Bending Metal. How can metal sheets and pipes be bent so that their strength and performance are preserved?
|
|
- Gabriel Davis
- 6 years ago
- Views:
Transcription
1 Bending Metal How can metal sheets and pipes be bent so that their strength and performance are preserved? Bending Metal page: 1 of 16 Contents Initial Problem Statement 2 Narrative 3-8 Solutions 9-14 Appendices 15-16
2 Bending Metal Initial Problem Statement Many manufactured and engineered products make use of metal sheets or pipes that are bent to form part of a structure or working mechanism. When a metal sheet is bent the inner side is compressed and the outer side is stretched. The amount of stretch depends upon how the bend is made. For a sharp crease in a metal sheet, the stretching can be extreme and can tear the outer side of the metal, weakening the product. Bending a pipe in such a manner not only weakens it structurally, it also constricts the pipe making it less effective for carrying fluids. How can metal sheets and pipes be bent so that their strength and performance are preserved? Bending Metal page: 2 of 16
3 Narrative Introduction Multimedia The animation Bending Metal Animation is available to introduce this example. Hint Activity 1 You have to manufacture a metal bracket that can be used to hold together two pieces of wood in the following way. What would your design look like if you wanted to avoid a sharp crease in the metal? Figure 1. You need to have metal that lays flat against both pieces of wood. Bending Metal page: 3 of 16
4 2. Bending the metal To avoid sharp creases in metal plates and pipes they are usually bent around the arc of a circle to reduce the stretching on the outer side. Figure 2. The radius of the circle around which the bend is made is called the bend radius. Figure 3. Bending Metal page: 4 of 16
5 Activity 2 Consider the design below which has flat sides of length a and b. Would the length of metal you require to it be (A) a + b? (B) more than (a + b)? (C) less than (a + b)? Figure 4. Bending Metal page: 5 of 16
6 3. Bending allowance To account for the metal curving around the bend you need to take the length of the flat sections and add a bend allowance, s, so that the actual length is given by: l = a+ b+ s The problem now is how to calculate the bend allowance and hence how much metal is required to make the fabrication. Discussion Looking again at a schematic of our simple design, the material on the inside is compressed at the bend so is a little shorter than the original piece of metal before bending. The metal on the outside is stretched so that it is a little longer than the original piece of metal before bending. The dotted line in the diagram is called the neutral line. What can you say about the length of the metal on the neutral line inside the metal bar? Figure 5. Bending Metal page: 6 of 16
7 Activity 3 In the design shown below the metal thickness, t, is 4 mm and the lengths a and b are 400 mm and 600 mm respectively. These sides form an internal angle of 120. The bend radius is 25 mm. Assuming the neutral line is along the centre-line of the metal what length of metal should we start with? Hint Figure 6. Remember the dotted neutral line neither stretches nor compresses. The length of this line is therefore the same in the flat and bent configurations. Hint Hint What is the radius of curvature on the neutral line? The 120 angle is not the angle through which the metal is bent. Identify this angle and calculate its value. What do you notice about its value? Hint Activity 4 Write down a general expression for the bending allowance, s, of a piece of metal of thickness t, bent through an angle θ with a bend radius r. Remember where the neutral line is. Bending Metal page: 7 of 16
8 4. More complex designs Activity 5 Work out the total length of metal for the following design. Multimedia Figure 7. The resource Bending Metal Interactive is available to show different configurations. See appendix 1. Bending Metal page: 8 of 16
9 Solution Introduction Activity 1 solution One way would be to use two pieces of metal and then weld them at the appropriate angle. You would have to be sure that the weld was strong for this to be a reliable solution. Another method would be to make it out of a single piece of metal but instead of making a sharp crease, make the bend around cylinder so that the curve is gentler. Figure 8. Bending Metal page: 9 of 16
10 2. Bending the metal Activity 2 solution The length of metal is greater than (a + b) as the metal has to curve around the bend. Bending Metal page: 10 of 16
