doi: /j.issn <J!K LMN PO 7! T IL 18 IL 18BP" IL 18R'0= = 1), 1),M 1),= 1), 1,2)#, 1)# 1) 4 S FG "* AE )S T # SS 2

Size: px
Start display at page:

Download "doi: /j.issn <J!K LMN PO 7! T IL 18 IL 18BP" IL 18R'0= = 1), 1),M 1),= 1), 1,2)#, 1)# 1) 4 S FG "* AE )S T # SS 2"

Transcription

1 doi: /j.issn <J!K LMN PO 7! T IL 18 IL 18BP" IL 18R'0= = 1), 1),M 1),= 1), 1,2)#, 1)# 1) 4 S FG "* AE )S T # SS #$%&':,,1971 5,,!," * + L:? E,E mail:zhanghuiyun2003@126.com;,, ,,! C ',"*+,:?E,E mail:shoahenghe@hotmail.com? $R ;? AB;IL 18;IL 18BP;IL 18R R392.8 ':89? $ R (AR+AS) '? A B IL 18 IL 18BPQ IL 18R E :K 13M AR+AS 'Q 14 ( C ) Y,H A B N 8 9 Y S Q ( Q )? A B IL 18 + IL 18BP + Q IL AX&' ;

2 JournalofZhengzhouUniversity(MedicalSciences) Sept Vol.52 No R + AB MD b(mfi),? (: C,Y S AR+AS '? AB IL 18 + Q IL 18BP + AB M (P=0.001)Q 44.1%(P=0.048),IL 18 + AB MFIab 29.1%(P=0.001),IL 18BP + AB MFI] 32.3%(P<0.001), IL 18R + AB MD MFI S (P>0.05) C AR+AS '? AB IL 18 IL 18BPD IL 18RE (P> 0.05) AR+AS '? AB IL 18 + Q IL 18BP + AB M (r=0.622,p<0.001) ):? AB E IL 18Q IL 18BP Jc AR+AS &H ExpresionsofIL 18,IL 18BPandIL 18Rinbloodeosinophil enriched populationsfrompatientswithalergicrhinitiscomplicatedwithasthma WANGLing 1),HUYalin 1),YANGRuiming 1),WANGJunling 1),ZHANGHuiyun 1,2),HEShaoheng 1) 1)AlergyandClinicalImmunologyResearchCenter,theFirstAfiliatedHospital,JinzhouMedicalUniver sity,jinzhou,liaoning )CentralLaboratory,SuzhouXiangchengPeople'sHospital,Suzhou, Jiangsu Keywords alergicrhinitiscomplicatedwithasthma;eosinophil;il 18;IL 18BP;IL 18R Abstract Aim:ToinvestigateexpressionsofIL 18,IL 18BPandIL 18R inbloodeosinophil enrichedpopulations from patientswithalergicrhinitiscomplicatedwithasthma(ar+as)aswelasthecorelationamongthem.methods: Bloodsampleswerecolectedfrom 13AR+ASpatientsand14healthycontrols.ProportionsandMFIofIL 18 +,IL 18BP + andil 18R + celsinbloodeosinophil enrichedpopulationsfrom 2groupsweredetectedbyflowcytometry.Re sults:comparedwithhealthycontrols,proportionsofil 18 + andil 18BP + celsineosinophil enrichedpopulationsfrom AR+ASpatientswereincreasedby5.821folds(P=0.001)and44.1%(P=0.048)whenculturedwithmedium only, MFIofIL 18 + celsineosinophil enrichedpopulationsfrom AR+ASpatientswasincreasedby29.1%(P=0.001),and MFIofIL 18BP + celswasdecreasedby32.3% (P<0.001);whiletheproportionandMFIofIL 18R + celsdidnot changesignificantly(p>0.05).proportionsofil 18 + andil 18BP + eosinophilswerecorelatedmoderately(r=0.622, P<0.001)ineosinophil enrichedpopulationsfromar+aspatients.conclusion:il 18 + andil 18BP + eosinophilsare likelytoplayakeyroleinar+as. Q? E?E,5' ONcR, a? AB E AB,c?E E &H [1 2] "* [3],L? RF G 0J] Q :,^_? AB E [4], c? A Bc Q &H AB P(inter leukin,il) 18 IL 1 E Z 1 [5] " * [6],IL 18? A B b ` A W IL 8 FGE ;.? 'E L IL 18Q IL 18R) [7] ;G ' IL 18 [8] ;? ' IL 18 [1] IL 18< $ (IL 18 bindingprotein,il 18BP) IL 18EA? 4F, IL [9] ' b C AR+AS '? A B IL 18 IL 18RQ IL 18BP E "* &']^? $R (AR+AS) 'Y S Q? A B IL 18 IL 18R Q IL 18BP ES, S 5'c AR+ASE &H +, 1 * 1.1 F:PE/Cy7 CD14 PerCP CD16 ZombieAquaFixableViabilityKit BV510 4 IgG 4@ FcRJ F AB B P A (BFA) Biolegend(USA),PE IL 18 APC IL 18R R&DSystems(USA), 4 IL 18BP Ab cam(uk), Q * ) + Q _! " # ( ),PBS Solarbio(USA),Cytofix/Cytoperm TM > / F > BD Biosciences Pharmigen (USA),? ALK ABELLO (Denmark), H F \: L (ThermoScientific,USA), (, ),FACSVerse AB\(BDBio sciences,usa)

