UTAH INSTRUCTIONAL MATERIALS

Instuctional Materials Evaluation Criteria (name and grade of the core document used to align):
Pre-Calculus Core
Title: Algebra and Trigonometry
ISBN: 0131959948 Copyright: 2007 Publisher:
Prentice Hall 		Grade: 10-12
Overall percentage of the Utah State Core Curriculum: 85% match

Standard I: Students will acquire number sense and perform fundamental operations with complex numbers.
Percentage of coverage for Standard 1: 100%
Objectives Indicators: Covered Yes Covered No
1.1 -- Compute fluently with vectors and complex numbers.

a. Add, and subtract vectors using a variety of techniques.

X
  
 

b. Perform scalar multiplication on vectors using a variety of techniques.

X  

c. Multiply complex numbers in polar form.

X  
 

d. Write complex numbers in polar form and use DeMoivre's Theorem to find roots of complex numbers.

X
  
1.2 -- Represent complex numbers and vectors in a variety of ways.

a. Represent vectors graphically and symbolically.

X  
 

b. Represent complex numbers in rectangular and polar form and convert between rectangular and polar form.

X  
Standard II: Students will use the language of algebra to analyze and represent relationships, including real-life relationships.
Percentage of coverage for Standard II: 80%
2.1 -- Analyze exponential, polynomial, rational, logarithmic, piece­wise, and trigonometric functions Identify the domain, range, and other attributes of families of functions and their inverses.

a. Simplify expressions using a variety of approaches and techniques .

X  
 

b. Identify vector-valued functions using a variety of approaches.

   
 

c. Raise a binomial to a power using the Binomial Theorem.

X
  
 

d. Relate the Binomial Theorem to combinations and Pascal's Triangle.

X  
2.2 -- Use functions to solve problems and describe mathematical relationships.

a. Solve equations and inequalities involving exponential, logarithmic, power, polynomial, rational, and trigonometric functions that reflect real-world situations.

X  
 

b. Relate logarithmic and exponential functions.

X  
 

c. Combine and compose functions using algebraic methods or by using technology when appropriate.

X  
 

d. Identify the domain and range of a function resulting from the combination or composition of functions.

X  
 

e. Given a real-world relationship, Identify a family or families of functions that model that relationship.

X  
2.3 -- Analyze the behavior of functions.

a. Approximate instantaneous rates of change and find average rates of change using graphical and numerical data.

  X (Average is covered but not instantaneos)
 

b. Determine intervals over which a function is increasing or decreasing.

X  
 

c. Identify and analyze graphical features of functions such as x- and y- intercepts, zeros (roots), asymptotes, holes, local, global, and end behavior.

X (could not find global)  
 

d. Relate the graphical representation of discontinuities and end-behavior to the concept of limit.

  X (not really related to the concept of limit)
 

e. Identify the effects of changing the parameters in transformations of functions.

X  
2.4 -- Analyze the behavior of sequences and series.

a. Identify a sequence as an infinite string of numbers.

X  
 

b. Understand that a sequence can be defined as a function with the domain of natural numbers.

X  
 

c. Understand the various notations of sequences and series.

X  
 

d. Identify and accurately express arithmetic and geometric sequences.

X  
 

e. Identify a geometric series as convergent or divergent .

  X (does not use the words "converge" or "diverge")
 

f. Identify a geometric series as convergent or divergent .

  X
Standard III: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.
Percentage of coverage for Standard III: 100%
3.1 -- Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

a. Determine and analyze the equations and characteristics of conic sections using their geometric definitions.

X  
 

b. Solve problems using the geometric properties of vectors.

X  
3.2 --Solve problems using trigonometry.

a. Define the six trigonometric functions using the unit circle.

X  
 

b. Develop trigonometric identities using definitions, the Pythagorean Theorem or other relationships.

X  

c. Simplify trigonometric expressions and solve trigonometric equations using identities.

X
Standard IV: Students will select and utilize measurement tools and techniques needed to apply mathematical formulas for addressing real-life problems.
Percentage of coverage for Standard IV: 0%
4.1 -- Understand measurable attributes of objects and the units, systems, and processes of measurement.

a. Compare and contrast linear and exponential scales.


X
Standard V: Students will draw reasonable conclusions using concepts, relationships, and algorithms of probability.
Percentage of coverage for Standard V: 75%
5.1 -- Apply basic concepts of probability.

a. Relate the Binomial Theorem to combinations and Pascal's Triangle .

  X (these are mentioned only briefly)
 

b. Differentiate between, and calculate probabilities of, independent and dependent events .

X  

c. Calculate probabilities of compound events.

X  

d. Calculate and interpret the expected value mean of simple discrete random variables.

  X