11 3. Bending allowance First construct a fully labelled diagram. Figure 9. The first thing to do is work out the bend allowance. This is the length of the curved arc of metal. To do this you need to work out the length r and the angle θ. The length r is the radius of the neutral line. The length of the arc on this circle gives you the bend allowance. The angle θ can tell you what fraction of a complete circle the arc makes. You can use this to work out the arc length which, by definition is the bend allowance, s, by multiplying this fraction by the circumference of a circle of radius r: s = c θ 360 where c is the circumference of the circle of radius r. The circumference of a circle is given by: c= 2πr Substituting into the expression for bend allowance, s θ θ πθ s = c = 2πr = r The value of θ is such that the sum of θ and the internal angle between the flat sides equals 180. Bending Metal page: 11 of 16
12 Using the values of r = 27 and θ = 60 in the expression for the bend allowance, s, gives πθ π s = r = = ( mm) ( 1 d.p) So that the total length of metal, l, is given by l = a+ b+ s = = ( mm) The angle θ through which the metal is bent is calculated by considering the angles in the diagram. C Method 1: triangles B Figure 10. D 120 The angle θ is given by AOC. BDC = = 60 Looking at triangle BCD: BDC+ DCB + 90 = 180 so DCB= BDC = = 30 Now note that DCB= ACO=30 Looking at triangle AOC: AOC+ ACO + 90 = 180 an expression for ACO so θ A O but AOC = θ, and you have just found θ + OAD+ ADB+ DBO=360 θ + OAD DBO=360 θ =360 θ = = 60 Bending Metal page: 12 of 16
13 Method 2: quadrilaterals Consider the quadrilateral OADB. The angles of a quadrilateral sum to 360 θ + OAD+ ADB+ DBO=360 θ + OAD DBO=360 θ =360 θ = = 60 The value of θ is such that the sum of θ and the internal angle between the flat sides equals 180. Using the values of r = 27 and θ = 60 in the expression for the bend allowance, s, gives πθ π s = r = = ( mm) ( 1 d.p) So that the total length of metal, l, is given by l = a+ b+ s = = ( mm) Activity 4 solution The bend allowance is made by considering the arc length of the neutral line which runs down the centre of the metal. Therefore, the bend radius of the neutral line is given by the bend radius plus half the thickness of the metal: t rneutral = r+ 2 The bend allowance, s, is the arc length on the neutral line. This is given by the fraction of the circumference that a bend of angle q makes so that πθ πθ t s = rneutral = r Bending Metal page: 13 of 16
14 4. More complex designs Activity 5 solution This design is an extension of the previous one. The additional lengths are 800 mm from the upper flat and the bend allowance for the upper curve, which need to be added to the value calculated previously. The angle between the left flat and the upper flat is shown as 60. Using the rule that the arc angle plus the internal angle equal 180 it is seen that the arc angle is 120. The that the bend allowance on the upper curve is therefore given by πθ π s = r = = ( mm) ( 1 d.p) Note that the inner bend radius is 50 mm but the neutral line has a radius of this plus half the material thickness; hence an effective radius of 52 mm. The total length is then where the was calculated in the previous activity. Bending Metal page: 14 of 16
15 Appendix 1 using the interactives Bending Metal Interactive This resource demonstrates the calculation of metal length required to produce a bend sheet. At the bottom of the screen is a bar that lets you choose whether you want to try finding a variable for a single bend of metal, a double bend of metal or a bar of metal with a random number of bends. Figure 11. You will be given the information for each known variable and are required to fill in the missing value into the empty box. You can use the diagram to help you do this, giving your answer to the nearest whole value. You can check your answer by clicking on the Check button in the bottom right hand corner of the screen. Bending Metal page: 15 of 16
16 Appendix 2 mathematical coverage PL objectives Use trigonometry and coordinate geometry to solve engineering problems Use both degrees and radians and convert between them Use algebra to solve engineering problems Solve problems involving ratio and proportion Solve problems involving area, perimeter and volume Bending Metal page: 16 of 16
Trial version. The AC Transformer. How is a transformer designed to change the voltage from one given level to another? Student.
