Chapter 6.7
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This document discusses how to graph linear inequalities in two variables. It explains that to shade the graph of an inequality, you should pick a point not on the line and test it in the original inequality. If the point makes the inequality true, shade the side it is on. If false, shade the side it is not on. The document also lists homework problems from pages 409-410 involving graphing linear inequalities in two variables.
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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.
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This document provides instructions for simplifying radical expressions, including basic operations with radicals, examples of simplifying radical expressions, and homework assignments involving simplifying radicals from pages 713 and 3-21 of the textbook. Students are asked to complete odd numbered problems 3, 7, 9, 17, 19, 23, 25 from page 713 and problems 27 through 53 from page 3-21.
5.1
This document discusses several fundamental trigonometric identities including basic trigonometric identities, quotient identities, Pythagorean identities, cofunction identities, odd-even identities, and other identities. These identities relate trigonometric functions and are important tools for working with and simplifying trigonometric expressions.
Section 6.4
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Alg 2 section 1.6
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Lesson 6.4
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Chapter 3.5
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This document provides an overview of topics in algebra including:
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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).
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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.
11.1 and 11.2
This document provides instructions for simplifying radical expressions, including basic operations with radicals, examples of simplifying radical expressions, and homework assignments involving simplifying radicals from pages 713 and 3-21 of the textbook. Students are asked to complete odd numbered problems 3, 7, 9, 17, 19, 23, 25 from page 713 and problems 27 through 53 from page 3-21.
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This document discusses several fundamental trigonometric identities including basic trigonometric identities, quotient identities, Pythagorean identities, cofunction identities, odd-even identities, and other identities. These identities relate trigonometric functions and are important tools for working with and simplifying trigonometric expressions.
Section 6.4
This document discusses solving compound inequalities, which involve two separate inequalities joined by "and" or "or". It provides examples of writing and solving compound inequalities, including graphing the solutions. One example asks the reader to write and solve a compound inequality describing possible temperatures in degrees Fahrenheit on Mars, between -133 degrees Celsius and 27 degrees Celsius.
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Lesson 6.4
The document discusses inverse relations and functions. An inverse relation interchanges the input and output values of the original relation and swaps the domain and range. The graph of an inverse function is a reflection of the original relation across the line y=x. A function has an inverse function if and only if its graph passes the horizontal line test, meaning no horizontal line intersects the graph more than once.
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3) Methods for graphing and solving linear and quadratic equations (finding intercepts, using a graphing calculator, extracting roots, using the quadratic formula).
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Section 1.5
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- 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.
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Section 4.2
This document provides homework assignments from a math textbook. Students are assigned problems on vertex form and intercept form of graphs from pages 240-245 with problems #5, 21-31 odd, 33, 35, 44-46, 57, 60. Additional problems on the same topics are assigned from pages 249-251 including problems #13-21 odd, 25-41 odd, and 54.
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This section discusses properties of quadratic functions including their graphs, minimum and maximum values, and axis of symmetry. It covers labeling key features such as the vertex on the graph of a quadratic function in standard form and identifying the axis of symmetry.
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Section 1.3
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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 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.
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 in a data set. The range is the difference between the greatest and least values. Examples are given of calculating each for a set of monthly temperature data.
Pc sections p.6-p.7
This document lists key properties of numbers and operations covered in two sections. Section P.6 covers commutative and associative properties of addition and multiplication as well as the distributive property of multiplication over addition and subtraction. Section P.7 directs students to complete specific math problems from two different pages focusing on odd numbered questions.
Alg 1 sections 1.5-1.6
1. This document discusses different ways to represent functions including equations, tables, and mapping diagrams. It provides examples of each.
2. Strategies for solving problems are outlined, including using formulas, patterns, and drawing diagrams. Specific math problems are provided as examples.
3. Homework assignments are listed at the end, including problem numbers from pages 31-32 and 38-39.
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.
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.
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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.
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The document provides instructions for performing mathematical operations including addition, subtraction, multiplication, and division. It lists common words and phrases used to indicate each operation, such as "add", "subtract", "double", and "divide". It then provides two examples of multi-step operations where the reader writes down a number and performs successive operations of doubling, adding, subtracting, and dividing the number.
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Chapter 6.7
- 2. Graph Linear Inequalities in Two Variables •
- 3. Graph Linear Inequalities in Two Variables Shading Pick a point not on the line. Test the point in the original inequality. If it is a true inequality, shade the side the point is in. If it is a false inequality, shade the side the point is not in.
- 4. Graph Linear Inequalities in Two Variables •
- 5. Graph Linear Inequalities in Two Variables •
- 6. Homework Pages 409 – 410 #23-35 odd, 41, 43, 53