K.S.E.E.B., Malleshwaram, Bangalore SSLC Model Question Paper-1 (2015) Mathematics
|
|
- Beryl McCoy
- 6 years ago
- Views:
Transcription
1 K.S.E.E.B., Malleshwaam, Bangaloe SSLC Model Question Pape-1 (015) Mathematics Max Maks: 80 No. of Questions: 40 Time: Hous 45 minutes Code No. : 81E Fou altenatives ae given fo the each question. Choose the coect altenative and wite the complete answe along with its alphabet in the space povided. 1 mak 8 = 8 1. Which one of the following is a coect elationship? (a) np nc! (b) nc np! (c) np nc! (d) nc np!. Pobability of getting 3 heads o 3 tails in tossing a coin 3 times is, (a) 1 8 (b) 1 (c) 3 8 (d) The sides of two simila tiangle ae in the atio : 3. Then thei aeas ae in the atio (a) 9 : 4 (b) 4 : 9 (c) : 3 (d) 3 : 4. If A B then, A B is (a) A B (c) B (b) B A (d) A 5. Mean and standad deviation of a data ae 48 and 1 espectively. The coefficient of vaiation is, (a) 48 (b) 4 (c) 15 (d) 5 K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 1
2 6. If ax bx c 0 has equal oots. Then c is equal to (a) (c) b 4a b a (b) (d) b a b 4a 7. In the adjoining figue, D and E ae the mid points of AB and AC espectively. If DE = 4 cm, then BC is equal to (a) 4 cm (b) 6 cm (c) 8 cm (d) 1 cm 8. 1 tan 60 is equal to (a) 1 (b) (c) 16 (d) 4 II 1 mak 6 = 6 9. Expess 676 as the poduct of pime factos. 10. Find the zeoes of the polynomial 4a Fo the equation 143 x 1, find the value of x. 1. Fom the quadatic equation whose oots ae 3 and In ABC. ABC 90 and BD AC. If BD = 8 cm and AD = 4 cm, find CD. K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1
3 14. O is the cente of the cicle. P is extenal point. If AP = 8 cm, AP = BP and APB 60 then find the length of the chod AB. III maks 16 = In a school, the stength of 8 th, 9 th and 10 th standads ae espectively 48, 4 and 60. Find the least numbe of books equied to be distibuted equally among the students of 8 th, 9 th and 10 th standad. 16. In a town 85% of the people speak English, 40% speak Kannada and 0% speak Hindi. Also 4% speak English and Kannada, 3% speak Kannada and Hindi and 10% speak English and Hindi. Find the pecentage of people who can speak all the thee languages. 17. Find the sum of all natual numbes between 1 and 01 which ae divisible by The 10 th tem of a G.P. is 30 and 6 th tem is 0. Find the pogession. 19. It is equied to seat 5 men and 4 women in a ow so that the women occupy the even places. How many such aangements ae possible? 0. How many maximum diagonals that can be dawn in a octagon? Eveybody in a function shakes hand with eveybody else. The total numbe of handshakes is 45. Find the numbe of pesons in the function. K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 3
4 1. Thee ae ed and yellow flowes in a basket. A child picks up at andom thee flowes. What is the pobability of picking up both the yellow flowes?. Rationalise the denominato and simplify: Multiply: Solve by using fomula: 15m 11m 0. 81E If one oot of the equation 3p 16q. x px q 0 is 3 times the othe, then pove that 5. Find the value of sin30 tan 45 cosec60 sec30 cos60 cot Find the slope of the line pependicula to the line joining the points (1, 7) and ( 4, 3). 7. A point P (, 1) is equidistant fom the points (a, 7) and ( 3, a). Find a. 8. Daw a cicle of adius 4 cm and constuct a pai of tangents such that angle between them is Daw the gaph (netwok) fo the following: Nodes = 7, Regions = 5, Acs = Daw a plan fo the ecodings fom the suveyo s field wok book given below: (Scale 5 m = 1 cm) To D metes to C to E to B 100 Fom A K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 4