The AC Transformer How is a transformer designed to change the voltage from one given level to another? The AC Transformer page: 1 of 11 Contents Initial Problem Statement 2 Narrative 3-6 Notes 7-9 Appendices
More informationTrial version. Microphone Sensitivity
Microphone Sensitivity Contents To select a suitable microphone a sound engineer will look at a graph of directional sensitivity. How can the directional sensitivity of a microphone be plotted in a clear
More informationI.G.C.S.E. Solving Linear Equations. You can access the solutions from the end of each question
I.G.C.S.E. Solving Linear Equations Inde: Please click on the question number you want Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 You can access the solutions
More information1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle
Pre- Calculus Mathematics 12 5.1 Trigonometric Functions Goal: 1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle Measuring Angles: Angles in Standard
More information13-3The The Unit Unit Circle
13-3The The Unit Unit Circle Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Find the measure of the reference angle for each given angle. 1. 120 60 2. 225 45 3. 150 30 4. 315 45 Find the exact value
More informationName: A Trigonometric Review June 2012
Name: A Trigonometric Review June 202 This homework will prepare you for in-class work tomorrow on describing oscillations. If you need help, there are several resources: tutoring on the third floor of
More informationF I C ~ Shrinking on a V-block. Builders Bookstore
F I C 5-20. ~ Shrinking on a V-block. hammer downward against the upper edge directly over the "V" (figure 5-20). While hammering, move the angle back and forth across the V-block to comprese the material
More informationMathematics. Foundation. Set E Paper 2 (Calculator)
Mark scheme Ch 1 Mathematics oundation Set E Paper 2 (Calculator) 80 marks 1 expression 1 Award 1 mark for correct answer. Students often find the distinction between these terms difficult. 2 6 11 1 Award
More informationModule 1G: Creating a Circle-Based Cylindrical Sheet-metal Lateral Piece with an Overlaying Lateral Edge Seam And Dove-Tail Seams on the Top Edge
Inventor (10) Module 1G: 1G- 1 Module 1G: Creating a Circle-Based Cylindrical Sheet-metal Lateral Piece with an Overlaying Lateral Edge Seam And Dove-Tail Seams on the Top Edge In Module 1A, we have explored
More informationAngles and Angle Measure
Angles and Angle Measure An angle θ is in standard position if the vertex of the angle is at the origin and the initial arm lies along the positive x-axis. The terminal arm can lie anywhere along the arc
More informationUnit 10 Arcs and Angles of Circles
Lesson 1: Thales Theorem Opening Exercise Vocabulary Unit 10 Arcs and Angles of Circles Draw a diagram for each of the vocabulary words. Definition Circle The set of all points equidistant from a given
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Trigonometry Final Exam Study Guide Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a polar equation is given. Select the polar
More information6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date
6.00 Trigonometry Geometry/Circles Basics for the ACT Name Period Date Perimeter and Area of Triangles and Rectangles The perimeter is the continuous line forming the boundary of a closed geometric figure.
More informationPrint n Play Collection. Of the 12 Geometrical Puzzles
Print n Play Collection Of the 12 Geometrical Puzzles Puzzles Hexagon-Circle-Hexagon by Charles W. Trigg Regular hexagons are inscribed in and circumscribed outside a circle - as shown in the illustration.
More informationTrigonometry. An Overview of Important Topics
Trigonometry An Overview of Important Topics 1 Contents Trigonometry An Overview of Important Topics... 4 UNDERSTAND HOW ANGLES ARE MEASURED... 6 Degrees... 7 Radians... 7 Unit Circle... 9 Practice Problems...
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 1F Centre Number Tuesday 6 January 2015 Afternoon Time: 2 hours Candidate Number
More informationh r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.
ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this
More informationTrade of Metal Fabrication. Module 5: Pipe Fabrication Unit 6: Pipe Development Unequal Diameter 'T' Piece Phase 2
Trade of Metal Fabrication Module 5: Pipe Fabrication Unit 6: Pipe Development Unequal Diameter 'T' Piece Phase 2 Table of Contents List of Figures... 4 List of Tables... 4 Document Release History...
