PYTHAGORAS THEOREM. Answers. Edexcel GCSE Mathematics (Linear) 1MA0


 Buck Mason
 1 years ago
 Views:
Transcription
1 Edexel GSE Mthemtis (Liner) 1M0 nswers PYTHGORS THEOREM Mterils required for exmintion Ruler grduted in entimetres nd millimetres, protrtor, ompsses, pen, H penil, erser. Tring pper my e used. Items inluded with question ppers Nil Instrutions Use lk ink or llpoint pen. Fill in the oxes t the top of this pge with your nme, entre numer nd ndidte numer. nswer ll questions. nswer the questions in the spes provided there my e more spe thn you need. lultors my e used. Informtion The mrks for eh question re shown in rkets use this s guide s to how muh time to spend on eh question. Questions lelled with n sterisk (*) re ones where the qulity of your written ommunition will e ssessed you should tke prtiulr re on these questions with your spelling, puntution nd grmmr, s well s the lrity of expression. dvie Red eh question refully efore you strt to nswer it. Keep n eye on the time. Try to nswer every question. hek your nswers if you hve time t the end.
2 1. PQR is rightngled tringle. PQ = 16 m. PR = 8 m. lulte the length of QR. Give your nswer orret to 2 deiml ples. ² + 8² = 16² ² + 64 = 256 ² = 192 = m 2. X 3.2 m Y 1.7 m Digrm NOT urtely drwn Z XYZ is rightngled tringle. XY = 3.2 m. XZ = 1.7 m. lulte the length of YZ. 1.7² + 3.2² = ² ² = = m
3 3. Digrm NOT urtely drwn 8 m is rightngled tringle. = 8 m, = 11 m. lulte the length of. 11 m 11² + 8² = ² ² = 185 = m m L Digrm NOT urtely drwn ngle MLN = 90. LM = 3.7 m. MN = 6.3 m. 6.3 m Work out the length of LN. M N 3.7² + ² = 6.3² ² = ² = 26 = LN =... m
4 5. 10 m 17 m Digrm NOT urtely drwn D is retngle. = 17 m. D = 10 m. D lulte the length of the side D. Give your nswer orret to one deiml ple. ² + 10² = 17² ² = 289 ² = 189 = m 6. Digrm NOT urtely drwn The digrm shows three ities. Norwih is 168 km due Est of Leiester. York is 157 km due North of Leiester. lulte the distne etween Norwih nd York. Give your nswer orret to the nerest kilometre. 168² + 157² = ² ² = ² = = km
5 7. retngulr television sreen hs width of 45 m nd height of 34 m. Digrm NOT urtely drwn Work out the length of the digonl of the sreen. Give your nswer orret to the nerest entimetre. 45² + 34² = ² ² = ² = 3181 = m (4 mrks) 8. 7 m 7 m 4² + ² = 7² 16 + ² = 49 ² = 33 = M 8 m Work out the length, in entimetres, of M. Give your nswer orret to 2 deiml ples. Digrm NOT urtely drwn 5.74 m
6 m D 1.9 m 3.2 m Digrm NOT urtely drwn D is trpezium. D is prllel to. ngle = ngle = 90. D = 2.1 m, = 1.9 m, D = 3.2 m. Work out the length of. = = ² + 1.9² = 3.2² ² = ² = 6.63 = m (4 mrks) m 6 m Digrm NOT urtely drwn is rightngled tringle. = 6 m. = 9 m. Work out the length of. 6² + ² = 9² 36 + ² = 81 ² = 45 = m
7 11. 10m 20m Digrm NOT urtely drwn In tringle, = 10 m = 20 m ngle = 90 Work out the length of. You must stte the units in your nswer. 20² + 10² = ² ² = ² = 500 = m... (4 mrks) 12. X 5.6 m Y 10.5 m Z In the tringle XYZ XY = 5.6 m YZ = 10.5 m ngle XYZ = 90 Work out the length of XZ. 10.5² + 5.6² = ² ² = ² = = 11.9 Digrm NOT urtely drwn m
8 13. D is trpezium. 6 8 D = 10 m = 9 m D = 3 m ngle = ngle D = 90 8 lulte the length of. ² + 6² = 10² ² + 36 = 100 ² = 64 = 8 8² + 9² = ² = ² ² = 145 = m 14. ldder is 6 m long. The ldder is pled on horizontl ground, resting ginst vertil wll. ( 5 mrks) The instrutions for using the ldder sy tht the ottom of the ldder must not e loser thn 1.5 m from the ottom of the wll. How fr up the wll n the ldder reh? Give your nswer orret to 1 deiml ple. h² + 1.5² = 6² h² = 36 h² = h = h m (4 mrks)
The remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More informationState the size of angle x. Sometimes the fact that the angle sum of a triangle is 180 and other angle facts are needed. b y 127
ngles 2 CHTER 2.1 Tringles Drw tringle on pper nd lel its ngles, nd. Ter off its orners. Fit ngles, nd together. They mke stright line. This shows tht the ngles in this tringle dd up to 180 ut it is not
More informationEnd of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.