5 IV 3 maks 6 = Daw Pie chat to epesent the following data: 81E Name of the spot Numbe of students Foot ball 35 Tennis 14 Volley ball 16 Hockey 7 3. Find the diviso g(x), when the polynomial 3 P x 4x x 10x is divided by g(x) and the quotient and emainde obtained ae x 4x 1 and 5 espectively. If the quotient obtained on dividing 4 8x x 6x 7 by x 1 is 3 4x px qx 3 then find the value of p, q and also the emainde. 33. If two cicles touch each othe intenally thei centes and the point of contact ae collinea. Pove. 34. In the tapezium ABCD, AB DC and AED BEC. The pove that AD = BC. D, E and F ae the mid-points of sides of ABC. P, Q, R ae the mid points of sides DEF. This pocess of making the mid-points and foming a new tiangle is continued. How ae the aeas of these tiangles elated? K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 5
6 35. Show that: tan 1 tan cot 1. Show that sec A 1 sin A sec A tan A A medicine capsule is in the shape of a cylinde with two hemisphees stuck to each of its ends. The length of the capsule is 14 mm and the width is 5 mm. Find the suface aea. The diamete of the intenal and extenal sufaces of a hollow hemispheical shell ae 6 cm and 10 cm espectively. It is melted and ecast into a solid cone of diamete 14 cm. Find the height of the cone. V 4 maks 4 = In an A.P. whose fist tem is the sum of fist five tems is one fouth the sum of the next five tems. Show that T 0 11 and also find S 0. Sum of thee tems in a G.P. is 31 and thei poduct is 15. Find the numbes. 38. A man tavels a distance of 196 km by tain and etuns in a ca which tavels at a speed of 1 km/hou moe than the tain. If the total jouney takes 11 hous, find the aveage speed of the tain and the ca espectively. 39. In a ight angled tiangle, the squae on the hypotenuse is equal to the sum of the squaes on the othe two sides. Pove. 40. Constuct a tansvese common tangent to two cicles of adii 4 cm and cm having thei cente 10 cm apat. Measue the length of the TCT and veify by calculation. * * * K.S.E.E.B., Malleshwaam, Bangaloe, Mathematics Model Question Pape-1 6
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 informationd 4 x x 170 n 20 R 8 A 200 h S 1 y 5000 x 3240 A 243
nswes: (1984-8 HKMO Final Events) eated by: M. Fancis Hung Last updated: 4 pil 017 Individual Events SI a I1 a I a 1 I3 a 4 I4 a I t 8 b 4 b 0 b 1 b 16 b 10 u 13 c c 9 c 3 c 199 c 96 v 4 d 1 d d 16 d 4
More informationEXTRA HOTS PROBLEMS. (5 marks) Given : t 3. = a + (n 1)d = 3p 2q + (n 1) (q p) t 10. = 3p 2q + (10 1) (q p) = 3p 2q + 9 (q p) = 3p 2q + 9q 9p = 7q 6p
MT EDUCARE LTD. EXTRA HOTS PROBLEMS HOTS SUMS CHAPTER : - ARITHMETIC PROGRESSION AND GEOMETRIC PROGRESSION. If 3 d tem of an A.P. is p and the 4 th tem is q. Find its n th tem and hence find its 0 th tem.
More informationWhen two numbers are written as the product of their prime factors, they are in factored form.
10 1 Study Guide Pages 420 425 Factos Because 3 4 12, we say that 3 and 4 ae factos of 12. In othe wods, factos ae the numbes you multiply to get a poduct. Since 2 6 12, 2 and 6 ae also factos of 12. The
More informationMotithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100
Motithang Highe Seconday School Thimphu Thomde Mid Tem Examination 016 Subject: Mathematics Full Maks: 100 Class: IX Witing Time: 3 Hous Read the following instuctions caefully In this pape, thee ae thee
More information3.6 Applied Optimization
.6 Applied Optimization Section.6 Notes Page In this section we will be looking at wod poblems whee it asks us to maimize o minimize something. Fo all the poblems in this section you will be taking the
More information(n 1)n(n + 1)(n + 2) + 1 = (n 1)(n + 2)n(n + 1) + 1 = ( (n 2 + n 1) 1 )( (n 2 + n 1) + 1 ) + 1 = (n 2 + n 1) 2.