More informationKey Stage 3 Mathematics. Common entrance revision
Key Stage 3 Mathematics Key Facts Common entrance revision Number and Algebra Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess Check Too Big/Too
More informationOne of the classes that I have taught over the past few years is a technology course for
Trigonometric Functions through Right Triangle Similarities Todd O. Moyer, Towson University Abstract: This article presents an introduction to the trigonometric functions tangent, cosecant, secant, and
More informationSurface Developments. Sacramento City College Engineering Design Technology. Surface Developments 1
Surface Developments Sacramento City College Engineering Design Technology Surface Developments 1 Surface Developments A surface development is a full-size layout of an object made on a single flat plane.
More informationSheet metal tutorial. To set the bend radius Right click on the first sheet metal icon in the command manager and specify a bend radius or 1mm.
Sheet metal tutorial In the following tutorial you will cover the basic features of the Solid Works sheet metal tool by modelling the component shown opposite. Activating Sheet metal mode Sheet metal components
More informationMethods in Mathematics (Linked Pair Pilot)
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Methods in Mathematics (Linked Pair Pilot) Unit 2 Geometry and Algebra Monday 11 November 2013
More informationClass 5 Geometry O B A C. Answer the questions. For more such worksheets visit
ID : in-5-geometry [1] Class 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) The set square is in the shape of. (2) Identify the semicircle that contains 'C'. A C O B
More informationName Period No. Geometry Unit Review with Application Problems
Name Period No. Geometry Unit Review with Application Problems For problems 1-3, find the area of each figure. Show all steps. 1) 2) 4) Draw a parallelogram with an area of 50 sq. units in the 3) coordinate
More informationSheet Metal OverviewChapter1:
Sheet Metal OverviewChapter1: Chapter 1 This chapter describes the terminology, design methods, and fundamental tools used in the design of sheet metal parts. Building upon these foundational elements
More informationIntermediate Mathematics League of Eastern Massachusetts
Meet #5 March 2006 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2006 Category 1 Mystery You may use a calculator today. 1. The combined cost of a movie ticket and popcorn is $8.00.
More informationExercise 1. Consider the following figure. The shaded portion of the circle is called the sector of the circle corresponding to the angle θ.
1 Radian Measures Exercise 1 Consider the following figure. The shaded portion of the circle is called the sector of the circle corresponding to the angle θ. 1. Suppose I know the radian measure of the
More informationUNIT 3 CIRCLES AND VOLUME Lesson 4: Finding Arc Lengths and Areas of Sectors Instruction
Prerequiite Skill Thi leon require the ue of the following kill: finding the circumference of a circle undertanding cale factor in imilar hape uing ratio and proportion Introduction All circle are imilar;
More information4.3. Trigonometric Identities. Introduction. Prerequisites. Learning Outcomes
Trigonometric Identities 4.3 Introduction trigonometric identity is a relation between trigonometric expressions which is true for all values of the variables (usually angles. There are a very large number
More informationof the whole circumference.
TRIGONOMETRY WEEK 13 ARC LENGTH AND AREAS OF SECTORS If the complete circumference of a circle can be calculated using C = 2πr then the length of an arc, (a portion of the circumference) can be found by
More informationIntermediate Mathematics League of Eastern Massachusetts
Meet #5 March 2009 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2009 Category 1 Mystery 1. Sam told Mike to pick any number, then double it, then add 5 to the new value, then
More informationWARM UP. 1. Expand the expression (x 2 + 3) Factor the expression x 2 2x Find the roots of 4x 2 x + 1 by graphing.