End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte Complete the missing numers in the sequenes elow. 8 30 3 28 2 9 25 00 75 25 2 Put irle round ll of the following shpes whih hve 3 shded.
More informationRightangled triangles
13 13A Pythgors theorem 13B Clulting trigonometri rtios 13C Finding n unknown side 13D Finding ngles 13E Angles of elevtion nd depression Rightngled tringles Syllus referene Mesurement 4 Rightngled tringles
More informationThe Pythagorean Theorem
The Pythgoren Theorem Pythgors ws Greek mthemtiin nd philosopher, orn on the islnd of Smos (. 58 BC). He founded numer of shools, one in prtiulr in town in southern Itly lled Crotone, whose memers eventully
More informationAngles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example
2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel
More informationInterior and exterior angles add up to 180. Level 5 exterior angle
22 ngles n proof Ientify interior n exterior ngles in tringles n qurilterls lulte interior n exterior ngles of tringles n qurilterls Unerstn the ie of proof Reognise the ifferene etween onventions, eﬁnitions
More informationSECTION 72 Law of Cosines
516 7 Additionl Topis in Trigonometry h d sin s () tn h h d 50. Surveying. The lyout in the figure t right is used to determine n inessile height h when seline d in plne perpendiulr to h n e estlished
More informationPROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions
PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * hllenge questions e The ll will strike the ground 1.0 s fter it is struk. Then v x = 20 m s 1 nd v y = 0 + (9.8 m s 2 )(1.0 s) = 9.8 m s 1 The speed
More informationThe Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationSine and Cosine Ratios. For each triangle, find (a) the length of the leg opposite lb and (b) the length of the leg adjacent to lb.
 Wht You ll ern o use sine nd osine to determine side lengths in tringles... nd Wh o use the sine rtio to estimte stronomil distnes indiretl, s in Emple Sine nd osine tios hek Skills You ll Need for Help
More informationLesson 12.1 Trigonometric Ratios
Lesson 12.1 rigonometric Rtios Nme eriod Dte In Eercises 1 6, give ech nswer s frction in terms of p, q, nd r. 1. sin 2. cos 3. tn 4. sin Q 5. cos Q 6. tn Q p In Eercises 7 12, give ech nswer s deciml
More information4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter
More informationSOLVING EQUATIONS BY FACTORING
316 (560) Chpter 5 Exponents nd Polynomils 5.9 SOLVING EQUATIONS BY FACTORING In this setion The Zero Ftor Property Applitions helpful hint Note tht the zero ftor property is our seond exmple of getting
More informationChapter. Contents: A Constructing decimal numbers
Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting
More informationMathematics Reference Sheet. (Pack of 10)
Mthemtis Referene Sheet (Pk of 0 Mthemtis Referene Sheet Use the informtion elow to nswer questions on the Mthemtis test. Cirle π. Are = Cirumferene = h Surfe Are = +h Retngle Trpezoid Are = lw Perimeter
More informationUNCORRECTED SAMPLE PAGES
6 Chpter Length, re, surfe re n volume Wht you will lern 6A Length n perimeter 6B Cirumferene of irles n perimeter of setors 6C Are of qurilterls n tringles 6D Are of irles 6E Perimeter n re of omposite
More informationLesson 2.1 Inductive Reasoning
Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10,
More informationEXAMPLE EXAMPLE. Quick Check EXAMPLE EXAMPLE. Quick Check. EXAMPLE RealWorld Connection EXAMPLE
 Wht You ll Lern To use the Pthgoren Theorem To use the onverse of the Pthgoren Theorem... nd Wh To find the distne etween two doks on lke, s in Emple The Pthgoren Theorem nd Its onverse hek Skills You
More informationThe Triangle and its Properties
THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three
More informationMATH PLACEMENT REVIEW GUIDE
MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your
More informationVectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a.
