Subject Area___MathB________________________________ Grade Level ___10-12     

b) follow and judge the validity of logical arguments

c) use symbolic logic in the construction of valid arguments

d) construct proofs based on deductive reasoning
2. Numbers and Numeration
 
a) understand and use rational and irrational numbers

b) recognize the order of real numbers

c) apply the properties of the real numbers to various subsets of numbers

 
3. Operations
 
a) use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions

b) develop an understanding of and use the composition of functions and transformations

c) explore and use negative exponents on integers and algebraic expressions

d) use field properties to justify mathematical procedures

e) use transformations on figures and functions in the coordinate plane

 
4. Modeling/Multiple Representation
 
a) represent problem situations symbolically by using algebraic expressions, sequences, tree diagrams, geometric figures, and graphs

b) manipulate symbolic representations to explore concepts at an abstract level

c) choose appropriate representations to facilitate the solving of a problem

d) use learning technologies to make and verify geometric conjectures

e) justify the procedures for basic geometric constructions

f) investigate transformations in the coordinate plane

g) develop meaning for basic conic sections

h) develop and apply the concept of basic loci to compound loci

i) use graphing utilities to create and explore geometric and algebraic models

j) model real-world problems with systems of equations and inequalities

 
5. Measurement
 
a) derive and apply formulas to find measures such as length, area, volume, `  weight, time, and angle in real-world contexts

b) choose the appropriate tools for measurement

c) use dimensional analysis techniques

d) use statistical methods including measures of central tendency to describe and compare data

e) use trigonometry as a method to measure indirectly

f) apply proportions to scale drawings, computer-assisted design blueprints, and direct variation in order to compute indirect measurements

g) relate absolute value, distance between two points, and the slope of a line to the coordinate plane

h) understand error in measurement and its consequence on subsequent calculations

i) use geometric relationships in relevant measurement problems involving geometric concepts

 
6. Uncertainty
 
a) judge the reasonableness of results obtained from applications in algebra, geometry, trigonometry, probability, and statistics

b) judge the reasonableness of a graph produced by a calculator or computer

c) use experimental or theoretical probability to represent and solve problems involving uncertainty

d) use the concept of random variable in computing probabilities

e) determine probabilities using permutations and combinations

 
7. Patterns/Functions
 
a) use function vocabulary and notation

b) represent and analyze functions using verbal descriptions, tables, equations, and graphs

c) translate among the verbal descriptions, tables, equations and graphic forms of functions

d) analyze the effect of parametric changes on the graphs of functions

e) apply linear, exponential, and quadratic functions in the solution of problems

f) apply and interpret transformations to functions

g) model real-world situations with the appropriate function

h) apply axiomatic structure to algebra and geometry

j) use computers and graphing calculators to analyze mathematical phenomena

 
 
Standard 6—Interconnectedness: Common Themes. Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.
 
The Key Ideas for Standard Six are
1.  Systems Thinking—Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions.
 
2.  Models—Models are simplified representations of objects, structure, or systems used in analysis, explanation, interpretation, or design.
 
 
3.  Magnitude and Scale—The grouping of magnitudes of size, time, frequency, and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes in scale that affect the behavior and design of systems.
 
 
4.  Equilibrium and Stability—Equilibrium is a state of stability due either to a lack of changes (static equilibrium) or a balance between opposing forces (dynamic equilibrium).
 
 
5.  Patterns of Change—Identifying patterns of change is necessary for making predictions about future behavior and conditions.
 
 
6.  Optimization—In order to arrive at the best solution that meets criteria within constraints, it is often necessary to make trade-offs.
 
 
National Standards: National Standards (published by the National Council of Teachers of Mathematics) are directly in line with our state standards and can be found at NCTM.ORG.
 
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Review for Math B Exam

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