/ 25 - :,,,

Size: px
Start display at page:

Download "/ 25 - :,,,"

Transcription

1 - 2011

2 / 25 - :,,,

3

4 PLANIX

5

6 6

7 - ; 7

8

9 - - 9

10 . 10

11 11

12 1 :

13

14 167,0, 150,1, 150,3, , ,. 14

15 . (8) - 7) 15

16 16

17 l, (1) L ; l L. 17

18 ). 18

19 1.1. h. 1 l 4 1, M L t = M (1) l L H H h 7 (2) º43' 20" 18º 10' 56" º 44' 27" 18º 12' 18" º 43' 58" 18º 12' 50" º43''20" 18º 10' 56" max º 31.5º 31º º 166º 165.5º º 71.º 71.5º = ; + ; ; = -. 1º -1 19

20 1:25 000, h = 5 d h i h d, d i d i i 1: : max =. 275 cd

21 ( - 21

22 . 2 N, N, N ).. 22

23 N N N r + ; (2) = +. (3) = +. (4) (5) 23

24 , 1:2 000? - r AB r AB ; rab 1 24

25 . h d. h, H H h, (6) B, d l. 25

26 160 d l B 150. l h h (7) d 3.. h 26

27 , d h d. (8) i d h h i tg =, (9) d. d =

28 , ( h d., (10) i. h i

29 a1, 12,23, 3r, a, r, t, b ab». u udmu q, u t u udmu. 29

30 ( 1, 2, ).,. 9, 1, 2. 30

31

32 (. 6-4 ). ( -. 32

33 . - - M (). 33

34 1: , 1: , 1: , 1: : , 2, 3,

35 . 1:50000, 1:25000, 1: , 2,..., (70). -87-(

36 2 (

37 36º00' 35º40' 35º20' 35º00' 34º40' 34º00' 33º00' 30º00' 31º00' 32º00' 33º00' 34º00' 36º00' 36º00' V 24 35º40' 35º20' 35º00' 34º40' 35º00' 35º30' 34º00' 33º00' 1: : : : : V º00' º00' 30º00' 31º00' 32º00' 33º00' 34º00' 35º00' 35º30' 36º00' =_35º35'35" ; = 35º35'35" º20' 35º15' 35º17'30" 35º10' 35º00' º17'30" 35º15' 35º10' 1: : : : º00' 35º30' 35º33'45" 35º37'30" 35º45' 36º00'

38 º30'00" 85º11'15" 49º30'00" 85º15'00" 49º27'30" 85º15'00" 49º27'30" 85º11'15"

39 , , 2,, 16, : , 1:2000, 1:1000, 39

40 ); 1:200. (2 2 S. 40

41 N 1 N 2 S S ( N 1 N2 ) (11) 1:100) l 1, l 2,, l, S a l l... l ), (12) ( 1 2 n l 1 l 1 ll 33 1:100. l 7 l 5 l 9 l n 41

42 - ; (13) ; 2 (14) (15) S ABC = p( pa)( pb)( p c). (16) , 1 1 S S 1 1 S ( ) ( ), 2 ( ) ( ) 1, (17) 2 ( ) ( ). 2 S S S 1 1 S 1 1. (18)

43 0. n ( ) i i 1 i 1 i1 S 2, (19) n ( ) i i1 i 1 i1 S 2, (20)

44 5 3,

45 ( ) S S ( n n ), (21) o S ) S0. (22) ( n n0 ). 45

46 . 0 r = n-n 0 r ( r r 1 2 ) r S0 r PLANIX 5. PLANIX 5 ( HOLD HOLD. MEMO ND. Batt 46

47 PLANIX 5 E ND cm 2 2 cm 2 = in 2. in 2 2 cm 2 = in. 2 C C

48 : START «0». HOLD END AVER END AVER. ONCE-C OFF - READI READI cm 2 READI in 2 READI cm 2 = in

49 cm 2 = in 2, cm 2 = in 2 READI READI cm 2 in 2. READI START «0».,. END AVER END «0».. ONCE-C «0». END, ). PLANIX 5 49

50 . PLANIX Start 0 READY 63.7 cm 2 END MEMO 0 READY MEMO 64.0 cm 2 END MEMO 0 READY MEMO 63.8 cm 2 END MEMO 0 READY MEMO 64 cm 2 END MEMO 0 READY MEMO 63.9 cm 2 END MEMO 0 READY MEMO 64.1 cm 2 AVER 63.9 READY cm 2 Start 0 READY 40.6 cm 2 END MEMO 0 READY MEMO 40.5 cm 2 END MEMO 0 READY MEMO 40.4 cm 2 END MEMO 0 READY MEMO 40.6 cm 2 AVER READY cm

