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Mathematics Curriculum Standards
3103 - Algebra II
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Internet Resources |
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Create and analyze scatter-plots of non-linear and transcendental functions.
3103.1.1 |
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Compare and contrast sampling techniques and identify the best technique for a given situation.
3103.1.2 |
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Use calculators to identify regression equations for nonlinear data.
3103.1.3 |
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Identify the weaknesses of calculators and other technologies in representing non-linear data, such as graphs approaching vertical asymptotes, and use alternative techniques to identify these issues and correctly solve problems.
3103.1.4 |
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Determine the accuracy and reliability of a mathematical model.
3103.1.5 |
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Use graphical representations to perform operations on complex numbers.
3103.1.6 |
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Use the unit circle to determine the exact value of trigonometric functions for commonly used angles (0°, 30°, 45°, 60°…).
3103.1.7 |
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Understand and describe the inverse relationship between exponential and logarithmic functions.
3103.1.8 |
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Translate the syntax of technology to appropriate mathematical notation for non-linear and transcendental functions.
3103.1.9 |
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Interpret the results of mathematical modeling in various contexts to answer questions.
3103.1.10 |
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Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic) of non-linear and transcendental functions to solve problems, to model mathematical ideas, and to communicate solution strategies.
SPI 3103.1.1
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Recognize and describe errors in data collection and analysis as well as identifying
representations of data as being accurate or misleading.
SPI 3103.1.2 |
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Use technology tools to identify and describe patterns in data using non-linear and transcendental functions that approximate data as well as using those functions to solve contextual problems.
SPI 3103.1.3 |
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Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely to effectively communicate reasoning in the process of solving problems via mathematical modeling with both linear and non-linear functions.
SPI 3103.1.4 |
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Mathematics Curriculum Standards
3103 - Algebra II
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Internet Resources |
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Understand that to solve certain problems and equations, the real number system needs to be extended from real numbers to complex numbers.
3103.2.1 |
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Define and give examples of each of the types of numbers in the complex number system.
3103.2.2 |
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Identify and apply properties of complex numbers (including simplification and standard form).
3103.2.3 |
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Add and subtract complex numbers.
3103.2.4 |
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Multiply complex numbers.
3103.2.5 |
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Define and utilize the complex conjugates to write the quotient of two complex numbers in standard form.
3103.2.6 |
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Graph complex numbers in the complex plane and recognize differences and similarities with the graphical representations of real numbers graphed on the number line.
3103.2.7 |
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Solve quadratic equations over the complex number system.
3103.2.8 |
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Find and describe geometrically the absolute value of a complex number.
3103.2.9 |
- Absolute Value lesson from Purple Math
- Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball
  on 9/4/08
- Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- Solving Absolute Value Equations - a lesson from Purple Math
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Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers.
3103.2.10 |
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Understand the capabilities and limitations of technology. Make estimations without a calculator to detect potential errors.
3103.2.11 |
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Select and use appropriate methods to make estimations without technology when solving contextual problems.
3103.2.12 |
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Analyze and evaluate contextual situations involving any type of number from the complex number system.
3103.2.13 |
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Describe any number in the complex number system.
SPI 3103.2.1 |
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Compute with all real and complex numbers.
SPI 3103.2.2 |
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Use the number system, from real to complex, to solve equations and contextual
problems.
SPI 3103.2.3 |
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National Library of Virtual Manipulatives |
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Number & Operations [Grades 9-12]
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Mathematics Curriculum Standards
3103 - Algebra II
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Internet Resources |
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Perform operations on algebraic expressions and justify the procedures.
3103.3.1 |
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Determine the domain of a function represented in either symbolic or graphical form.
3103.3.2 |
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Determine and graph the inverse of a function with and without technology.
3103.3.3 |
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Analyze the effect of changing various parameters on functions and their graphs.
3103.3.4 |
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Graph piece-wise and step functions.
3103.3.5 |
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Simplify expressions and solve equations containing radicals.
3103.3.6 |
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Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula.
3103.3.7 |
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Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology.
3103.3.8 |
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Find an equation for a parabola when given its graph or when given its roots.
3103.3.9 |
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Given a quadratic equation use the discriminant to determine the nature of the roots.
3103.3.10 |
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Describe and articulate the characteristics and parameters of a parent function.
3103.3.11 |
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Understand the relationship between real zeros of a function and the x-intercepts of its graph.
3103.3.12 |
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Solve problems using exponential functions requiring the use of logarithms for their solutions.
3103.3.13 |
- Basic Log Rules from Purple Math
- College Algebra - a tutorial on Logarithmic Properties with several examples and practice problems
- Exponential functions - a review of logarithms from SOS Math
- Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes
- Properties of Logarithms from SOS Math
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Define and use arithmetic and geometric sequences and series including using sigma and pi notation.
3103.3.14 |
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Find the sum of an geometric series whose common ratio, r, is in the interval (-1,1).
3103.3.15 |
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Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems.
3103.3.16 |
- Exponential functions - a review of logarithms from SOS Math
- Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes
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Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems.
3103.3.17 |
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Solve compound inequalities involving disjunction and conjunction and linear inequalities containing absolute values.
3103.3.18 |
- Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
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Solve linear programming problems.
3103.3.19 |
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Understand the relationships between the equations of conic sections and their graphs.
3103.3.20 |
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Factor polynomials using a variety of methods including the factor theorem, synthetic division, long division, sums and differences of cubes, and grouping.