WARM UP Monday, December 8, 2014 1. Expand the expression (x 2 + 3) 2 2. Factor the expression x 2 2x 8 3. Find the roots of 4x 2 x + 1 by graphing. 1 2 3 4 5 6 7 8 9 10 Objectives Distinguish between
More informationMethods in Mathematics Unit 1: Methods 1
Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 1: Methods 1 Practice Paper Time: 1 hour 45 minutes Foundation Tier Paper Reference 5MM1F/01
More informationAGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School
AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved AGS Math Algebra 2 Grade
More informationSquares Multiplication Facts: Square Numbers
LESSON 61 page 328 Squares Multiplication Facts: Square Numbers Name Teacher Notes: Introduce Hint #21 Multiplication/ Division Fact Families. Review Multiplication Table on page 5 and Quadrilaterals on
More informationTrial version. Resistor Production. How can the outcomes be analysed to optimise the process? Student. Contents. Resistor Production page: 1 of 15
Resistor Production How can the outcomes be analysed to optimise the process? Resistor Production page: 1 of 15 Contents Initial Problem Statement 2 Narrative 3-11 Notes 12 Appendices 13-15 Resistor Production
More informationth Grade Test. A. 128 m B. 16π m C. 128π m
1. Which of the following is the greatest? A. 1 888 B. 2 777 C. 3 666 D. 4 555 E. 6 444 2. How many whole numbers between 1 and 100,000 end with the digits 123? A. 50 B. 76 C. 99 D. 100 E. 101 3. If the
More informationTapered or Conical Tee
TRADE OF Industrial Insulation PHASE 2 Module 2 Geometry & Pattern Development UNIT: 9 Produced by In cooperation with subject matter expert: Michael Kelly SOLAS 2014 Table of Contents Unit Objective...
More informationWe will study all three methods, but first let's review a few basic points about units of measurement.
WELCOME Many pay items are computed on the basis of area measurements, items such as base, surfacing, sidewalks, ditch pavement, slope pavement, and Performance turf. This chapter will describe methods
More informationTrial version. The AC Transformer. How is a transformer designed to change the voltage from one given level to another? Teacher.
The AC Transformer How is a transformer designed to change the voltage from one given level to another? The AC Transformer page: 1 of 15 Contents Initial Problem Statement 2 arrative 3-6 otes 7-9 Solutions
More informationWire and tube Drawing
Wire and tube Drawing Drawing is an operation in which the cross-section of solid rod, wire or tubing is reduced or changed in shape by pulling it through a die. The principle of this procedure consist
More informationEssential Mathematics Practice Problems for Exam 5 Chapter 8
Math 254B Essential Mathematics Practice Problems for Eam 5 Chapter 8 Name Date This eam is closed book and closed notes, ecept for the Geometry Formula sheet that is provided by the instructor. You can
More informationSheet Metal OverviewChapter1:
Sheet Metal OverviewChapter1: Chapter 1 This chapter describes the terminology, design methods, and fundamental tools used in the design of sheet metal parts. Building upon these foundational elements
More informationCore Learning Standards for Mathematics Grade 6
Core Learning Standards for Mathematics Grade 6 Write and evaluate numerical expressions involving whole-number exponents. Write, read, and evaluate expressions; identify parts of an expression using mathematical
More information3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.
1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationGeometry. Practice Pack
Geometry Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Lines and Angles Practice 1.1 What Is Geometry?........................ 1 Practice 1.2 What Is Geometry?........................ 2 Practice
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *5164933141* CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) October/November 2017 1 hour
More informationThursday 2 November 2017 Morning Time allowed: 1 hour 30 minutes
Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature GCSE MATHEMATICS Foundation Tier Paper 1 Non-Calculator F Thursday 2 November 2017 Morning
More informationSketching Fundamentals
Sketching Fundamentals Learning Outcome When you complete this module you will be able to: Make basic engineering sketches of plant equipment. Learning Objectives Here is what you will be able to do when
More informationHonors Geometry Summer Math Packet
Honors Geometry Summer Math Packet Dear students, The problems in this packet will give you a chance to practice geometry-related skills from Grades 6 and 7. Do your best to complete each problem so that
More informationUK SENIOR MATHEMATICAL CHALLENGE
UK SENIOR MATHEMATICAL CHALLENGE Tuesday 8 November 2016 Organised by the United Kingdom Mathematics Trust and supported by Institute and Faculty of Actuaries RULES AND GUIDELINES (to be read before starting)
More informationFerris Wheel Activity. Student Instructions:
Ferris Wheel Activity Student Instructions: Today we are going to start our unit on trigonometry with a Ferris wheel activity. This Ferris wheel will be used throughout the unit. Be sure to hold on to
More informationUNIT PLAN. Grade Level: Unit #: 7 Unit Name: Circles
UNIT PLAN Subject: Geometry Grade Level: 10-12 Unit #: 7 Unit Name: Circles Big Idea/Theme: The understanding of properties of circles, the lines that intersect them, and the use of their special segments
More informationMAT01A1. Appendix D: Trigonometry
MAT01A1 Appendix D: Trigonometry Dr Craig 12 February 2019 Introduction Who: Dr Craig What: Lecturer & course coordinator for MAT01A1 Where: C-Ring 508 acraig@uj.ac.za Web: http://andrewcraigmaths.wordpress.com
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *9105218512* CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2017 Candidates
More informationEstimating Tolerance Accuracy (Rounding, including sig. fig.) Scientific notation
S3 Pathways for learning in Maths Pathway 1 (Lower) Pathway 2 (Middle) Pathway 3 (Upper) Targets Complete coverage of level 3 experiences and outcomes in Mathematics Cover level 4 experiences and outcomes
More informationUnderstanding Angles. Estimate and determine benchmarks for angle measure.