51 51

52 n S n a a i 1 = (250 2 ; S ; S 2 2 ( ) = ; S 2. n Y n -1 - n+1 Y n+1 -Y n-1 (Y n+1 -Y n-1 ) Y n -1 - n+1)

53 ... S = r = n-n 0 r ( r r 1 2 ) r. S r S a n l i s 1 l i n ls 1 = = = S a n l s 1 =

54

55

56 r 14. 0, 1:2 000, 1:5 000? 56

57 57

58 58

59 :1000, 1: :2000; 1:1000; 1:

60

GCSE (9-1) Grade 6. Circle Theorems 2

GCSE (9-1) Grade 6. Circle Theorems 2 Name:.. Total Marks: GCSE (9-1) Grade 6 Circle Theorems 2 Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name. Answer all questions. Answer the questions

More information

LLT Education Services

LLT Education Services 8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the

More information

Kevin James. MTHSC 3110 Section 2.1 Matrix Operations

Kevin James. MTHSC 3110 Section 2.1 Matrix Operations MTHSC 3110 Section 2.1 Matrix Operations Notation Let A be an m n matrix, that is, m rows and n columns. We ll refer to the entries of A by their row and column indices. The entry in the i th row and j

More information

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below. 0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,

More information

Lecture 5: NAND, NOR and XOR Gates, Simplification of Algebraic Expressions

Lecture 5: NAND, NOR and XOR Gates, Simplification of Algebraic Expressions EE210: Switching Systems Lecture 5: NAND, NOR and XOR Gates, Simplification of Algebraic Expressions Prof. YingLi Tian Feb. 15, 2018 Department of Electrical Engineering The City College of New York The

More information

+ R 2 where R 1. MULTIPLE CHOICE QUESTIONS (MCQ's) (Each question carries one mark)

+ R 2 where R 1. MULTIPLE CHOICE QUESTIONS (MCQ's) (Each question carries one mark) 2. C h p t e r t G l n c e is the set of ll points in plne which re t constnt distnce from fixed point clled centre nd constnt distnce is known s rdius of circle. A tngent t ny point of circle is perpendiculr

More information

Page 1 of 15. Website: Mobile:

Page 1 of 15. Website:    Mobile: Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5

More information

4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF?

4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF? Name:!!!!!!!!!!!!! Geo(2) GEOMETRY (2) REVIEW FOR FINAL EXAM #2 1. If ABC is similar to ADE, then AB AD =? AE. Which replaces the? to make the statement true? A. AC!! B. AE!! C. DE!! D. BC 2. In ABC,

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

Lecture 10: The Normal Distribution. So far all the random variables have been discrete.

Lecture 10: The Normal Distribution. So far all the random variables have been discrete. Lecture 10: The Normal Distribution 1. Continuous Random Variables So far all the random variables have been discrete. We need a different type of model (called a probability density function) for continuous

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

NATIONAL SENIOR CERTIFICATE MEMORANDUM MATHEMATICS MEMORANDUM P2 SEPTEMBER 2016 GRADE 12

NATIONAL SENIOR CERTIFICATE MEMORANDUM MATHEMATICS MEMORANDUM P2 SEPTEMBER 2016 GRADE 12 NATIONAL SENIOR CERTIFICATE MEMORANDUM MATHEMATICS MEMORANDUM P SEPTEMBER 06 GRADE This memo consists of 5 pages Income Maths Memo / P September 06 QUESTION.. 700 answer ().. 700 answer ().. 45 minutes

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

AFM Midterm Review I Fall Determine if the relation is a function. 1,6, 2. Determine the domain of the function. . x x

AFM Midterm Review I Fall Determine if the relation is a function. 1,6, 2. Determine the domain of the function. . x x AFM Midterm Review I Fall 06. Determine if the relation is a function.,6,,, 5,. Determine the domain of the function 7 h ( ). 4. Sketch the graph of f 4. Sketch the graph of f 5. Sketch the graph of f

More information

Exercises, II part Exercises, II part

Exercises, II part Exercises, II part Inference: 12 Jul 2012 Consider the following Joint Probability Table for the three binary random variables A, B, C. Compute the following queries: 1 P(C A=T,B=T) 2 P(C A=T) P(A, B, C) A B C 0.108 T T

