Answers to Exercises. c 2 2ab b 2 2ab a 2 c 2 a 2 b 2

Size: px
Start display at page:

Download "Answers to Exercises. c 2 2ab b 2 2ab a 2 c 2 a 2 b 2"

Transcription

1 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 squre is re of tringle re of smll squre. c b (b ) c b b b c b b b c 9 8. Smple nswer: Yes, ABC XYZ b SSS. Both tringles re right tringles, so ou cn use the Pthgoren Theorem to find tht CB ZY cm cm Mrk the unnmed ngles s shown in the figure below. B the Liner Pir Conjecture, p 0 80, so p 0. B AIA, m q. B the Tringle Sum Conjecture, q p n 80. Substitute m q nd p 0 to get m 0 n 80. m n 0. m 0 p q n Or use the Eterior Angle Conjecture to get q n 0. B AIA, q m. Substituting, m n 0.., b 7, c 0, d, e 90, f 7, g 7, h 7, n 7, r, s 7, t 7, u, v 7. Possible eplntion: B the Tngent Conjecture, the qudrilterl contining g hs two right ngles formed b rdii intersecting tngent lines. Using c 0 nd the Qudrilterl Sum Conjecture, g , so g 7. The ngle mesures e nd f nd the mesure of the inscribed ngle tht intercepts the rc with mesure u sum to 80. Using e 90 nd f 7, the inscribed ngle mesures. Using the Inscribed Angle Conjecture, u.. T T Answers to Eercises ANSWERS TO EXERCISES 05

2 Answers to Eercises LESSON 9.. es. es. no. no 5. no. no 7. no 8. No, the given lengths re not Pthgoren triple cm 0. units. 7. m., 8, 0. 0 cm.. ft cm. 0 m 7. cm 7b. 7.8 cm 8. Smple nswer: The numbers given stisf the Pthgoren Theorem, so the tringle is right tringle; but the right ngle should be inscribed in n rc of 80. Thus the tringle is not right tringle. 9. Smple nswer: (BD) 7; (BC) (BD) 9 08; then (AB) (BC) (AC) ( 08 ), so ABC is right tringle b the Converse of the Pthgoren Theorem. 0. centroid. 0. Becuse mdcf 90, mdce (90 ). Becuse DCE is isosceles, mdec (90 ). md 80 (90 ).Becuse D is centrl ngle,.therefore,.. The pth from C to M to T lies on stright line nd therefore must be shorter thn the pth from C to A to T. P C. 790 squre units A U M T B 0 ANSWERS TO EXERCISES

3 USING YOUR ALGEBRA SKILLS Answers will vr. Possible nswer: The length of the hpotenuse of n isosceles right tringle with legs of length units is 8 units. This is the sme s,or. 7. The hpotenuse represents 5 units. In the second right tringle, the legs hve lengths nd, so the hpotenuse hs length 0.The length of the hpotenuse is twice the length of the hpotenuse of the smller tringle, so Possible nswer: A right tringle with legs of lengths nd units hs hpotenuse of length 0 units. A right tringle with legs of lengths nd units hs hpotenuse of length Possible nswer: A right tringle with legs of lengths nd units hs hpotenuse of length units. 0 0.,. Becuse is twice s long s,, so Answers to Eercises ANSWERS TO EXERCISES 07

4 Answers to Eercises. 7 cm. cm. 0 cm, 5 cm. 0 cm, 0 cm 5. cm, 7 cm. 7 cm 7. cm cm, 00 cm 9. cm 0., LESSON 9.. A tringle must hve sides whose lengths re multiples of,, nd. The tringle shown does not reflect this rule.. Possible nswer: Use nd possible nswer: 8. Possible nswer: Use 5 nd 5.. c Strt with the Pthgoren Theorem. c Combine like terms. c Tke the squre root of both sides m 9.7 m m Construct n isosceles right tringle with legs of length, construct tringle with legs of lengths nd,nd construct right tringle with legs of lengths nd Ares:.5 cm,8 cm,.5 cm ; tht is, the sum of the res of the semicircles on the two legs is equl to the re of the semicircle on the hpotenuse.. 7. chih. Etend the rs tht form the right ngle. m m5 80 b the Liner Pir Conjecture, nd it s given tht m5 90. m 90. m m m m m m m 90. m m b AIA. m m CDA, AEC, AEB, BFA, BFC 5b. MDB, MEB, MEC, MFC, MFA ANSWERS TO EXERCISES

