4.1 4.2 Notes A
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The document provides instruction and examples for calculating slope between two points on a graph. It defines slope as "rise over run", or the change in the y-values divided by the change in the x-values between two points. Examples are given for finding the slope between points, identifying positive and negative slopes, and special cases where the slope is zero or undefined. Students are asked to provide their own examples comparing slopes and complete an exit slip with slope problems.
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4.1 4.2 Notes B
This document appears to be notes from a math lesson that discusses slope. It includes examples of calculating slope between different points, the definition of slope as "rise over run", and special cases like undefined and zero slopes. The homework assigned is to complete practice problems calculating and applying slopes from pages 311-312 and 317-318 of the textbook.
001 area, perimeter
The document provides formulas and examples for calculating the perimeter and area of various geometric shapes. It defines perimeter and area, lists common formulas, and provides examples of calculating:
- The area of a rectangle using the formula A=bh
- The area of a triangle using the formula A=(1/2)bh
- The area of an irregular shape by finding the sum of the areas of its individual parts
- The perimeter of an irregular shape by finding the total distance around it
Lesson 2.7 measuring volume
1. The document discusses different formulas for calculating the volume of various 3D shapes including cubes, rectangular prisms, cylinders, pyramids, cones, and spheres.
2. Examples are provided for each shape to demonstrate how to apply the volume formulas in practice.
3. Recognizing the appropriate volume formula and computing the volume using the formula are important for finding the volume of different solids.
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This document discusses the volume formulas for pyramids and cones. It provides examples of calculating the volumes of different pyramids and cones using their base areas and heights. It also notes that tripling the height of a cone triples its volume, while tripling the radius increases the volume nine-fold.
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This document provides information about calculating the surface area and volume of spheres. It defines key terms related to spheres such as radius, diameter, center, and hemisphere. It gives the formulas for calculating the surface area (S=4πr^2) and volume (V=4/3πr^3) of spheres. Examples are provided to demonstrate how to use the formulas to find the surface area of a baseball and the radius of a ball bearing given its original volume as a cylinder.
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1. The document discusses the surface area formulas for various shapes including cylinders, cubes, cuboids, and cones.
2. It provides examples of calculating the surface area of a cylinder given its height and radius. The surface area equals 2πr^2 + 2πrh.
3. The document explains that a cuboid has 6 faces - two for the top and bottom, two for the sides, and two for the front and back. The total surface area is the sum of the areas of all 6 faces.
SURFACE AREAS AND VOLUMES OF SOLID FIGURES - MENSURATION
This document discusses surface areas and volumes of solid figures. It begins by defining surface area as the measure of the boundary of a solid figure, while volume is the measure of the space enclosed. It then discusses cuboids and cubes, providing formulas for their surface areas and volumes. The surface area of a cuboid is 2(lb + bh + hl) and its volume is lbh. The surface area of a cube of side a is 6a2 and its volume is a3. Several examples are given applying these formulas to problems involving cuboids, cubes, and other solids.
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cube cuboid and cylinder is found .here you can learn surface area and volume of these 3 dimensional figures.it also includes basic information on the basic properties of these figures
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4.1 4.2 Notes B
This document appears to be notes from a math lesson that discusses slope. It includes examples of calculating slope between different points, the definition of slope as "rise over run", and special cases like undefined and zero slopes. The homework assigned is to complete practice problems calculating and applying slopes from pages 311-312 and 317-318 of the textbook.
001 area, perimeter
The document provides formulas and examples for calculating the perimeter and area of various geometric shapes. It defines perimeter and area, lists common formulas, and provides examples of calculating:
- The area of a rectangle using the formula A=bh
- The area of a triangle using the formula A=(1/2)bh
- The area of an irregular shape by finding the sum of the areas of its individual parts
- The perimeter of an irregular shape by finding the total distance around it
Lesson 2.7 measuring volume
1. The document discusses different formulas for calculating the volume of various 3D shapes including cubes, rectangular prisms, cylinders, pyramids, cones, and spheres.
2. Examples are provided for each shape to demonstrate how to apply the volume formulas in practice.
3. Recognizing the appropriate volume formula and computing the volume using the formula are important for finding the volume of different solids.
Volume pyramid notes
This document discusses the volume formulas for pyramids and cones. It provides examples of calculating the volumes of different pyramids and cones using their base areas and heights. It also notes that tripling the height of a cone triples its volume, while tripling the radius increases the volume nine-fold.