3103.3.21 |
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Determine the number and possible types of zeros for a polynomial function and find the rational roots.
3103.3.22 |
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Understand the connection between the roots, zeros, x-intercepts, factors of polynomials, and solutions of polynomial equations.
3103.3.23 |
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Add, subtract and multiply polynomials; divide a polynomial by a lower degree
polynomial.
SPI 3103.3.1 |
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Solve quadratic equations and systems, and determine roots of a higher order
polynomial.
SPI 3103.3.2 |
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Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents.
SPI 3103.3.3 |
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Use the formulas for the general term and summation of finite arithmetic and both finite and infinite geometric series.
SPI 3103.3.4 |
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Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent.
SPI 3103.3.5 |
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Combine functions (such as polynomial, rational, radical and absolute value expressions) by addition, subtraction, multiplication, division, or by composition and evaluate at specified values of their variables.
SPI 3103.3.6 |
- Determining the Sign of Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
- Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball on 9/4/08
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Identify whether a function has an inverse, whether two functions are inverses of each other, and/or explain why their graphs are reflections over the line y = x.
SPI 3103.3.7 |
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Solve systems of three linear equations in three variables.
SPI 3103.3.8 |
- Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball on 9/4/08
- Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball on 9/4/08
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Graph the solution set of two or three linear or quadratic inequalities.
SPI 3103.3.9 |
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Identify and/or graph a variety of functions and their transformations.
SPI 3103.3.10 |
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Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph.
SPI 3103.3.11 |
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Interpret graphs that depict real-world phenomena.
SPI 3103.3.12 |
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Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations.
SPI 3103.3.13 |
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Solve problems involving the binomial theorem and its connection to Pascal’s Triangle, combinatorics, and probability.
SPI 3103.3.14 |
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National Library of Virtual Manipulatives |
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Algebra [Grades 9-12]
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Mathematics Curriculum Standards
3103 - Algebra II
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Internet Resources |
Checks for Understanding (Formative/Summative Assessment)
4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 |
Convert between radians and degrees and vice versa.
3103.4.1
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Determine the period and the amplitude of a periodic function.
3103.4.2 |
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Extend the trigonometric functions to periodic functions on the real line by defining them as functions on the unit circle.
3103.4.3 |
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Understand the relationship between the radius, the central angle, and radian measure.
3103.4.4 |
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Determine the domain and range of the six trigonometric functions given a graph.
3103.4.5 |
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Know and be able to use the fundamental trigonometric identities, including the Pythagorean identities, reciprocal identities, sum of sine and cosine, and odd and even identities.
3103.4.6 |
- Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math
- How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
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Exhibit knowledge of unit circle trigonometry.
SPI 3103.4.1 |
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Match graphs of basic trigonometric functions with their equations.
SPI 3103.4.2 |
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Describe and articulate the characteristics and parameters of parent trigonometric functions to solve contextual problems.
SPI 3103.4.3 |
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National Library of Virtual Manipulatives |
- Geometry [Grades 9-12]
- Measurement [Grades 9-12]
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Data Analysis, Statistics, & Probability
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Mathematics Curriculum Standards
3103 - Algebra II
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Internet Resources |
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Collect, represent and describe both linear and non-linear data developed from contextual situations.
3103.5.1 |
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Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns.
3103.5.2 |
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Read and interpret data from a two-way table.
3103.5.3 |
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Understand the impact of various sampling methods and use them to draw valid conclusions.
3103.5.4 |
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Calculate measures of central tendency and spread (variance and standard deviation).
3103.5.5 |
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Use technology to find the appropriate regression equation for both linear and non-linear data.
3103.5.6 |
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Recognize when the correlation coefficient measures goodness of fit and does not imply causation.
3103.5.7 |
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Know the Empirical Rule for one, two and three standard deviations for a normal distribution.
3103.5.8 |
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Use data to detect patterns.
3103.5.9 |
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Design simple experiments to collect data to answer questions of interest.
3103.5.10 |
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Evaluate published data by considering the source, the design of the study and the analysis and representation (or misrepresentation) of the data.
3103.5.11 |
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Investigate bias and the phrasing of questions during data acquisition to formulate reasonable conclusions.
3103.5.12 |
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Apply both theoretical and experimental probability to analyze the likelihood of an event.
3103.5.13 |
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Compute, compare and explain summary statistics for distributions of data including measures of center and spread.
SPI 3103.5.1 |
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Compare data sets using graphs and summary statistics.
SPI 3103.5.2 |
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Analyze patterns in a scatter-plot and describe relationships in both linear and non-linear data.
SPI 3103.5.3 |
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Apply the characteristics of the normal distribution.
SPI 3103.5.4 |
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Determine differences between randomized experiments and observational studies.
SPI 3103.5.5 |
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Find the regression curve that best fits both linear and non-linear data (using technology such as a graphing calculator) and use it to make predictions.
SPI 3103.5.6 |
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Determine/recognize when the correlation coefficient measures goodness of fit.
SPI 3103.5.7 |
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Apply probability concepts such as conditional probability and independent events to calculate simple probability.
SPI 3103.5.8 |
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National Library of Virtual Manipulatives |
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Data Analysis & Probability [Grades 9-12]
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a site for teachers | 
a PowerPoint show | 
a Word document
sound | 
video format | 
a quiz | 