5 LESSON 9.. No. The spce digonl of the bo is bout.5 in.. 0 m. 50 km/h. 8 ft 5. re: 0 m ; cost: $700. surfce re of prism 7 80 cm.8 cm ; surfce re of clinder 78 cm 5.0 cm 7. cm 0.8 cm ft;. lb 9. 0 ft-lb 9b. 0 lb 9c. 0 lb 0. bout. ft... units. 8 cm 5. Drw rdii CD nd CB. ABC ADC 90. For qudrilterl ABCD, 5 90 mc 90 0, so mc. BD but 0.., 7. SAA 8. orthocenter PO Answers to Eercises ANSWERS TO EXERCISES 09

6 LESSON units. 5 units. units. 5 m units. isosceles 7. rectngle prllelogrm H D A C B 8 0 E F b. Circle A: ( ) ( ) ; Circle B: ( ) c. ( h) ( k) (r). ( ) 5. Center is (0, ), r 9.. ( ) ( ) 8 5. units 5b. 7 units 5c. ( ) ( ) z (z ). 8.5 units 7. units 8. n (n ) (n ) (n ) k, m.,, Answers to Eercises 9. kite K 8 J 8 0 L 0. squre I G. 9 cm. The ngle of rottion is pproimtel 77. Connect two pirs of corresponding points. Construct the perpendiculr bisector of ech segment. The point where the perpendiculr bisectors meet is the center of rottion.. An long digonl of regulr hegon divides it into two congruent qudrilterls. Ech ngle of regulr hegon is ( ) 80 0, nd the digonl divides two of the 0 ngles into 0 ngles. Look t the digonl s trnsversl. The lternte interior ngles re congruent, thus the opposite sides of regulr hegon re prllel. 8 P M O 0 0 N (0, ) (, ) (, ) Circle A (, ) Circle B 0 ANSWERS TO EXERCISES

7 LESSON cm 5.5 cm. (8 ) m 9. m. 5 cm cm. 0 cm 77.0 cm 5. m 5. m. (5 8) cm 0.5 cm 7. cm 9. cm 8. (0 8) m 8.5 m 9. 0 cm 0. Possible proof: Given: Circle C with tngents AM nd AN Show: AM AN M. cm. cm cm 8.8 cm. 7 cm 7. Inscribed circle: cm. Circumscribed circle: cm. The re of the circumscribed circle is four times s gret s the re of the inscribed circle ( ) ( ) 0. The dimeter is the trnsversl, nd the chords re prllel b the Converse of the Prllel Lines Conjecture. The chords re congruent becuse the cn be shown to be the sme distnce from the center. (Drw perpendiculr from ech chord to the center nd use AAS nd CPCTC.) Smple construction: C N Add MC,NC nd AC to the digrm s shown. B the Tngent Conjecture, M nd N re right ngles, so AMC nd ANC re right tringles. Using the Pthgoren Theorem, (AM) (MC) (AC) nd (AN) (NC) (AC).Solvingfor AM nd AN, AM (AC) (MC) nd AN (AC).BecuseMC (NC) nd NC re rdii of the sme circle, the hve the sme lengths. So, substitute MC for NC in the second eqution: AN (AC) (MC) AM.Therefore, AM AN.. 8 m. cm 08 cm. 9 cm A. Becuse crpenter s squre hs right ngle nd both rdii re perpendiculr to the tngents, squre is formed. The rdius is 0 in., therefore the dimeter is 0 in. 0 in. d 0 in. 0 in. 0 in. 0 in. b. Possible nswer: Mesure the circumference with string nd divide b.. 5 Answers to Eercises ANSWERS TO EXERCISES

8 Answers to Eercises CHAPTER 9 REVIEW. 0 cm. 0 cm. obtuse. cm 5.,., cm. cm 8. d cm 7.0 cm 9. cm 0. 7 in. in. cm 75. cm. ( ) cm.8 cm..8 cm. isosceles right 5. No. The closest she cn come to cmp is 0 km.. No. The 5 cm digonl is the longer digonl. 7.. km; 8 min 8. es 9. 9 ft 0. 5 ft. 50 mi. 707 m. nd 8. m 5.. No. If ou reflect one of the right tringles into the center piece, ou ll see tht the re of the kite is lmost hlf gin s lrge s the re of ech of the other tringles. Etr The qurter-circle gives the mimum re. Tringle: s 5 A s Squre: _ s A s s s Qurter-circle: s s r r s A s s s s s s s s 5 _ s s m 0. 0 Or students might compre res b ssuming the short leg of the tringle is. The re of ech tringle is then 0.87 nd the re of the kite is.7.. ; 0; 0. The rule is n if n is even, but 0 if n is odd. ANSWERS TO EXERCISES

