Ratio and Proportion Long-Term Memory Review Review 1
|
|
|
- April Clemence Whitehead
- 7 years ago
- Views:
Transcription
1 Rtio nd Proportion Review 1 1. Provide omplete response to eh of the following:. A rtio ompres two.. A proportion sets two rtios to eh other.. Wht re similr figures? 2. Drw two similr figures. D A 14 m E 15 m F 3. The tringles in the figure ove re similr. B 21 m C. nd re mesures of orresponding sides.. nd re mesures of nother pir of orresponding sides. 4. Find the vlue of. A. 7 m B. 8 m C. 10 m D. m Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
2 Rtio nd Proportion Review 2 1. Provide omplete response to eh of the following:. A rtio ompres two.. A proportion sets two rtios to eh other.. Wht re similr figures? 2. Drw two similr figures. D A 14 m E 15 m F B 21 m C 3. USE the figure ove: We know tht ABC DEF. Write four different proportions tht n used to solve for. 15 m 21 m 14 m m 15 m 14 m 21 m One wy Seond wy Third wy Fourth wy 4. A mn who is 6 feet tll sts shdow tht is feet long. At the sme time, tree sts shdow tht is 33 feet long. Use the drwing elow to help you find the height of the tree? Lel the following: ) tree, ) tree s shdow, ) mn, nd d) mn s shdow. Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
3 Rtio nd Proportion Review 3 1. Provide omplete response to eh of the following:. A rtio ompres two.. A proportion sets two rtios to eh other.. Wht re similr figures? 2. Drw two similr figures. 3. In one seson, ity s sketll tem won 60 gmes nd lost 20 gmes.. Wht is the rtio of gmes won to gmes lost? ANSWER: This question n e written in following different wys: 60 won 60 won to 20 lost; or 60 won: 20 lost: or 20 lost. Wht is the totl numer of gmes plyed?. Wht is the rtio of gmes won to gmes plyed? d. Wht is the rtio of gmes lost to gmes plyed? 4. There re only dogs nd ts t the lol niml resue enter. The rtio of dogs to ts eing dopted tody t the niml resue enter is 7 to 5. If there re 120 totl nimls up for doption, how mny dogs re there? 5. The retngles t the right re similr. Write four different proportions tht n e used to solve for. 12 m 6 m 4 m 12 m 6 m 4 m One wy Seond wy Third wy Fourth wy Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
4 Rtio nd Proportion Review 4 1. Provide omplete response to eh of the following:. A rtio ompres two.. A proportion sets two rtios to eh other.. Wht re similr figures? 2. Drw two similr figures. USE the figure on the right for questions 3-4. The two retngles t the right re similr. 3. Write four different proportions tht n used to solve for? One wy Seond wy Third wy Fourth wy 4. Wht is the vlue of? A. B. C. D. 5. In one seson, ity s sketll tem won 60 gmes nd lost 20 gmes.. Wht is the totl numer of gmes plyed?. Wht is the rtio of gmes won to gmes plyed?. Wht is the rtio of gmes lost to gmes plyed? d. In the ity, sell tem hd the sme rtio of wins to losses s the ove sketll tem, ut they plyed 120 totl gmes during the seson. How mny gmes did the sell tem win nd lose? 6. A new winter ot is on sle for 20% off the originl prie. If sle prie is $176 fter the 20% disount, then wht is the originl prie of the ot? Use the proportion elow to help you solve the prolem. 80 sle prie (%pid) sle prie ($pid) 100 totl prie (%originl) totl prie ($originl) Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
5 Rtio nd Proportion Quiz 1. Provide omplete response to the following questions:. A rtio ompres two.. A proportion sets two rtios to eh other.. Wht re similr figures? d. Drw two similr figures. Use the figure on the right for questions The retngles re similr.. nd re mesures of orresponding sides.. nd re mesures of the other pir of orresponding sides. 6 m 12 m 3. Write four different proportions tht n e used to solve for? 4 m 12 m 6 m 12 m 4 m 6 m 4 m One wy Seond wy Third wy Fourth wy 4. Find the vlue of. A. 2 m B. 8 m C. 10 m D. 18 m 5. A new lether ot is on sle for 20% off the originl prie. If sle prie is $160 fter the 20% disount, then wht is the originl prie of the ot? Use the proportion elow to help you solve the prolem. 80 sle prie (%pid) sle prie ($pid) 100 totl prie (%originl) totl prie ($originl) 6. A mn who is 6 feet tll sts shdow tht is feet long. At the sme time, tree sts shdow tht is 33 feet long. Drw piture to represent this sitution nd find the height of the tree? Lel the digrm. 7. The two retngles t the right re similr. Wht is the vlue of? A. B. C. D. Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
6 Rtio nd Proportion ANSWERS Review 1 - Answers 1.. numers. equl. Similr figures re figures tht re the sme shpe, ut my e different sizes; ngles re ongruent, sides re proportionl 2. Answers my vry nd nd 4. C. 10 m Review 2 - Answers 1.. numers. equl. Similr figures re figures tht re the sme shpe, ut my e different sizes; ngles re ongruent, sides re proportionl 2. Answers my vry m 21 m 14 m m 14 m 15 m 21 m m 15 m 14 m 21 m 14 m 21 m m 15 m One wy Seond wy Third wy Fourth wy 4. 6 ft: Mn X ft: tree 6 33 ft: Mn shdow 33 ft: Tree s shdow 18 ft Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