3 600 ( ) $/> 13M AR+AS ', 11M, 2M, 51(9~61), 38(3~55), 3(0.2~30.0)a;? 9M,? 10M,? 5M ' 14, 3, 11, 26(23~29) "*, 4 I 1 E, ' D! 2 "*C? ARE $ 2015 " #$ B E [10],ASE $ 2015 ^ 0 - (GlobalInitiativefor Asthma,GINA) _ 'Da 2 % H4,Da 1Q A _ E RS "*C K 10mL Y, EDTA4JFEK,HIS 1.3 PO 7! IL 18 IL 18BP/ IL 18R' R ^ 6 BFA Q ( 1.0 mg/l),37 1h;1400r/minL, A B Z : Q FcRJ F,,1 15min, 4 CD14 CD16Q IL 15min A B,L H > / > A B, 4 IL 18Q 4 IL 18BP4@, BV510 4 IgG4@, A B \ 8 9 IL 18 + IL 18BP + Q IL 18R + AB MD b(mfi) 1.4 ]^_`S H SPSS13.0 / H / Kruskal WalisH8 Y S Q 2 "*C? AB IL 18 + IL 18BP + Q IL 18R + A B E M Q MFI E, _ 'H Mann Whitney U H& / AR+AS '? AB IL 18 + IL 18BP + Q IL 18R + AB M* E? 8 α= ( ! T IL 18 + IL 18BP + " IL 18R + cp'c < 1~ 3 C,AR+AS 'Y S? A B IL 18 + A B M 5.821,IL 18BP + A B E M 44.1%,IL 18R + AB M S AR+AS 'Q C? AB IL 18 + IL 18BP + D IL 18R + AB M QRGS/<JTU 7! T IL 18 + 'cp % Y S (2.108,7.938) C (1.372,7.745) (1.833,7.940) (1.521,10.745) Y S (5.770,26.400) AR+AS (7.080,16.400) (6.448,18.000) (7.060,19.000) : C Y S,P= QRGS/<JTU 7! T IL 18BP + 'cp % Y S (17.100,46.900) C (20.150,51.550) (26.600,66.600) (29.900,55.600) Y S (30.300,66.700) AR+AS (31.800,70.000) (20.150,57.225) (20.510,61.900) : C Y S,P= QRGS/<JT U 7! T IL 18R + 'cp % Y S (3.643,8.093) C (4.135,8.395) (3.425,9.010) (4.335,9.110) Y S (3.640,8.770) AR+AS (4.500,11.900) (5.515,8.455) (5.370,12.500) : C Y S,P> ! T IL 18 + IL 18BP + " IL 18R + MFIc < 4~6 C,AR+AS ' Y S? A B IL 18 + A B E MFI 29.1%,IL 18BP + A B E MFI] 32.3%, IL 18R + ABE MFI S :, Q C IL 18BP + ABE MFI]

4 JournalofZhengzhouUniversity(MedicalSciences) Sept Vol.52 No QRGS/<JT U 7! T IL 18 + ' MFI Y S ( , ) C ( , ) ( , ) ( , ) Y S ( , ) AR+AS ( , ) ( , ) ( , ) : C Y S,P= QRGS/<JT U 7! T IL 18BP + ' MFI Y S ( , ) C ( , ) ( , ) ( , ) Y S ( , ) AR+AS ( , ) ( , ) ( , ) : C Y S,P< QRGS/<JT U 7! T IL 18R + ' MFI Y S ( , ) C ( , ) ( , ) ( , ) Y S ( , ) AR+AS ( , ) ( , ) ( , ) : C Y S,P> AR +AS 7! T IL 18 + cp/ IL 18BP + cp' Y S,AR+AS '? AB IL 18BP + Q IL 18 + AB M,r=0.662,P< ;) AR+AS D E R? E _"* [1]? ' IL 18,: ' IL 18 [11],<$ "* AR+AS '? A B IL 18 +?ABE M, c R? E ' IL 18 E J? AB_ IL 18&?AB W,? AB b`a W IL 8 [6] FGE [12] ; E IL 18!? IgE Z,R Th2A B W IL 4 IL 5Q IL 13 E ;IL 18? E E [13 14] IL 18$ AB FE IL 18R 'D. 0 J " * [15] G 'L? ABa R _ IL 18R a _"* [16] OVA. V IL 18 A B IL 18R,; "* C,AR+AS '? AB IL 18 +?ABE M,? AB IL 18R +? A B E M C, R, c? AB E IL 18 J$ E ABQ? AB FE IL 18Rc AR+AS "* IL 18BP IL 18E A? 4 F [9], IL 18< $ ] E? ; " * AR+AS ' IL 18BP +? ABE M C, I IL 18E ; O AR+AS '? A B IL 18 + A B MFIa b,il 18BP + A B MFI], c IL 18Q IL 18BP * E J AR+AS, AR+ASE01 :,"* AR+AS '? A B IL 18 +?AB M Q IL 18BP +? A B M (r=0.662), c E IL 18? AB$Z IL 18BP -,? AB E IL 18Q IL 18BP Jc AR+AS &H [1] LUCASCD,DORWARD DA,SHARMA S,etal.Wogonin induceseosinophilapoptosisandatenuatesalergicairway inflammation[j].am JRespirCritCareMed,2015,191 (6):626 [2] GANGWARRS,FRIEDMANS,SEAFM.Mastcelsande osinophilsinalergy:closefriendsorjustneighbors[j]. EurJPharmacol,2016,778:77 [3] FULKERSON PC,ROTHENBERG ME.Targetingeosino philsinalergy,inflammationandbeyond[j].natrev DrugDiscov,2013,12(2):117