9 . in./s. in./s. true. true 5. Flse. The hpotenuse is of length.. true 7. flse; AB ( ) ( ) 8. Flse. A glide reflection is combintion of trnsltion nd reflection. 9. Flse. Equilterl tringles, squres, nd regulr hegons cn be used to crete monohedrl tesselltions. 0. true. D. B. A. C 5. C. D 7. See flowchrt below. 8. W B 8-bll 9. cm ; 7.7 cm cm.9 cm 5. bout 55.9 m 5. bout.5 cm 5. 8 cm 5. ft N S A Cue bll E Answers to Eercises 7. (Chpter 9 Review) ABCD is rectngle Given D B Definition of rectngle ABCD is prllelogrm Definition of rectngle DA CB Definition of prllelogrm AC AC 5 DAC BCA AIA Conjecture 7 ABC CDA SAA Congruence Conjecture Sme segment ANSWERS TO EXERCISES

+ 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

MEP Practice Book ES3. 1. Calculate the size of the angles marked with a letter in each diagram. None to scale

MEP 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 information

GEOMETRICAL PROPERTIES OF ANGLES AND CIRCLES, ANGLES PROPERTIES OF TRIANGLES, QUADRILATERALS AND POLYGONS:

GEOMETRICAL PROPERTIES OF ANGLES AND CIRCLES, ANGLES PROPERTIES OF TRIANGLES, QUADRILATERALS AND POLYGONS: GEOMETRICL PROPERTIES OF NGLES ND CIRCLES, NGLES PROPERTIES OF TRINGLES, QUDRILTERLS ND POLYGONS: 1.1 TYPES OF NGLES: CUTE NGLE RIGHT NGLE OTUSE NGLE STRIGHT NGLE REFLEX NGLE 40 0 4 0 90 0 156 0 180 0

More information

MDPT Practice Test 1 (Math Analysis)

MDPT 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 information

Unit 5 Review. For each problem (1-4) a and b are segment lengths; x and y are angle measures.

Unit 5 Review. For each problem (1-4) a and b are segment lengths; x and y are angle measures. For ech problem (1-4) nd b re segment lengths; x nd y re ngle mesures. 1. Figure is Prllelogrm 2. Figure is Squre 21 36 16 b 104 3 2 6 b = 21 b = 16 x = 104 y = 40 = 3 2 b = 6 x = 45 y = 90 3. Figure is

More information

Answers for Lesson 3-1, pp Exercises

Answers for Lesson 3-1, pp Exercises Answers for Lesson -, pp. Eercises * ) PQ * ) PS * ) PS * ) PS * ) SR * ) QR * ) QR * ) QR. nd with trnsversl ; lt. int. '. nd with trnsversl ; lt. int. '. nd with trnsversl ; sme-side int. '. nd with

More information

Chapter 12. Lesson Geometry Worked-Out Solution Key. Prerequisite Skills (p. 790) A 5 } perimeter Guided Practice (pp.

Chapter 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 information

2) Three noncollinear points in Plane M. [A] A, D, E [B] A, B, E [C] A, B, D [D] A, E, H [E] A, H, M [F] H, A, B

2) Three noncollinear points in Plane M. [A] A, D, E [B] A, B, E [C] A, B, D [D] A, E, H [E] A, H, M [F] H, A, B Review Use the points nd lines in the digrm to identify the following. 1) Three colliner points in Plne M. [],, H [],, [],, [],, [],, M [] H,, M 2) Three noncolliner points in Plne M. [],, [],, [],, [],,

More information

15 - TRIGONOMETRY Page 1 ( Answers at the end of all questions )

15 - 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 information

3 x x 3x x. 3x x x 6 x 3. PAKTURK 8 th National Interschool Maths Olympiad, h h

3 x x 3x x. 3x x x 6 x 3. PAKTURK 8 th National Interschool Maths Olympiad, h h PAKTURK 8 th Ntionl Interschool Mths Olmpid,.9. Q: Evlute 6.9. 6 6 6... 8 8...... Q: Evlute bc bc. b. c bc.9.9b.9.9bc Q: Find the vlue of h in the eqution h 7 9 7.. bc. bc bc. b. c bc bc bc bc......9 h

More information

Log1 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?

