3 x x 3x x. 3x x x 6 x 3. PAKTURK 8 th National Interschool Maths Olympiad, h h
|
|
- Osborn Rogers
- 6 years ago
- Views:
Transcription
1 PAKTURK 8 th Ntionl Interschool Mths Olmpid,.9. Q: Evlute Q: Evlute bc bc. b. c bc.9.9b.9.9bc Q: Find the vlue of h in the eqution h bc. bc bc. b. c bc bc bc bc h 7 7 h Q: Which of the following is not fctor of b b 6 9 h b b b b b Q: Age of fther is nd his son is ers old. After how mn ers the ge of fther will be triple of his son : b then nswer b
2 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q6: Find the multiplictive inverse of if /76 / Q8: ISMOISMOISMO... find the 767 th letter or digit in the sequence? I M nd 7th term is Q9: ABCD is squre nd equilterl tringle. Find BCE is n 76 Q7: Ech of the nine pths in prk is m long. Ann wnts to go from A to B without going long n pth more thn once. Wht is the length of the longest route she cn choose? 6 9m 8m 7m 6m
3 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: Which of the following is lws n even number where n is positive integer? 7(n+) 7(n+) 7(n+) 7(7n+) 7n 7n n Q: Evlute Q: If 6 nd thn 6 6 6? 6 Q: If Frhn leves now nd drive t 8km/h, he cn be in Lhore in time for his ppointment. On the other hnd, if he ets first nd leves in hlf n hour, he will hve to drive t km/h to mke his ppointment. How fr is he to Lhore? km km km km Q: I think of number, subtrct 7 from it, divide the result b, nd then dd. If this gives finl result of, find the originl number d 8t t. 8t t t 8t t t.hrs Q: A wter tnk cn be filled b one pipe in hours nd it cn be emptied b nother pipe in hours. If both pipes re open, how long will it tke to fill the tnk? d 8t 8. km hrs
4 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q6: Evlute. Q9: If [ AK [ AC,[ BF //[ CE nd, m ACD m DCE m FKB then, 9.. m FDC? Q7: If nd the,... n? n n nn nn nn... n n n Q8: If n, then find the mimum nd minimum vlue of n? (n is n integer) 9 nd - nd -6 9 nd -6 nd - Q: Evlute ? - - n ? n 6 n min n... 9 n n m n 9 9 9
5 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: If is the result of then, which of the followings in terms of 9 7 Emple: ++=6 or ++++= The numbers which re squres of nturl numbers re clled perfect squres. Which of the following numbers is neither tringulr nor perfect squre? Emple: 6 is squre of Q: Sibtin evlutes. for nd 7 Which of the following epressions hs the sme vlue when nd Q: In the figure, rectngulr prism hs been removed from lrger prism with dimensions cm, cm nd cm. Find the vlume of the remining solid in cubic centimeters. 8 6 Q: Informtion: The numbers which cn be written s the sum of the integers from to n for n=,,,,... re clled tringulr numbers. cm
6 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: Find the re of given figure if BD is cm Are of ABCD cm, Are of AKFE cm 6 6 6, Are of LMNC cm 9, shded re cm , cm 6cm cm 6cm Q7: The figure shosw cube. Wht is the mesure of ngle EFL? Are of ABD cm, Are of BDC 6 cm, totl re cm cm cm, 6 7 Q6: In the figure, ABCD, AKFE nd LMNC re squres. Find the re of the shded region Q8: Find the vlume in cubic centimeters of the solid with the given dimensions. cm 99cm 78cm 86cm
7 PAKTURK 8 th Ntionl Interschool Mths Olmpid, AD 69 AD 69 AD cm 66cm 68cm 7cm 7cm Q: Simplif b. b V cm b b b b Q9: Wht is the mesurement of the ngle between the hour-hnd nd the minute- hnd t the time :? 6 8 b b b b. b b Angle between to is. If ever 6 minutes it moves then in minutes it will move. Totl mkes + =. Q: Find the distnce between A nd D Q: There re two different ws from the cit A, to the cit B. There re different ws from the cit B, to the cit C. There re two different ws from the cit A to the cit C tht re not pssing through the cit B. How mn different ws re there from the cit A to the cith C? 6 8 cm cm cm cm
