Variable Dry Run (for Python)

Size: px
Start display at page:

Download "Variable Dry Run (for Python)"

Transcription

1 Vrile Dr Run (for Pthon) Age group: Ailities ssumed: Time: Size of group: Focus Vriles Assignment Sequencing Progrmming 7 dult Ver simple progrmming, sic understnding of ssignment nd vriles minutes depending on student eperience unlimited Sllus Links This ctivit is pproprite for n sllus im out lerning to progrm t n level tht requires n understnding of vriles nd ssignment. Summr Set series of dr run eercises where students hve to step through short frgments of code working out wht the do on pper. This is n importnt ctivit to do fter eplining vriles nd ssignment. It reinforces understnding nd helps identif fult mentl models so the cn e fied. Being le to do this kind of dr run for n new construct is n importnt prerequisite to eing le to ctull write code. Technicl Terms Assignment, Vrile, Vlue, Sequencing. Mterils Dr run eercise sheets Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

2 Wht to do The Gr: Use the Bo Vrile ctivit s the grd to this one, giving students n understnding of vriles nd ssignment tht this ctivit reinforces. The ctivit: Hve the clss dr run the given series of short progrms on pper (see the eercise sheets provided t the end). Use these to determine wht ech student understnds. As ech finishes the sheet, mrk them on the spot, nd fi n prolems. It is vitl tht n incorrect mentl model is corrected stright w. Common misunderstndings to look out for include: - tht vrile still holds its originl vlue fter n ssignment, - tht ssignment works coping left to right, - tht sequence of ssignments ll hppen together - tht sequence of ssignments cn hppen in n order - tht oth left hnd side nd right hnd side chnge - tht it is like mthemticl equlit just mking oth sides the sme so tht future chnges to one chnge the other - tht vrile cn hold ll the vlues ever ssigned to it If students get n wrong, find out wht the hve misunderstood, if it is not lck of cre over detil, nd eplin the correct mentl model nd their misunderstnding to them. This cn e done stepping through one of the eercises with them. Hve them redo the sheet once the re hpp the do now understnd. Vritions nd Etensions Student written progrms Hve students write their own simple progrms using ssignment nd then dr run them. Dr Run Tles Do similr eercises ut now using more compct tle formt to record the dr run, with one column per vrile, crossing out vlues nd moving to the net row s the re replced. Further Reding Computing without computers A free ooklet Pul Curzon on progrmming, dt structures nd lgorithms eplined using links to everd concepts. Aville from Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

3 Links to other ctivities Bo Vriles Eecute run simple progrms tht involve vriles nd ssignment running them on computer mde of students. Students with oes ct s vriles s vlues re copied etween them following the instructions of progrm. You phsicll demonstrte the cretion of vriles, how ccessing vrile involves tking cop of its vlue, nd how storing vlues in vrile destros n previous vlue stored. The swp puzzle Solve puzzle, coming up with n lgorithm tht our tem cn follow fster thn none else. This gives w to introduce the ide of the solution to prolem eing set of instructions tht llow others to solve it with no understnding. It lso eplores how different lgorithms cn solve the sme prolem ut m not e equll good some m e fster. The intelligent piece of pper Tke prt in test of intelligence ginst n intelligent piece of pper! This is good introduction to wht n lgorithms is nd how computer progrm is just n lgorithm. It cn lso e used to strt discussion on wht it would men for computer to e intelligent. It cn led on to n unplugged progrmming ctivit creting winning instructions. The Invisile Plming Trick Tech trick where the mgicin invisil moves crd etween 2 piles. This is fun w to introduce the ide of n lgorithm, showing how lgorithms re series of steps tht if followed precisel led to something (in this cse mgicl) eing gurnteed to hppen even if the person (or computer) following the lgorithm doesn t know wht the re doing. Live demonstrtion of this ctivit Teching London Computing give live sessions for techers demonstrting this nd our other ctivities. See for detils. Videos of some ctivities re lso ville or in preprtion. Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

4 Dr Run Eercises (Pthon) 1. Wht re the finl vlues stored in nd fter the following code frgment hs eecuted? = 5 = 7 = The finl vlue of is The finl vlue of is Solve this doing dr run, filling in the vlue in the oes = 5 hs eecuted the vriles hold the following vlues: = 7 hs eecuted the vriles hold the following vlues: = hs eecuted the vriles hold the following vlues: Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

