Chapter 3.5
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This section discusses one-to-one properties and order of magnitude comparisons. It provides examples of calculating the order of magnitude between Pluto and Mercury's distance from the sun, and comparisons between meters and kilometers, the weight of a horse and mouse, and populations of New York City and Earmuff Junction. Newton's Law of Cooling is also mentioned as a topic for a later part of the chapter.
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Parametric equations allow functions to be defined using a third variable t, called a parameter, to define both x and y values. For example, a function can be defined parametrically as x=f(t) and y=g(t). Inverse functions relate each element of an ordered pair (x,y) to another ordered pair by reflecting points across the line y=x. This is known as the inverse reflection principle. Inverse functions satisfy the horizontal line test, meaning each x value corresponds to only one y value.
2.1 lesson
This document discusses different types of real numbers including rational numbers, irrational numbers, integers, and whole numbers. It defines rational numbers and discusses their properties such as opposites and absolute value. It also explains what conditional statements are, noting they have a hypothesis and conclusion in an "if-then" format and can be proven true or false with a counterexample. Examples of conditional statements involving rational numbers and absolute value are provided. Students are assigned practice problems from lessons 2.2, 2.3, and 2.4.
Section 1.3
This document discusses graphing the 12 basic functions in mathematics. It provides an example of graphing the 12 basic functions and mentions that graphing these functions is an example. The document repeats the phrase "Graph the 12 Basic Functions" three times.
Alg 2 sections 2.1
This document discusses relations and functions. It defines a relation as a mapping or pairing of input and output values, with the input set called the domain and output set called the range. Relations can be represented through tables, mapping diagrams, ordered pairs, and graphs. The document defines a function as a special type of relation where each input has exactly one output; if any input has more than one output it is not a function. Examples of functions and non-functions are provided. Homework problems from the textbook are listed at the end.
Section 1.1
The document discusses mathematical modeling and functions. It defines a mathematical model as a structure that approximates real-world phenomena to study or predict behavior. It then discusses numerical, algebraic and graphical models. It also discusses functions, including defining them, representing them with equations, graphs and mappings, and determining their domains and ranges. It provides examples of finding domains and ends with homework problems assigned.
Section 1.1
The document discusses mathematical modeling and functions. It defines mathematical modeling as using mathematical structures to approximate real-world phenomena in order to study or predict behavior. It then discusses different types of mathematical models like numerical, algebraic and graphical models. The rest of the document focuses on defining and representing functions, including discussing domain and range, and ways to find the domain of a function either algebraically or graphically. It concludes by listing specific homework problems.
Alg2 section 1.7
This document discusses how to solve absolute value equations and inequalities in 3 sections: the first section explains absolute value, the second section provides instructions for solving absolute value equations, and the third section gives directions for solving absolute value inequalities and includes an application example.
Pa section 1.6
The document defines and provides examples of calculating the median, mode, and range of data sets. It explains that the median is the middle value of a data set in numerical order, or the mean of the two middle values for an even number of values. The mode is the value that occurs most frequently. The range is the difference between the greatest and least values. Examples are provided to demonstrate calculating each metric for temperature and score data sets.
Alg 2 section 1.6
The document discusses solving linear inequalities and includes three topics: forms of linear inequalities, compound inequalities, and homework assigned which includes odd numbered problems 23 through 33 and 37 through 47 on page 45 of the text.
Alg2 sections 1.4-1.5
This document provides an overview of rewriting formulas and equations. It includes sections on common formulas, solving for variables, examples to practice, and application problems. Formulas covered include distance, temperature, areas of shapes, and circumference. It also discusses strategies for problem solving like using formulas, patterns, and diagrams. Sample problems are provided for average speed, finding heights from a pattern, and positioning posters on a wall. The document concludes with assigned homework problems.
Pc sections p.4-p.5
This document provides an overview of topics in algebra including:
1) Different forms of equations for lines (slope-intercept, point-slope, etc.) and quadratics (general, vertex).
2) How to determine if lines are parallel or perpendicular.
3) Methods for graphing and solving linear and quadratic equations (finding intercepts, using a graphing calculator, extracting roots, using the quadratic formula).
4) An example word problem on investing money with different interest rates and determining the amount to invest to earn a target return.
5) Assigned homework problems from the textbook.
Pa sections 1-2
This document provides instructions for performing common mathematical operations like addition, subtraction, multiplication, and division. It includes examples of writing down a number and then performing sequential operations on it like doubling, adding or subtracting other numbers, dividing, and subtracting the original number. The document also lists common words used to indicate different operations and directs the reader to specific math problems to complete on designated pages.
Alg1 sections 1.1-1.2
This document summarizes key concepts from sections 1 and 2 of chapter 1 including:
- PEMDAS order of operations with parentheses, exponents, multiplication/division, addition/subtraction.
- Definitions of powers/exponents as repeated multiplication with a base and exponent.
- Examples of evaluating expressions and algebraic equations.
- Formulas for estimating a frog's jump distance, points earned in soccer, and adult height based on childhood height.
- Practice problems listed for pages 5-7 and 10-12.
Pc sections p.1-p.3
This document provides an overview of number types including real numbers, imaginary numbers, rational numbers, irrational numbers, integers, whole numbers, and natural numbers. It also covers interval notation and types of intervals. Key concepts covered include the x-axis, y-axis, origin, ordered pairs, coordinates, quadrants, absolute value, distance formula, midpoint formula, and the standard form of a circle. Practice problems are assigned from pages 9-10, 17-19, and 25-27 of the text.
Alg2 sections 1, 2, and3
This document provides an overview of key concepts from the first three sections of an Algebra 2 textbook. It introduces different types of real numbers like integers, rational numbers, and irrational numbers. It discusses how to plot numbers on a real number line and use the order of operations. Properties of real numbers are defined, including closure, commutative, associative, identity, inverse, and distributive. The document also covers unit analysis, numerical and algebraic expressions, solving linear equations, and key vocabulary terms. Homework problems are assigned from various textbook pages.
Alg1 sections 1.1-1.2
This document summarizes key concepts from the first chapter of a math textbook. It begins by explaining the order of operations using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). It then defines powers and exponents. Several examples of evaluating expressions and solving equations are provided. The document concludes by listing vocabulary terms and practice problems for students to complete.
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Chapter 3.5
- 1. Equations Solving and Modeling Chapter 3 section 5
- 2. One to One Properties •
- 3. Examples • •
- 4. Order of Magnitude The common logarithm of a positive quantity. Pluto is 5.9 x 1012 meters from the sun, Mercury is 5.79 x 1010 meters from the sun. Pluto’s distance from the sun is 2 orders of magnitude greater than Mercury. • A kilometer is orders of magnitude longer than a meter. • A horse weighting 400 kg is orders of magnitude heavier than a mouse weighting 40 g. • New York City with 8 million people is orders of magnitude bigger than Earmuff Junction with a population of 8.
- 5. Newton’s Law of Cooling •