Log1 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 information

/ 3, then (A) 3(a 2 m 2 + b 2 ) = 4c 2 (B) 3(a 2 + b 2 m 2 ) = 4c 2 (C) a 2 m 2 + b 2 = 4c 2 (D) a 2 + b 2 m 2 = 4c 2

/ 3, then (A) 3(a 2 m 2 + b 2 ) = 4c 2 (B) 3(a 2 + b 2 m 2 ) = 4c 2 (C) a 2 m 2 + b 2 = 4c 2 (D) a 2 + b 2 m 2 = 4c 2 SET I. If the locus of the point of intersection of perpendiculr tngents to the ellipse x circle with centre t (0, 0), then the rdius of the circle would e + / ( ) is. There re exctl two points on the

More information

Andrew Ryba Math Intel Research Final Paper 6/7/09 (revision 6/17/09)

Andrew Ryba Math Intel Research Final Paper 6/7/09 (revision 6/17/09) Andrew Ryb Mth ntel Reserch Finl Pper 6/7/09 (revision 6/17/09) Euler's formul tells us tht for every tringle, the squre of the distnce between its circumcenter nd incenter is R 2-2rR, where R is the circumrdius

More information

Algebra & Functions (Maths ) opposite side

Algebra & 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 information

GEOMETRY OF THE CIRCLE TANGENTS & SECANTS

GEOMETRY OF THE CIRCLE TANGENTS & SECANTS Geometry Of The ircle Tngents & Secnts GEOMETRY OF THE IRLE TNGENTS & SENTS www.mthletics.com.u Tngents TNGENTS nd N Secnts SENTS Tngents nd secnts re lines tht strt outside circle. Tngent touches the

More information

Level 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 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 information

ICSE Board Class IX Mathematics Paper 4 Solution

ICSE Board Class IX Mathematics Paper 4 Solution ICSE Bord Clss IX Mthemtics Pper Solution SECTION A (0 Mrks) Q.. () Consider x y 6 5 5 x y 6 5 5 0 6 0 6 x y 6 50 8 5 6 7 6 x y 6 7 6 x y 6 x 7,y (b) Dimensions of the brick: Length (l) = 0 cm, bredth

More information

JEE 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 information

What s in Chapter 13?

What 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 information

IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB

IMPORTANT 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 information

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

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 information

13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS

13.3 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 information

Time : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 S E CT I O N - A

Time : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 S E CT I O N - A Time : hours 0 - Mthemtics - Mrch 007 Mrks : 100 Pg - 1 Instructions : 1. Answer ll questions.. Write your nswers ccording to the instructions given below with the questions.. Begin ech section on new

More information

Coimisiún na Scrúduithe Stáit State Examinations Commission

Coimisiún 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 information

Form 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 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 information

8Similarity 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.

8Similarity 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 information

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF DOWNLOAD FREE FROM www.tekoclsses.com, PH.: 0 903 903 7779, 98930 5888 Some questions (Assertion Reson tpe) re given elow. Ech question contins Sttement (Assertion) nd Sttement (Reson). Ech question hs

More information

Set 1 Paper 2. 1 Pearson Education Asia Limited 2017

Set 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 information

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES SECTION MULTIPLE CHOICE QUESTIONS QUESTION QUESTION

More information

Alg. Sheet (1) Department : Math Form : 3 rd prep. Sheet

Alg. 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 information

A LEVEL TOPIC REVIEW. factor and remainder theorems

A 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 information

Math 1102: Calculus I (Math/Sci majors) MWF 3pm, Fulton Hall 230 Homework 2 solutions

Math 1102: Calculus I (Math/Sci majors) MWF 3pm, Fulton Hall 230 Homework 2 solutions Mth 1102: Clculus I (Mth/Sci mjors) MWF 3pm, Fulton Hll 230 Homework 2 solutions Plese write netly, nd show ll work. Cution: An nswer with no work is wrong! Do the following problems from Chpter III: 6,

More information

Lesson-5 ELLIPSE 2 1 = 0

Lesson-5 ELLIPSE 2 1 = 0 Lesson-5 ELLIPSE. An ellipse is the locus of point which moves in plne such tht its distnce from fied point (known s the focus) is e (< ), times its distnce from fied stright line (known s the directri).

More information

8Similarity 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.

8Similarity 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 information

Use the diagram to identify each angle pair as a linear pair, vertical angles, or neither.