8 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: In the given figure, wht is the vlue of ngle o? 7m m m m 9 7 Are of Shded Region=Are of Rectngle-(Are of smll circles+are of big circle) cm Q: In the figure, O is the center of the circle. Find the re of the shded region. Q: The figure below shows circulr pools in rectngulr grden. The dimeters of the circles re 6 m nd m nd the side lengths of the grden re m nd m. The rest of the grden is covered in grss. How much of the grden is covered in grss? cm 6cm cm 8cm Are of tringle(with perpendiculr sides)= 8 8 cm
9 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q6: Find the perimeter of the shded region Q8: A gs sttion gives % discount on gsoline. The net month it gives nother % discount on the new price. Find the totl percentge of discount on the originl price. 6% % 6% 66% st : then 66cm 7cm 78cm 8cm 6% discount Perimeter of the shded region= cm Q9: In school referendum % of techers nd 98% of students s YES. All the students nd techers prticipte in the referendum. Referendum results s 9% YES. Find the rtio of the number of students to the number of the techers. 8 Q7: Find the re of trpezoid Let Techers : nd Students : be cm. cm 7 cm 7 cm 8 8 : : Are of trpezium=/ Sum of prllel sides height cm
10 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: Wht is M PN \? Q: A regulr hegon is divided in to 6 equilterl tringles. If one side of the hegon is 6 cm wht is the totl perimeter of tringles? 6 cm 7 cm 8 cm cm {,,} {,,,} {,,,,9} {,,,,6,7,8,9} M \ P N,,,,,9 \,,,,9 Q: One of the students sks the ge of Khwrizmi. His nswer is : "When I ws t our ge ou were ers old nd when ou re t m ge, I will be 66 ers old." Accordingl, wht is the student's current ge? 8 6 Totl Perimeter: 8One side of tringle= 86=8cm.? Q: -7 Pst Present Future Student -k Khwrizmi -k +k=66 -k=+m nd -k+m= then m=k, -k=+m nd -k=+k, -k= nd +k=66 solutions =8 nd k=8 then Student s current ge=-k=8-8=
11 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q:...? Q6: If. b nd. b.7 then, evlute b..7 Q: Onder, Tner nd Serht re plnning to go to trip. The shre the cost of the trip in the rtio ::6 respectivel. If hlf of Serht`s shre is 6 Rs, how much less is Onder going to p thn Tner? Q7: If the numbers in the figure re ordered with rule then which number will come in plce of question mrk? Rs. Rs. Rs. Rs. Serht s shre: 6=Rs., Totl shre is: 6Totl Serht ' s Totl Rs. Onder ' s Rs.8 Tner ' s Rs. 8 Tner ' s Onder ' s 8 Rs.
12 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q8: During n rt lesson, Mudessir creted repeted pttern on piece of pper s shown below, The re of the shded prt is... Q: If b c 8 9 b c 8 then, find the vlue of. b c cm cm cm cm Are of tringles: Q9: cm, is the vlue of nd then, wht b c 8 b c b c b c 8 8 b c 6
1 (=0.5) I3 a 7 I4 a 15 I5 a (=0.5) c 4 N 10 1 (=0.5) N 6 A 52 S 2
Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Individul Events SI 900 I 0 I (=0.5) I 7 I4 5 I5 80 b 7 b b 5 b 6 b 8 b 4 c c 4 c 0 x (=0.5) c 4 N 0 d 9 d 5 d 5 y d
More informationWhat s in Chapter 13?
Are nd volume 13 Wht s in Chpter 13? 13 01 re 13 0 Are of circle 13 03 res of trpeziums, kites nd rhomuses 13 04 surfce re of rectngulr prism 13 05 surfce re of tringulr prism 13 06 surfce re of cylinder
More informationLog1 Contest Round 3 Theta Individual. 4 points each 1 What is the sum of the first 5 Fibonacci numbers if the first two are 1, 1?