Paabola Volume 5, Issue (017) Solutions 151 1540 Q151 Take any fou consecutive whole numbes, multiply them togethe and add 1. Make a conjectue and pove it! The esulting numbe can, fo instance, be expessed
More informationGCSE MATHEMATICS FORMULAE SHEET HIGHER TIER
Pythagoas Volume of cone = Theoem c a a + b = c hyp coss section adj b opp length Intenational GCSE MATHEMATICS FORMULAE SHEET HIGHER TIER Cuved suface aea of cone = adj = hyp opp = hyp opp = adj o sin
More informationAustralian Intermediate Mathematics Olympiad 2017
Austalian Intemediate Mathematics Olympiad 207 Questions. The numbe x is when witten in base b, but it is 22 when witten in base b 2. What is x in base 0? [2 maks] 2. A tiangle ABC is divided into fou
More informationMath Section 4.2 Radians, Arc Length, and Area of a Sector
Math 1330 - Section 4. Radians, Ac Length, and Aea of a Secto The wod tigonomety comes fom two Geek oots, tigonon, meaning having thee sides, and mete, meaning measue. We have aleady defined the six basic
More information4.3 Area of a Sector. Area of a Sector Section
ea of a Secto Section 4. 9 4. ea of a Secto In geomety you leaned that the aea of a cicle of adius is π 2. We will now lean how to find the aea of a secto of a cicle. secto is the egion bounded by a cental
More information1. Show that the volume of the solid shown can be represented by the polynomial 6x x.
7.3 Dividing Polynomials by Monomials Focus on Afte this lesson, you will be able to divide a polynomial by a monomial Mateials algeba tiles When you ae buying a fish tank, the size of the tank depends
More information(A) 2log( tan cot ) [ ], 2 MATHEMATICS. 1. Which of the following is correct?
MATHEMATICS. Which of the following is coect? A L.P.P always has unique solution Evey L.P.P has an optimal solution A L.P.P admits two optimal solutions If a L.P.P admits two optimal solutions then it
More informationFORMULAE. 8. a 2 + b 2 + c 2 ab bc ca = 1 2 [(a b)2 + (b c) 2 + (c a) 2 ] 10. (a b) 3 = a 3 b 3 3ab (a b) = a 3 3a 2 b + 3ab 2 b 3
FORMULAE Algeba 1. (a + b) = a + b + ab = (a b) + 4ab. (a b) = a + b ab = (a + b) 4ab 3. a b = (a b) (a + b) 4. a + b = (a + b) ab = (a b) + ab 5. (a + b) + (a b) = (a + b ) 6. (a + b) (a b) = 4ab 7. (a
More informationOLYMON. Produced by the Canadian Mathematical Society and the Department of Mathematics of the University of Toronto. Issue 9:2.
OLYMON Poduced by the Canadian Mathematical Society and the Depatment of Mathematics of the Univesity of Toonto Please send you solution to Pofesso EJ Babeau Depatment of Mathematics Univesity of Toonto
More informationOnline Mathematics Competition Wednesday, November 30, 2016
Math@Mac Online Mathematics Competition Wednesday, Novembe 0, 206 SOLUTIONS. Suppose that a bag contains the nine lettes of the wod OXOMOXO. If you take one lette out of the bag at a time and line them
More informationLesson-7 AREAS RELATED TO CIRCLES
Lesson- RES RELTE T IRLES Intoduction cicle is a plane figue bounded by one line () such that the distance of this line fom a fixed point within it (point ), emains constant thoughout That is constant.
More informationNo. 32. R.E. Woodrow. As a contest this issue we give the Junior High School Mathematics
334 THE SKOLIAD CORNER No. 32 R.E. Woodow As a contest this issue we give the Junio High School Mathematics Contest, Peliminay Round 1998 of the Bitish Columbia Colleges which was witten Mach 11, 1998.
More informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,
R Pena Towe, Road No, Contactos Aea, Bistupu, Jamshedpu 8, Tel (657)89, www.penaclasses.com IIT JEE Mathematics Pape II PART III MATHEMATICS SECTION I Single Coect Answe Type This section contains 8 multiple
More informationThe CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Galois Contest. Wednesday, April 12, 2017
The ENTRE fo EDUATIN in MATHEMATIS and MPUTING cemc.uwateloo.ca 2017 Galois ontest Wednesday, Apil 12, 2017 (in Noth Ameica and South Ameica) Thusday, Apil 13, 2017 (outside of Noth Ameica and South Ameica)
More informationPDF Created with deskpdf PDF Writer - Trial ::
A APPENDIX D TRIGONOMETRY Licensed to: jsamuels@bmcc.cun.edu PDF Ceated with deskpdf PDF Wite - Tial :: http://www.docudesk.com D T i g o n o m e t FIGURE a A n g l e s Angles can be measued in degees
More informationRelated Rates - the Basics
Related Rates - the Basics In this section we exploe the way we can use deivatives to find the velocity at which things ae changing ove time. Up to now we have been finding the deivative to compae the
More informationHeronian Triangles of Class K: Congruent Incircles Cevian Perspective
Foum Geometicoum Volume 5 (05) 5. FORUM GEOM ISSN 534-78 Heonian Tiangles of lass K: onguent Incicles evian Pespective Fank M. Jackson and Stalislav Takhaev bstact. We elate the popeties of a cevian that
More informationSMT 2013 Team Test Solutions February 2, 2013
1 Let f 1 (n) be the numbe of divisos that n has, and define f k (n) = f 1 (f k 1 (n)) Compute the smallest intege k such that f k (013 013 ) = Answe: 4 Solution: We know that 013 013 = 3 013 11 013 61
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Chapte 7-8 Review Math 1316 Name SHORT ANSWER. Wite the wod o phase that best completes each statement o answes the question. Solve the tiangle. 1) B = 34.4 C = 114.2 b = 29.0 1) Solve the poblem. 2) Two
More informationNo. 39. R.E. Woodrow. This issue we give another example of a team competition with the problems
282 THE SKOLIAD CORNER No. 39 R.E. Woodow This issue we give anothe example of a team competition with the poblems of the 998 Floida Mathematics Olympiad, witten May 4, 998. The contest was oganized by
More informationProblem 1: Multiple Choice Questions
Mathematics 102 Review Questions Poblem 1: Multiple Choice Questions 1: Conside the function y = f(x) = 3e 2x 5e 4x (a) The function has a local maximum at x = (1/2)ln(10/3) (b) The function has a local
More informationAMC 10 Contest B. Solutions Pamphlet. Wednesday, FEBRUARY 21, American Mathematics Competitions
The MATHEMATICAL ASSOCIATION of AMERICA Ameican Mathematics Competitions 8 th Annual Ameican Mathematics Contest 10 AMC 10 Contest B Solutions Pamphlet Wednesday, FEBRUARY 21, 2007 This Pamphlet gives
More information2 x 8 2 x 2 SKILLS Determine whether the given value is a solution of the. equation. (a) x 2 (b) x 4. (a) x 2 (b) x 4 (a) x 4 (b) x 8
5 CHAPTER Fundamentals When solving equations that involve absolute values, we usually take cases. EXAMPLE An Absolute Value Equation Solve the equation 0 x 5 0 3. SOLUTION By the definition of absolute
More information1.6. Trigonometric Functions. 48 Chapter 1: Preliminaries. Radian Measure
48 Chapte : Peliminaies.6 Tigonometic Functions Cicle B' B θ C A Unit of cicle adius FIGURE.63 The adian measue of angle ACB is the length u of ac AB on the unit cicle centeed at C. The value of u can
More informationFREE Download Study Package from website: &
.. Linea Combinations: (a) (b) (c) (d) Given a finite set of vectos a b c,,,... then the vecto xa + yb + zc +... is called a linea combination of a, b, c,... fo any x, y, z... R. We have the following
More informationMATH Non-Euclidean Geometry Exercise Set 3: Solutions
MATH 68090 NonEuclidean Geomety Execise Set : Solutions Pove that the opposite angles in a convex quadilateal inscibed in a cicle sum to 80º Convesely, pove that if the opposite angles in a convex quadilateal
More informationCh 6 Worksheet L1 Key.doc Lesson 6.1 Tangent Properties
Lesson 6.1 Tangent Popeties Investigation 1 Tangent onjectue If you daw a tangent to a cicle, then Daw a adius to the point of tangency. What do you notice? pependicula Would this be tue fo all tangent
More informationBerkeley Math Circle AIME Preparation March 5, 2013
Algeba Toolkit Rules of Thumb. Make sue that you can pove all fomulas you use. This is even bette than memoizing the fomulas. Although it is best to memoize, as well. Stive fo elegant, economical methods.
