TECHNICAL DATA 3. (equilateral triangle, pentagon, hexagon, octagon, polygon) a. (equilateral triangle. pentagon. B! r. hexagon. octogan.

Similar documents
Actual Formula Test #1 Test #2 Formula. (x h) 2 + (y k) 2 = r 2 General equation of a circle

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

GEOMETRY Properties of lines

D Properties and Measurement

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

Appendix D: Formulas, Properties and Measurements

SPECIALIST MATHEMATICS

1.3 Using Formulas to Solve Problems

Letter STUDENT NUMBER SPECIALIST MATHEMATICS. Written examination 2. Number of questions and mark allocations may vary from the information indicated.

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

AP Calculus BC Review Applications of Integration (Chapter 6) noting that one common instance of a force is weight

Geometry. A. Right Triangle. Legs of a right triangle : a, b. Hypotenuse : c. Altitude : h. Medians : m a, m b, m c. Angles :,

A 2 ab bc ca. Surface areas of basic solids Cube of side a. Sphere of radius r. Cuboid. Torus, with a circular cross section of radius r

SPECIALIST MATHEMATICS

Letter STUDENT NUMBER SPECIALIST MATHEMATICS. Number of questions and mark allocations may vary from the information indicated. Written examination 1

SPECIALIST MATHEMATICS

SPECIALIST MATHEMATICS

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

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

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

SPECIALIST MATHEMATICS

Classwork. Opening Exercises 1 2. Note: Figures not drawn to scale. 1. Determine the volume for each figure below.

SPECIALIST MATHEMATICS

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

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

What s in Chapter 13?

LUMS School of Science and Engineering

( ) 2 ( ) 9.80 m s Pa kg m 9.80 m s m

Answers: ( HKMO Heat Events) Created by: Mr. Francis Hung Last updated: 15 December 2017

MDPT Practice Test 1 (Math Analysis)

Angles and triangles. Chapter Introduction Angular measurement Minutes and seconds

Shape and measurement

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

+ r Position Velocity

Nonlocal Boundary Value Problem for Nonlinear Impulsive q k Symmetric Integrodifference Equation

T h e C S E T I P r o j e c t

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

*GMT62* *20GMT6201* Mathematics. Unit T6 Paper 2 (With calculator) Higher Tier [GMT62] MONDAY 11 JUNE 3.00 pm 4.15 pm. 1 hour 15 minutes.

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

Practice SAC. Unit 4 Further Mathematics: Geometry and Trigonometry Module

MATHEMATICS (Part II) (Fresh / New Course)

1 Review: Volumes of Solids (Stewart )

Clicks, concurrency and Khoisan

SPECIALIST MATHEMATICS

Mathematics Extension 2

Answers for Lesson 3-1, pp Exercises

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

Math 10 C. Measurement Test ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.

Complete E3. Copyright Mathster.com Licensed to Matthew Moss High School, Rochdale. 2) Round to 2 significant figures [7] g) 0.

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

QUEEN S COLLEGE Yearly Examination,

Solutions to Problems Integration in IR 2 and IR 3

Copyright Birkin Cars (Pty) Ltd

MATHEMATICAL METHODS (CAS) Written Examination 1

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Geometry Honors Final Exam Review June 2018

SPECIALIST MATHEMATICS

Big idea in Calculus: approximation

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION

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

HYPERBOLA. AIEEE Syllabus. Total No. of questions in Ellipse are: Solved examples Level # Level # Level # 3..

Algebra & Functions (Maths ) opposite side

5.5 Trigonometric Equations

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii

Copyright Birkin Cars (Pty) Ltd

( ) ) in 2 ( ) ) in 3

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID

Chapter 6 Area and Volume

Copyright Birkin Cars (Pty) Ltd

P49361A Pearson Education Ltd.