Use the diagram to identify each angle pair as a linear pair, vertical angles, or neither. inl xm Review hpter 1 6 & hpter 9 Nme Use the points nd lines in the digrm to identify the following. 1) Three colliner points in Plne M. [],, H [],, [],, [],, [],, M [] H,, M 2) Three noncolliner points

More information

CONIC SECTIONS. Chapter 11

CONIC 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 information

Prerequisite Knowledge Required from O Level Add Math. d n a = c and b = d

Prerequisite Knowledge Required from O Level Add Math. d n a = c and b = d Prerequisite Knowledge Required from O Level Add Mth ) Surds, Indices & Logrithms Rules for Surds. b= b =. 3. 4. b = b = ( ) = = = 5. + b n = c+ d n = c nd b = d Cution: + +, - Rtionlising the Denomintor

More information

Pre-AP Geometry Worksheet 5.2: Similar Right Triangles

Pre-AP Geometry Worksheet 5.2: Similar Right Triangles ! re-a Geometr Worksheet 5.2: Similr Right Tringles Nme: te: eriod: Solve. Show ll work. Leve nswers s simplified rdicls on #1-5. For #6, round to the nerer tenth. 12!! 6! 1) =! 8! 6! 2) = 18! 8! w!+!9!

More information

Lesson 4.1 Triangle Sum Conjecture

Lesson 4.1 Triangle Sum Conjecture Lesson 4.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q 2., y 3., b 31 82 p 98 q 28 53 y 17 79 23 50 b 4. r, s, 5., y 6. y t t s r 100 85 100 y 30 4 7 y 31 7. s 8.

More information

Precalculus Due Tuesday/Wednesday, Sept. 12/13th Mr. Zawolo with questions.

Precalculus Due Tuesday/Wednesday, Sept. 12/13th  Mr. Zawolo with questions. Preclculus Due Tuesd/Wednesd, Sept. /th Emil Mr. Zwolo (isc.zwolo@psv.us) with questions. 6 Sketch the grph of f : 7! nd its inverse function f (). FUNCTIONS (Chpter ) 6 7 Show tht f : 7! hs n inverse

More information

LUMS School of Science and Engineering

LUMS 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 information

4. Statements Reasons

4. Statements Reasons Chpter 9 Answers Prentie-Hll In. Alterntive Ativity 9-. Chek students work.. Opposite sides re prllel. 3. Opposite sides re ongruent. 4. Opposite ngles re ongruent. 5. Digonls iset eh other. 6. Students

More information

Shape and measurement

Shape 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 information

USA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year

USA 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 information

CET MATHEMATICS 2013

CET MATHEMATICS 2013 CET MATHEMATICS VERSION CODE: C. If sin is the cute ngle between the curves + nd + 8 t (, ), then () () () Ans: () Slope of first curve m ; slope of second curve m - therefore ngle is o A sin o (). The

More information

Faith Scholarship Service Friendship

Faith 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 information

THE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES

THE 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 information

8.6 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

8.6 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 information

MORE FUNCTION GRAPHING; OPTIMIZATION. (Last edited October 28, 2013 at 11:09pm.)

MORE FUNCTION GRAPHING; OPTIMIZATION. (Last edited October 28, 2013 at 11:09pm.) MORE FUNCTION GRAPHING; OPTIMIZATION FRI, OCT 25, 203 (Lst edited October 28, 203 t :09pm.) Exercise. Let n be n rbitrry positive integer. Give n exmple of function with exctly n verticl symptotes. Give

More information

Chapter 4 Trigonometric Functions

Chapter 4 Trigonometric Functions Chter Trigonometric Functions Chter Trigonometric Functions Section. Angles nd Their Mesures Exlortion. r. rdins ( lengths of ted). No, not quite, since the distnce r would require iece of ted times s

More information

JEE(MAIN) 2015 TEST PAPER WITH SOLUTION (HELD ON SATURDAY 04 th APRIL, 2015) PART B MATHEMATICS

JEE(MAIN) 2015 TEST PAPER WITH SOLUTION (HELD ON SATURDAY 04 th APRIL, 2015) PART B MATHEMATICS JEE(MAIN) 05 TEST PAPER WITH SOLUTION (HELD ON SATURDAY 0 th APRIL, 05) PART B MATHEMATICS CODE-D. Let, b nd c be three non-zero vectors such tht no two of them re colliner nd, b c b c. If is the ngle

More information

SOLUTION OF TRIANGLES

SOLUTION OF TRIANGLES SOLUTION OF TIANGLES DPP by VK Sir B.TEH., IIT DELHI VK lsses, -9-40, Indr Vihr, Kot. Mob. No. 989060 . If cos A + cosb + cos = then the sides of the AB re in A.P. G.P H.P. none. If in tringle sin A :

More information

3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles.