8.1 Understanding ngles YOU WILL NEED compass pipe cleaners protractor EXPLORE Devise a method to estimate the measure of any central angle in a circle without using a protractor. Explain how your method
More informationMETHOD 1: METHOD 2: 4D METHOD 1: METHOD 2:
4A Strategy: Count how many times each digit appears. There are sixteen 4s, twelve 3s, eight 2s, four 1s, and one 0. The sum of the digits is (16 4) + + (8 2) + (4 1) = 64 + 36 +16+4= 120. 4B METHOD 1:
More informationMath Problem Set 5. Name: Neal Nelson. Show Scored View #1 Points possible: 1. Total attempts: 2
Math Problem Set 5 Show Scored View #1 Points possible: 1. Total attempts: (a) The angle between 0 and 60 that is coterminal with the 69 angle is degrees. (b) The angle between 0 and 60 that is coterminal
More informationTrigonometry. David R. Wilkins
Trigonometry David R. Wilkins 1. Trigonometry 1. Trigonometry 1.1. Trigonometric Functions There are six standard trigonometric functions. They are the sine function (sin), the cosine function (cos), the
More informationThe year 5 entrance test is based on IGCSE paper type questions, a selection of which can be found below. Answer ALL TWENTY TWO questions.
The year 5 entrance test is based on IGCSE paper type questions, a selection of which can be found below. Answer ALL TWENTY TWO questions. All formulas will be provided. A calculator is required. The entrance
More informationActivity: Fold Four Boxes
ctivity: Fold Four Boxes 1. Cut out your copy of the crease pattern for the square-base twist box but only cut along the solid lines. 2. Look at this key: mountain crease valley crease When folded, a mountain
More informationModule 3 Selection of Manufacturing Processes
Module 3 Selection of Manufacturing Processes Lecture 4 Design for Sheet Metal Forming Processes Instructional objectives By the end of this lecture, the student will learn the principles of several sheet
More informationExcel / Education. GCSE Mathematics. Paper 5B (Calculator) Higher Tier. Time: 2 hours. Turn over
Excel / Education GCSE Mathematics Paper 5B (Calculator) Higher Tier Time: 2 hours 5B Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil,
More informationASSIGNMENT ON TRIGONOMETRY LEVEL 1 (CBSE/NCERT/STATE BOARDS) Find the degree measure corresponding to the following radian measures :
ASSIGNMENT ON TRIGONOMETRY LEVEL 1 (CBSE/NCERT/STATE BOARDS) Find the degree measure corresponding to the following radian measures : (i) c 1 (ii) - c (iii) 6 c (iv) c 11 16 Find the length of an arc of
More informationOutcome 7 Review. *Recall that -1 (-5) means
Outcome 7 Review Level 2 Determine the slope of a line that passes through A(3, -5) and B(-2, -1). Step 1: Remember that ordered pairs are in the form (x, y). Label the points so you can substitute into
More informationTrigonometry LESSON ONE - Degrees and Radians Lesson Notes
8 = 6 Trigonometry LESSON ONE - Degrees and Radians Example : Define each term or phrase and draw a sample angle. Angle in standard position. b) Positive and negative angles. Draw. c) Reference angle.