Vectors mesurement which onl descries the mgnitude (i.e. size) of the oject is clled sclr quntit, e.g. Glsgow is 11 miles from irdrie. vector is quntit with mgnitude nd direction, e.g. Glsgow is 11 miles
More informationKEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001
KEY SKILLS INFORMATION TECHNOLOGY Level 3 Question Pper 29 Jnury 9 Ferury 2001 WHAT YOU NEED This Question Pper An Answer Booklet Aess to omputer, softwre nd printer You my use ilingul ditionry Do NOT
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationGeometry 71 Geometric Mean and the Pythagorean Theorem
Geometry 71 Geometric Men nd the Pythgoren Theorem. Geometric Men 1. Def: The geometric men etween two positive numers nd is the positive numer x where: = x. x Ex 1: Find the geometric men etween the
More informationFormal Languages and Automata Exam
Forml Lnguges nd Automt Exm Fculty of Computers & Informtion Deprtment: Computer Science Grde: Third Course code: CSC 34 Totl Mrk: 8 Dte: 23//2 Time: 3 hours Answer the following questions: ) Consider
More informationPractice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn
Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationLecture 5. Inner Product
Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right
More informationFinite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh
Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is
More informationNational Firefighter Ability Tests And the National Firefighter Questionnaire
Ntionl Firefighter Aility Tests An the Ntionl Firefighter Questionnire PREPARATION AND PRACTICE BOOKLET Setion One: Introution There re three tests n questionnire tht mke up the NFA Tests session, these
More informationScan Tool Software Applications Installation and Updates
Sn Tool Softwre Applitions Instlltion nd Updtes Use this doument to: Unlok softwre pplitions on Sn Tool Instll new softwre pplitions on Sn Tool Instll the NGIS Softwre Suite pplitions on Personl Computer
More informationCalculating Principal Strains using a Rectangular Strain Gage Rosette
Clulting Prinipl Strins using Retngulr Strin Gge Rosette Strin gge rosettes re used often in engineering prtie to determine strin sttes t speifi points on struture. Figure illustrtes three ommonly used
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More information DAY 1  Website Design and Project Planning
Wesite Design nd Projet Plnning Ojetive This module provides n overview of the onepts of wesite design nd liner workflow for produing wesite. Prtiipnts will outline the sope of wesite projet, inluding
More informationReleased Assessment Questions, 2015 QUESTIONS
Relesed Assessmet Questios, 15 QUESTIONS Grde 9 Assessmet of Mthemtis Ademi Red the istrutios elow. Alog with this ooklet, mke sure you hve the Aswer Booklet d the Formul Sheet. You my use y spe i this
More informationThe art of Paperarchitecture (PA). MANUAL
The rt of Pperrhiteture (PA). MANUAL Introution Pperrhiteture (PA) is the rt of reting threeimensionl (3D) ojets out of plin piee of pper or ror. At first, esign is rwn (mnully or printe (using grphil
More informationStart Here. IMPORTANT: To ensure that the software is installed correctly, do not connect the USB cable until step 17. Remove tape and cardboard
Strt Here 1 IMPORTANT: To ensure tht the softwre is instlled correctly, do not connect the USB cle until step 17. Follow the steps in order. If you hve prolems during setup, see Trouleshooting in the lst
More informationLesson 4.1 Triangle Sum Conjecture
Lesson 4.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q 2., y 3., b 31 82 p 98 q 28 53 y 17 79 23 50 b 4. r, s, 5., y 6. y t t s r 100 85 100 y 30 4 7 y 31 7. s 8.