SSC Mains Mock Test 227 [Answer with Solution]

Satellite Orbits. Orbital Mechanics. Circular Satellite Orbits

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

USA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year

Identifying and Classifying 2-D Shapes

Eigen Values and Eigen Vectors of a given matrix

CONNECTED RATE OF CHANGE PACK

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,

GCSE APPLICATIONS OF MATHEMATICS (LINKED PAIR)

ENGI 4430 Surface Integrals Page and 0 2 r

Homework: Study 6.2 #1, 3, 5, 7, 11, 15, 55, 57

No. Diagram Given Condition Conclusion Abbreviation a and b are adjacent angles on a straight a b 180. a, b and c are angles at a point

*GMT41* *24GMT4101* Mathematics. Unit T4 (With calculator) Higher Tier [GMT41] WEDNESDAY 6 JUNE 9.15 am am. 2 hours.

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

Kansas City Area Teachers of Mathematics 2015 KCATM Math Competition GEOMETRY GRADE 7

CET MATHEMATICS 2013

IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB

CBSE CLASS X MATH -SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1.

SSC Mains Mock Test 226 [Answer with Solution]

FORMULAE. 8. a 2 + b 2 + c 2 ab bc ca = 1 2 [(a b)2 + (b c) 2 + (c a) 2 ] 10. (a b) 3 = a 3 b 3 3ab (a b) = a 3 3a 2 b + 3ab 2 b 3

Class X Delhi Math Set-3 Section A

CHAPTER 1 CENTRES OF MASS

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION

1. Use. What are the vertices of A.,, B.,, C.,, D.,,

Calculating Tank Wetted Area Saving time, increasing accuracy

ICSE Board Class IX Mathematics Paper 4 Solution

Circles. Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: Angles & Arcs Class Work

Lesson 4.1 Triangle Sum Conjecture

Not for reproduction

Reference. Reference. Properties of Equality. Properties of Segment and Angle Congruence. Other Properties. Triangle Inequalities

Transcription:

T SHEET /7/7 :5 M Pge..e. Contuction Ceicl FORMULE TECHNICL T SH EQUILTERL TRINGLE TECHNICL T SHEET HEXGON foule (equiltel tingle octgon, olygon) 5 5 5, T SHEET /7/7 :5 M Pge e.55.8.8 (equiltel tingle, entgon, egon, octgon, olygon) C CE PENTGON equiltel tingle foule entgon C B Q egon 5 8 + 5-5 Q + 5 Contuction: octogn B.5, BC B, C CE E, TECHNICL T SHEET.55 5 8.8 OCTGON Contuction: + 5 (equiltel tingle, entgon, egon, octgon, olygon) - 5 + 5 B.5, BC B, C CE equiltel tingle.55.8 entgon.8 C B tn.5 ~.5.5 E co.5 ~.95.9 ~.8 co.5 ~ equil B o.5.9.8.55.8 olygon..e. i n ISO 9:8 egitee cony PO Bo 5, Bokug Not, co,.5 Sout ~ fic.9 Weite: www.e.co.z Tel: +7() 9 ~.8 un Jonneug Ce co Town.5 Pot Elizet Et Lonon Bloefontein Geoge.8 tn.5 ~.5 egon + + octogn + + e o Totl ufce e Genete ufce e V Volue..e. i n ISO 9 : Regitee Co..e. Contuction olygon Ceicl Liite P.O. Bo 5, Iiingo, 7

T SHEET /7/7 :5 M Pge POLYGON NNULUS TECHNICL T SHEET SHEET /7/7 :5 M Pge + + + + foule ( ) ( + ) - ~.785 U (cicle, nnulu, ecto o egent of cicle, elli cic CIRCLE SECTOR OF CIRCLE TECHNICL T SHEET ecto of cicle ( ) nnu foule ~.785 Cicu U ( ) ( + ) - ( + ) α (cicle, nnulu, ecto - of cicle, egent of cicle, ellie) 8 α α α α α ( α α in cicul eue) 8 in ( + ) ( - in) + 8 ( - co ) 8 tn ( in cicul eue ) V Volue ecto of cicle..e. i n ISO 9:8 egitee cony PO Bo 5, + Bokug Not,, Sout fic U ~.785 Weite: www.e.co.z Tel: +7() 9 un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge ( + ) + # # 8 + + # + 5 ( in cicul eue) cicle nnulu e o Totl ufce e Genete ufce e ecto o egent o elli