008 009 Log1 Contest Round Thet Individul Nme: points ech 1 Wht is the sum of the first Fiboncci numbers if the first two re 1, 1? If two crds re drwn from stndrd crd deck, wht is the probbility of drwing
More informationAnswers to Exercises. c 2 2ab b 2 2ab a 2 c 2 a 2 b 2
Answers to Eercises CHAPTER 9 CHAPTER LESSON 9. CHAPTER 9 CHAPTER. c 9. cm. cm. b 5. cm. d 0 cm 5. s cm. c 8.5 cm 7. b cm 8.. cm 9. 0 cm 0. s.5 cm. r cm. 7 ft. 5 m.. cm 5.,, 5. 8 m 7. The re of the lrge
More informationfractions Let s Learn to
5 simple lgebric frctions corne lens pupil retin Norml vision light focused on the retin concve lens Shortsightedness (myopi) light focused in front of the retin Corrected myopi light focused on the retin
More informationShape and measurement
C H A P T E R 5 Shpe nd mesurement Wht is Pythgors theorem? How do we use Pythgors theorem? How do we find the perimeter of shpe? How do we find the re of shpe? How do we find the volume of shpe? How do
More informationPre Regional Mathematical Olympiad, 2016 Delhi Region Set C
Pre Regionl Mthemticl Olympid, 06 Delhi Region Set C Mimum Mrks: 50 Importnt Note: The nswer to ech question is n integer between 0 nd 06. Ech Cndidte must write the finl nswer (in the spce provided) s,
More informationForm 5 HKCEE 1990 Mathematics II (a 2n ) 3 = A. f(1) B. f(n) A. a 6n B. a 8n C. D. E. 2 D. 1 E. n. 1 in. If 2 = 10 p, 3 = 10 q, express log 6
Form HK 9 Mthemtics II.. ( n ) =. 6n. 8n. n 6n 8n... +. 6.. f(). f(n). n n If = 0 p, = 0 q, epress log 6 in terms of p nd q.. p q. pq. p q pq p + q Let > b > 0. If nd b re respectivel the st nd nd terms
More informationMinnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017
Minnesot Stte University, Mnkto 44 th Annul High School Mthemtics Contest April, 07. A 5 ft. ldder is plced ginst verticl wll of uilding. The foot of the ldder rests on the floor nd is 7 ft. from the wll.
More informationPROPERTIES OF AREAS In general, and for an irregular shape, the definition of the centroid at position ( x, y) is given by
PROPERTES OF RES Centroid The concept of the centroid is prol lred fmilir to ou For plne shpe with n ovious geometric centre, (rectngle, circle) the centroid is t the centre f n re hs n is of smmetr, the
More information10 If 3, a, b, c, 23 are in A.S., then a + b + c = 15 Find the perimeter of the sector in the figure. A. 1:3. A. 2.25cm B. 3cm
HK MTHS Pper II P. If f ( x ) = 0 x, then f ( y ) = 6 0 y 0 + y 0 y 0 8 y 0 y If s = ind the gretest vlue of x + y if ( x, y ) is point lying in the region O (including the boundry). n [ + (n )d ], then
More informationMEP Practice Book ES3. 1. Calculate the size of the angles marked with a letter in each diagram. None to scale
ME rctice ook ES3 3 ngle Geometr 3.3 ngle Geometr 1. lculte the size of the ngles mrked with letter in ech digrm. None to scle () 70 () 20 54 65 25 c 36 (d) (e) (f) 56 62 d e 60 40 70 70 f 30 g (g) (h)
More information12.1 Introduction to Rational Expressions
. Introduction to Rtionl Epressions A rtionl epression is rtio of polynomils; tht is, frction tht hs polynomil s numertor nd/or denomintor. Smple rtionl epressions: 0 EVALUATING RATIONAL EXPRESSIONS To
More informationChapter 12. Lesson Geometry Worked-Out Solution Key. Prerequisite Skills (p. 790) A 5 } perimeter Guided Practice (pp.
Chpter 1 Prerequisite Skills (p. 790) 1. The re of regulr polygon is given by the formul A 5 1 p P, where is the pothem nd P is the perimeter.. Two polygons re similr if their corresponding ngles re congruent
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils
More informationMDPT Practice Test 1 (Math Analysis)
MDPT Prctice Test (Mth Anlysis). Wht is the rdin mesure of n ngle whose degree mesure is 7? ) 5 π π 5 c) π 5 d) 5 5. In the figure to the right, AB is the dimeter of the circle with center O. If the length
More information5.2 Exponent Properties Involving Quotients
5. Eponent Properties Involving Quotients Lerning Objectives Use the quotient of powers property. Use the power of quotient property. Simplify epressions involving quotient properties of eponents. Use
More informationIf C = 60 and = P, find the value of P. c 2 = a 2 + b 2 2abcos 60 = a 2 + b 2 ab a 2 + b 2 = c 2 + ab. c a
Answers: (000-0 HKMO Finl Events) Creted : Mr. Frncis Hung Lst updted: 0 June 08 Individul Events I P I P I P I P 5 7 0 0 S S S S Group Events G G G G 80 00 0 c 8 c c c d d 6 d 5 d 85 Individul Event I.,
More informationDownloaded From:
Downloded From: www.jsuniltutoril.weel.com UNIT-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES Like the crest of pecock so is mthemtics t the hed of ll knowledge.. At certin time in deer prk, the numer of
More informationList all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.