More informationPage 1 of 6 Physics II Exam 1 155 points Name Discussion day/time Pat I. Questions 110. 8 points each. Multiple choice: Fo full cedit, cicle only the coect answe. Fo half cedit, cicle the coect answe and
More information06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )
06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math Pecalculus Ch. 6 Review Name SHORT ANSWER. Wite the wod o phase that best completes each statement o answes the question. Solve the tiangle. ) ) 6 7 0 Two sides and an angle (SSA) of a tiangle ae
More informationSection 8.2 Polar Coordinates
Section 8. Pola Coodinates 467 Section 8. Pola Coodinates The coodinate system we ae most familia with is called the Catesian coodinate system, a ectangula plane divided into fou quadants by the hoizontal
More informationPolar Coordinates. a) (2; 30 ) b) (5; 120 ) c) (6; 270 ) d) (9; 330 ) e) (4; 45 )
Pola Coodinates We now intoduce anothe method of labelling oints in a lane. We stat by xing a oint in the lane. It is called the ole. A standad choice fo the ole is the oigin (0; 0) fo the Catezian coodinate
More informationEuclidean Figures and Solids without Incircles or Inspheres
Foum Geometicoum Volume 16 (2016) 291 298. FOUM GEOM ISSN 1534-1178 Euclidean Figues and Solids without Incicles o Insphees Dimitis M. Chistodoulou bstact. ll classical convex plana Euclidean figues that
More information4.3 Right Triangle Trigonometry
Section. Right Tiangle Tigonomet 77. Right Tiangle Tigonomet The Si Tigonometic Functions Ou second look at the tigonometic functions is fom a ight tiangle pespective. Conside a ight tiangle, with one
More informationThe geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
More informationTrigonometry Standard Position and Radians
MHF 4UI Unit 6 Day 1 Tigonomety Standad Position and Radians A. Standad Position of an Angle teminal am initial am Angle is in standad position when the initial am is the positive x-axis and the vetex
More informationCh 6 Worksheet L1 Shorten Key Lesson 6.1 Tangent Properties
Lesson 6.1 Tangent Popeties Investigation 1 Tangent Conjectue If you daw a tangent to a cicle, then Daw a adius to the point of tangency. What do you notice? pependicula Would this be tue fo all tangent
More informationof the contestants play as Falco, and 1 6
JHMT 05 Algeba Test Solutions 4 Febuay 05. In a Supe Smash Bothes tounament, of the contestants play as Fox, 3 of the contestants play as Falco, and 6 of the contestants play as Peach. Given that thee
More informationNo. 48. R.E. Woodrow. Mathematics Contest of the British Columbia Colleges written March 8, Senior High School Mathematics Contest
341 THE SKOLIAD CORNER No. 48 R.E. Woodow This issue we give the peliminay ound of the Senio High School Mathematics Contest of the Bitish Columbia Colleges witten Mach 8, 2000. My thanks go to Jim Totten,
More informationUniversal Gravitation
Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between
More informationPractice Problems Test 3
Pactice Poblems Test ********************************************************** ***NOTICE - Fo poblems involving ʺSolve the Tiangleʺ the angles in this eview ae given by Geek lettes: A = α B = β C = γ
More informationF g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N
Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the
More informationPhysics 2212 GH Quiz #2 Solutions Spring 2016
Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying
More informationMAP4C1 Exam Review. 4. Juno makes and sells CDs for her band. The cost, C dollars, to produce n CDs is given by. Determine the cost of making 150 CDs.
MAP4C1 Exam Review Exam Date: Time: Room: Mak Beakdown: Answe these questions on a sepaate page: 1. Which equations model quadatic elations? i) ii) iii) 2. Expess as a adical and then evaluate: a) b) 3.
More informationRandom Variables and Probability Distribution Random Variable
Random Vaiables and Pobability Distibution Random Vaiable Random vaiable: If S is the sample space P(S) is the powe set of the sample space, P is the pobability of the function then (S, P(S), P) is called
More informationworking pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50
woking pages fo Paul Richads class notes; do not copy o ciculate without pemission fom PGR 2004/11/3 10:50 CHAPTER7 Solid angle, 3D integals, Gauss s Theoem, and a Delta Function We define the solid angle,
More informationGraphs of Sine and Cosine Functions
Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the
More informationMath 1105: Calculus I (Math/Sci majors) MWF 11am / 12pm, Campion 235 Written homework 3
Math : alculus I Math/Sci majos MWF am / pm, ampion Witten homewok Review: p 94, p 977,8,9,6, 6: p 46, 6: p 4964b,c,69, 6: p 47,6 p 94, Evaluate the following it by identifying the integal that it epesents:
More informationBetween any two masses, there exists a mutual attractive force.
YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce
More informationSides and Angles of Right Triangles 6. Find the indicated side length in each triangle. Round your answers to one decimal place.
