphs of the form y=AsinB(x-C)+D and
  • y=AcosB(x-C)+D.
  • Measurement of Angles: Convert between degrees and radians.
  • Sine and Cosine Functions: To graph and find values of trigonometric functions.

 

Polynomials: ( Unit Two- Advanced Mathematics- Brown/Robbins)

 

  • Roots of Polynomial Equations: Use synthetic division and apply the Factor Theorem and Remainder Theorem.
  • Rational Roots of Polynomial Equations: To find rational and irrational roots of a polynomial equation.
  • Completing the Square: Solve quadratics applying quadratic formula.

 

Trigonometric functions: ( Unit Six- Advanced Mathematics- Brown/Robbins)

  • Other Trigonometric Functions: Apply the six trig. Functions.
  • Trigonometric Identities: Simplify, apply and prove trigonometric relationships and identities.
  • Trigonometric Equations: Solve trigonometric equations.