5 602 ( ) [4] EL SHAZLY AE,RONCARATIP,LEJEUNE M,etal. Tyrosinekinaseinhibitionisanimportantfactorforgene expressionofcrth2inhumaneosinophilsandlympho cytes:a novelmechanism forexplainingeosinophilsre cruitmentbytheneuro immuneaxisinalergicrhinitis[j]. IntImmunopharmacol,2017,45:180 [5] KAWAYAMA T,OKAMOTO M,IMAOKA H,etal.Inter leukin 18inpulmonaryinflammatorydiseases[J].JInter feroncytokineres,2012,32(10):443 [6] WANG W,TANAKA T,OKAMURA H,etal.Interleukin 18enhancestheproductionofinterleukin 8byeosinophils [J].EurJImmunol,2001,31(4):1010 [7] XU D,CHAN WL,LEUNG BP,etal.Selectiveexpression andfunctionsofinterleukin18receptoronthelper(th) type1butnotth2cels[j].jexpmed,1998,188(8): 1485 [8] SIMSJE,SMITHDE.TheIL 1family:regulatorsofimmu nity[j].natrevimmunol,2010,10(2):89 [9] SAWADAM,KAWAYAMAT,IMAOKAH,etal.IL 18in ducesairwayhyperesponsivenessandpulmonaryinflamma tionviacd4 + TcelandIL 13[J].PLoSOne,2013,8 (1):e54623 [10]SEIDMANMD,GURGELRK,LINSY,etal.Clinicalprac ticeguideline: alergicrhinitisexecutivesummary[j]. OtolaryngolHeadNeckSurg,2015,152(2):197 [11]BLOM L,POULSEN LK.IL 1familymembersIL 18and IL 33upregulatetheinflammatorypotentialofdiferentiated humanth1andth2cultures[j].jimmunol,2012,189 (9):4331 [12]PORTER LM,COWBURN AS,FARAHIN,etal.Hypoxia causesil 8secretion,CharcotLeydencrystalformation, andsuppressionofcorticosteroid inducedapoptosisinhu maneosinophils[j].clinexpalergy,2017,47(6):770 [13]DINARELLOCA,NOVICKD,KIM S,etal.Interleukin 18 andil 18bindingprotein[J].FrontImmunol,2013,4:289 [14]SANDERSNL,MISHRA A.Roleofinterleukin 18inthe pathophysiologyofalergicdiseases[j].cytokinegrowth FactorRev,2016,32:31 [15]WANG J,ZHANG H,ZHENG W,etal.CorelationofIL 18withtryptaseinatopicasthmaandinductionofmastcel accumulation by IL 18[J].Mediators Inflamm,2016, 2016: [16]VERHAEGHE B,GEVAERTP,HOLTAPPELSG,etal. Up regulationofil 18 in alergicrhinitis[j].alergy, 2002,57(9):825 ( >?@)

Expanding brackets and factorising

Expanding brackets and factorising CHAPTER 8 Epanding brackets and factorising 8 CHAPTER Epanding brackets and factorising 8.1 Epanding brackets There are three rows. Each row has n students. The number of students is 3 n 3n. Two students

More information

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3 - - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f

More information

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

More information

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 2. Let ABCD be a cyclic quadrilateral inscribed in a circle

More information

trawhmmry ffimmf,f;wnt

trawhmmry ffimmf,f;wnt r nsr rwry fff,f;wn My 26, $51 Swe, k "Te Srwberry Cp f e Vr,, c) [ re ers 6 (, r " * f rn ff e # s S,r,* )er*,3n*,.\ ) x 8 2 n v c e 6 r D r, } e ;s 1 :n..< Z r : 66 3 X f; 1r_ X r { j r Z r 1r 3r B s

More information

MEP Pupil Text 13-19, Additional Material. Gradients of Perpendicular Lines

MEP Pupil Text 13-19, Additional Material. Gradients of Perpendicular Lines Graphs MEP Pupil Text -9, Additional Material.B Gradients of Perpendicular Lines In this section we explore the relationship between the gradients of perpendicular lines and line segments. Worked Example

More information

Algebraic Expressions

Algebraic Expressions Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly

More information

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths 1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles

More information

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between

More information

CCE PR Revised & Un-Revised

CCE PR Revised & Un-Revised D CCE PR Revised & Un-Revised 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 08 S.S.L.C. EXAMINATION, JUNE, 08 :. 06. 08 ] MODEL ANSWERS : 8-K Date :. 06. 08 ] CODE

More information

A B CDE F B FD D A C AF DC A F

A B CDE F B FD D A C AF DC A F International Journal of Arts & Sciences, CD-ROM. ISSN: 1944-6934 :: 4(20):121 131 (2011) Copyright c 2011 by InternationalJournal.org A B CDE F B FD D A C A BC D EF C CE C A D ABC DEF B B C A E E C A

More information

Implementation of erythroid lineage analysis by flow cytometry in diagnostic models for myelodysplastic syndromes