Mth Anlysis CP WS 4.X- Section 4.-4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether - is root of 0. Show
More information2 Calculate the size of each angle marked by a letter in these triangles.
Cmridge Essentils Mthemtics Support 8 GM1.1 GM1.1 1 Clculte the size of ech ngle mrked y letter. c 2 Clculte the size of ech ngle mrked y letter in these tringles. c d 3 Clculte the size of ech ngle mrked
More information1. Extend QR downwards to meet the x-axis at U(6, 0). y
In the digrm, two stright lines re to be drwn through so tht the lines divide the figure OPQRST into pieces of equl re Find the sum of the slopes of the lines R(6, ) S(, ) T(, 0) Determine ll liner functions
More informationUSA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year
1/1/21. Fill in the circles in the picture t right with the digits 1-8, one digit in ech circle with no digit repeted, so tht no two circles tht re connected by line segment contin consecutive digits.
More informationR(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of
Higher Mthemtics Ojective Test Prctice ook The digrm shows sketch of prt of the grph of f ( ). The digrm shows sketch of the cuic f ( ). R(, 8) f ( ) f ( ) P(, ) Q(, ) S(, ) Wht re the domin nd rnge of
More informationMATHEMATICS AND STATISTICS 1.2
MATHEMATICS AND STATISTICS. Apply lgebric procedures in solving problems Eternlly ssessed 4 credits Electronic technology, such s clcultors or computers, re not permitted in the ssessment of this stndr
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More informationLesson 1: Quadratic Equations
Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring
More informationLevel I MAML Olympiad 2001 Page 1 of 6 (A) 90 (B) 92 (C) 94 (D) 96 (E) 98 (A) 48 (B) 54 (C) 60 (D) 66 (E) 72 (A) 9 (B) 13 (C) 17 (D) 25 (E) 38
Level I MAML Olympid 00 Pge of 6. Si students in smll clss took n em on the scheduled dte. The verge of their grdes ws 75. The seventh student in the clss ws ill tht dy nd took the em lte. When her score
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time llowed Two hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions
More informationEquations and Inequalities
Equtions nd Inequlities Equtions nd Inequlities Curriculum Redy ACMNA: 4, 5, 6, 7, 40 www.mthletics.com Equtions EQUATIONS & Inequlities & INEQUALITIES Sometimes just writing vribles or pronumerls in
More informationIndividual Events I3 a 10 I4. d 90 angle 57 d Group Events. d 220 Probability
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 I 800 I Individul Events I 0 I4 no. of routes 6 I5 + + b b 0 b b c *8 missing c 0 c c See the remrk 600 d d 90 ngle 57
More information8Similarity ONLINE PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8.4 re nd volume scle fctors 8. Review Plese refer to the Resources t in the Prelims section of your eookplus for comprehensive step-y-step
More information15 - TRIGONOMETRY Page 1 ( Answers at the end of all questions )
- TRIGONOMETRY Pge P ( ) In tringle PQR, R =. If tn b c = 0, 0, then Q nd tn re the roots of the eqution = b c c = b b = c b = c [ AIEEE 00 ] ( ) In tringle ABC, let C =. If r is the inrdius nd R is the
More informationA-Level Mathematics Transition Task (compulsory for all maths students and all further maths student)
A-Level Mthemtics Trnsition Tsk (compulsory for ll mths students nd ll further mths student) Due: st Lesson of the yer. Length: - hours work (depending on prior knowledge) This trnsition tsk provides revision
More informationTHE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES
THE 08 09 KENNESW STTE UNIVERSITY HIGH SHOOL MTHEMTIS OMPETITION PRT I MULTIPLE HOIE For ech of the following questions, crefully blcken the pproprite box on the nswer sheet with # pencil. o not fold,
More informationLesson 1.6 Exercises, pages 68 73
Lesson.6 Exercises, pges 68 7 A. Determine whether ech infinite geometric series hs finite sum. How do you know? ) + +.5 + 6.75 +... r is:.5, so the sum is not finite. b) 0.5 0.05 0.005 0.0005... r is:
More information8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims
More informationAlg. Sheet (1) Department : Math Form : 3 rd prep. Sheet
Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (,
More informationCat Solved Paper. Fresh Paper. No. of Questions : 50 Time : 40 min
t Solved Pper Fresh Pper No. of Questions : 50 Time : 0 min Note Ech wrong nswer crry rd negtive mrk. irections for question number to 5 : nswer the questions independently of ech other. 9 6 5. The infinite
More information1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE
ELEMENTARY ALGEBRA nd GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the exmples, work the prolems, then check your nswers t the end of ech topic. If you don t get the nswer given, check
More informationTO: Next Year s AP Calculus Students
TO: Net Yer s AP Clculus Students As you probbly know, the students who tke AP Clculus AB nd pss the Advnced Plcement Test will plce out of one semester of college Clculus; those who tke AP Clculus BC
More informationIs there an easy way to find examples of such triples? Why yes! Just look at an ordinary multiplication table to find them!