7 Rtio nd Proportion Review 3 - Answers 1.. numers. equl. Similr figures re figures tht re the sme shpe, ut my e different sizes; ngles re ongruent, sides re proportionl 2. Answers my vry won to 20 lost. 60: dog 7 (dog) 7 totl dogs m 6 m 4 m m 4 m 12 m 6 m 12 m m 6 m 4 m 6 m 4 m 12 m m One wy Seond wy Third wy Fourth wy Review 4 - Answers 1.. numers. equl. Similr figures re figures tht re the sme shpe, ut my e different sizes; ngles re ongruent, sides re proportionl 2. Answers my vry. 3. One wy Seond wy Third wy Fourth wy Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
8 Rtio nd Proportion 4. A Wht is the totl numer of gmes plyed? 80. Wht is the rtio of gmes won to gmes plyed? 60 to 80. Wht is the rtio of gmes lost to gmes plyed? d. In the ity, sell tem hd the sme rtio of wins to losses s the ove sketll tem, ut they plyed 120 totl gmes during the seson. How mny gmes did the sell tem win nd lose? 3 ; won 90, lost ; 80=17600; =$ Quiz - Answers 1.. numers. equl. Similr figures re figures tht re the sme shpe, ut my e different sizes; ngles re ongruent, sides re proportionl 2. Answers my vry One wy Seond wy Third wy Fourth wy 4. B. 8 m ; 80=1600; =$ ; =198; =18; The tree is 18 ft. tll A. Produed y the Southern Nevd Regionl Professionl Development Progrm (SNRPDP) June 09
Ratio 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
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
Lesson 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,
PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
Angles 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
Geometry 7-1 Geometric Mean and the Pythagorean Theorem
Geometry 7-1 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
Words Symbols Diagram. abcde. a + b + c + d + e
Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To
Section 5-4 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
Chapter. 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
50 MATHCOUNTS LECTURES (10) RATIOS, RATES, AND PROPORTIONS
0 MATHCOUNTS LECTURES (0) RATIOS, RATES, AND PROPORTIONS BASIC KNOWLEDGE () RATIOS: Rtios re use to ompre two or more numers For n two numers n ( 0), the rtio is written s : = / Emple : If 4 stuents in
Released 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
How To Find The Re Of Tringle
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,
A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
Interior 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
End 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.
Chapter. 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
1. 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
Lesson 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.
10.6 Applications of Quadratic Equations
10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,
Operations 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
SOLVING EQUATIONS BY FACTORING
316 (5-60) 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
Reasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right.
Order of Opertions r of Opertions Alger P lese Prenthesis - Do ll grouped opertions first. E cuse Eponents - Second M D er Multipliction nd Division - Left to Right. A unt S hniqu Addition nd Sutrction
c b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00
Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt volume @ 0.200 m 3, isohori. Pressure inreses from 2.00 10 5 P to 5.00 10 5 P. Seond: Constnt ressure @ 5.00 10 5 P, isori. olume
Practice 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?
addition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.
APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The
Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
Maximum 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
. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2
7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6
Angles 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
Experiment 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
MATH 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
Binary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy
P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
If 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
One Minute To Learn Programming: Finite Automata
Gret Theoreticl Ides In Computer Science Steven Rudich CS 15-251 Spring 2005 Lecture 9 Fe 8 2005 Crnegie Mellon University One Minute To Lern Progrmming: Finite Automt Let me tech you progrmming lnguge
Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur
Module 5 Three-hse A iruits Version EE IIT, Khrgur esson 8 Three-hse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (-7), the study of iruits, onsisting of the liner elements resistne,
GENERAL APPLICATION FOR FARM CLASSIFICATION
SCHEDULE 1 (section 1) Plese return to: DEADLINE: Plese return this form to your locl BC Assessment office y Octoer 31. Assessment Roll Numer(s) GENERAL APPLICATION FOR FARM CLASSIFICATION Section 23 (1)
Graphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
The Cat in the Hat. by Dr. Seuss. A a. B b. A a. Rich Vocabulary. Learning Ab Rhyming
MINI-LESSON IN TION The t in the Ht y Dr. Seuss Rih Voulry tme dj. esy to hndle (not wild) LERNING Lerning Rhyming OUT Words I know it is wet nd the sun is not sunny. ut we n hve Lots of good fun tht is
Cypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
Homework 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}.
Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
NQF 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:.................................