Implementation of erythroid lineage analysis by flow cytometry in diagnostic models for myelodysplastic syndromes Publishe Ahea of Print on September 22, 2016, as oi:10.3324/haematol.2016.147843. Copyright 2016 Ferrata Storti Founation. Implementation of erythroi lineage analysis by flow cytometry in iagnostic moels

More information

Advanced Digital Design with the Verilog HDL, Second Edition Michael D. Ciletti Prentice Hall, Pearson Education, 2011

Advanced Digital Design with the Verilog HDL, Second Edition Michael D. Ciletti Prentice Hall, Pearson Education, 2011 Problem 2-1 Recall that a minterm is a cube in which every variable appears. A Boolean expression in SOP form is canonical if every cube in the expression has a unique representation in which all of the

More information

COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use

COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE I. Length of a Line Segment: The distance between two points A ( x1, 1 ) B ( x, ) is given b A B = ( x x1) ( 1) To find the length of a line segment joining

More information

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES Mathematics SKE, Strand J STRAND J: TRANSFORMATIONS, VECTORS and MATRICES J4 Matrices Text Contents * * * * Section J4. Matrices: Addition and Subtraction J4.2 Matrices: Multiplication J4.3 Inverse Matrices:

More information

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ

More information

Properties of Isosceles and Equilateral Triangles

Properties of Isosceles and Equilateral Triangles Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg

More information

Hanoi Open Mathematical Olympiad

Hanoi Open Mathematical Olympiad HEXAGON inspiring minds always Let x = 6+2 + Hanoi Mathematical Olympiad 202 6 2 Senior Section 20 Find the value of + x x 7 202 2 Arrange the numbers p = 2 2, q =, t = 2 + 2 in increasing order Let ABCD

More information

Created by T. Madas 2D VECTORS. Created by T. Madas

Created by T. Madas 2D VECTORS. Created by T. Madas 2D VECTORS Question 1 (**) Relative to a fixed origin O, the point A has coordinates ( 2, 3). The point B is such so that AB = 3i 7j, where i and j are mutually perpendicular unit vectors lying on the

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

Class IX : Math Chapter 11: Geometric Constructions Top Concepts 1. To construct an angle equal to a given angle. Given : Any POQ and a point A.

Class IX : Math Chapter 11: Geometric Constructions Top Concepts 1. To construct an angle equal to a given angle. Given : Any POQ and a point A. 1 Class IX : Math Chapter 11: Geometric Constructions Top Concepts 1. To construct an angle equal to a given angle. Given : Any POQ and a point A. Required : To construct an angle at A equal to POQ. 1.

More information

Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.

Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line

More information

1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?

1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? 1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined

More information

Day 31 Bellringer. (a) 2 and 7. (b) 3 and 7. (c) 3 and 6. Page 1

Day 31 Bellringer. (a) 2 and 7. (b) 3 and 7. (c) 3 and 6. Page 1 Day 31 Bellringer 1. In the figure below lines PQ and RS are parallel. State whether the following angles are corresponding, alternate interior or alternate exterior angles. P R 1 2 3 4 5 6 7 8 Q S (a)

More information

PYTHAGORAS THEOREM PYTHAGORAS THEOREM IN A RIGHT ANGLED TRIANGLE, THE SQUARE ON HYPOTENUSE IS EQUAL TO SUM OF SQUARES ON OTHER TWO SIDES

PYTHAGORAS THEOREM PYTHAGORAS THEOREM IN A RIGHT ANGLED TRIANGLE, THE SQUARE ON HYPOTENUSE IS EQUAL TO SUM OF SQUARES ON OTHER TWO SIDES PYTHAGORAS THEOREM PYTHAGORAS THEOREM IN A RIGHT ANGLED TRIANGLE, THE SQUARE ON HYPOTENUSE IS EQUAL TO SUM OF SQUARES ON OTHER TWO SIDES EXERCISE 2.1 *THE SIDES OF A RIGHT ANGLED TRIANGLE CONTAINING THE

More information

UNIT-8 SIMILAR TRIANGLES Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. 1. ABC is a right-angled triangle, right-angled

More information

Solutions I.N. Herstein- Second Edition

Solutions I.N. Herstein- Second Edition Solutions I.N. Herstein- Second Edition Sadiah Zahoor 25, July 2016 Please email me if any corrections at sadiahzahoor@cantab.net. Problem 0.1. In the following determine whether the systems described

More information

Chapter 10. Properties of Circles

Chapter 10. Properties of Circles Chapter 10 Properties of Circles 10.1 Use Properties of Tangents Objective: Use properties of a tangent to a circle. Essential Question: how can you verify that a segment is tangent to a circle? Terminology:

More information

Geometry Chapter 3 & 4 Test

Geometry Chapter 3 & 4 Test Class: Date: Geometry Chapter 3 & 4 Test Use the diagram to find the following. 1. What are three pairs of corresponding angles? A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 8 & 6, and 2 & 4 B. angles

More information

Solution Of Class 10 th CBSE SA-II Board (Set-1)Mathematics

Solution Of Class 10 th CBSE SA-II Board (Set-1)Mathematics L.K. Gupta (Mathematic Classes) www.poineermathematics.com. MOBILE: 98155771, 461771 Solution Of Class 10 th CBSE SA-II Board (Set-1)Mathematics 1. (k 1) k = (k + 1) (k 1) k 1 k = k + 1 k + 1 k 1 = k.