5 2. Wht re the finl vlues stored in nd fter the following code frgment hs eecuted? = 5 = 7 = The finl vlue of is The finl vlue of is Solve this doing dr run, filling in the vlue in the oes = 5 hs eecuted the vriles hold the following vlues: = 7 hs eecuted the vriles hold the following vlues: = hs eecuted the vriles hold the following vlues: Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

6 3. Wht re the finl vlues stored in nd fter the following code frgment hs eecuted? = 7 = 5 = The finl vlue of is The finl vlue of is Solve this doing dr run, filling in the vlue in the oes = 7 hs eecuted the vriles hold the following vlues: = 5 hs eecuted the vriles hold the following vlues: = hs eecuted the vriles hold the following vlues: Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

7 4. Wht re the finl vlues stored in red nd lue fter the following code frgment hs eecuted? red = red lue = ellow red = lue The finl vlue of red is The finl vlue of lue is Solve this doing dr run, filling in the vlue in the oes red = red hs eecuted the vriles hold the following vlues: red lue = ellow hs eecuted the vriles hold the following vlues: red lue red = lue hs eecuted the vriles hold the following vlues: red lue Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

8 5. Wht re the finl vlues stored in nd fter the following code frgment hs eecuted? = 7 = 5 = = 3 The finl vlue of is The finl vlue of is Solve this doing dr run, filling in the vlue in the oes = 7 hs eecuted the vriles hold the following vlues: = 5 hs eecuted the vriles hold the following vlues: = hs eecuted the vriles hold the following vlues: = 3 hs eecuted the vriles hold the following vlues: Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

9 6. Wht re the finl vlues in, nd z fter the following code frgment hs eecuted? = 1 = 2 z = 3 = = The finl vlue of is The finl vlue of is The finl vlue of z is Solve this doing dr run, filling in the vlue in the oes = 1 hs eecuted the vriles hold the following vlues: = 2 hs eecuted the vriles hold the following vlues: z = 3 hs eecuted the vriles hold the following vlues: z = hs eecuted the vriles hold the following vlues: z = hs eecuted the vriles hold the following vlues: z Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

10 7. Wht re the finl vlues in one, two nd three fter the following code frgment hs eecuted? one = 1 two = 3 three = 2 one = two two = three The finl vlue of one is The finl vlue of two is The finl vlue of three is Solve this doing dr run, filling in the vlue in the oes one = 1 hs eecuted the vriles hold the following vlues: one two = 3 hs eecuted the vriles hold the following vlues: one two three = 2 hs eecuted the vriles hold the following vlues: one two three one = two hs eecuted the vriles hold the following vlues: one two three two = three hs eecuted the vriles hold the following vlues: one two three Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

11 8. Wht re the finl vlues in, nd c fter the following hs eecuted? = 9 = 7 c = 8 = c = c = The finl vlue of is The finl vlue of is The finl vlue of c is Solve this doing dr run, filling in the vlue in the oes = 9 hs eecuted the vriles hold the following vlues: = 7 hs eecuted the vriles hold the following vlues: c = 8 hs eecuted the vriles hold the following vlues: c = c hs eecuted the vriles hold the following vlues: c = hs eecuted the vriles hold the following vlues: c c = hs eecuted the vriles hold the following vlues: c Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

12 9. Wht re the finl vlues in, nd c fter the following hs eecuted? = 1 = 2 c = 3 c = c = = The finl vlue of is The finl vlue of is The finl vlue of c is Solve this doing dr run, filling in the vlue in the oes = 1 hs eecuted the vriles hold the following vlues: = 2 hs eecuted the vriles hold the following vlues: c = 3 hs eecuted the vriles hold the following vlues: c c = hs eecuted the vriles hold the following vlues: c c = hs eecuted the vriles hold the following vlues: c = hs eecuted the vriles hold the following vlues: c Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

13 10. Wht re the finl vlues in, nd z fter the following hs eecuted? = 3 = 2 z = 3 z = = = z The finl vlue of is The finl vlue of is The finl vlue of z is Solve this doing dr run, filling in the vlue in the oes = 3 hs eecuted the vriles hold the following vlues: = 2 hs eecuted the vriles hold the following vlues: z = 3 hs eecuted the vriles hold the following vlues: z z = hs eecuted the vriles hold the following vlues: z = hs eecuted the vriles hold the following vlues: z = z hs eecuted the vriles hold the following vlues: z Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