More informationEnterprise Digital Signage Create a New Sign
Enterprise Digitl Signge Crete New Sign Intended Audiene: Content dministrtors of Enterprise Digitl Signge inluding stff with remote ess to sign.pitt.edu nd the Content Mnger softwre pplition for their
More informationChapter. Fractions. Contents: A Representing fractions
Chpter Frtions Contents: A Representing rtions B Frtions o regulr shpes C Equl rtions D Simpliying rtions E Frtions o quntities F Compring rtion sizes G Improper rtions nd mixed numers 08 FRACTIONS (Chpter
More informationPreparing the PW5. The following is a stepby procedure for assembly and disassembly
Prepring the PW5 The following is stepy ystep proedure for ssemly nd disssemly Begin with opening the triler Otin the keys from the green ox in the wll power ox. Untie the restrining ropes t eh side
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More informationMaximum area of polygon
Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is
More information1. Area under a curve region bounded by the given function, vertical lines and the x axis.
Ares y Integrtion. Are uner urve region oune y the given funtion, vertil lines n the is.. Are uner urve region oune y the given funtion, horizontl lines n the y is.. Are etween urves efine y two given
More information1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.
. Definition, Bsi onepts, Types. Addition nd Sutrtion of Mtries. Slr Multiplition. Assignment nd nswer key. Mtrix Multiplition. Assignment nd nswer key. Determinnt x x (digonl, minors, properties) summry
More informationTJ Publishers Advantage Business Centre 132134 Great Ancoats Street Manchester M4 6DE
TJ Pulishers Advntge Business Centre 132134 Gret Anots Street Mnhester M4 6DE Tel: 0141 880 6839 Fx: 0870 124 9189 emil: teejypulishers@tinternet.om we pge: www.teejypulishers.o.uk TeeJy Pulishers 2014
More informationOxCORT v4 Quick Guide Revision Class Reports
OxCORT v4 Quik Guie Revision Clss Reports This quik guie is suitble for the following roles: Tutor This quik guie reltes to the following menu options: Crete Revision Clss Reports pg 1 Crete Revision Clss
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments  they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationLISTENING COMPREHENSION
PORG, přijímí zkoušky 2015 Angličtin B Reg. číslo: Inluded prts: Points (per prt) Points (totl) 1) Listening omprehension 2) Reding 3) Use of English 4) Writing 1 5) Writing 2 There re no extr nswersheets
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationTiming/Synchronizing/ Adjusting (3 Cylinder Models)
Timing/Synhronizing/ Adjusting (3 Cylinder Models) Speifitions 70, 75 nd 80 Models Seril Numer nd Aove U.S. B239242 Belgium 9502135 Cnd A730007 Full Throttle RPM Rnge 47505250 Idle RPM (in FORWARD Ger)
More informationFurther applications of area and volume
2 Further pplitions of re n volume 2A Are of prts of the irle 2B Are of omposite shpes 2C Simpson s rule 2D Surfe re of yliners n spheres 2E Volume of omposite solis 2F Error in mesurement Syllus referene
More informationIf two triangles are perspective from a point, then they are also perspective from a line.
Mth 487 hter 4 Prtie Prolem Solutions 1. Give the definition of eh of the following terms: () omlete qudrngle omlete qudrngle is set of four oints, no three of whih re olliner, nd the six lines inident
More informationStudent Access to Virtual Desktops from personally owned Windows computers
Student Aess to Virtul Desktops from personlly owned Windows omputers Mdison College is plesed to nnoune the ility for students to ess nd use virtul desktops, vi Mdison College wireless, from personlly
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationLecture 15  Curve Fitting Techniques
Lecture 15  Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting  motivtion For root finding, we used given function to identify where it crossed zero where does fx
More informationNCERT INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS. Trigonometric Ratios of the angle A in a triangle ABC right angled at B are defined as:
INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS (A) Min Concepts nd Results Trigonometric Rtios of the ngle A in tringle ABC right ngled t B re defined s: side opposite to A BC sine of A = sin A = hypotenuse
More informationH SERIES. Area and Perimeter. Curriculum Ready. www.mathletics.com
Are n Perimeter Curriulum Rey www.mthletis.om Copyright 00 3P Lerning. All rights reserve. First eition printe 00 in Austrli. A tlogue reor for this ook is ville from 3P Lerning Lt. ISBN 7886307 Ownership
More informationHeron s Formula for Triangular Area
Heron s Formul for Tringulr Are y Christy Willims, Crystl Holom, nd Kyl Gifford Heron of Alexndri Physiist, mthemtiin, nd engineer Tught t the museum in Alexndri Interests were more prtil (mehnis, engineering,
More informationFAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University
SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility
More informationSection 55 Solving Right Triangles*
55 Solving Right Tringles 379 79. Geometry. The re of retngulr nsided polygon irumsried out irle of rdius is given y A n tn 80 n (A) Find A for n 8, n 00, n,000, nd n 0,000. Compute eh to five deiml
More informationMath 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.
Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose
More informationRadius of the Earth  Radii Used in Geodesy James R. Clynch Naval Postgraduate School, 2002
dius of the Erth  dii Used in Geodesy Jmes. Clynh vl Postgrdute Shool, 00 I. Three dii of Erth nd Their Use There re three rdii tht ome into use in geodesy. These re funtion of ltitude in the ellipsoidl
More informationPure C4. Revision Notes
Pure C4 Revision Notes Mrch 0 Contents Core 4 Alger Prtil frctions Coordinte Geometry 5 Prmetric equtions 5 Conversion from prmetric to Crtesin form 6 Are under curve given prmetriclly 7 Sequences nd
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls : The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N):  counting numers. {,,,,, } Whole Numers (W):  counting numers with 0. {0,,,,,, } Integers (I): 
More informationHealth and Social Care
Write your name here Surname Other names Edexcel GSE entre Number andidate Number Health and Social are Unit 1: Understanding Personal Development and Relationships Wednesday 25 January 2012 fternoon Time:
More informationVolumes by Cylindrical Shells: the Shell Method
olumes Clinril Shells: the Shell Metho Another metho of fin the volumes of solis of revolution is the shell metho. It n usull fin volumes tht re otherwise iffiult to evlute using the Dis / Wsher metho.
More information10 AREA AND VOLUME 1. Before you start. Objectives
10 AREA AND VOLUME 1 The Tower of Pis is circulr bell tower. Construction begn in the 1170s, nd the tower strted lening lmost immeditely becuse of poor foundtion nd loose soil. It is 56.7 metres tll, with
More informationQuick Reference Guide: Onetime Account Update
Quick Reference Guide: Onetime Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)
More information1 Fractions from an advanced point of view
1 Frtions from n vne point of view We re going to stuy frtions from the viewpoint of moern lger, or strt lger. Our gol is to evelop eeper unerstning of wht n men. One onsequene of our eeper unerstning
More informationSOLVING QUADRATIC EQUATIONS BY FACTORING
6.6 Solving Qudrti Equtions y Ftoring (6 31) 307 In this setion The Zero Ftor Property Applitions 6.6 SOLVING QUADRATIC EQUATIONS BY FACTORING The tehniques of ftoring n e used to solve equtions involving
More informationTHE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION.
THE LONGITUDINAL FIELD IN THE GTEM 175 AND THE NATURE OF THE TERMINATION. Benjmin Guy Loder Ntionl Physil Lbortory, Queens Rod, Teddington, Middlesex, Englnd. TW11 LW Mrtin Alexnder Ntionl Physil Lbortory,
More informationVectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m
. Slr prout (ot prout): = osθ Vetors Summry Lws of ot prout: (i) = (ii) ( ) = = (iii) = (ngle etween two ientil vetors is egrees) (iv) = n re perpeniulr Applitions: (i) Projetion vetor: B Length of projetion
More informationIntroduction. Teacher s lesson notes The notes and examples are useful for new teachers and can form the basis of lesson plans.