More information

Properties of Quadrilaterals

Properties of Quadrilaterals Properties of Quadrilaterals 1 Proving Properties of Parallelograms Given: ABC is a parallelogram Prove: AB C and A BC A B C Statements Reasons 1. 1. Given 2. AB C and A BC 2. 3. AB CB and CB AB 3. 4.

More information

Collinearity/Concurrence

Collinearity/Concurrence Collinearity/Concurrence Ray Li (rayyli@stanford.edu) June 29, 2017 1 Introduction/Facts you should know 1. (Cevian Triangle) Let ABC be a triangle and P be a point. Let lines AP, BP, CP meet lines BC,

More information

G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2

G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2 Regents Exam Questions www.jmap.org Name: 1 In square GEOM, the coordinates of G are (2, 2) and the coordinates of O are ( 4,2). Determine and state the coordinates of vertices E and M. [The use of the

More information

CHAPTER 5 : THE STRAIGHT LINE

CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 CHAPTER 5 : THE STRAIGHT LINE 1. In the diagram, PQ is a straight line. P 4 2 4 3 2 1 0 1 2 2 2. Find (a) the -intercept, (b) the gradient, of the straight line. Q (5,18) Q Answer :a).. b) 3

More information

Maharashtra State Board Class IX Mathematics Geometry Board Paper 1 Solution

Maharashtra State Board Class IX Mathematics Geometry Board Paper 1 Solution Maharashtra State Board Class IX Mathematics Geometry Board Paper Solution Time: hours Total Marks: 40. i. Let the measure of each interior opposite angle be x. Since, Sum of two interior opposite angles

More information

Mathematics. Exercise 9.3. (Chapter 9) (Sequences and Series) Question 1: Find the 20 th and n th terms of the G.P. Answer 1:

Mathematics. Exercise 9.3. (Chapter 9) (Sequences and Series) Question 1: Find the 20 th and n th terms of the G.P. Answer 1: ( : A step towards free education) Exercise 9.3 Question 1: Find the 20 th and n th terms of the G.P. Answer 1: The given G.P. is Here, a = First term = r = Common ratio = Question 2: Find the 12 th term

More information

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here

More information

Matrix Algebra. Learning Objectives. Size of Matrix

Matrix Algebra. Learning Objectives. Size of Matrix Matrix Algebra 1 Learning Objectives 1. Find the sum and difference of two matrices 2. Find scalar multiples of a matrix 3. Find the product of two matrices 4. Find the inverse of a matrix 5. Solve a system

More information

Homework 3/ Solutions

Homework 3/ Solutions MTH 310-3 Abstract Algebra I and Number Theory S17 Homework 3/ Solutions Exercise 1. Prove the following Theorem: Theorem Let R and S be rings. Define an addition and multiplication on R S by for all r,

More information

Geometry Facts Circles & Cyclic Quadrilaterals

Geometry Facts Circles & Cyclic Quadrilaterals Geometry Facts Circles & Cyclic Quadrilaterals Circles, chords, secants and tangents combine to give us many relationships that are useful in solving problems. Power of a Point Theorem: The simplest of

More information

Narayana IIT Academy

Narayana IIT Academy INDIA Sec: Sr. IIT_IZ Jee-Advanced Date: 8--7 Time: 9: AM to : Noon 5_P MDEL Max.Marks:64 KEY SHEET PHYSICS 3 3 5 4 9 5 8 6 5 7 9 8 4 9 ABC ACD BD BC 3 ABD 4 BC 5 BCD 6 ABC 7 ABC 8 CD 9 A-PRST B-PST C-PRS

More information

Republic of tlre Ph?lippines OEPARTMENT OF EDUCATION

Republic of tlre Ph?lippines OEPARTMENT OF EDUCATION Repb re Ph?ppnes OPARTMT O DATO Ren V& AABARZO w ss Ds ABYA TORADT TO: ROM SBT: DAT Asssn Shs Dsn Speenen O he Sr emne n Operns Dbn O he nr:m mpemenn Dsbn Pb n Pre emenry, Senry n Senr h Sr es Ahers neme

More information

chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true? chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "

More information

1 / 23

1 / 23 CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper

More information

Geometry CP Semester 1 Review Packet. answers_december_2012.pdf

Geometry CP Semester 1 Review Packet.  answers_december_2012.pdf Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: http://www.hfhighschool.org/assets/1/7/sem_1_review_packet

More information

I N A C O M P L E X W O R L D

I N A C O M P L E X W O R L D IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e

More information

8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ. 8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral

More information

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation

More information

1. (a) q = 4, r = 1. (b) q = 0, r = 0. (c) q = 5, r = (a) q = 9, r = 3. (b) q = 15, r = 17. (c) q = 117, r = 11.