3 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 information

MATHEMATICS AND STATISTICS 1.6

MATHEMATICS AND STATISTICS 1.6 MTHMTIS N STTISTIS 1.6 pply geometri resoning in solving prolems ternlly ssessed 4 redits S 91031 inding unknown ngles When finding the size of unknown ngles in figure, t lest two steps of resoning will

More information

2 Calculate the size of each angle marked by a letter in these triangles.

2 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 information

Essential Question What conjectures can you make about perpendicular lines?

Essential Question What conjectures can you make about perpendicular lines? 3. roofs with erpendiculr Lines Essentil Question Wht conjectures cn ou ke out perpendiculr lines? Writing onjectures Work with prtner. Fold piece of pper in hlf twice. Lel points on the two creses, s

More information

Section 1.3 Triangles

Section 1.3 Triangles Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior

More information

1 cos. cos cos cos cos MAT 126H Solutions Take-Home Exam 4. Problem 1

1 cos. cos cos cos cos MAT 126H Solutions Take-Home Exam 4. Problem 1 MAT 16H Solutions Tke-Home Exm 4 Problem 1 ) & b) Using the hlf-ngle formul for cosine, we get: 1 cos 1 4 4 cos cos 8 4 nd 1 8 cos cos 16 4 c) Using the hlf-ngle formul for tngent, we get: cot ( 3π 1 )

More information

Minnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017

Minnesota 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 information

QUANTITATIVE REASONING

QUANTITATIVE REASONING Quntittive Resoning QUNTITTIVE RESONING The quntittive resoning section tests your bility to use numbers nd mthemticl concepts to solve quntittive problems, nd your bility to nlyze dt presented in different

More information

Geometry AP Book 8, Part 2: Unit 3

Geometry AP Book 8, Part 2: Unit 3 Geometry ook 8, rt 2: Unit 3 IMRTNT NTE: For mny questions in this unit, there re multiple correct nswers, e.g. line segment cn e written s, RST is the sme s TSR, etc. Where pproprite, techers should e

More information

03 Qudrtic Functions Completing the squre: Generl Form f ( x) x + x + c f ( x) ( x + p) + q where,, nd c re constnts nd 0. (i) (ii) (iii) (iv) *Note t

03 Qudrtic Functions Completing the squre: Generl Form f ( x) x + x + c f ( x) ( x + p) + q where,, nd c re constnts nd 0. (i) (ii) (iii) (iv) *Note t A-PDF Wtermrk DEMO: Purchse from www.a-pdf.com to remove the wtermrk Add Mths Formule List: Form 4 (Updte 8/9/08) 0 Functions Asolute Vlue Function Inverse Function If f ( x ), if f ( x ) 0 f ( x) y f

More information

( ) Straight line graphs, Mixed Exercise 5. 2 b The equation of the line is: 1 a Gradient m= 5. The equation of the line is: y y = m x x = 12.

( ) Straight line graphs, Mixed Exercise 5. 2 b The equation of the line is: 1 a Gradient m= 5. The equation of the line is: y y = m x x = 12. Stright line grphs, Mied Eercise Grdient m ( y ),,, The eqution of the line is: y m( ) ( ) + y + Sustitute (k, ) into y + k + k k Multiply ech side y : k k The grdient of AB is: y y So: ( k ) 8 k k 8 k

More information

On the diagram below the displacement is represented by the directed line segment OA.

On the diagram below the displacement is represented by the directed line segment OA. Vectors Sclrs nd Vectors A vector is quntity tht hs mgnitude nd direction. One exmple of vector is velocity. The velocity of n oject is determined y the mgnitude(speed) nd direction of trvel. Other exmples

More information

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

More information

If 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

If 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 information

Drill Exercise Find the coordinates of the vertices, foci, eccentricity and the equations of the directrix of the hyperbola 4x 2 25y 2 = 100.