Vectors. 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
Review Problems for the Final of Math 121, Fall 2014
Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since
Seeking Equilibrium: Demand and Supply
SECTION 1 Seeking Equilirium: Demnd nd Supply OBJECTIVES KEY TERMS TAKING NOTES In Setion 1, you will explore mrket equilirium nd see how it is rehed explin how demnd nd supply intert to determine equilirium
LISTENING 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
CUBIC-FOOT VOLUME OF A LOG
CUBIC-FOOT VOLUME OF A LOG Wys to clculte cuic foot volume ) xylometer: tu of wter sumerge tree or log in wter nd find volume of wter displced. ) grphic: exmple: log length = 4 feet, ech section feet in
Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
SECTION 7-2 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
Exercises in KS3 Mathematics Levels 7-8. R Joinson
Exercises in KS Mthemtics Levels 7-8 R Joinson Sumbooks Northwy Chester CH 8BB Exercises in KS Mthemtics - Levels 7 nd 8 First Published 00 Copyright R Joinson nd Sumbooks This pckge of worksheets is sold
Project Recovery. . It Can Be Done
Project Recovery. It Cn Be Done IPM Conference Wshington, D.C. Nov 4-7, 200 Wlt Lipke Oklhom City Air Logistics Center Tinker AFB, OK Overview Mngement Reserve Project Sttus Indictors Performnce Correction
Math 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
AAPT UNITED STATES PHYSICS TEAM AIP 2010
2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD
Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
H 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 78--86-30-7 Ownership
Physics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
AREA 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.
Mathematics. 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
Pure 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
ONLINE 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
Brillouin Zones. Physics 3P41 Chris Wiebe
Brillouin Zones Physics 3P41 Chris Wiebe Direct spce to reciprocl spce * = 2 i j πδ ij Rel (direct) spce Reciprocl spce Note: The rel spce nd reciprocl spce vectors re not necessrily in the sme direction
1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
Use 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
Unit 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): -
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
SOLVING 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
Introduction. 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
and thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
Answer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your
, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
10 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
Polynomial 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 +
Chap.6 Surface Energy
Chp.6 urfe Energy (1) Bkground: Consider the toms in the bulk nd surfe regions of rystl: urfe: toms possess higher energy sine they re less tightly bound. Bulk: toms possess lower energy sine they re muh
Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
ALGEBRAIC FRACTIONS,AND EQUATIONS AND INEQUALITIES INVOLVING FRACTIONS
CHAPTER ALGEBRAIC FRACTIONS,AND EQUATIONS AND INEQUALITIES INVOLVING FRACTIONS Although people tody re mking greter use of deciml frctions s they work with clcultors, computers, nd the metric system, common
Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
Radius 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
Econ 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
1 GSW IPv4 Addressing
1 For s long s I ve een working with the Internet protools, people hve een sying tht IPv6 will e repling IPv4 in ouple of yers time. While this remins true, it s worth knowing out IPv4 ddresses. Even when
MA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!
MA 5800 Lesson 6 otes Summer 06 Rememer: A logrithm is n eponent! It ehves like n eponent! In the lst lesson, we discussed four properties of logrithms. ) log 0 ) log ) log log 4) This lesson covers more
6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of
PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
Review. Scan Conversion. Rasterizing Polygons. Rasterizing Polygons. Triangularization. Convex Shapes. Utah School of Computing Spring 2013
Uth Shool of Computing Spring 2013 Review Leture Set 4 Sn Conversion CS5600 Computer Grphis Spring 2013 Line rsteriztion Bsi Inrementl Algorithm Digitl Differentil Anlzer Rther thn solve line eqution t
EQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint
Applications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
PHY 140A: Solid State Physics. Solution to Homework #2
PHY 140A: Solid Stte Physics Solution to Homework # TA: Xun Ji 1 October 14, 006 1 Emil: jixun@physics.ucl.edu Problem #1 Prove tht the reciprocl lttice for the reciprocl lttice is the originl lttice.
In order to master the techniques explained here it is vital that you undertake the practice exercises provided.
Tringle formule m-ty-tringleformule-009-1 ommonmthemtilprolemistofindthenglesorlengthsofthesidesoftringlewhen some,utnotllofthesequntitiesreknown.itislsousefultoeletolultethere of tringle from some of
COMPLEX FRACTIONS. section. Simplifying Complex Fractions
58 (6-6) Chpter 6 Rtionl Epressions undles tht they cn ttch while working together for 0 hours. 00 600 6 FIGURE FOR EXERCISE 9 95. Selling. George sells one gzine suscription every 0 inutes, wheres Theres
1 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
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
0.1 Basic Set Theory and Interval Notation
0.1 Bsic Set Theory nd Intervl Nottion 3 0.1 Bsic Set Theory nd Intervl Nottion 0.1.1 Some Bsic Set Theory Notions Like ll good Mth ooks, we egin with definition. Definition 0.1. A set is well-defined
KEY 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
CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001
CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic
Quick 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 S-epressions. The representtion o n S-epression n e roken into two piees, the
Small Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
SUPPLEMENTARY MATERIAL
SUPPLEMENTARY MATERIAL Lyer-speifi exittory iruits differentilly ontrol reurrent network dynmis in the neoortex Rirdo Beltrmo, Giuli D Urso, Mro Dl Mshio, Psqulin Frisello, Seren Bovetti, Yonne Clovis,