1. (a) q = 4, r = 1. (b) q = 0, r = 0. (c) q = 5, r = (a) q = 9, r = 3. (b) q = 15, r = 17. (c) q = 117, r = 11. 000 Chapter 1 Arithmetic in 1.1 The Division Algorithm Revisited 1. (a) q = 4, r = 1. (b) q = 0, r = 0. (c) q = 5, r = 3. 2. (a) q = 9, r = 3. (b) q = 15, r = 17. (c) q = 117, r = 11. 3. (a) q = 6, r =

More information

CHEM 108 (Spring-2008) Exam. 3 (105 pts)

CHEM 108 (Spring-2008) Exam. 3 (105 pts) CHEM 08 (Spring-008) Exam. (05 pts) Name: --------------------------------------------------------------------------, CLID # -------------------------------- LAST NAME, First (Circle the alphabet segment

More information

1 / 24

1 / 24 CBSE-XII-017 EXAMINATION CBSE-X-01 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instuctions : 1. All questions are compulsory.. The question paper consists of 34 questions

More information

Coordinate Geometry. Exercise 13.1

Coordinate Geometry. Exercise 13.1 3 Exercise 3. Question. Find the distance between the following pairs of points (i) ( 3) ( ) (ii) ( 5 7) ( 3) (iii) (a b) ( a b) Solution (i) Let A( 3 ) and B( ) be the given points. Here x y 3and x y

More information

Example. Addition, subtraction, and multiplication in Z are binary operations; division in Z is not ( Z).

Example. Addition, subtraction, and multiplication in Z are binary operations; division in Z is not ( Z). CHAPTER 2 Groups Definition (Binary Operation). Let G be a set. A binary operation on G is a function that assigns each ordered pair of elements of G an element of G. Note. This condition of assigning

More information

Objective Mathematics

Objective Mathematics Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is

More information

Subject : MATHEMATICS

Subject : MATHEMATICS CCE RF 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 05 S. S. L. C. EXAMINATION, MARCH/APRIL, 05 : 06. 04. 05 ] MODEL ANSWERS : 8-E Date : 06. 04. 05 ] CODE NO.

More information

Angles of Elevation and Depression

Angles of Elevation and Depression Angles of Elevation and Depression Study the following figure carefully. angle of elevation angle of depression When we see an object above us, the angle between our line of sight and the horizontal is

More information

page 1 Total ( )

page 1 Total ( ) A B C D E F Costs budget of [Claimant / Defendant] dated [ ] Estimated page 1 Work done / to be done Pre-action Disbs ( ) Time ( ) Disbs ( ) Time ( ) Total ( ) 1 Issue /statements of case 0.00 0.00 CMC

More information

Advanced Placement. Chemistry. Integrated Rates

Advanced Placement. Chemistry. Integrated Rates Advanced Placement Chemistry Integrated Rates 204 47.90 9.22 78.49 (26) 50.94 92.9 80.95 (262) 52.00 93.94 83.85 (263) 54.938 (98) 86.2 (262) 55.85 0. 90.2 (265) 58.93 02.9 92.2 (266) H Li Na K Rb Cs Fr

More information

Pre-Regional Mathematical Olympiad Solution 2017

Pre-Regional Mathematical Olympiad Solution 2017 Pre-Regional Mathematical Olympiad Solution 07 Time:.5 hours. Maximum Marks: 50 [Each Question carries 5 marks]. How many positive integers less than 000 have the property that the sum of the digits of

More information

1. (a) q = 4, r = 1. (b) q = 0, r = 0. (c) q = 5, r = (a) q = 9, r = 3. (b) q = 15, r = 17. (c) q = 117, r = 11.

1. (a) q = 4, r = 1. (b) q = 0, r = 0. (c) q = 5, r = (a) q = 9, r = 3. (b) q = 15, r = 17. (c) q = 117, r = 11. 000 Chapter 1 Arithmetic in 1.1 The Division Algorithm Revisited 1. (a) q = 4, r = 1. (b) q = 0, r = 0. (c) q = 5, r = 3. 2. (a) q = 9, r = 3. (b) q = 15, r = 17. (c) q = 117, r = 11. 3. (a) q = 6, r =

More information

Solutions. S1. Ans.(c) Sol. Try Using option and divide With given option

Solutions. S1. Ans.(c) Sol. Try Using option and divide With given option Solutions S1. Ans.(c) Try Using option and divide 64329 With given option S2. Ans.(a) Let the fraction be x/y. According to the questions, x y of 4 7 + 4 7 = 15 14 x y 4 7 + 4 7 = 15 14 x y 4 7 = 1 2 x

More information

SUMMATIVE ASSESSMENT I, IX / Class IX

SUMMATIVE ASSESSMENT I, IX / Class IX I, 0 SUMMATIVE ASSESSMENT I, 0 0 MATHEMATICS / MATHEMATICS MATHEMATICS CLASS CLASS - IX - IX IX / Class IX MA-0 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 8 6 0 0 (iii) 8 (iv) (v) General Instructions:

More information

Created by T. Madas MIXED SURD QUESTIONS. Created by T. Madas

Created by T. Madas MIXED SURD QUESTIONS. Created by T. Madas MIXED SURD QUESTIONS Question 1 (**) Write each of the following expressions a single simplified surd a) 150 54 b) 21 7 C1A, 2 6, 3 7 Question 2 (**) Write each of the following surd expressions as simple

More information

Faculty of Natural and Agricultural Sciences Chemistry Department. Semester Test 1. Analytical Chemistry CMY 283. Time: 120 min Marks: 100 Pages: 6

Faculty of Natural and Agricultural Sciences Chemistry Department. Semester Test 1. Analytical Chemistry CMY 283. Time: 120 min Marks: 100 Pages: 6 Faculty of Natural and Agricultural Sciences Chemistry Department Semester Test 1 Analytical Chemistry CMY 283 Date: 5 September 2016 Lecturers : Prof P Forbes, Dr Laurens, Mr SA Nsibande Time: 120 min