Geom12point6 97
This document provides information about calculating the surface area and volume of spheres. It defines key terms related to spheres such as radius, diameter, center, and hemisphere. It gives the formulas for calculating the surface area (S=4πr^2) and volume (V=4/3πr^3) of spheres. Examples are provided to demonstrate how to use the formulas to find the surface area of a baseball and the radius of a ball bearing given its original volume as a cylinder.
Maths p.p.t
1. The document discusses the surface area formulas for various shapes including cylinders, cubes, cuboids, and cones.
2. It provides examples of calculating the surface area of a cylinder given its height and radius. The surface area equals 2πr^2 + 2πrh.
3. The document explains that a cuboid has 6 faces - two for the top and bottom, two for the sides, and two for the front and back. The total surface area is the sum of the areas of all 6 faces.
SURFACE AREAS AND VOLUMES OF SOLID FIGURES - MENSURATION
This document discusses surface areas and volumes of solid figures. It begins by defining surface area as the measure of the boundary of a solid figure, while volume is the measure of the space enclosed. It then discusses cuboids and cubes, providing formulas for their surface areas and volumes. The surface area of a cuboid is 2(lb + bh + hl) and its volume is lbh. The surface area of a cube of side a is 6a2 and its volume is a3. Several examples are given applying these formulas to problems involving cuboids, cubes, and other solids.
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The document discusses different types of 2D and 3D shapes. It defines rectangles, squares, triangles, and hexagons as plane or 2D figures. Cuboids, cubes, and cylinders are defined as solid or 3D figures. Solid figures are made up of plane surfaces or figures. The surface area of solids is calculated by finding the total area of these plane figures. Formulas are provided to calculate the surface area of cuboids and cubes. Practice questions are included for students to calculate surface areas of shapes based on given measurements.
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11.1 11.2 notes a
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This document provides instruction on writing and graphing linear equations in different forms. It begins with a review of equivalent forms of linear equations, including point-slope, slope-intercept, and standard form. Students are then given examples of writing equations of lines given a point and slope, or two points. The document concludes with examples of graphing lines by using the point-slope and slope-intercept forms to easily find points and draw the line. Students are challenged to graph a line given in standard form and explain their process.
April 1
This document provides an agenda and notes for a math class that is reviewing quadratic functions and equations. It includes warm-up problems to solve quadratic equations algebraically and graphically, identifies an upcoming test on sections 10.1-10.3, and provides class work where students must show the steps to graph quadratic functions using a table of values.
Demo slides in math editedppt
The document thanks God for his love and care, and asks that they multiply his good works through love, respect, faith, and by sharing talents with others so that they can be united as one in God's family. It prays that they subtract unworthy behavior and evil works, and divide God's gifts to help others.
Pc 2.1 notes
This document defines quadratic equations as polynomial functions of degree 2, where the highest exponent is 2. It explains that a quadratic equation can be written in standard form as f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic equation is a parabola. Key features of a parabola include its axis of symmetry, which is the line that bisects the parabola, and its vertex, which is the highest or lowest point of the parabola. The document provides examples of finding the vertex and axis of symmetry of parabolas given their equations and of writing the equation of a parabola
Algebreviewer
This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.
Algebreviewer
This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.
Module 2 properties of quadrilaterals
This document discusses properties of quadrilaterals, specifically rectangles, squares, and rhombuses. It provides 3 learning objectives: 1) derive properties of diagonals of special quadrilaterals, 2) verify conditions for a quadrilateral to be a parallelogram, and 3) solve problems involving these shapes. It then presents true/false questions to assess prior knowledge, worked examples demonstrating properties and problem solving, and additional practice problems. The key properties covered are that rectangle and square diagonals are congruent and perpendicular, and rhombus diagonals bisect opposite angles and are perpendicular.
1.1a
The document provides examples for translating words into algebraic expressions and equations. It gives several word problems describing real-world situations and shows how to represent each with variables and equations. The problems are solved by graphing the lines represented by the equations on a coordinate plane and finding their point of intersection. This identifies the solution that satisfies both equations simultaneously. The document demonstrates how to set up and solve systems of linear equations to find unknown values described in word problems.