More information

Downloaded from

Downloaded from Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar

More information

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. () Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other

More information

11. Concentric Circles: Circles that lie in the same plane and have the same center.

11. Concentric Circles: Circles that lie in the same plane and have the same center. Circles Definitions KNOW THESE TERMS 1. Circle: The set of all coplanar points equidistant from a given point. 2. Sphere: The set of all points equidistant from a given point. 3. Radius of a circle: The

More information

[BIT Ranchi 1992] (a) 2 (b) 3 (c) 4 (d) 5. (d) None of these. then the direction cosine of AB along y-axis is [MNR 1989]

[BIT Ranchi 1992] (a) 2 (b) 3 (c) 4 (d) 5. (d) None of these. then the direction cosine of AB along y-axis is [MNR 1989] VECTOR ALGEBRA o. Let a i be a vector which makes an angle of 0 with a unit vector b. Then the unit vector ( a b) is [MP PET 99]. The perimeter of the triangle whose vertices have the position vectors

More information

Probability theory and mathematical statistics:

Probability theory and mathematical statistics: N.I. Lobachevsky State University of Nizhni Novgorod Probability theory and mathematical statistics: Geometric probability Practice Associate Professor A.V. Zorine Geometric probability Practice 1 / 7

More information

WHITE KNUCKLE RIDE AN INTRODUCTION TO DYNAMICS

WHITE KNUCKLE RIDE AN INTRODUCTION TO DYNAMICS WHITE KNUCKLE RIDE AN INTRODUCTION TO DYNAMICS P R E A M B L E The original version of White Knuckle Ride is run as a Laboratory Group Research Project, undertaken by students in small groups. There are

More information

Practice Assessment Task SET 3

Practice Assessment Task SET 3 PRACTICE ASSESSMENT TASK 3 655 Practice Assessment Task SET 3 Solve m - 5m + 6 $ 0 0 Find the locus of point P that moves so that it is equidistant from the points A^-3, h and B ^57, h 3 Write x = 4t,

More information

Lecture 3 : Probability II. Jonathan Marchini

Lecture 3 : Probability II. Jonathan Marchini Lecture 3 : Probability II Jonathan Marchini Puzzle 1 Pick any two types of card that can occur in a normal pack of shuffled playing cards e.g. Queen and 6. What do you think is the probability that somewhere

More information

Chapter 6: Structural Analysis

Chapter 6: Structural Analysis Chapter 6: Structural Analysis APPLICATIONS Trusses are commonly used to support a roof. For a given truss geometry and load, how can we determine the forces in the truss members and select their sizes?

More information

UNDERSTANDING RULER AND COMPASS CONSTRUCTIONS WITH FIELD THEORY

UNDERSTANDING RULER AND COMPASS CONSTRUCTIONS WITH FIELD THEORY UNDERSTANDING RULER AND COMPASS CONSTRUCTIONS WITH FIELD THEORY ISAAC M. DAVIS Abstract. By associating a subfield of R to a set of points P 0 R 2, geometric properties of ruler and compass constructions

More information

Announcements. Exam 1 Review

Announcements. Exam 1 Review Announcements Quiz today Exam Monday! You are allowed one 8.5 x 11 in cheat sheet of handwritten notes for the exam (front and back of 8.5 x 11 in paper) Handwritten means you must write them by hand,

More information

DESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80

DESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80 DESIGN OF THE QUESTION PAPER Mathematics Class X Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage to Content/ Subject Units : S.No. Content

More information

Class X Delhi Math Set-3 Section A

Class X Delhi Math Set-3 Section A Class X Delhi Math Set-3 Section A 1. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30. The distance of the car from the base of the tower (in m.) is:

More information

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont.

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont. 2.8 Proving angle relationships cont. ink.notebook page 84 page 83 2.8 cont. page 85 page 86 Lesson Objectives Standards Lesson Notes 2.8 Proving Angle Relationships Cont. Press the tabs to view details.