Drill Exercise Find the coordinates of the vertices, foci, eccentricity and the equations of the directrix of the hyperbola 4x 2 25y 2 = 100. Drill Exercise - 1 1 Find the coordintes of the vertices, foci, eccentricit nd the equtions of the directrix of the hperol 4x 5 = 100 Find the eccentricit of the hperol whose ltus-rectum is 8 nd conjugte

More information

PROPERTIES OF AREAS In general, and for an irregular shape, the definition of the centroid at position ( x, y) is given by

PROPERTIES 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 information

Mathematics Extension 2

Mathematics Extension 2 00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mthemtics Etension Generl Instructions Reding time 5 minutes Working time hours Write using blck or blue pen Bord-pproved clcultors my be used A tble of stndrd

More information

42nd International Mathematical Olympiad

42nd International Mathematical Olympiad nd Interntionl Mthemticl Olympid Wshington, DC, United Sttes of Americ July 8 9, 001 Problems Ech problem is worth seven points. Problem 1 Let ABC be n cute-ngled tringle with circumcentre O. Let P on

More information

1. If * is the operation defined by a*b = a b for a, b N, then (2 * 3) * 2 is equal to (A) 81 (B) 512 (C) 216 (D) 64 (E) 243 ANSWER : D

1. If * is the operation defined by a*b = a b for a, b N, then (2 * 3) * 2 is equal to (A) 81 (B) 512 (C) 216 (D) 64 (E) 243 ANSWER : D . If * is the opertion defined by *b = b for, b N, then ( * ) * is equl to (A) 8 (B) 5 (C) 6 (D) 64 (E) 4. The domin of the function ( 9)/( ),if f( ) = is 6, if = (A) (0, ) (B) (-, ) (C) (-, ) (D) (, )

More information

10 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

10 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 information

CHAPTER 6 Introduction to Vectors

CHAPTER 6 Introduction to Vectors CHAPTER 6 Introduction to Vectors Review of Prerequisite Skills, p. 73 "3 ".. e. "3. "3 d. f.. Find BC using the Pthgoren theorem, AC AB BC. BC AC AB 6 64 BC 8 Net, use the rtio tn A opposite tn A BC djcent.

More information

from X to GH. 17. What is the distance from M(9, 4) to N( 1, 2)? of A?geometry Review #1 for MP3 Exam A If MX 21.6, find LZ and MW.

from X to GH. 17. What is the distance from M(9, 4) to N( 1, 2)? of A?geometry Review #1 for MP3 Exam A If MX 21.6, find LZ and MW. Nme te _ lss GJ. Find m JX dtnce Eplin ngles re similr. why. Foundtions for. from X G. continued PQR UTS 0. mesure twice mesure 7. Wht dtnce from M9 ) its complement. Wht N ) Nme:_ mesure geometry Review

More information

R(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

R(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 information

Triangles The following examples explore aspects of triangles:

Triangles The following examples explore aspects of triangles: Tringles The following exmples explore spects of tringles: xmple 1: ltitude of right ngled tringle + xmple : tringle ltitude of the symmetricl ltitude of n isosceles x x - 4 +x xmple 3: ltitude of the

More information

T 1 T 2 T 3 T 4 They may be illustrated by triangular patterns of numbers (hence their name) as shown:

T 1 T 2 T 3 T 4 They may be illustrated by triangular patterns of numbers (hence their name) as shown: TOPIC 3: VISUAL EXPLANATIONS (PROOFS) (Pge references to Proof re to Bndll, P R et l, Proof in Mthemtics, KMEP, 2002). 3. The tringulr numbers form the sequence, 3, 6, 0,, 2,... T T 2 T 3 T 4 The m be

More information

Problem 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:

Problem 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 information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

More information

Similarity and Congruence

Similarity and Congruence Similrity nd ongruence urriculum Redy MMG: 201, 220, 221, 243, 244 www.mthletics.com SIMILRITY N ONGRUN If two shpes re congruent, it mens thy re equl in every wy ll their corresponding sides nd ngles

More information

A-Level Mathematics Transition Task (compulsory for all maths students and all further maths student)

A-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 information

Room: Portable # 2 Phone: MATHEMATICS 9

Room: Portable # 2 Phone: MATHEMATICS 9 Techer: Mr. A. Tsui Emil: tsui_ndrew@surreyschools.c Room: Portble # 2 Phone: 604-574-7407 MATHEMATICS 9 Mth 9 will build on concepts covered in Mth 8 nd introduce new skills which will be epnded on in

More information

JUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson

JUST 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 information

9.5 Start Thinking. 9.5 Warm Up. 9.5 Cumulative Review Warm Up

9.5 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 information

US01CMTH02 UNIT Curvature

US01CMTH02 UNIT Curvature Stu mteril of BSc(Semester - I) US1CMTH (Rdius of Curvture nd Rectifiction) Prepred by Nilesh Y Ptel Hed,Mthemtics Deprtment,VPnd RPTPScience College US1CMTH UNIT- 1 Curvture Let f : I R be sufficiently

More information

A B= ( ) because from A to B is 3 right, 2 down.