14 Answers 1. The finl vlue of is: 7 The finl vlue of is: 7 2. The finl vlue of is: 5 The finl vlue of is: 5 3. The finl vlue of is: 5 The finl vlue of is: 5 4. The finl vlue of red is: The finl vlue of lue is: ellow ellow 5. The finl vlue of is: 3 The finl vlue of is: 5 6. The finl vlue of is: 1 The finl vlue of is: 1 The finl vlue of z is: 3 7. The finl vlue of one is: 3 The finl vlue of two is: 2 The finl vlue of three is: 2 8. The finl vlue of is: 8 The finl vlue of is: 8 The finl vlue of c is: 8 9. The finl vlue of is: 2 The finl vlue of is: 2 The finl vlue of c is: The finl vlue of is: 2 The finl vlue of is: 3 The finl vlue of z is: 2 Computer Science ctivities with sense of fun: Assignment Dr Run V1.1 (28 M 2014) Creted Pul Curzon, Queen Mr, Universit of London for

Binary Representation of Numbers Autar Kaw

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

More information

Reasoning to Solve Equations and Inequalities

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

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

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

More information

EQUATIONS OF LINES AND PLANES

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

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

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

More information

Homework 3 Solutions

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}.

More information

Rotational Equilibrium: A Question of Balance

Rotational Equilibrium: A Question of Balance Prt of the IEEE Techer In-Service Progrm - Lesson Focus Demonstrte the concept of rottionl equilirium. Lesson Synopsis The Rottionl Equilirium ctivity encourges students to explore the sic concepts of

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

Experiment 6: Friction

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

More information

Warm-up for Differential Calculus

Warm-up for Differential Calculus Summer Assignment Wrm-up 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 information

Answer, Key Homework 10 David McIntyre 1

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

More information

Quick Reference Guide: One-time Account Update

Quick Reference Guide: One-time Account Update Quick Reference Guide: One-time 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 information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

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 +

More information

One Minute To Learn Programming: Finite Automata

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

More information

Econ 4721 Money and Banking Problem Set 2 Answer Key

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

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

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

More information

Angles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example

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

More information

Graphs on Logarithmic and Semilogarithmic Paper

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

More information

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

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

More information

Words Symbols Diagram. abcde. a + b + c + d + e

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

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

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

More information

Health insurance marketplace What to expect in 2014

Health insurance marketplace What to expect in 2014 Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum

More information

Algebra Review. How well do you remember your algebra?

Algebra Review. How well do you remember your algebra? Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

Integration. 148 Chapter 7 Integration

Integration. 148 Chapter 7 Integration 48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but

More information

5 a LAN 6 a gateway 7 a modem

5 a LAN 6 a gateway 7 a modem STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet

More information

Health insurance exchanges What to expect in 2014

Health insurance exchanges What to expect in 2014 Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount

More information

SPECIAL PRODUCTS AND FACTORIZATION

SPECIAL PRODUCTS AND FACTORIZATION MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come

More information

Vectors 2. 1. Recap of vectors

Vectors 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 information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

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

More information

Morgan Stanley Ad Hoc Reporting Guide

Morgan Stanley Ad Hoc Reporting Guide spphire user guide Ferury 2015 Morgn Stnley Ad Hoc Reporting Guide An Overview For Spphire Users 1 Introduction The Ad Hoc Reporting tool is ville for your reporting needs outside of the Spphire stndrd

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of

More information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Section 5-4 Trigonometric Functions

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

More information

Operations with Polynomials

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

More information

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful Pentominoes Bruce Bguley Cscde Mth Systems, LLC Astrct. Pentominoes nd their reltives the polyominoes, polycues, nd polyhypercues will e used to explore nd pply vrious importnt mthemticl concepts. In this

More information

Helicopter Theme and Variations

Helicopter 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 information

New Internet Radio Feature

New Internet Radio Feature XXXXX XXXXX XXXXX /XW-SMA3/XW-SMA4 New Internet Rdio Feture EN This wireless speker hs een designed to llow you to enjoy Pndor*/Internet Rdio. In order to ply Pndor/Internet Rdio, however, it my e necessry

More information

Lec 2: Gates and Logic

Lec 2: Gates and Logic Lec 2: Gtes nd Logic Kvit Bl CS 34, Fll 28 Computer Science Cornell University Announcements Clss newsgroup creted Posted on we-pge Use it for prtner finding First ssignment is to find prtners Due this

More information

Object Semantics. 6.170 Lecture 2

Object Semantics. 6.170 Lecture 2 Object Semntics 6.170 Lecture 2 The objectives of this lecture re to: to help you become fmilir with the bsic runtime mechnism common to ll object-oriented lnguges (but with prticulr focus on Jv): vribles,

More information

Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right.