More information

Dispersion and how to control it

Dispersion and how to control it Dispersion and how to control it Group velocity versus phase velocity Angular dispersion Prism sequences Grating pairs Chirped mirrors Intracavity and extra-cavity examples 1 Pulse propagation and broadening

More information

1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD

1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD Chapter. Geometry Problems. LINE SEGMENTS Theorem : If ABC A B C, then the ratio of the areas is as follows: S ABC a b c ( ) ( ) ( ) S a b A BC c a a b c and b c Theorem : If DE//BC, then ABC ADE and AD

More information

ASIAN MATHS OLYMPIAD

ASIAN MATHS OLYMPIAD ASIAN ATHS OLYPIAD Full Name: Date: School Name: IC No.: Time: Class: Rules and Regulations (Please read the following rules and regulations carefully) 1. Please fill in your FULL name correctly, IC No.,

More information

1. a) 28 integers are chosen from the interval [104, 208]. Show that there exit two of them having a

1. a) 28 integers are chosen from the interval [104, 208]. Show that there exit two of them having a NMTC STAGE-II 0 JUNIOR GROUP (IX AND X) Note : Answer as many questions as possible. Elegant and noval solution will get extra credits. Diagrams and explanations should be given wherever necessary. Fill

More information

GEOMETRY CHAPTER 2: Deductive Reasoning

GEOMETRY CHAPTER 2: Deductive Reasoning GEOMETRY CHAPTER 2: Deductive Reasoning NAME Page 1 of 34 Section 2-1: If-Then Statements; Converses Conditional Statement: If hypothesis, then conclusion. hypothesis conclusion converse conditional statement

More information

POINT. Preface. The concept of Point is very important for the study of coordinate

POINT. Preface. The concept of Point is very important for the study of coordinate POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates

More information

2002 MAML Olympiad Level 1 Questions (A) 5 (B) 7 (C) 11 (D) 17 (E) 19 (C) (D) 12 5 (A) 87 (B) 124 (C) 127 (D) 131 (E) 141

2002 MAML Olympiad Level 1 Questions (A) 5 (B) 7 (C) 11 (D) 17 (E) 19 (C) (D) 12 5 (A) 87 (B) 124 (C) 127 (D) 131 (E) 141 . What is the largest prime factor of ( )? 00 MAML Olympiad Level Questions (A) 5 (B) 7 (C) (D) 7 (E) 9. Simplify: (A) 9 + + + + (B) 5 (C) 6 (D) 5 (E) 9. Suppose $0 is placed in a box today. Every three

More information

Documentation for the RUG-IV CMIs: Logic Version 1.02

Documentation for the RUG-IV CMIs: Logic Version 1.02 Documentation for the RUG-IV CMIs: Logic Version 1.02 January 4, 2012 This documentation includes the CMI sets (sets E03 and E04) based on the Medicare Part A rates in the Final Rule for FY2012. Note that

More information

2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is

2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is . If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time

More information

Objective Mathematics

Objective Mathematics . In BC, if angles, B, C are in geometric seq- uence with common ratio, then is : b c a (a) (c) 0 (d) 6. If the angles of a triangle are in the ratio 4 : :, then the ratio of the longest side to the perimeter

More information

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

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

MOMENT OF A COUPLE. Today s Objectives: Students will be able to a) define a couple, and, b) determine the moment of a couple.

MOMENT OF A COUPLE. Today s Objectives: Students will be able to a) define a couple, and, b) determine the moment of a couple. MOMENT OF A COUPLE Today s Objectives: Students will be able to a) define a couple, and, b) determine the moment of a couple. In Class activities: Check Homework Reading Quiz Applications Moment of a Couple

More information

1985B4. A kilogram sample of a material is initially a solid at a temperature of 20 C. Heat is added to the sample at a constant rate of 100

1985B4. A kilogram sample of a material is initially a solid at a temperature of 20 C. Heat is added to the sample at a constant rate of 100 1985B4. A 0.020-kilogram sample of a material is initially a solid at a temperature of 20 C. Heat is added to the sample at a constant rate of 100 joules per second until the temperature increases to 60

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

Model Answer Paper 24(24 1) 2 12

Model Answer Paper 24(24 1) 2 12 ICSE X SUBJECT : MATHEMATICS Marks : 80 Exam No. : MT/ICSE/Semi Prelim II- Set-B-00 Model Answer Paper Time : ½ hrs. SECTION I (40 Marks) A. (a) Maturity value ` 0,000 No. of months (n) 4 months Rate of

More information

(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5).

(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5). ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit www.edugain.com Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height. Find the ratio

More information

Calculation of Power and Flow Capacity of Rotor / Stator Devices in VisiMix RSD Program.