Chapte 7 Peequisite Skills BLM 7-1.. Convet a Beaing to an Angle in Standad Position 1. Convet each beaing to an angle in standad position on the Catesian gaph. a) 68 127 c) 215 d) 295 e) N40 W f) S65
More informationKCET 2015 TEST PAPER WITH ANSWER KEY (HELD ON TUESDAY 12 th MAY, 2015) MATHEMATICS ALLEN Y (0, 14) (4) 14x + 5y ³ 70 y ³ 14and x - y ³ 5 (2) (3) (4)
KET 0 TEST PAPER WITH ANSWER KEY (HELD ON TUESDAY th MAY, 0). If a and b ae the oots of a + b = 0, then a +b is equal to a b () a b a b () a + b Ans:. If the nd and th tems of G.P. ae and esectively, then
More information612 MHR Principles of Mathematics 9 Solutions. Optimizing Measurements. Chapter 9 Get Ready. Chapter 9 Get Ready Question 1 Page 476.
Chapte 9 Optimizing Measuements Chapte 9 Get Ready Chapte 9 Get Ready Question Page 476 a) P = w+ l = 0 + 0 = 0 + 40 = 60 A= lw = 0 0 = 00 The peimete is 60 cm, and the aea is 00 cm. b) P = w+ l = 5. 8
More informationALL INDIA TEST SERIES
Fom Classoom/Integated School Pogams 7 in Top 0, in Top 00, 54 in Top 00, 06 in Top 500 All India Ranks & 4 Students fom Classoom /Integated School Pogams & 7 Students fom All Pogams have been Awaded a
More information11.2. Area of a Circle. Lesson Objective. Derive the formula for the area of a circle.
11.2 Aea of a Cicle Lesson Objective Use fomulas to calculate the aeas of cicles, semicicles, and quadants. Lean Deive the fomula fo the aea of a cicle. A diamete divides a cicle of adius into 2 semicicles.
More informationElectrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
More information5.8 Trigonometric Equations
5.8 Tigonometic Equations To calculate the angle at which a cuved section of highwa should be banked, an enginee uses the equation tan =, whee is the angle of the 224 000 bank and v is the speed limit
More informationΔt The textbook chooses to say that the average velocity is
1-D Motion Basic I Definitions: One dimensional motion (staight line) is a special case of motion whee all but one vecto component is zeo We will aange ou coodinate axis so that the x-axis lies along the
More informationRECTIFYING THE CIRCUMFERENCE WITH GEOGEBRA
ECTIFYING THE CICUMFEENCE WITH GEOGEBA A. Matín Dinnbie, G. Matín González and Anthony C.M. O 1 Intoducction The elation between the cicumfeence and the adius of a cicle is one of the most impotant concepts
More informationAuchmuty High School Mathematics Department Advanced Higher Notes Teacher Version
The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!
More informationMarkscheme May 2017 Calculus Higher level Paper 3
M7/5/MATHL/HP3/ENG/TZ0/SE/M Makscheme May 07 Calculus Highe level Pape 3 pages M7/5/MATHL/HP3/ENG/TZ0/SE/M This makscheme is the popety of the Intenational Baccalaueate and must not be epoduced o distibuted
More informationAP Physics 1 - Circular Motion and Gravitation Practice Test (Multiple Choice Section) Answer Section
AP Physics 1 - Cicula Motion and Gaitation Pactice est (Multiple Choice Section) Answe Section MULIPLE CHOICE 1. B he centipetal foce must be fiction since, lacking any fiction, the coin would slip off.
More informationCircular Orbits. and g =
using analyse planetay and satellite motion modelled as unifom cicula motion in a univesal gavitation field, a = v = 4π and g = T GM1 GM and F = 1M SATELLITES IN OBIT A satellite is any object that is
More informationCh 6 Worksheets L2 Shortened Key Worksheets Chapter 6: Discovering and Proving Circle Properties
Woksheets Chapte 6: Discoveing and Poving Cicle Popeties Lesson 6.1 Tangent Popeties Investigation 1 Tangent Conjectue If you daw a tangent to a cicle, then Daw a adius to the point of tangency. What do
More informationMODULE 5a and 5b (Stewart, Sections 12.2, 12.3) INTRO: In MATH 1114 vectors were written either as rows (a1, a2,..., an) or as columns a 1 a. ...