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

More information

Section 7-4 Translation of Axes

Section 7-4 Translation of Axes 62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the

More information

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.

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

More information

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,

More information

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one. 5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued

More information

How To Study The Effects Of Music Composition On Children

How To Study The Effects Of Music Composition On Children C-crcs Cognitive - Counselling Reserch & Conference Services (eissn: 2301-2358) Volume I Effects of Music Composition Intervention on Elementry School Children b M. Hogenes, B. Vn Oers, R. F. W. Diekstr,

More information

Introduction to Integration Part 2: The Definite Integral

Introduction to Integration Part 2: The Definite Integral Mthemtics Lerning Centre Introduction to Integrtion Prt : The Definite Integrl Mr Brnes c 999 Universit of Sdne Contents Introduction. Objectives...... Finding Ares 3 Ares Under Curves 4 3. Wht is the

More information

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems Gene Expression Progrmming: A New Adptive Algorithm for Solving Prolems Cândid Ferreir Deprtmento de Ciêncis Agráris Universidde dos Açores 9701-851 Terr-Chã Angr do Heroísmo, Portugl Complex Systems,

More information

Welch Allyn CardioPerfect Workstation Installation Guide

Welch Allyn CardioPerfect Workstation Installation Guide Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.5 or lter For network instlltion, plese refer to

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define

More information

Distributions. (corresponding to the cumulative distribution function for the discrete case).

Distributions. (corresponding to the cumulative distribution function for the discrete case). Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive

More information

Chapter. Contents: A Constructing decimal numbers

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

More information

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks

More information

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time

More information

Java CUP. Java CUP Specifications. User Code Additions You may define Java code to be included within the generated parser:

Java CUP. Java CUP Specifications. User Code Additions You may define Java code to be included within the generated parser: Jv CUP Jv CUP is prser-genertion tool, similr to Ycc. CUP uilds Jv prser for LALR(1) grmmrs from production rules nd ssocited Jv code frgments. When prticulr production is recognized, its ssocited code

More information

JaERM Software-as-a-Solution Package

JaERM Software-as-a-Solution Package JERM Softwre-s--Solution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock

More information

DATABASDESIGN FÖR INGENJÖRER - 1056F

DATABASDESIGN FÖR INGENJÖRER - 1056F DATABASDESIGN FÖR INGENJÖRER - 06F Sommr 00 En introuktionskurs i tssystem http://user.it.uu.se/~ul/t-sommr0/ lt. http://www.it.uu.se/eu/course/homepge/esign/st0/ Kjell Orsorn (Rusln Fomkin) Uppsl Dtse

More information

and thus, they are similar. If k = 3 then the Jordan form of both matrices is

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

More information

Recognition Scheme Forensic Science Content Within Educational Programmes

Recognition Scheme Forensic Science Content Within Educational Programmes Recognition Scheme Forensic Science Content Within Eductionl Progrmmes one Introduction The Chrtered Society of Forensic Sciences (CSoFS) hs been ccrediting the forensic content of full degree courses

More information

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

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.

More information

AREA OF A SURFACE OF REVOLUTION

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.

More information

The remaining two sides of the right triangle are called the legs of the right triangle.

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 information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

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

More information

NQF Level: 2 US No: 7480

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:.................................

More information

Network Configuration Independence Mechanism

Network Configuration Independence Mechanism 3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting

More information

Quick Guide to Lisp Implementation

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

More information

Integration by Substitution

Integration 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 information

SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1470 - COLLEGE ALGEBRA (4 SEMESTER HOURS)

SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1470 - COLLEGE ALGEBRA (4 SEMESTER HOURS) SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 470 - COLLEGE ALGEBRA (4 SEMESTER HOURS). COURSE DESCRIPTION: Polynomil, rdicl, rtionl, exponentil, nd logrithmic functions

More information

Firm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach

Firm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

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.................................................