Calculation of Power and Flow Capacity of Rotor / Stator Devices in VisiMix RSD Program. Calculation of Power and Flow Capacity of Rotor / Stator Devices in VisiMix RSD Program. L.N.Braginsky, D.Sc. (Was invited to be presented on the CHISA 2010-13th Conference on Process Integration, Modelling

More information

43603F. General Certificate of Secondary Education Foundation Tier June Unit 3. (JUN F01) WMP/Jun12/43603F F

43603F. General Certificate of Secondary Education Foundation Tier June Unit 3. (JUN F01) WMP/Jun12/43603F F Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Foundation Tier June 2012 Pages 3 4 5 Mark Mathematics

More information

the coordinates of C (3) Find the size of the angle ACB. Give your answer in degrees to 2 decimal places. (4)

the coordinates of C (3) Find the size of the angle ACB. Give your answer in degrees to 2 decimal places. (4) . The line l has equation, 2 4 3 2 + = λ r where λ is a scalar parameter. The line l 2 has equation, 2 0 5 3 9 0 + = µ r where μ is a scalar parameter. Given that l and l 2 meet at the point C, find the

More information

Year 11 Math Homework

Year 11 Math Homework Yimin Math Centre Year 11 Math Homework Student Name: Grade: Date: Score: Table of contents 8 Year 11 Topic 8 Trigonometry Part 5 1 8.1 The Sine Rule and the Area Formula........................... 1 8.1.1

More information

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 4

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 4 07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 y intercept of the line (c) 0 By slope intercept form, The equation of the line is y m + c y (4) + (0) y 4 MT - GEOMETRY - SEMI

More information

SECTION A(1) k k 1= = or (rejected) k 1. Suggested Solutions Marks Remarks. 1. x + 1 is the longest side of the triangle. 1M + 1A

SECTION A(1) k k 1= = or (rejected) k 1. Suggested Solutions Marks Remarks. 1. x + 1 is the longest side of the triangle. 1M + 1A SECTION A(). x + is the longest side of the triangle. ( x + ) = x + ( x 7) (Pyth. theroem) x x + x + = x 6x + 8 ( x )( x ) + x x + 9 x = (rejected) or x = +. AP and PB are in the golden ratio and AP >

More information

Unit 7 Probability M2 13.1,2,4, 5,6

Unit 7 Probability M2 13.1,2,4, 5,6 + Unit 7 Probability M2 13.1,2,4, 5,6 7.1 Probability n Obj.: I will be able to determine the experimental and theoretical probabilities of an event, or its complement, occurring. n Vocabulary o Outcome

More information

ENGR-1100 Introduction to Engineering Analysis. Lecture 19

ENGR-1100 Introduction to Engineering Analysis. Lecture 19 ENGR-1100 Introduction to Engineering Analysis Lecture 19 SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS Today s Objectives: Students will be able to: In-Class Activities: a) Define a simple

More information

1. Peter cuts a square out of a rectangular piece of metal. accurately drawn. x + 2. x + 4. x + 2

1. Peter cuts a square out of a rectangular piece of metal. accurately drawn. x + 2. x + 4. x + 2 1. Peter cuts a square out of a rectangular piece of metal. 2 x + 3 Diagram NOT accurately drawn x + 2 x + 4 x + 2 The length of the rectangle is 2x + 3. The width of the rectangle is x + 4. The length

More information

SAMPLE QUESTION PAPER 11 Class-X ( ) Mathematics

SAMPLE QUESTION PAPER 11 Class-X ( ) Mathematics SAMPLE QUESTION PAPER 11 Class-X (2017 18) Mathematics GENERAL INSTRUCTIONS (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided into four sections A, B,C and D. (iii)

More information

Geometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula.

Geometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. Geometry AIR Test Mar 14-3:07 PM Congruence and Proof 33-39% coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. missing sides on triangles (trig ratios,

More information

Probability Review I

Probability Review I Probability Review I Harvard Math Camp - Econometrics Ashesh Rambachan Summer 2018 Outline Random Experiments The sample space and events σ-algebra and measures Basic probability rules Conditional Probability

More information

Discrete Mathematics. Chapter 4. Relations and Digraphs Sanguk Noh

Discrete Mathematics. Chapter 4. Relations and Digraphs Sanguk Noh Discrete Mathematics Chapter 4. Relations and Digraphs Sanguk Noh Table Product sets and partitions Relations and digraphs Paths in relations and digraphs Properties of relations Equivalence relations

More information

Lesson 7.6 Exercises, pages

Lesson 7.6 Exercises, pages Lesson 7.6 Exercises, pages 658 665 A. Write each expression as a single trigonometric ratio. a) sin (u u) b) sin u sin u c) sin u sin u d) cos u cos u sin U cos U e) sin u sin u f) sin u sin u sin U 5.