MODULE 5a and 5b (Stewat, Sections 2.2, 2.3) INTRO: In MATH 4 vectos wee witten eithe as ows (a, a2,..., an) o as columns a a 2... a n and the set of all such vectos of fixed length n was called the vecto
More informationRadian Measure CHAPTER 5 MODELLING PERIODIC FUNCTIONS
5.4 Radian Measue So fa, ou hae measued angles in degees, with 60 being one eolution aound a cicle. Thee is anothe wa to measue angles called adian measue. With adian measue, the ac length of a cicle is
More informationPhysics 11 Chapter 20: Electric Fields and Forces
Physics Chapte 0: Electic Fields and Foces Yesteday is not ous to ecove, but tomoow is ous to win o lose. Lyndon B. Johnson When I am anxious it is because I am living in the futue. When I am depessed
More informationUse Properties of Tangents
opeties of icles 1010.1 Use opeties of Tangents 10.2 Find c Measues 10.3 pply opeties of hods 10.4 Use Inscibed ngles and olygons 10.5 pply Othe ngle elationships in icles 10.6 Find egment Lengths in icles
More informationBASIC ALGEBRA OF VECTORS
Fomulae Fo u Vecto Algeba By Mi Mohammed Abbas II PCMB 'A' Impotant Tems, Definitions & Fomulae 01 Vecto - Basic Intoduction: A quantity having magnitude as well as the diection is called vecto It is denoted
More informationArea of Circles. Fold a paper plate in half four times to. divide it into 16 equal-sized sections. Label the radius r as shown.
-4 Aea of Cicles MAIN IDEA Find the aeas of cicles. Fold a pape plate in half fou times to New Vocabulay Label the adius as shown. Let C secto Math Online glencoe.com Exta Examples Pesonal Tuto Self-Check
More informationJEE(MAIN) 2018 TEST PAPER WITH SOLUTIONS (HELD ON SUNDAY 08 th APRIL, 2018) PART B MATHEMATICS ALLEN
. The integal sin cos 5 5 (sin cos sin sin cos cos ) is equal to () ( tan ) C () cot C () cot C () ( tan ) C (whee C is a constant of integation) Ans. () Let I sin cos d [(sin cos )(sin cos )] sin cos
More informationChapter 5: Trigonometric Functions of Angles
Chapte 5: Tigonometic Functions of Angles In the pevious chaptes we have exploed a vaiety of functions which could be combined to fom a vaiety of shapes. In this discussion, one common shape has been missing:
More informationCurrent Balance Warm Up
PHYSICS EXPERIMENTS 133 Cuent Balance-1 Cuent Balance Wam Up 1. Foce between cuent-caying wies Wie 1 has a length L (whee L is "long") and caies a cuent I 0. What is the magnitude of the magnetic field
More informationtransformation Earth V-curve (meridian) λ Conical projection. u,v curves on the datum surface projected as U,V curves on the projection surface
. CONICAL PROJECTIONS In elementay texts on map pojections, the pojection sufaces ae often descibed as developable sufaces, such as the cylinde (cylindical pojections) and the cone (conical pojections),
More informationGeometry Contest 2013
eomety ontet 013 1. One pizza ha a diamete twice the diamete of a malle pizza. What i the atio of the aea of the lage pizza to the aea of the malle pizza? ) to 1 ) to 1 ) to 1 ) 1 to ) to 1. In ectangle
More information0606 ADDITIONAL MATHEMATICS 0606/01 Paper 1, maximum raw mark 80
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Intenational Geneal Cetificate of Seconday Education MARK SCHEME fo the Octobe/Novembe 009 question pape fo the guidance of teaches 0606 ADDITIONAL MATHEMATICS
More informationMCV4U Final Exam Review. 1. Consider the function f (x) Find: f) lim. a) lim. c) lim. d) lim. 3. Consider the function: 4. Evaluate. lim. 5. Evaluate.
MCVU Final Eam Review Answe (o Solution) Pactice Questions Conside the function f () defined b the following gaph Find a) f ( ) c) f ( ) f ( ) d) f ( ) Evaluate the following its a) ( ) c) sin d) π / π
More information2 Cut the circle along the fold lines to divide the circle into 16 equal wedges. radius. Think About It
Activity 8.7 Finding Aea of Cicles Question How do you find the aea of a cicle using the adius? Mateials compass staightedge scissos Exploe 1 Use a compass to daw a cicle on a piece of pape. Cut the cicle
More informationAP * PHYSICS B. Circular Motion, Gravity, & Orbits. Teacher Packet
AP * PHYSICS B Cicula Motion, Gavity, & Obits Teache Packet AP* is a tademak of the College Entance Examination Boad. The College Entance Examination Boad was not involved in the poduction of this mateial.