More information

Chapter 3: Stoichiometry

Chapter 3: Stoichiometry Chapter 3: Stoichiometry Chem 6A Michael J. Sailor, UC San Diego 1 Announcements: Thursday (Sep 29) quiz: Bring student ID or we cannot accept your quiz! No notes, no calculators Covers chapters 1 and

More information

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39 NAME: Date: HOMEWORK: C1 Question Obtained 1 2 3 4 5 6 7 8 9 10 Total/100 A 80 B 70 C 60 D 50 E 40 U 39 1. Figure 2 y A(1, 7) B(20, 7) D(8, 2) O x C(p, q) The points A(1, 7), B(20, 7) and C(p, q) form

More information

Math 4377/6308 Advanced Linear Algebra

Math 4377/6308 Advanced Linear Algebra 2.3 Composition Math 4377/6308 Advanced Linear Algebra 2.3 Composition of Linear Transformations Jiwen He Department of Mathematics, University of Houston jiwenhe@math.uh.edu math.uh.edu/ jiwenhe/math4377

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

AREAS OF PARALLELOGRAMS AND TRIANGLES

AREAS OF PARALLELOGRAMS AND TRIANGLES AREAS OF PARALLELOGRAMS AND TRIANGLES Main Concepts and Results: The area of a closed plane figure is the measure of the region inside the figure: Fig.1 The shaded parts (Fig.1) represent the regions whose

More information

Anycast Latency How many sites are enough?

Anycast Latency How many sites are enough? Anycast atency How many sites are enough? Presented by Ricardo de Oliveira Schmidt October 25, 2016 Madrid, Spain Presentation copyright 2016 by Ricardo de Oliveira Schmidt Reference: Anycast atency: How

More information

Problems and Solutions

Problems and Solutions 46 th Canadian Mathematical Olympiad Wednesday, April 2, 204 Problems and Solutions. Let a, a 2,..., a n be positive real numbers whose product is. Show that the sum a a 2 + + a ( + a )( + a 2 ) + a 3

More information

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION. Sunday, March 14, 2004 Time: hours No aids or calculators permitted.

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION. Sunday, March 14, 2004 Time: hours No aids or calculators permitted. THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION Sunday, March 1, Time: 3 1 hours No aids or calculators permitted. 1. Prove that, for any complex numbers z and w, ( z + w z z + w w z +

More information

Circle the letters only. NO ANSWERS in the Columns!

Circle the letters only. NO ANSWERS in the Columns! Chemistry 1304.001 Name (please print) Exam 5 (100 points) April 18, 2018 On my honor, I have neither given nor received unauthorized aid on this exam. Signed Date Circle the letters only. NO ANSWERS in

More information

LINEAR SYSTEMS AND MATRICES

LINEAR SYSTEMS AND MATRICES CHAPTER 3 LINEAR SYSTEMS AND MATRICES SECTION 3. INTRODUCTION TO LINEAR SYSTEMS This initial section takes account of the fact that some students remember only hazily the method of elimination for and

More information

COMPOSITIO MATHEMATICA

COMPOSITIO MATHEMATICA COMPOSITIO MATHEMATICA OSWALD WYLER Order in projective and in descriptive geometry Compositio Mathematica, tome 11 (1953), p. 60-70 Foundation Compositio

More information

Udaan School Of Mathematics Class X Chapter 10 Circles Maths

Udaan School Of Mathematics Class X Chapter 10 Circles Maths Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in

More information

7.2. Matrix Multiplication. Introduction. Prerequisites. Learning Outcomes

7.2. Matrix Multiplication. Introduction. Prerequisites. Learning Outcomes Matrix Multiplication 7.2 Introduction When we wish to multiply matrices together we have to ensure that the operation is possible - and this is not always so. Also, unlike number arithmetic and algebra,

More information

SOLVED PROBLEMS. 1. The angle between two lines whose direction cosines are given by the equation l + m + n = 0, l 2 + m 2 + n 2 = 0 is

SOLVED PROBLEMS. 1. The angle between two lines whose direction cosines are given by the equation l + m + n = 0, l 2 + m 2 + n 2 = 0 is SOLVED PROBLEMS OBJECTIVE 1. The angle between two lines whose direction cosines are given by the equation l + m + n = 0, l 2 + m 2 + n 2 = 0 is (A) π/3 (B) 2π/3 (C) π/4 (D) None of these hb : Eliminating

More information

Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1

Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1 Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1 1 Triangles: Basics This section will cover all the basic properties you need to know about triangles and the important points of a triangle.

More information

ANSWER KEY & SOLUTIONS

ANSWER KEY & SOLUTIONS PRE-HALFYEARLY ASSESSMENT- [P-H-A MATHS SYLLABUS] ANSWER KEY & SOLUTIONS General Instructions:. The question paper comprises of four sections, A, B, C & D.. All questions are compulsory. 3. Section A Q

More information

5. Introduction to Euclid s Geometry

5. Introduction to Euclid s Geometry 5. Introduction to Euclid s Geometry Multiple Choice Questions CBSE TREND SETTER PAPER _ 0 EXERCISE 5.. If the point P lies in between M and N and C is mid-point of MP, then : (A) MC + PN = MN (B) MP +