PUSHING PYTHAGORAS 009 Jmes Tnton A triple of integers ( bc,, ) is clled Pythgoren triple if exmple, some clssic triples re ( 3,4,5 ), ( 5,1,13 ), ( ) fond of ( 0,1,9 ) nd ( 119,10,169 ). + b = c. For
More informationAlgebra & Functions (Maths ) opposite side
Instructor: Dr. R.A.G. Seel Trigonometr Algebr & Functions (Mths 0 0) 0th Prctice Assignment hpotenuse hpotenuse side opposite side sin = opposite hpotenuse tn = opposite. Find sin, cos nd tn in 9 sin
More informationSample pages. 9:04 Equations with grouping symbols
Equtions 9 Contents I know the nswer is here somewhere! 9:01 Inverse opertions 9:0 Solving equtions Fun spot 9:0 Why did the tooth get dressed up? 9:0 Equtions with pronumerls on both sides GeoGebr ctivity
More information50. Use symmetry to evaluate xx D is the region bounded by the square with vertices 5, Prove Property 11. y y CAS
68 CHAPTE MULTIPLE INTEGALS 46. e da, 49. Evlute tn 3 4 da, where,. [Hint: Eploit the fct tht is the disk with center the origin nd rdius is smmetric with respect to both es.] 5. Use smmetr to evlute 3
More informationPART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.
PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic
More informationMath 153: Lecture Notes For Chapter 5
Mth 5: Lecture Notes For Chpter 5 Section 5.: Eponentil Function f()= Emple : grph f ) = ( if = f() 0 - - - - - - Emple : Grph ) f ( ) = b) g ( ) = c) h ( ) = ( ) f() g() h() 0 0 0 - - - - - - - - - -
More informationSSC Mains Mock Test 227 [Answer with Solution]
SS Mins Mock Test 7 [nswer with Solution]. (D) E ccording to question, G 00 00 8 0 G GF, F D Let, GF GF Now, eterior ngle FGE FGE FEG Now, eterior ngle D In DE, + + 80º 80º 7 5º (ppro.). () I st digit
More informationLesson 2.4 Exercises, pages
Lesson. Exercises, pges A. Expnd nd simplify. ) + b) ( ) () 0 - ( ) () 0 c) -7 + d) (7) ( ) 7 - + 8 () ( 8). Expnd nd simplify. ) b) - 7 - + 7 7( ) ( ) ( ) 7( 7) 8 (7) P DO NOT COPY.. Multiplying nd Dividing
More information1. Twelve less than five times a number is thirty three. What is the number
Alger 00 Midterm Review Nme: Dte: Directions: For the following prolems, on SEPARATE PIECE OF PAPER; Define the unknown vrile Set up n eqution (Include sketch/chrt if necessr) Solve nd show work Answer
More informationIndividual Contest. English Version. Time limit: 90 minutes. Instructions:
Elementry Mthemtics Interntionl Contest Instructions: Individul Contest Time limit: 90 minutes Do not turn to the first pge until you re told to do so. Write down your nme, your contestnt numer nd your
More informationChapter 1: Fundamentals
Chpter 1: Fundmentls 1.1 Rel Numbers Types of Rel Numbers: Nturl Numbers: {1, 2, 3,...}; These re the counting numbers. Integers: {... 3, 2, 1, 0, 1, 2, 3,...}; These re ll the nturl numbers, their negtives,
More informationUNIT-4. File downloaded from For the things of this world cannot be made known without a knowledge of mathematics.
