Lesson 2.1 Inductive Reasoning



Similar documents
Angles 2.1. Exercise Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example

Interior and exterior angles add up to 180. Level 5 exterior angle

The remaining two sides of the right triangle are called the legs of the right triangle.

MATH PLACEMENT REVIEW GUIDE

Lesson 4.1 Triangle Sum Conjecture

Maximum area of polygon

1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.

Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right.

End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.

Geometry 7-1 Geometric Mean and the Pythagorean Theorem

H SERIES. Area and Perimeter. Curriculum Ready.

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

Ratio and Proportion

SOLVING EQUATIONS BY FACTORING

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Chapter. Contents: A Constructing decimal numbers

Volumes by Cylindrical Shells: the Shell Method

SECTION 7-2 Law of Cosines

50 MATHCOUNTS LECTURES (10) RATIOS, RATES, AND PROPORTIONS

Operations with Polynomials

84 cm 30 cm. 12 in. 7 in. Proof. Proof of Theorem 7-4. Given: #QXY with 6 Prove: * RS * XY

UNCORRECTED SAMPLE PAGES

Section 5-4 Trigonometric Functions

Reasoning to Solve Equations and Inequalities

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

How To Find The Re Of Tringle

Words Symbols Diagram. abcde. a + b + c + d + e

SOLVING QUADRATIC EQUATIONS BY FACTORING

Review. Scan Conversion. Rasterizing Polygons. Rasterizing Polygons. Triangularization. Convex Shapes. Utah School of Computing Spring 2013

The art of Paperarchitecture (PA). MANUAL

1 Fractions from an advanced point of view

Factoring Polynomials

Section 7-4 Translation of Axes

Unit 6: Exponents and Radicals

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m

AREA OF A SURFACE OF REVOLUTION

c b N/m 2 (0.120 m m 3 ), = J. W total = W a b + W b c 2.00

RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS

Answer, Key Homework 10 David McIntyre 1

Introduction. Teacher s lesson notes The notes and examples are useful for new teachers and can form the basis of lesson plans.

A.7.1 Trigonometric interpretation of dot product A.7.2 Geometric interpretation of dot product

Math 314, Homework Assignment Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Homework 3 Solutions

Chapter. Fractions. Contents: A Representing fractions

Angles and Triangles

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

EQUATIONS OF LINES AND PLANES

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Quick Guide to Lisp Implementation

Lecture 3 Gaussian Probability Distribution

Calculating Principal Strains using a Rectangular Strain Gage Rosette

Further applications of area and volume

The Pythagorean Theorem

Graphs on Logarithmic and Semilogarithmic Paper

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Learning Outcomes. Computer Systems - Architecture Lecture 4 - Boolean Logic. What is Logic? Boolean Logic 10/28/2010

Pure C4. Revision Notes

1.2 The Integers and Rational Numbers

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn

Radius of the Earth - Radii Used in Geodesy James R. Clynch Naval Postgraduate School, 2002

Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur

Thinking out of the Box... Problem It s a richer problem than we ever imagined

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Active Directory Service

NQF Level: 2 US No: 7480

If two triangles are perspective from a point, then they are also perspective from a line.

Vectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a.

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

32. The Tangency Problem of Apollonius.

Released Assessment Questions, 2015 QUESTIONS

MA Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!

MATH 150 HOMEWORK 4 SOLUTIONS

10.6 Applications of Quadratic Equations

Vectors Recap of vectors

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS

1 GSW IPv4 Addressing

Rotating DC Motors Part II

Math Review for Algebra and Precalculus

Experiment 6: Friction

Orthopoles and the Pappus Theorem

Solving BAMO Problems

Physics 43 Homework Set 9 Chapter 40 Key

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES

5.6 POSITIVE INTEGRAL EXPONENTS

2. Properties of Functions

KEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001

9 CONTINUOUS DISTRIBUTIONS

WHAT HAPPENS WHEN YOU MIX COMPLEX NUMBERS WITH PRIME NUMBERS?