More information

University of Melbourne Schools Mathematics Competition 2004 Senior Solutions

University of Melbourne Schools Mathematics Competition 2004 Senior Solutions University of Melbourne Schools Mathematics Competition 004 Senior Solutions 1. Jane and her friends are standing in a circle. It turns out that both neighbours of each child are the same gender. If there

More information

d. The numerator comes from part c and the denominator from part b: =. 14

d. The numerator comes from part c and the denominator from part b: =. 14 Solution to assignmet 2 a Because order is important, we ll use P 8, 8(7)() b Order doesn t matter here, so we use C, 59,775 8 2 c From each group we choose 2: 8, 2 2 2 8, d The numerator comes from part

More information

Investigation of acid stratification in lead-acid batteries

Investigation of acid stratification in lead-acid batteries Investigation of acid stratification in lead-acid batteries Development of an electrochemical sensor array for online measurement of acid stratification Abderrezak Hammouche, Juergen Bauer, Stephan A.

More information

SV-2, SV-1, AVS, AVSL, SI Grilles

SV-2, SV-1, AVS, AVSL, SI Grilles Grilles SV-2, SV-1, AVS, AVS-L TECHNICAL DATA - 2004 page 351 SV-2, SV-1, AVS, AVSL, SI Grilles SV-2 SV-1 47 (H-17) x (W-17) (H-12) x (W-12) AVS, SI AVSL S SV, AVS, AVSL and SI grilles are designed for

More information

Fall Inverse of a matrix. Institute: UC San Diego. Authors: Alexander Knop

Fall Inverse of a matrix. Institute: UC San Diego. Authors: Alexander Knop Fall 2017 Inverse of a matrix Authors: Alexander Knop Institute: UC San Diego Row-Column Rule If the product AB is defined, then the entry in row i and column j of AB is the sum of the products of corresponding

More information

B. L. Raktoe and W. T. Federer Cornell University ABSTRACT

B. L. Raktoe and W. T. Federer Cornell University ABSTRACT On Irregular 1_ Fractions of a 2m Factorial 2n B. L. Raktoe and W. T. Federer Cornell University ABSTRACT A rigorous definition of regular and irregular fractional replicates from an sm factorial is presented.

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

More information

DESIGN OF THE QUESTION PAPER Mathematics Class X

DESIGN OF THE QUESTION PAPER Mathematics Class X SET-I DESIGN OF THE QUESTION PAPER Mathematics Class X Time : 3 Hours Maximum Marks : 80 Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage

More information

S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP.

S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP. F R A N K L IN M A D IS O N S U E R O B E R T LE IC H T Y A LY C E C H A M B E R L A IN T W IN C R E E K M A R T Z -PA U L L IN C O R A O W E N M E A D O W L A R K W R E N N LA N T IS R E D R O B IN F

More information

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 909/1 Paper 1 May/June 01 MARK SCHEME Maximum Mark: 5 Published This mark scheme is published

More information

Lecture 1. ABC of Probability

Lecture 1. ABC of Probability Math 408 - Mathematical Statistics Lecture 1. ABC of Probability January 16, 2013 Konstantin Zuev (USC) Math 408, Lecture 1 January 16, 2013 1 / 9 Agenda Sample Spaces Realizations, Events Axioms of Probability

More information

Solutions and Ions. Pure Substances

Solutions and Ions. Pure Substances Class #4 Solutions and Ions CHEM 107 L.S. Brown Texas A&M University Pure Substances Pure substance: described completely by a single chemical formula Fixed composition 1 Mixtures Combination of 2 or more

More information

Diagnostic Tests Study Guide

Diagnostic Tests Study Guide California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra

More information

Permutation. Permutation. Permutation. Permutation. Permutation

Permutation. Permutation. Permutation. Permutation. Permutation Conditional Probability Consider the possible arrangements of the letters A, B, and C. The possible arrangements are: ABC, ACB, BAC, BCA, CAB, CBA. If the order of the arrangement is important then we