File downloded from http://jsuniltutoril.weely.com UNIT- For the things of this world cnnot e mde known without knowledge of mthemtics.. Solve y fctoriztion. - + ( ) = 0 Ans: + ( - ) = 0. [( + ) + ( -
More informationReview Factoring Polynomials:
Chpter 4 Mth 0 Review Fctoring Polynomils:. GCF e. A) 5 5 A) 4 + 9. Difference of Squres b = ( + b)( b) e. A) 9 6 B) C) 98y. Trinomils e. A) + 5 4 B) + C) + 5 + Solving Polynomils:. A) ( 5)( ) = 0 B) 4
More information13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS
33 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS As simple ppliction of the results we hve obtined on lgebric extensions, nd in prticulr on the multiplictivity of extension degrees, we cn nswer (in
More informationSet 1 Paper 2. 1 Pearson Education Asia Limited 2017
. A. A. C. B. C 6. A 7. A 8. B 9. C. D. A. B. A. B. C 6. D 7. C 8. B 9. C. D. C. A. B. A. A 6. A 7. A 8. D 9. B. C. B. D. D. D. D 6. D 7. B 8. C 9. C. D. B. B. A. D. C Section A. A (68 ) [ ( ) n ( n 6n
More informationSummer Work Packet for MPH Math Classes
Summer Work Pcket for MPH Mth Clsses Students going into Pre-clculus AC Sept. 018 Nme: This pcket is designed to help students sty current with their mth skills. Ech mth clss expects certin level of number
More informationARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac
REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b
More informationMath Sequences and Series RETest Worksheet. Short Answer
Mth 0- Nme: Sequences nd Series RETest Worksheet Short Answer Use n infinite geometric series to express 353 s frction [ mrk, ll steps must be shown] The popultion of community ws 3 000 t the beginning
More informationBefore we can begin Ch. 3 on Radicals, we need to be familiar with perfect squares, cubes, etc. Try and do as many as you can without a calculator!!!
Nme: Algebr II Honors Pre-Chpter Homework Before we cn begin Ch on Rdicls, we need to be fmilir with perfect squres, cubes, etc Try nd do s mny s you cn without clcultor!!! n The nth root of n n Be ble
More informationDistance And Velocity
Unit #8 - The Integrl Some problems nd solutions selected or dpted from Hughes-Hllett Clculus. Distnce And Velocity. The grph below shows the velocity, v, of n object (in meters/sec). Estimte the totl
More informationAdding and Subtracting Rational Expressions
6.4 Adding nd Subtrcting Rtionl Epressions Essentil Question How cn you determine the domin of the sum or difference of two rtionl epressions? You cn dd nd subtrct rtionl epressions in much the sme wy
More informationGoals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite
Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite
More informationIMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB
` K UKATP ALLY CE NTRE IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB 7-8 FIITJEE KUKATPALLY CENTRE: # -97, Plot No, Opp Ptel Kunt Hud Prk, Vijngr Colon, Hderbd - 5 7 Ph: -66 Regd
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More information3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles.
3 ngle Geometry MEP Prtie ook S3 3.1 Mesuring ngles 1. Using protrtor, mesure the mrked ngles. () () (d) (e) (f) 2. Drw ngles with the following sizes. () 22 () 75 120 (d) 90 (e) 153 (f) 45 (g) 180 (h)
More informationBelievethatyoucandoitandyouar. Mathematics. ngascannotdoonlynotyetbelieve thatyoucandoitandyouarehalfw. Algebra
Believethtoucndoitndour ehlfwtherethereisnosuchthi Mthemtics ngscnnotdoonlnotetbelieve thtoucndoitndourehlfw Alger therethereisnosuchthingsc nnotdoonlnotetbelievethto Stge 6 ucndoitndourehlfwther S Cooper
More informationJUST THE MATHS SLIDES NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 13.12 INTEGRATION APPLICATIONS 12 (Second moments of n re (B)) b A.J.Hobson 13.12.1 The prllel xis theorem 13.12.2 The perpendiculr xis theorem 13.12.3 The rdius of grtion
More informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationLUMS School of Science and Engineering
LUMS School of Science nd Engineering PH- Solution of ssignment Mrch, 0, 0 Brvis Lttice Answer: We hve given tht c.5(î + ĵ + ˆk) 5 (î + ĵ + ˆk) 0 (î + ĵ + ˆk) c (î + ĵ + ˆk) î + ĵ + ˆk + b + c î, b ĵ nd
More informationHQPD - ALGEBRA I TEST Record your answers on the answer sheet.