Integration by Substitution

4.11 Inner Product Spaces

Brillouin Zones. Physics 3P41 Chris Wiebe

e.g. f(x) = x domain x 0 (cannot find the square root of negative values)

Review Problems for the Final of Math 121, Fall 2014

Transcription:

Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10, 90,, 6. 1,, 9, 7, 81,, 7. 1,, 14, 0,,, For Eerises 8 10, use inutive resoning to rw the net two shpes in eh piture pttern. 8. 9. 10. ( 1, ) (, 1) (, 1) For Eerises 11 1, use inutive resoning to test eh onjeture. Deie if the onjeture seems true or flse. If it seems flse, give ounteremple. 11. he squre of numer is lrger thn the numer. 1. Ever multiple of 11 is plinrome, tht is, numer tht res the sme forwr n kwr. 1. he ifferene of two onseutive squre numers is n o numer. 10 CAPER Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

Lesson. Fining the nth erm Nme Perio Dte For Eerises 1 4, tell whether the rule is liner funtion. 1.. f(n) 8 1 9 6. 4. h(n) 9 6 9 g(n) 14 11 8 j(n) 1 1 0 1 For Eerises n 6, omplete eh tle.. 6. f(n) 7n 1 g(n) 8n For Eerises 7 9, fin the funtion rule for eh sequene. hen fin the 0th term in the sequene. 7. 8. 9. 6... n... 0 f(n) 9 1 17 1 9...... 6... n... 0 g(n) 6 1 4 9 14 19...... 6... n... 0 h(n) 6. 7 7. 8 8. 9...... 10. Use the figures to omplete the tle.... n... 0 Numer of tringles 1 9...... 11. Use the figures ove to omplete the tle. Assume tht the re of the first figure is 1 squre unit.... n... 0 Are of figure 1 4 16...... Disovering Geometr Prtie Your Skills CAPER 11 008 Kenll unt Pulishing

Lesson. Mthemtil Moeling Nme Perio Dte 1. Drw the net figure in this pttern.. ow mn smll squres will there e in the 10th figure?. ow mn in the th figure?. Wht is the generl funtion rule for this pttern?. If ou toss oin, ou will get he or til. Cop n omplete the geometri moel to show ll possile results of three onseutive tosses.. ow mn sequenes of results re possile?. ow mn sequenes hve etl one til?. Assuming he or til is equll likel, wht is the proilit of getting etl one til in three tosses?. If there re 1 people sitting t roun tle, how mn ifferent pirs of people n hve onverstions uring inner, ssuming the n ll tlk to eh other? Wht geometri figure n ou use to moel this sitution? 4. ournment gmes n results re often isple using geometri moel. wo emples re shown elow. Sketh geometri moel for tournment involving tems n tournment involving 6 tems. Eh tem must hve the sme hne to win. r to hve s few gmes s possile in eh tournment. Show the totl numer of gmes in eh tournment. Nme the tems,,... n numer thegmes 1,,... 1 1 tems, gmes (roun roin) 4 tems, gmes (single elimintion) 1 CAPER Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

Lesson.4 Deutive Resoning Nme Perio Dte 1. ABC is equilterl. Is ABD equilterl? Eplin our nswer. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem? B C A D. A n D re omplementr. A n E re supplementr. Wht n ou onlue out D n E? Eplin our nswer. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem?. Whih figures in the lst group re whtnots? Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem?.... e. f. Whtnots Not whtnots Whih re whtnots? 4. Solve eh eqution for. Give reson for eh step in the proess. Wht tpe of resoning, inutive or eutive, o ou use when solving these prolems?. 4 ( ) 8. 19 ( 1). A sequene egins 4, 1, 6, 11.... Give the net two terms in the sequene. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem?. Fin rule tht genertes the sequene. hen give the 0th term in the sequene. Wht tpe of resoning, inutive or eutive, o ou use when solving this prolem? Disovering Geometr Prtie Your Skills CAPER 1 008 Kenll unt Pulishing

Lesson. Angle Reltionships Nme Perio Dte For Eerises 1 6, fin eh lettere ngle mesure without using protrtor. 1... 11 1 8 40 70 4. e. 6. 1 70 e 18 110 100 For Eerises 7 10, tell whether eh sttement is lws (A), sometimes (S), or never (N) true. 7. he sum of the mesures of two ute ngles equls the mesure of n otuse ngle. 8. If XAY n PAQ re vertil ngles, then either X, A, n P or X, A, n Q re olliner. 9. If two ngles form liner pir, then the re omplementr. 10. If sttement is true, then its onverse is true. For Eerises 11 1, fill in eh lnk to mke true sttement. 11. If one ngle of liner pir is otuse, then the other is. 1. If A B n the supplement of B hs mesure, then m A. 1. If P is right ngle n P n Q form liner pir, then m Q is. 14. If S n re omplementr n n U re supplementr, then U is (n) ngle. 1. Swithing the if n then prts of sttement hnges the sttement to its. 14 CAPER Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