More information

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff Protocol Anlysis 17-654/17-764 Anlysis of Softwre Artifcts Kevin Bierhoff Tke-Awys Protocols define temporl ordering of events Cn often be cptured with stte mchines Protocol nlysis needs to py ttention

More information

MATH 150 HOMEWORK 4 SOLUTIONS

MATH 150 HOMEWORK 4 SOLUTIONS MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

Thinking out of the Box... Problem It s a richer problem than we ever imagined

Thinking out of the Box... Problem It s a richer problem than we ever imagined From the Mthemtics Techer, Vol. 95, No. 8, pges 568-574 Wlter Dodge (not pictured) nd Steve Viktor Thinking out of the Bo... Problem It s richer problem thn we ever imgined The bo problem hs been stndrd

More information

MA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!

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

More information

body.allow-sidebar OR.no-sidebar.home-page (if this is the home page).has-custom-banner OR.nocustom-banner .IR OR.no-IR

body.allow-sidebar OR.no-sidebar.home-page (if this is the home page).has-custom-banner OR.nocustom-banner .IR OR.no-IR body.llow-sidebr OR.no-sidebr.home-pge (if this is the home pge).hs-custom-bnner OR.nocustom-bnner.IR OR.no-IR #IDENTIFIER_FOR_THIS_SITE div#pge-continer.depends_on_page_ty PE llow-sidebr mens tht there

More information

Assessing authentically in the Graduate Diploma of Education

Assessing authentically in the Graduate Diploma of Education Assessing uthenticlly in the Grdute Diplom of Eduction Dr Mree DinnThompson Dr Ruth Hickey Dr Michelle Lsen WIL Seminr JCU Nov 12 2009 Key ides plnning process tht embeds uthentic ssessment, workintegrted

More information

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University

FAULT 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 information

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding 1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde

More information

Lecture 5. Inner Product

Lecture 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 information

OPTIMA QUADRANT / OFFSET QUADRANT

OPTIMA QUADRANT / OFFSET QUADRANT OPTIMA QUADRANT / OFFSET QUADRANT 71799 00 / Issue 1 / 15 Y Z DIMENSIONS Check the enclosure size in the tle elow mtches the showertry instlltion. = Widths: 800 Door = 780-805mm 900 Door = 880-905mm Y

More information

0.1 Basic Set Theory and Interval Notation

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

More information

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00

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

More information

Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials

Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic

More information

Introduction. Teacher s lesson notes The notes and examples are useful for new teachers and can form the basis of lesson plans.

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

More information

Clipping & Scan Conversion. CSE167: Computer Graphics Instructor: Steve Rotenberg UCSD, Fall 2005

Clipping & Scan Conversion. CSE167: Computer Graphics Instructor: Steve Rotenberg UCSD, Fall 2005 Clipping & Scn Conersion CSE167: Computer Grphics Instructor: Stee Rotenberg UCSD, Fll 2005 Project 2 Render 3D hnd (mde up of indiidul boxes) using hierrchicl trnsformtions (push/pop) The hnd should perform

More information

CallPilot 100/150 Upgrade Addendum

CallPilot 100/150 Upgrade Addendum CllPilot 100/150 Relese 3.0 Softwre Upgrde Addendum Instlling new softwre onto the CllPilot 100/150 Feture Crtridge CllPilot 100/150 Upgrde Addendum Prerequisites lptop or desktop computer tht cn ccept

More information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information

trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007

trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007 trdemrk nd symbol guidelines trdemrk guidelines The trdemrk Cn be plced in either of the two usul configurtions but horizontl usge is preferble. Wherever possible the trdemrk should be plced on blck bckground.

More information

Data Compression. Lossless And Lossy Compression

Data Compression. Lossless And Lossy Compression Dt Compression Reduce the size of dt. ƒ Reduces storge spce nd hence storge cost. Compression rtio = originl dt size/compressed dt size ƒ Reduces time to retrieve nd trnsmit dt. Lossless And Lossy Compression

More information

Start Here. IMPORTANT: To ensure that the software is installed correctly, do not connect the USB cable until step 17. Remove tape and cardboard

Start 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 information

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES

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

More information

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control Chpter 5 Configurtion of ISDN Protocols This chpter provides instructions for configuring the ISDN protocols in the SP201 for signling conversion. Use the sections tht reflect the softwre you re configuring.

More information

1.2 The Integers and Rational Numbers

1.2 The Integers and Rational Numbers .2. THE INTEGERS AND RATIONAL NUMBERS.2 The Integers n Rtionl Numers The elements of the set of integers: consist of three types of numers: Z {..., 5, 4, 3, 2,, 0,, 2, 3, 4, 5,...} I. The (positive) nturl

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Rotating DC Motors Part II

Rotating DC Motors Part II Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors

More information