HQPD - ALGEBRA I TEST Record your nswers on the nswer sheet. Choose the best nswer for ech. 1. If 7(2d ) = 5, then 14d 21 = 5 is justified by which property? A. ssocitive property B. commuttive property
More information9.5 Start Thinking. 9.5 Warm Up. 9.5 Cumulative Review Warm Up
9.5 Strt Thinking In Lesson 9.4, we discussed the tngent rtio which involves the two legs of right tringle. In this lesson, we will discuss the sine nd cosine rtios, which re trigonometric rtios for cute
More informationJEE Advnced Mths Assignment Onl One Correct Answer Tpe. The locus of the orthocenter of the tringle formed the lines (+P) P + P(+P) = 0, (+q) q+q(+q) = 0 nd = 0, where p q, is () hperol prol n ellipse
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationAlgebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1
Algebr Rediness PLACEMENT Frction Bsics Percent Bsics Algebr Bsics CRS Algebr CRS - Algebr Comprehensive Pre-Post Assessment CRS - Algebr Comprehensive Midterm Assessment Algebr Bsics CRS - Algebr Quik-Piks
More informationy = f(x) This means that there must be a point, c, where the Figure 1
Clculus Investigtion A Men Slope TEACHER S Prt 1: Understnding the Men Vlue Theorem The Men Vlue Theorem for differentition sttes tht if f() is defined nd continuous over the intervl [, ], nd differentile
More informationA LEVEL TOPIC REVIEW. factor and remainder theorems
A LEVEL TOPIC REVIEW unit C fctor nd reminder theorems. Use the Fctor Theorem to show tht: ) ( ) is fctor of +. ( mrks) ( + ) is fctor of ( ) is fctor of + 7+. ( mrks) +. ( mrks). Use lgebric division
More informationCONIC SECTIONS. Chapter 11
CONIC SECTIONS Chpter. Overview.. Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig..). Fig.. Suppose we rotte the line m round
More information1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE
ELEMENTARY ALGEBRA nd GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the exmples, work the prolems, then check your nswers t the end of ech topic. If you don t get the nswer given, check
More informationSpecial Numbers, Factors and Multiples
Specil s, nd Student Book - Series H- + 3 + 5 = 9 = 3 Mthletics Instnt Workooks Copyright Student Book - Series H Contents Topics Topic - Odd, even, prime nd composite numers Topic - Divisiility tests
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission
M 30 Coimisiún n Scrúduithe Stáit Stte Exmintions Commission LEAVING CERTIFICATE EXAMINATION, 005 MATHEMATICS HIGHER LEVEL PAPER ( 300 mrks ) MONDAY, 3 JUNE MORNING, 9:30 to :00 Attempt FIVE questions
More informationMATH STUDENT BOOK. 10th Grade Unit 5
MATH STUDENT BOOK 10th Grde Unit 5 Unit 5 Similr Polygons MATH 1005 Similr Polygons INTRODUCTION 3 1. PRINCIPLES OF ALGEBRA 5 RATIOS AND PROPORTIONS 5 PROPERTIES OF PROPORTIONS 11 SELF TEST 1 16 2. SIMILARITY
More informationLoudoun Valley High School Calculus Summertime Fun Packet
Loudoun Vlley High School Clculus Summertime Fun Pcket We HIGHLY recommend tht you go through this pcket nd mke sure tht you know how to do everything in it. Prctice the problems tht you do NOT remember!
More informationLogarithms. Logarithm is another word for an index or power. POWER. 2 is the power to which the base 10 must be raised to give 100.