Similar to 4.1 4.2 Notes A (20)
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Unit 1 test 2.9 notes b
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
2.2 2.3 notes a
The document describes a numeric pattern where each row contains consecutive odd integers centered around 1. It asks students to conjecture the pattern and sum of terms in each row. It also provides homework questions on conditional statements, deductive reasoning, and analyzing the truth value of related conditional statements.
Unit 1 test 2.9 notes a
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
2.8 notes a
1. The document discusses solving equations by backtracking. It begins by defining an equation and identifying true and false equations. It then discusses the concept of solutions - the values that make the equation true.
2. Examples are provided to illustrate finding solutions to equations by reversing the steps of number tricks. Backtracking involves working backwards through the operations to determine the starting value.
3. Readers are instructed to solve sample equations by listing the number trick steps and then reversing the steps through backtracking to find the solution values.
Chapter 1 rev notes (a)
This document provides homework questions and a review packet for a chapter. It lists 7 numbered sections that appear to be questions or tasks related to reviewing material from the first chapter. The document aims to help students review and reinforce their understanding of the concepts covered in the initial chapter through completing the homework and review activities.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations (translations, reflections, rotations, and dilations) and provides examples of identifying each type using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. It includes examples of using the midpoint formula to find the midpoint of a segment and using given midpoints and endpoints to find missing endpoints.
3. There are also examples of using the Pythagorean theorem and distance formula to find the length of a segment between two points.
1.5 1.6 notes a
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6. Students are asked to work on vocabulary and postulates after the quiz.
2. Examples are given for finding midpoints and distances between points on a coordinate plane using formulas like the midpoint formula, Pythagorean theorem, and distance formula.
3. Homework assignments include problems from the textbook on the topics of formulas in geometry, midpoints, and distance.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
2.4 notes b
1. Students were asked to put math problems on the board from previous homework. The document then provides examples of expressions and teaches how to simplify them using order of operations and properties like the distributive property. Students are asked to simplify sample expressions involving variables.
2. The document reviews that expressions need to have "like terms" to be simplified, such as terms with the same variables. Students practice simplifying expressions with multiple variables and terms by combining like terms.
3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
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4.1 4.2 Notes A
- 1. Open er!!! January 4th & 5th: 4.1 Getting Started with Slope Open your books to 1. With your partner, determine which roof is the page 309. steepest. Then write down how you might explain how you decided which roof is the steepest to a person who does not understand the words steep or slope. (4 minutes) 2a. What are the rise and run of the gable end? 2c. What is the mathematical process we would need to follow to find the length of each of the vertical boards? 1
- 2. For You to Explore: Take 4 minutes to discuss and record your ideas for Tony and Sasha's bike trip. Be prepared to share your ideas with the rest of the class. 3a. Who rode faster, Tony or Sasha? Explain. 3b. What does the intersection of the lines represent? 3c. How many miles did Sasha travel in an hour? 3d. How many miles did Tony travel in an hour? Checkpoint: Draw After each equation is shown, "draw" the general that graph! shape of the corresponding graph in the air with your finger. a. y =x b. y = x2 c. y = 5x + 2 d. y = x3 + 5 e. y = 4x2 ‐ 13 + 2x ‐ 7 f. y = 2(13 ‐ 7x) 2
- 3. 4.2 Pitch and Slope Using pitch and slope: Pitch: Used by _________ to describe the steepness of a roof. • • Slope: Used by _____________ to describe the steepness of a line between two points in the Cartesian plane. • • Finding the slope Find the slope of the line that connects A(3,1) and between 2 points: B (7,9). Find two other points, S and T, such that m(S, T) is the same as m(A, B). Is m(S, T) = m(T, S)? Finding slope With your partner, find the slope between the points continued... R(7,2) and S (10,0). Defining Slope: Given the two points A (x1, y1) and B (x2, y2): m(A,B) = rise = y = y2 ‐ y1 run x x2 ‐ x1 Positive/ Negative Slope: Magnitude of Slope: Special slope cases: Find the slope between (4, 8) and (4, 2). Find the slope between (7,2) and (3,2) 3
- 4. Exit Slip: Write an example of two slopes for each of the Complete on a following statements: separate half‐sheet with your partner. a. a positive slope and a negative slope that is steeper b. a negative slope and a positive slope with the same steepness c. two pairs of points that have the same slope d. a pair of points whose slope is undefined. Homework: Pg. 311‐312 # 7,8, 10‐12, 13abc, & 14abc 317‐318 # 7abcd, 8bdef, 9, 10, 4