More information

GEOMETRY AND TRIGONOMETRY

GEOMETRY AND TRIGONOMETRY Name: Teacher: GEOMETRY AND TRIGONOMETRY Duration: 150 minutes Timeline for classes: Part A: 50 minutes for 20 multiple choice questions (answers to be submitted in the answer sheet). Each question is

More information

Probability- describes the pattern of chance outcomes

Probability- describes the pattern of chance outcomes Chapter 6 Probability the study of randomness Probability- describes the pattern of chance outcomes Chance behavior is unpredictable in the short run, but has a regular and predictable pattern in the long

More information

CBSE X Mathematics 2012 Solution (SET 1) Section B

CBSE X Mathematics 2012 Solution (SET 1) Section B CBSE X Mathematics 01 Solution (SET 1) Section B Q11. Find the value(s) of k so that the quadratic equation x kx + k = 0 has equal roots. Given equation is x kx k 0 For the given equation to have equal

More information

Juan Juan Salon. EH National Bank. Sandwich Shop Nail Design. OSKA Beverly. Chase Bank. Marina Rinaldi. Orogold. Mariposa.

Juan Juan Salon. EH National Bank. Sandwich Shop Nail Design. OSKA Beverly. Chase Bank. Marina Rinaldi. Orogold. Mariposa. ( ) X é X é Q Ó / 8 ( ) Q / ( ) ( ) : ( ) : 44-3-8999 433 4 z 78-19 941, #115 Z 385-194 77-51 76-51 74-7777, 75-5 47-55 74-8141 74-5115 78-3344 73-3 14 81-4 86-784 78-33 551-888 j 48-4 61-35 z/ zz / 138

More information

bending moment in the beam can be obtained by integration

bending moment in the beam can be obtained by integration q 0 L 4 B = - v(l) = CCC ( ) 30 EI Example 9-5 an overhanging beam ABC with a concentrated load P applied at the end determine the equation of deflection curve and the deflection C at the end flexural

More information

SURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS

SURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS SURA's Guides for rd to 1th Std for all Subjects in TM & EM Available 10 th STD. MARCH - 017 Public Exam Question Paper with Answers MATHEMATICS [Time Allowed : ½ Hrs.] [Maximum Marks : 100] SECTION -

More information

3/15/2010 ENGR 200. Counting

3/15/2010 ENGR 200. Counting ENGR 200 Counting 1 Are these events conditionally independent? Blue coin: P(H = 0.99 Red coin: P(H = 0.01 Pick a random coin, toss it twice. H1 = { 1 st toss is heads } H2 = { 2 nd toss is heads } given

More information

This section will help you revise previous learning which is required in this topic.

This section will help you revise previous learning which is required in this topic. Higher Portfolio Circle Higher 10. Circle Revision Section This section will help you revise previous learning which is required in this topic. R1 I can use the distance formula to find the distance 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

Set Notation and Axioms of Probability NOT NOT X = X = X'' = X

Set Notation and Axioms of Probability NOT NOT X = X = X'' = X Set Notation and Axioms of Probability Memory Hints: Intersection I AND I looks like A for And Union U OR + U looks like U for Union Complement NOT X = X = X' NOT NOT X = X = X'' = X Commutative Law A

More information

Lecture 3: Probability

Lecture 3: Probability Lecture 3: Probability 28th of October 2015 Lecture 3: Probability 28th of October 2015 1 / 36 Summary of previous lecture Define chance experiment, sample space and event Introduce the concept of the

More information

Complete Syllabus of Class XI & XII

Complete Syllabus of Class XI & XII Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-0005 Ph.: 0-7656 Fa : 0-767 MM : 0 Sample Paper : Campus Recruitment Test Time : ½ Hr. Mathematics (Engineering) Complete Syllabus of Class XI & XII

More information

Random Variables and Events

Random Variables and Events Random Variables and Events Data Science: Jordan Boyd-Graber University of Maryland SLIDES ADAPTED FROM DAVE BLEI AND LAUREN HANNAH Data Science: Jordan Boyd-Graber UMD Random Variables and Events 1 /

More information

Mathematics I. Exercises with solutions. 1 Linear Algebra. Vectors and Matrices Let , C = , B = A = Determine the following matrices:

Mathematics I. Exercises with solutions. 1 Linear Algebra. Vectors and Matrices Let , C = , B = A = Determine the following matrices: Mathematics I Exercises with solutions Linear Algebra Vectors and Matrices.. Let A = 5, B = Determine the following matrices: 4 5, C = a) A + B; b) A B; c) AB; d) BA; e) (AB)C; f) A(BC) Solution: 4 5 a)