Lesson.6 Speil Angles on Prllel Lines Nme Perio Dte For Eerises 1, use our onjetures to fin eh ngle mesure. 1... 4 6 4 For Eerises 4 6, use our onjetures to etermine whether 1, n eplin wh. If not enough informtion is given, write nnot e etermine. 4.. 6. 118 1 1 48 1 6 9 48 7. Fin eh ngle mesure. 44 78 f e 64 8. Fin. 9. Fin n. 160 18 4 4 Disovering Geometr Prtie Your Skills CAPER 1 008 Kenll unt Pulishing

11. Kite 4. Possile nswers: B... Q P A LESSON 1.8 Spe Geometr 1.. LESSON.1 Inutive Resoning 1. 0, 4. 1 1,6 1 4. 4, 4. 1, 1. 7, 60 6. 4, 79 7. 91, 140. Retngulr prism 4. Pentgonl prism 8. 9.. 6. 10. 7. 18 ues 8., 1 (, 1) LESSON 1.9 A Piture Is Worth housn Wors 1. 10 m Possile lotions A 1 m. Dor, Ellen, Chrles, Ani, Fre, Brue Gs Power 1 1 4 (1, ) 11. Flse; 1 1 4 1. Flse; 11 10 110, 11 1 1 1. rue LESSON. Fining the nth erm 1. Liner. Liner. Not liner 4. Liner. D E C A F B f (n) 9 16. ringles Aute tringles 6. g(n) 10 18 6 4 4 Isoseles tringles Slene tringles 7. f(n) 4n ; f(0) 0 8. f(n) n 11; f(0) 9 9. f(n) 1 n 6; f(0) 1 Disovering Geometr Prtie Your Skills ANSWERS 9 008 Kenll unt Pulishing

10.... n... 0 Numer 1 9 1 17... 4n... 197 of tringles 11.... n... 0 Are of figure 1 4 16 64 6... 4 n 1... 4 49 4. Answers will vr. Possile nswers: 1 6 10 8 4 e 7 9 tems, 10 gmes 1 4 e 6 f 7 6 tems, 7 gmes LESSON. Mthemtil Moeling 1. 1 4 6 f e.. 40. 10. f(n) n(n ), or f(n) n 4n. 8 sequenes. sequenes hve 1 til.. 8. 66 ifferent pirs. Use oegon showing sies n igonls. 6 tems, 6 gmes LESSON.4 Deutive Resoning 1. No. Eplntions will vr. Smple eplntion: Beuse ABC is equilterl, AB BC. Beuse C lies etween B n D, BD BC, so BD is not equl to AB. hus ABD is not equilterl, eutive resoning.. Answers will vr. m E m D (m E m D 90 ); eutive., e, f; inutive 4. Deutive. 4 ( ) 8 he originl eqution. 4 6 8 Distriutive propert. 6 8 Comining like terms. 6 8 Aition propert of equlit. Sutrtion propert of equlit. Division propert of equlit. 94 ANSWERS Disovering Geometr Prtie Your Skills 008 Kenll unt Pulishing

. 19 ( 1) he originl eqution. 19 ( 1) ( ) Multiplition propert of equlit. 19 6 10 Distriutive propert. 1 6 10 Comining like terms. 1 11 10 Aition propert of equlit. 11 11 Sutrtion propert of equlit. 1 Division propert of equlit... 16, 1; inutive. f(n) n 9; 41; eutive LESSON.1 Dupliting Segments n Angles 1. P. XY PQ RS X A Q. Possile nswer: 4. 18 9 Y R B B S LESSON. Angle Reltionships 1. 68, 11, 68. 17., 40,, 70 4. 90, 90, 4, 48, e 1. 0, 70, 0, 70, e 110 6. 70,, 7. Sometimes 8. Alws 9. Never 10. Sometimes 11. ute 1. 18 1. 90 14. otuse 1. onverse LESSON.6 Speil Angles on Prllel Lines. 6. B C D C D D C D LESSON. Construting Perpeniulr Bisetors 1.. Squre 1. 4, 4, 4. 11, 6, 11, 6. 7, 16 4. 1. 1 6. nnot e etermine 7. 10, 78, 8, 1, e 6, f 8 8. 80 9. 0, Disovering Geometr Prtie Your Skills ANSWERS 9 008 Kenll unt Pulishing