A B= ( ) because from A to B is 3 right, 2 down. 8. Vectors nd vector nottion Questions re trgeted t the grdes indicted Remember: mgnitude mens size. The vector ( ) mens move left nd up. On Resource sheet 8. drw ccurtely nd lbel the following vectors.

More information

( β ) touches the x-axis if = 1

( β ) touches the x-axis if = 1 Generl Certificte of Eduction (dv. Level) Emintion, ugust Comined Mthemtics I - Prt B Model nswers. () Let f k k, where k is rel constnt. i. Epress f in the form( ) Find the turning point of f without

More information

Mathematics Extension 1

Mathematics Extension 1 04 Bored of Studies Tril Emintions Mthemtics Etension Written by Crrotsticks & Trebl. Generl Instructions Totl Mrks 70 Reding time 5 minutes. Working time hours. Write using blck or blue pen. Blck pen

More information

First Semester Review Calculus BC

First Semester Review Calculus BC First Semester Review lculus. Wht is the coordinte of the point of inflection on the grph of Multiple hoice: No lcultor y 3 3 5 4? 5 0 0 3 5 0. The grph of piecewise-liner function f, for 4, is shown below.

More information

Chapter 7: Applications of Integrals

Chapter 7: Applications of Integrals Chpter 7: Applictions of Integrls 78 Chpter 7 Overview: Applictions of Integrls Clculus, like most mthemticl fields, egn with tring to solve everd prolems. The theor nd opertions were formlized lter. As

More information

Lesson 4.1 Triangle Sum Conjecture

Lesson 4.1 Triangle Sum Conjecture Lesson.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q., 3., 31 8 p 98 q 8 53 17 79 3 50. r, s, 5.,. t t 85 s 100 r 30 100 7 31 7. s 8. m 9. m s 7 35 m c c 10. Find

More information

Definition :- A shape has a line of symmetry if, when folded over the line. 1 line of symmetry 2 lines of symmetry

Definition :- A shape has a line of symmetry if, when folded over the line. 1 line of symmetry 2 lines of symmetry Symmetry Lines of Symmetry Definition :- A shpe hs line of symmetry if, when folded over the line the hlves of the shpe mtch up exctly. Some shpes hve more thn one line of symmetry : line of symmetry lines

More information

l 2 p2 n 4n 2, the total surface area of the

l 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 information

Instructor(s): Acosta/Woodard PHYSICS DEPARTMENT PHY 2049, Fall 2015 Midterm 1 September 29, 2015

Instructor(s): Acosta/Woodard PHYSICS DEPARTMENT PHY 2049, Fall 2015 Midterm 1 September 29, 2015 Instructor(s): Acost/Woodrd PHYSICS DEPATMENT PHY 049, Fll 015 Midterm 1 September 9, 015 Nme (print): Signture: On m honor, I hve neither given nor received unuthorized id on this emintion. YOU TEST NUMBE

More information

Cat Solved Paper. Fresh Paper. No. of Questions : 50 Time : 40 min

Cat 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 information

10.2 The Ellipse and the Hyperbola

10.2 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 information

Individual Events I3 a 10 I4. d 90 angle 57 d Group Events. d 220 Probability

Individual 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 information

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014 SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.

More information

1. If y 2 2x 2y + 5 = 0 is (A) a circle with centre (1, 1) (B) a parabola with vertex (1, 2) 9 (A) 0, (B) 4, (C) (4, 4) (D) a (C) c = am m.

1. If y 2 2x 2y + 5 = 0 is (A) a circle with centre (1, 1) (B) a parabola with vertex (1, 2) 9 (A) 0, (B) 4, (C) (4, 4) (D) a (C) c = am m. SET I. If y x y + 5 = 0 is (A) circle with centre (, ) (B) prbol with vertex (, ) (C) prbol with directrix x = 3. The focus of the prbol x 8x + y + 7 = 0 is (D) prbol with directrix x = 9 9 (A) 0, (B)

More information

JUST THE MATHS SLIDES NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson

JUST 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 information