On the other hand, if the vectors had been assigned values, then both of the above expressions would reduce to the same value, as long as the second expression had been copied and pasted from the "simplified" result of the former expression, but if the user typed in the second expression, then its value as a specific three-tuple would be computed correctly. Current releases[ edit ] As of Augustthere are two actively maintained Mathcad releases and a free express version available to consumers:
Algebra 2 Table of Contents Chapter 1: Fitting Functions to Tables 1A: Tables This investigation begins the Algebra 2 thread of functions and fitting. Students investigate how to use constant differences and other cues to fit linear and quadratic rules to input-output tables.
They use a functional modeling language on their calculator to model and experiment with functions. Fitting the Data Students begin to develop a statistical perspective, in the sense of thinking of data in terms of trends, rather than as individual points.
Students investigate whether or not a data set can be reasonably approximated by a linear function, and they study alternatives to linear trends. Students investigate relationships among mean, median, variance and standard deviation. Here, they investigate recursion in greater depth by analyzing a recursive function that determines the monthly payment on a loan.
Students also investigate the factorial function — a recursively-defined function with no simple closed form. Functions and Polynomials 2A: About Functions Students develop a "functional perspective: Students learn to decide whether a given pairing is a function from a table, a graph, or an equation.
Students also revisit notation and develop precise definitions of domain and range. Students investigate the arithmetic of functions, including composition. Inverse functions are introduced. Making it Fit 2C: Students learn the relationship between roots and factors of polynomials.
Students also learn to divide polynomials by monic linear polynomials. Advanced Factoring Students study various polynomial forms and methods for factoring them: Rational expressions are also introduced. Introduction to Complex Numbers Students encounter problems whose solutions require calculations with square roots of negative numbers, and they then extend the real numbers to include these square roots.
They investigate arithmetic of complex numbers. Complex Plane, Graphing, Complex Numbers This investigation offers an exploration of some more advanced topics in complex numbers, including in-depth investigations of magnitude and direction, roots of polynomials, and roots of unity.
The Complex Plane Students learn how to graph complex numbers, and how to interpret arithmetic geometrically.
Magnitude and direction are introduced. Gaussian Elimination Students solve systems of linear equations. Matrices and Gaussian elimination are introduced as tools for solving linear systems.
Matrix Algebra Students learn to solve matrix equations. Dot product is introduced. Students also learn to multiply matrices and find inverses of matrices, by hand and with their calculators. Applications of Matrix Multiplication Students learn to use matrices to represent sequences of geometric transformations, model the evolution of a system over time, and analyze sequences of repeated probabilities.
Exponential and Logarithmic Functions 5A: Working with Exponents This investigation begins with a review of laws of exponents, including a review of zero and negative exponents. Students investigate arithmetic and geometric sequences, and they use these to extend the laws of exponents to include rational exponents.
Exponential Functions Students explore exponential functions via tables and graphs.Algebra Lesson Plans; Listed below are links to some of the tests and exams that I administered to my Algebra II class in I gave two versions of each test and I have provided both an Adobe Acrobat PDF file and a Microsoft Word document of each version.
Test 6 Sections – (Factoring) Version 1 Microsoft Word Document. Algebra II A relation is a set of ordered pairs, where the set of x-coordinates is known as the domain and the set of y-coordinates is known as the range. A relation can be represented as a set of ordered pairs, a table, a graph, or by mapping.
Ordered Pairs (1, 2) (-2, 4) (0, -3) Table x y 1 2. Menu Pre-Algebra / Introducing Algebra / Evaluate expressions. A variable is a letter, for example x, y or z, that represents an unspecified number. $$6+x=12$$ To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
In the example above, the variable x is equal to 6 since 6. How does change in the slope affect the steepness of a line? Why is the slope of a horizontal line is zero? Algebra 2 Chapter 4 Practice Test 3 | Page 5.
\ L Û Û E à F â L Ù For #6‐7, a) solve and graph the inequality and b) write the solution: 6. Û3 T R28 Starting 6Equation: T. Browse over educational resources created by All Things Algebra in the official Teachers Pay Teachers store.