gent of cicle, ellie) cicle TECHNICL T SHEET foule nnulu SEGMENT OF CIRCLE ~.785 (cicle, nnulu, ecto of cicle, egent of cicle, ellie) cicle SQURE l eue) ( - in) tn l eue ).785 # + # + 5 # - + U α ( ) ( + ) α inin - ( + ) ( α - in) α) egent of cicle + 8 α α ( - co ) tn α 8 α ( α α in cicul eue ) ELLIPSE ( in cicul eue) i n ISO 9 : Regitee Cony. ecto of cicle 8 8 ellie Cicu U ~.785, Iiingo, 7 Wilco Ro, Iiingo, Tel. () 9 5 ( + ) + # # λ + λ + λ # + 5 in ( + ) ( - in) ( in cicul eue ) + 8 ( - co ) 8 + tn Reviion: -5-8 nnulu c ecto of cicle RECTNGLE egent of cicle ellie + 5 8 λ # 8 +, wee λ# - +..e. i n ISO 9 : Regitee Cony. e o Totl ufce e Genete ufce e Reviion: -5-8 V Volue..e. Contuction Ceicl Liite P.O. Bo 5, Iiingo, 7 Wilco Ro, Iiingo, Tel. () 9 5..e. i n ISO 9:8 egitee cony PO Bo 5, Bokug Not,, Sout fic Weite: www.e.co.z Tel: +7() 9 un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge

in ( + cot + foule ( - cot + + PRLLELOGRM α + + in α + + c ( - ) ( - ) ( - c) TRINGLE teziu in ( + cot + ( - cot + + c + tingle Q..e. i n ISO 9 : Regitee Cony. Q lle te TRPEZIUM + CYLINER tin Reviion: -5-8 ( + cot α +..e. Contuction Ceicl Liite P.O. Bo 5, Iiingo, 7 Wilco Ro, Iiingo, Tel. () 9 5 ( - cot α + + + c ( - ) ( - ) ( - c) c..e. i n ISO 9 : Regitee Cony...e. Contuction Ceicl Liite P.O. Bo 5, Iiingo, 7 Wilc ( - ) ( - ) ( - c) + + + c V + ( + ) Reviion: -5-8 e o Totl ufce e Genete ufce e V Volue..e. i n ISO 9:8 egitee cony PO Bo 5, Bokug Not,, Sout fic Weite: www.e.co.z Tel: +7() 9 un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge

V cyline TECHNICL T S ( + ) foule (cyline, ollow c futu of cone, V ollow cyline V SHEET /7/7 :5 M Pge ( - ) HOLLOW CYLINER FRUSTUM OF CONE ( + ) futu of cone CONE foule : V ( - ) V V ( + + ) - ( ( + ) ) + V V V cone ( + ) + ( + ) V ~ (. 89 - ) TECHNICL T SHEET (cyline, ollow cyline, cone, futu of cone, ee) V V SPHERE : cyline futu of cone ( + + ) V ( + ) V ( ) - ( + ) ( ) + + V ollow cyline ee cone ( - ) ( + + ) ( + ) - ( ) + f V V ( + ) + : : V ( + + ) ( + ) e o Totl ufce e Genete ufce e V Volue..e. Contuction Ceicl Liite P.O. Bo 5, Iiingo,..e. i n ISO 9:8 - egitee cony PO Bo 5, Bokug ( Not, ), + Sout fic Weite: www.e.co.z Tel: +7() 9 un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge V cone..e. i n ISO 9 : Regitee Cony. ~. 89 futu of cone..e. Contuction Ceicl Liite P.O. Bo 5, Iiingo, 7 Wilco Ro, Iiingo, Tel. () 9 5 Reviion: -5-8..e. i n ISO 9 : Regitee C V Reviion: -5-8 ee