Introduction Introduction The Key Stge 3 Mthemtics series covers the new Ntionl Curriculum for Mthemtics (SCAA: The Ntionl Curriculum Orders, DFE, Jnury 1995, 0 11 270894 3). Detiled curriculum references
More informationQuick Guide to Lisp Implementation
isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled Sepressions. The representtion o n Sepression n e roken into two piees, the
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationCambridge International Examinations Cambridge Secondary 1 Checkpoint
ambridge International Examinations ambridge Secondary 1 heckpoint NDIDTE NME ENTRE NUMER NDIDTE NUMER ENGLISH S SEOND LNGUGE Paper 3 Listening SPEIMEN PPER 1110/03 For Examination from 2015 approximately
More informationPlotting and Graphing
Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured
More informationBefore you can use the machine, read this Quick Setup Guide for the correct setup and installation.
Quik Setup Guide Strt Here MFC490CW Before you n use the mhine, red this Quik Setup Guide for the orret setup nd instlltion. WARNING Wrnings tell you wht to do to prevent possile personl injury. Importnt
More informationPaper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes
Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationAngles and Triangles
nges nd Tringes n nge is formed when two rys hve ommon strting point or vertex. The mesure of n nge is given in degrees, with ompete revoution representing 360 degrees. Some fmiir nges inude nother fmiir
More informationthe machine and check the components Starter Ink Cartridges Basic User s Guide Product Safety Guide Telephone Line Cord
Quik Setup Guide Strt Here MFCJ450DW MFCJ470DW Thnk you for hoosing Brother, your support is importnt to us nd we vlue your usiness. Your Brother produt is engineered nd mnuftured to the highest stndrds
More informationONLINE PAGE PROOFS. Trigonometry. 6.1 Overview. topic 6. Why learn this? What do you know? Learning sequence. measurement and geometry
mesurement nd geometry topic 6 Trigonometry 6.1 Overview Why lern this? Pythgors ws gret mthemticin nd philosopher who lived in the 6th century BCE. He is est known for the theorem tht ers his nme. It
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationBefore you can use the machine, please read this Quick Setup Guide for the correct setup and installation.
Quik Setup Guide Strt Here DCP365CN DCP373CW DCP375CW DCP377CW Before you n use the mhine, plese red this Quik Setup Guide for the orret setup nd instlltion. WARNING CAUTION Wrnings tell you wht to
More informationGRADE 4. Fractions WORKSHEETS
GRADE Frtions WORKSHEETS Types of frtions equivlent frtions This frtion wll shows frtions tht re equivlent. Equivlent frtions re frtions tht re the sme mount. How mny equivlent frtions n you fin? Lel eh
More informationhow do I? table of contents
hp dvd writer how do I? tle of ontents how do I know whih progrm to use? 1 english how do I opy dis? 2 how do I trnsfer my tpes to dis? 4 how do I rete DVD movie? 9 how do I edit DVD movie dis? 13 how
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationIntroductory Information. Setup Guide. Introduction. Space Required for Installation. Overview of Setup. The Manuals Supplied with This Printer ENG
Introdutory Informtion Introdution Setup Guide ENG Red this mnul efore ttempting to operte the printer. Keep this mnul in hndy lotion for future referene. Overview of Setup These re the steps in printer
More informationVolumes of solids of revolution
Volumes of solids of revolution We sometimes need to clculte the volume of solid which cn be obtined by rotting curve bout the xxis. There is strightforwrd technique which enbles this to be done, using
More informationAssembly & Installation Instructions: Impulse 2Leg Workcenter IM3E487830DX
Assemly & Instlltion Instrutions: Impulse Leg Workenter IM3E487830DX Prts Inluded, Frme Set A Impulse Bse Assemly Qty: D M5 0 mm Phillips Wood Srews Qty: 8 M0 35 mm Soket ed Srews Qty: 8 Box E Swith
More informationTeeJay Publishers Homework for Level F book Ch 59  Pythagoras
Chapter 59 Pythagoras Exerise 1 1. Find : Calulators should not be used anywhere in this Chapter unless you are otherwise instruted. (a) 3 2 (b) 5 2 () 2 2 (d) 1 2 (e) 10 2 (f) 9 2 (g) 11 2 (h) 12 2 (i)
More informationHow to Graphically Interpret the Complex Roots of a Quadratic Equation
Universit of Nersk  Linoln DigitlCommons@Universit of Nersk  Linoln MAT Em Epositor Ppers Mth in the Middle Institute Prtnership 7007 How to Grphill Interpret the Comple Roots of Qudrti Eqution Crmen
More information