More informationMark Scheme 4727 June 2006
Mak Scheme 77 June 006 77 Mak Scheme June 006 (a) Identity = + 0 i Invese = + i i = + i i 0 0 (b) Identity = 0 0 0 Invese = 0 0 i B Fo coect identity. Allow B Fo seen o implied + i = B Fo coect invese
More informationVariables and Formulas
64 Vaiales and Fomulas Vaiales and Fomulas DEFINITIONS & BASICS 1) Vaiales: These symols, eing lettes, actually epesent numes, ut the numes can change fom time to time, o vay. Thus they ae called vaiales.
More informationA Crash Course in (2 2) Matrices
A Cash Couse in ( ) Matices Seveal weeks woth of matix algeba in an hou (Relax, we will only stuy the simplest case, that of matices) Review topics: What is a matix (pl matices)? A matix is a ectangula
More information16.4 Volume of Spheres
Name Class Date 16.4 Volume of Sphees Essential Question: How can you use the fomula fo the volume of a sphee to calculate the volumes of composite figues? Exploe G.11.D Apply the fomulas fo the volume
More information( ) ( ) Review of Force. Part 1, Topic 1 Force Fields. Dr. Sven Achenbach - based on a script by Dr. Eric Salt - Outline. Review of Force. F r.
S. Achenbach: PHYS 55 (Pat, Topic ) Handouts p. Review of Foce Univesity of Saskatchewan Undegaduate Couse Phys 55 Intoduction to Electicity and Magnetism Basics F o F v denotes foce it is a thee dimensional
More informationHOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS?
6th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS? Cecília Sitkuné Göömbei College of Nyíegyháza Hungay Abstact: The
More informationPhysics 521. Math Review SCIENTIFIC NOTATION SIGNIFICANT FIGURES. Rules for Significant Figures
Physics 51 Math Review SCIENIFIC NOAION Scientific Notation is based on exponential notation (whee decimal places ae expessed as a powe of 10). he numeical pat of the measuement is expessed as a numbe
More informationPhysics 111 Lecture 5 (Walker: 3.3-6) Vectors & Vector Math Motion Vectors Sept. 11, 2009
Physics 111 Lectue 5 (Walke: 3.3-6) Vectos & Vecto Math Motion Vectos Sept. 11, 2009 Quiz Monday - Chap. 2 1 Resolving a vecto into x-component & y- component: Pola Coodinates Catesian Coodinates x y =
More information8.7 Circumference and Area
Page 1 of 8 8.7 Cicumfeence and Aea of Cicles Goal Find the cicumfeence and aea of cicles. Key Wods cicle cente adius diamete cicumfeence cental angle secto A cicle is the set of all points in a plane
More informationf h = u, h g = v, we have u + v = f g. So, we wish
Answes to Homewok 4, Math 4111 (1) Pove that the following examples fom class ae indeed metic spaces. You only need to veify the tiangle inequality. (a) Let C be the set of continuous functions fom [0,
More informationMENSURATION-III
MENSURATION-III CIRCLE: A cicle is a geometical figue consisting of all those points in a plane which ae at a given distance fom a fixed point in the same plane. The fixed point is called the cente and
More information- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.
- 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU
More informationPhysics Tutorial V1 2D Vectors
Physics Tutoial V1 2D Vectos 1 Resolving Vectos & Addition of Vectos A vecto quantity has both magnitude and diection. Thee ae two ways commonly used to mathematically descibe a vecto. y (a) The pola fom:,
More informationGeometry Unit 4b - Notes Triangle Relationships
Geomety Unit 4b - Notes Tiangle Relationships This unit is boken into two pats, 4a & 4b. test should be given following each pat. quidistant fom two points the same distance fom one point as fom anothe.
More information1) (A B) = A B ( ) 2) A B = A. i) A A = φ i j. ii) Additional Important Properties of Sets. De Morgan s Theorems :
Additional Impotant Popeties of Sets De Mogan s Theoems : A A S S Φ, Φ S _ ( A ) A ) (A B) A B ( ) 2) A B A B Cadinality of A, A, is defined as the numbe of elements in the set A. {a,b,c} 3, { }, while
More information