CHNICL T SHEET (cue, cuoi, lleleie, yi, futu of yi) CUBE PRLLELEPIPE cue foule V cuoi V (Cvliei incile) CUBOI V c lleleie PYRMI ( + c + c) c + + c yi V V c (Cvliei incile) ( + c + c) V futu of + yi + c ) e o Totl ufce e Genete ufce e V Volue Reviion: -5-8..e. i n ISO 9 : Regitee Cony...e. i n ISO 9:8 egitee cony PO Bo 5, Bokug Not,, Sout fic Weite: V www.e.co.z ( Tel: + +7() + 9 ) 5, Iiingo, 7 Wilco Ro, Iiingo, Tel. () 9 5 un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge ~ +

T SHEET /7/7 :5 M Pge TECHNICL T SHE FRUSTUM OF PYRMI foule SEGMENT OF SPHERE (zone of ee, egent ee wit cylinicl o ) V ( + + ) zone of ( + + ) T SHEET /7/7 :5 M Pge V ( + + ) ~ + Reviion: -5-8 V ( ( - ) + ) ( + ) egent o ZONE OF SPHERE zone of ee foule V ( + + ) ( + + ) V ( ( - ) + ) SECTOR V OF SPHERE TECHNICL T SHEET ( + ) (zone of ee, egent of ee, ecto of ee, ee wit cylinicl oe, ee wit conicl oe) V V ( R + ) zone of ee ( + ) V egent of ee ( + e o Totl ufce e Genete ufce e V Volue ecto of ee wit cyl ee wit c ( + )..e. i n ISO 9 : Regitee Cony...e. i n ISO 9:8 egitee cony PO Bo 5, Bokug Not,, Sout fic ecto of ee Weite: www.e.co.z V Tel: +7() 9..e. Contuction Ceicl Liite P.O. Bo 5, Iiingo, 7 Wilco un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge ( + )

TECHNICL T SHEET foule T SHEET /7/7 :5 M Pge (cyline, ollow cyline, cone, futu of cone, ee) SPHERE WITH CYLINRICL V BORING ee wit cylinicl oing TORUS tou TECHNICL T SHEET cyline V V ( - ) ( R + ) V V SPHERE WITH VCONICL BORING ee wit conicl oing V ( + ) ( + ) V ( - ) + : R ( + ) foule foule T SHEET /7/7 :5 M Pge tou ollow cyline (tou, lice cyline, ungul, el, ioi) V TECHNICL T SHE foule SLICE CYLINER lice cyline V cone (tou, lice cyline, to V V ( + ) - ( ( + ) ( - + ) + + + V V ~. ( 89 + ) V V ( R + )..e. i n ISO 9:8 egitee cony ioi PO Bo 5, Bokug V Not,, ( Sout fic + + ) Weite: www.e.co.z Tel: +7() 9 V..e. i n ISO 9 : Regitee Cony. un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge Ti foul y e ue fo clcultion involving oli own on foule cue n tu ee n t of ee. ( + ( + + ) ungul V el futu of cone V ee e o Totl ufce e Genete ufce e V Volue + + + V ( + ) lice c ung Reviion: -5

UNGUL BRREL V V ( + ) + + + PRISMOI V ( + + ) Ti foul y e ue fo clcultion involving oli own on foule cue n tu ee n t of ee. e o Totl ufce e Genete ufce e V Volue..e. i n ISO 9:8 egitee cony PO Bo 5, Bokug Not,, Sout fic Weite: www.e.co.z Tel: +7() 9 un Jonneug Ce Town Pot Elizet Et Lonon Bloefontein Geoge