More information2016 State Competition Target Round Problems 1 & 2
2016 State Competition Target Round Problems 1 & 2 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems, which will be presented
More information1 SLABBING, RENDERING, FLOATING AND SKIMMING
TRADE OF PLASTERING PHASE 2 Module 1 SLABBING, RENDERING, FLOATING AND SKIMMING UNIT: 10 Produced by In cooperation with subject matter expert: Terry Egan Some images & text courtesy of Gypsum Industries
More informationLesson 0.1 The Same yet Smaller
Lesson 0.1 The Same yet Smaller 1. Write an expression and find the total shaded area in each square. In each case, assume that the area of the largest square is 1. a. b. c. d. 2. Write an expression and
More information2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)
Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down
More information18.2 Geometric Probability
Name Class Date 18.2 Geometric Probability Essential Question: What is geometric probability? Explore G.13.B Determine probabilities based on area to solve contextual problems. Using Geometric Probability
More informationLesson 18: More Problems on Area and Circumference
Student Outcomes Students examine the meaning of quarter circle and semicircle. Students solve area and perimeter problems for regions made out of rectangles, quarter circles, semicircles, and circles,
More informationWheels Diameter / Conversion of Units
Note to the teacher On this page, students will learn about the relationships between wheel diameter, circumference, revolutions and distance. They will also convert measurement units and use fractions
More informationFRIDAY, 10 NOVEMBER 2017 MORNING 1 hour 30 minutes
Surname Centre Number Candidate Number Other Names 0 GCSE 3300U10-1 A17-3300U10-1 MATHEMATICS UNIT 1: NON-CALCULATOR FOUNDATION TIER FRIDAY, 10 NOVEMBER 2017 MORNING 1 hour 30 minutes For s use ADDITIONAL
More informationIntermediate Mathematics League of Eastern Massachusetts
Meet #5 April 2003 Intermediate Mathematics League of Eastern Massachusetts www.imlem.org Meet #5 April 2003 Category 1 Mystery You may use a calculator 1. In his book In an Average Lifetime, author Tom
More informationTenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7
EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional
More informationDaily Warmup. - x 2 + x x 2 + x Questions from HW?? (7x - 39) (3x + 17) 1. BD bisects ABC. Find the m ABC.
Daily Warmup Questions from HW?? B 1. BD bisects ABC. Find the m ABC. (3x + 17) (7x - 39) C 2. The figure below is a regular polygon. Find the value of x. - x 2 + x + 43 A D 4x 2 + x - 37 3. The measure
More informationSection 5.1 Angles and Radian Measure. Ever Feel Like You re Just Going in Circles?
Section 5.1 Angles and Radian Measure Ever Feel Like You re Just Going in Circles? You re riding on a Ferris wheel and wonder how fast you are traveling. Before you got on the ride, the operator told you
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission
2009. M26 Coimisiún na Scrúduithe Stáit State Examinations Commission LEAVING CERTIFICATE EXAMINATION, 2009 MATHEMATICS FOUNDATION LEVEL PAPER 2 ( 300 marks ) MONDAY, 8 JUNE MORNING, 9:30 to 12:00 Attempt
More informationTrade of Sheet Metalwork. Module 2: Geometry and Pattern Development Unit 3: Parallel Line Phase 2
Trade of Sheet Metalwork Module 2: Geometry and Pattern Development Unit 3: Parallel Line Phase 2 Table of Contents List of Figures... 4 List of Tables... 5 Document Release History... 6 Module 2 Geometry
More informationI look forward to seeing you on August 24!!
AP Physics 1 Summer Assignment Packet Welcome to AP Physics 1! Your summer assignment is below. You are to complete the entire packet and bring it with you on the first day of school (Monday August 24,
More informationMathematical Olympiad for Girls
UKMT UKMT UKMT United Kingdom Mathematics Trust Mathematical Olympiad for Girls Tuesday 2nd October 208 Organised by the United Kingdom Mathematics Trust These are polished solutions and do not illustrate
More information2005 Galois Contest Wednesday, April 20, 2005
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 2005 Galois Contest Wednesday, April 20, 2005 Solutions
More informationMATHS CHALLENGE 2010 SOLUTIONS PART 1
MATHS CHALLENGE 2010 SOLUTIONS PART 1 EASY 1 If five robots can make five new robots in five hours, how long would it take a hundred robots to make a hundred new robots? ANSWER: In five hours, each of
More informationSimple Solutions Mathematics. Level 2. Help Pages & Who Knows?