Logrithms. Logrithm is nother word for n inde or power. THIS IS A POWER STATEMENT BASE POWER FOR EXAMPLE : We lred know tht; = NUMBER 10² = 100 This is the POWER Sttement OR 2 is the power to which the
More informationMAC 1105 Final Exam Review
1. Find the distnce between the pir of points. Give n ect, simplest form nswer nd deciml pproimtion to three plces., nd, MAC 110 Finl Em Review, nd,0. The points (, -) nd (, ) re endpoints of the dimeter
More information10.2 The Ellipse and the Hyperbola
CHAPTER 0 Conic Sections Solve. 97. Two surveors need to find the distnce cross lke. The plce reference pole t point A in the digrm. Point B is meters est nd meter north of the reference point A. Point
More informationThe Trapezoidal Rule
_.qd // : PM Pge 9 SECTION. Numericl Integrtion 9 f Section. The re of the region cn e pproimted using four trpezoids. Figure. = f( ) f( ) n The re of the first trpezoid is f f n. Figure. = Numericl Integrtion
More informationGRADE 4. Division WORKSHEETS
GRADE Division WORKSHEETS Division division is shring nd grouping Division cn men shring or grouping. There re cndies shred mong kids. How mny re in ech shre? = 3 There re 6 pples nd go into ech bsket.
More informationEquations, expressions and formulae
Get strted 2 Equtions, epressions nd formule This unit will help you to work with equtions, epressions nd formule. AO1 Fluency check 1 Work out 2 b 2 c 7 2 d 7 2 2 Simplify by collecting like terms. b
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationFaith Scholarship Service Friendship
Immcult Mthemtics Summer Assignment The purpose of summer ssignment is to help you keep previously lerned fcts fresh in your mind for use in your net course. Ecessive time spent reviewing t the beginning
More information8.6 The Hyperbola. and F 2. is a constant. P F 2. P =k The two fixed points, F 1. , are called the foci of the hyperbola. The line segments F 1
8. The Hperol Some ships nvigte using rdio nvigtion sstem clled LORAN, which is n cronm for LOng RAnge Nvigtion. A ship receives rdio signls from pirs of trnsmitting sttions tht send signls t the sme time.
More informationObjective: Use the Pythagorean Theorem and its converse to solve right triangle problems. CA Geometry Standard: 12, 14, 15
Geometry CP Lesson 8.2 Pythgoren Theorem nd its Converse Pge 1 of 2 Ojective: Use the Pythgoren Theorem nd its converse to solve right tringle prolems. CA Geometry Stndrd: 12, 14, 15 Historicl Bckground
More informationJUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson
JUST THE MATHS UNIT NUMBE 13.1 INTEGATION APPLICATIONS 1 (Second moments of n re (B)) b A.J.Hobson 13.1.1 The prllel xis theorem 13.1. The perpendiculr xis theorem 13.1.3 The rdius of grtion of n re 13.1.4
More informationl 2 p2 n 4n 2, the total surface area of the
Week 6 Lectures Sections 7.5, 7.6 Section 7.5: Surfce re of Revolution Surfce re of Cone: Let C be circle of rdius r. Let P n be n n-sided regulr polygon of perimeter p n with vertices on C. Form cone
More informationIDENTITIES FORMULA AND FACTORISATION
SPECIAL PRODUCTS AS IDENTITIES FORMULA AND FACTORISATION. Find the product of : (i) (n + ) nd ((n + 5) ( + 0.) nd ( + 0.5) (iii) (y + 0.7) nd (y + 0.) (iv) + 3 nd + 3 (v) y + 5 nd 3 y + (iv) 5 + 7 nd +
More informationNat 5 USAP 3(b) This booklet contains : Questions on Topics covered in RHS USAP 3(b) Exam Type Questions Answers. Sourced from PEGASYS
Nt USAP This ooklet contins : Questions on Topics covered in RHS USAP Em Tpe Questions Answers Sourced from PEGASYS USAP EF. Reducing n lgeric epression to its simplest form / where nd re of the form (
More informationMath 1132 Worksheet 6.4 Name: Discussion Section: 6.4 Work
Mth 1132 Worksheet 6.4 Nme: Discussion Section: 6.4 Work Force formul for springs. By Hooke s Lw, the force required to mintin spring stretched x units beyond its nturl length is f(x) = kx where k is positive
More informationMath 113 Exam 2 Practice
Mth 3 Exm Prctice Februry 8, 03 Exm will cover 7.4, 7.5, 7.7, 7.8, 8.-3 nd 8.5. Plese note tht integrtion skills lerned in erlier sections will still be needed for the mteril in 7.5, 7.8 nd chpter 8. This
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More information