More information

CBSE MATHEMATICS (SET-2)_2019

CBSE MATHEMATICS (SET-2)_2019 CBSE 09 MATHEMATICS (SET-) (Solutions). OC AB (AB is tangent to the smaller circle) In OBC a b CB CB a b CB a b AB CB (Perpendicular from the centre bisects the chord) AB a b. In PQS PQ 4 (By Pythagoras

More information

8. Relax and do well.

8. Relax and do well. CHEM 1225 Exam III John III. Gelder April 8, 1999 Name TA's Name Lab Section INSTRUCTIONS: 1. This examination consists of a total of 7 different pages. The last two pages includes a periodic table and

More information

FINAL EXAM April 26, 2004

FINAL EXAM April 26, 2004 CM 1045 (11:15 am Lecture) Dr. Light FINAL EXAM April 26, 2004 Name (please print) Check your recitation section: Sec. 21 5:30-6:20 pm (Popovic) Sec. 24 3:30-4:20 pm (Giunta) Sec. 22 6:30-7:20 pm (Popovic)

More information

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 FOR HALF YEARLY EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX Chapter VSA (1 mark) SA I (2 marks) SA

More information

11. Prove that the Missing Strip Plane is an. 12. Prove the above proposition.

11. Prove that the Missing Strip Plane is an. 12. Prove the above proposition. 10 Pasch Geometries Definition (Pasch s Postulate (PP)) A metric geometry satisfies Pasch s Postulate (PP) if for any line l, any triangle ABC, and any point D l such that A D B, then either l AC or l

More information

Chapter. Algebra techniques. Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations.

Chapter. Algebra techniques. Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations. Chapter 2 Algebra techniques Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations. Page 1 2.1 What is algebra? In order to extend the usefulness of mathematical

More information

: t,.: -aa:.a. ). tt. 1. :...: :.- .AL. q" ul. ,.:sfilis$llx,i^4iir$irini: :ti. ) :;ti: i;: : : :,::;:., 1'1 ll, il:i ii I{OTARASTII:

: t,.: -aa:.a. ). tt. 1. :...: :.- .AL. q ul. ,.:sfilis$llx,i^4iir$irini: :ti. ) :;ti: i;: : : :,::;:., 1'1 ll, il:i ii I{OTARASTII: ,... ).. 1..... ".A,.X,^4 ),., 1'1, AD {AA ] AA { D ARA A ATARR HTARAR pv pb B V h p 217 A ( ' A S.. AAS S.A.. p v 29.11.217 S A.,,S SA, b pv A v.3199 pb ",, pz pz97.13 % p. Av v. 294115.11.211 S AABS

More information

Math 308 Practice Final Exam Page and vector y =

Math 308 Practice Final Exam Page and vector y = Math 308 Practice Final Exam Page Problem : Solving a linear equation 2 0 2 5 Given matrix A = 3 7 0 0 and vector y = 8. 4 0 0 9 (a) Solve Ax = y (if the equation is consistent) and write the general solution

More information

Homework 1/Solutions. Graded Exercises

Homework 1/Solutions. Graded Exercises MTH 310-3 Abstract Algebra I and Number Theory S18 Homework 1/Solutions Graded Exercises Exercise 1. Below are parts of the addition table and parts of the multiplication table of a ring. Complete both

More information

(Chapter 10) (Practical Geometry) (Class VII) Question 1: Exercise 10.1 Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only. Answer 1: To

More information

review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17

review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17 1. Revision Recall basic terms of algebraic expressions like Variable, Constant, Term, Coefficient, Polynomial etc. The coefficients of the terms in 4x 2 5xy + 6y 2 are Coefficient of 4x 2 is 4 Coefficient

More information

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism Periodic Properties Atomic & Ionic Radius Energy Electron Affinity We want to understand the variations in these properties in terms of electron configurations. The Periodic Table Elements in a column

More information

PERIODIC TABLE OF THE ELEMENTS

PERIODIC TABLE OF THE ELEMENTS Useful Constants and equations: K = o C + 273 Avogadro's number = 6.022 x 10 23 d = density = mass/volume R H = 2.178 x 10-18 J c = E = h = hc/ h = 6.626 x 10-34 J s c = 2.998 x 10 8 m/s E n = -R H Z 2

More information

Summary Slides for MATH 342 June 25, 2018

Summary Slides for MATH 342 June 25, 2018 Summary Slides for MATH 342 June 25, 2018 Summary slides based on Elementary Number Theory and its applications by Kenneth Rosen and The Theory of Numbers by Ivan Niven, Herbert Zuckerman, and Hugh Montgomery.

More information

CHAPTER 7. Solutions for Exercises

CHAPTER 7. Solutions for Exercises CHAPTER 7 Solutions for Exercises E7.1 (a) For the whole part we have: Quotient Remainders 23/2 11 1 11/2 5 1 5/2 2 1 2/2 1 0 1/2 0 1 Reading the remainders in reverse order we obtain: 23 10 = 10111 2

More information

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)

More information

Faculty of Natural and Agricultural Sciences Chemistry Department. Semester Test 1 MEMO. Analytical Chemistry CMY 283

Faculty of Natural and Agricultural Sciences Chemistry Department. Semester Test 1 MEMO. Analytical Chemistry CMY 283 Faculty of Natural and Agricultural Sciences Chemistry Department Semester Test 1 MEMO Analytical Chemistry CMY 283 Date: 5 September 2016 Lecturers : Prof P Forbes, Dr Laurens, Mr SA Nsibande Time: 90

More information