Simple Solutions Mathematics Level 2, 2nd semester Level 2 & Who Knows? 139 Vocabulary Arithmetic Operations Addition When you combine numbers, you add. The sign + means add. The answer to an addition
More informationStudy Guide and Intervention
- Study Guide and Intervention Write Mathematical Expressions In the algebraic expression, w, the letters and w are called variables. In algebra, a variable is used to represent unspecified numbers or
More informationExcel / Education. GCSE Mathematics. Paper 4B (Calculator) Foundation Tier. Time: 1 hour 30 minutes. Turn over
Excel / Education GCSE Mathematics Paper 4B (Calculator) Foundation Tier Time: 1 hour 30 minutes 4B Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses,
More informationTrade of Metal Fabrication. Module 6: Fabrication Drawing Unit 13: Parallel Line Development Phase 2
Trade of Metal Fabrication Module 6: Fabrication Drawing Unit 13: Parallel Line Development Phase 2 Table of Contents List of Figures... 4 List of Tables... 5 Document Release History... 6 Module 6 Fabrication
More informationFor AQA. Mathematics. Sample from Churchill Maths. General Certificate of Secondary Education. Calculator
Name Class Sample from For AQA General Certificate of Secondary Education Mathematics Paper 2A Calculator Higher Tier H For this paper you must have: a calculator mathematical instruments. Time allowed
More informationAlgebra 2/Trigonometry Review Sessions 1 & 2: Trigonometry Mega-Session. The Unit Circle
Algebra /Trigonometry Review Sessions 1 & : Trigonometry Mega-Session Trigonometry (Definition) - The branch of mathematics that deals with the relationships between the sides and the angles of triangles
More informationHeavy Plate Leveler improvement by coupling a model to a flatness gauge
Heavy Plate Leveler improvement by coupling a model to a flatness gauge Laurent Bodini, Siemens VAI Metals Technologies SAS, 51 rue Sibert, F-42403 Saint Chamond cedex Olaf Ehrich, Thyssenkrupp Steel,
More informationPractice Problems: Calculus in Polar Coordinates
Practice Problems: Calculus in Polar Coordinates Answers. For these problems, I want to convert from polar form parametrized Cartesian form, then differentiate and take the ratio y over x to get the slope,
More informationBending. the bend radius is measured to the inner surface of the bent part
Bending the bend radius is measured to the inner surface of the bent part there is a plane which separates the tension and compression zones. This plane is called neutral axis. The position of neutral
More informationConnected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6)
Core Standards of the Course Standard I Students will acquire number sense and perform operations with rational numbers. Objective 1 Represent whole numbers and decimals in a variety of ways. A. Change
More informationFind the value of the expressions. 3 x = 3 x = = ( ) 9 = 60 (12 + 8) 9 = = 3 9 = 27
PreAlgebra Concepts Important Concepts exponent In a power, the number of times a base number is used as a factor order of operations The rules which tell which operation to perform first when more than
More informationDecide how many topics you wish to revise at a time (let s say 10)
1 Minute Maths for the Higher Exam (grades B, C and D topics*) Too fast for a first-time use but... brilliant for topics you have already understood and want to quickly revise. for the Foundation Exam
More informationChapter 6: Periodic Functions
Chapter 6: Periodic Functions In the previous chapter, the trigonometric functions were introduced as ratios of sides of a right triangle, and related to points on a circle. We noticed how the x and y
More informationMake and Measure a Circle Without a Pattern
Published on Sew4Home Make and Measure a Circle Without a Pattern Editor: Liz Johnson Thursday, 25 August 2016 1:00 The circle is, in my humble opinion, the Queen of the geometric shapes. Don't get me
More information