More information

1. Matrices and Determinants

1. Matrices and Determinants Important Questions 1. Matrices and Determinants Ex.1.1 (2) x 3x y Find the values of x, y, z if 2x + z 3y w = 0 7 3 2a Ex 1.1 (3) 2x 3x y If 2x + z 3y w = 3 2 find x, y, z, w 4 7 Ex 1.1 (13) 3 7 3 2 Find

More information

Engineering Mechanics: Statics STRUCTURAL ANALYSIS. by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics

Engineering Mechanics: Statics STRUCTURAL ANALYSIS. by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics CHAPTER Engineering Mechanics: Statics STRUCTURAL ANALYSIS College of Engineering Department of Mechanical Engineering Tenth Edition 6a by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics Department

More information

ARC 202L. Not e s : I n s t r u c t o r s : D e J a r n e t t, L i n, O r t e n b e r g, P a n g, P r i t c h a r d - S c h m i t z b e r g e r

ARC 202L. Not e s : I n s t r u c t o r s : D e J a r n e t t, L i n, O r t e n b e r g, P a n g, P r i t c h a r d - S c h m i t z b e r g e r ARC 202L C A L I F O R N I A S T A T E P O L Y T E C H N I C U N I V E R S I T Y D E P A R T M E N T O F A R C H I T E C T U R E A R C 2 0 2 L - A R C H I T E C T U R A L S T U D I O W I N T E R Q U A

More information

MATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C.

MATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C. MATHEMATICS PAPER IB COORDINATE GEOMETRY(D &3D) AND CALCULUS. TIME : 3hrs Ma. Marks.75 Note: This question paper consists of three sections A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0.

More information

Transweb Educational Services Pvt. Ltd Tel:

Transweb Educational Services Pvt. Ltd     Tel: . An aeroplane flying at a constant speed, parallel to the horizontal ground, km above it, is observed at an elevation of 6º from a point on the ground. If, after five seconds, its elevation from the same

More information

Lecture 3: Matrix and Matrix Operations

Lecture 3: Matrix and Matrix Operations Lecture 3: Matrix and Matrix Operations Representation, row vector, column vector, element of a matrix. Examples of matrix representations Tables and spreadsheets Scalar-Matrix operation: Scaling a matrix

More information

1994 HKCEE MATHS Paper II

1994 HKCEE MATHS Paper II 99 HKCEE MATHS Paper II P. If f ( x) = x + x, then f ( x ) = 99 HKCEE MATHS Paper II 6 If x ( x + ) < ( x + ), then x x x + x x + x x + x If x y =, then x = x + + y + y + y + y y The L.M. of ( ) x y +

More information

C e. Negative. In a clockwise cycle, the work done on the gas is negative. Or for the cycle Qnet = +600 J and U = 0 so W = Q = 600 J

C e. Negative. In a clockwise cycle, the work done on the gas is negative. Or for the cycle Qnet = +600 J and U = 0 so W = Q = 600 J AP Physics Free Response Practice Thermodynamics ANSWERS 1983B4 Since T is constant, pbv B = p 0 V 0 and V B = 2V 0 gives p B = ½ p0 U = Q + W, since AB is isothermal, U = 0 and W = Q = 1000 J c. The entropy

More information

1.5 Gaussian Elimination With Partial Pivoting.

1.5 Gaussian Elimination With Partial Pivoting. Gaussian Elimination With Partial Pivoting In the previous section we discussed Gaussian elimination In that discussion we used equation to eliminate x from equations through n Then we used equation to

More information

[ ]:543.4(075.8) 35.20: ,..,..,.., : /... ;. 2-. ISBN , - [ ]:543.4(075.8) 35.20:34.

[ ]:543.4(075.8) 35.20: ,..,..,.., : /... ;. 2-. ISBN , - [ ]:543.4(075.8) 35.20:34. .. - 2-2009 [661.87.+661.88]:543.4(075.8) 35.20:34.2373-60..,..,..,..,.. -60 : /... ;. 2-. : -, 2008. 134. ISBN 5-98298-299-7 -., -,,. - «,, -, -», - 550800,, 240600 «-», -. [661.87.+661.88]:543.4(075.8)

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

Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES

Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Warm-Up 1.) What is the distance between the points (2, 3) and (5, 7). 2.) If < 1 and < 2 are complements, and m < 1 = 49, then what is

More information