MEMORANDUM ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT
|
|
- Doris Harrison
- 5 years ago
- Views:
Transcription
1 MATH MEMORANDUM ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT IIMVIWO ZEBANGA LESHUMI ELINANYE GRADE EXAMINATIONS GRAAD -EKSAMEN NOVEMBER 008 MATHEMATICS SECOND PAPER This memrandum cnsists f pages.
2 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION. AB ( x x) + (y y) frmula. ( ) + ( y y Gradient f AB x x 8 ( ) - ) () frmula (). tan m ,80,6. Equatin f AB : y y m(x x ) y ( -) - ( x ) y + - x + 8 y - x - tan ref. angle () frmula (). Crdinates f C: ( 0;- 8 ) ().6 Midpint f AB + 8 ; The crdinates f C x + x y + y ; ; 8 0; ; C is nt the midpint f AB frmula ; cnclusin () [8]
3 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) QUESTION x + x y + Midpint f PR : M ( ; ) + + M ; m PR y x - - y x - - (-) y M (- ; ) - (-) 6 mmq mpr. mmq ( - ) - PR QM Prduct f gradients - 6 Area bh Area f RMQ ( PR MQ) PR ( ) + ( ) MQ 0 0 Area f RMQ unit ( ) + ( + ) () - - cnclusin () PR 0 MQ 0 (). y x y x - gradient f the line gradient f the parallel line is Equatin f the parallel line is y y m( x x ) Substituting ( ; - ) y + ( x - ) y x - 7. m AB m BC OR M AB ½ 0 ( -) p 0 y ½ (x+) --(-) ( -) y ½ x+ p p Subst (;p) p ½ + gradient gradient f parallel line (; -) () m AB m BC () [8]
4 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION C (-;9) B (-6; 8) A (-; ) G(-;0) E(-;-) C(;9) 9 B(6; 8) A(; ) F(0;-) F A (-;) B (-6;8) C (-;9) ().. E(-;- ) F(0;-) G(- ;0) ().. D(-8;-6) ().. Rtatin clckwise arund rigin thrugh 90 clckwise arund rigin rtatin 90 ().. (-;-) ().. Scale factr ().. P ; Q ; R 7 ; () [7]
5 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) QUESTION.. OP (-) OP Applying Pythagras therem (). tan(80 + α ) tan α -.. β α - 90 sin β sin (α -90 ) sin (-(90 - α )) - sin(90 - α ) - cs α - ( - ) tan α () β α sin(90 - α ) - cs α ().. LHS sin x. cs x. sin x cs x sin x cs x RHS sin x cs x sin x - cs x ().. RHS sin y cs y cs y cs y ( + cs y)( - cs y) - cs y + cs y LHS cs y factrs simplificatin () []
6 6 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION. (- sin θ)(- sin θ) ( - sin θ) tan θ - sin θ sinθ csθ - cs θ - sin θ - sin θ - sin θ tan θ sinθ csθ (6). (- sin0 ) ( - cs 0 ) tan sin 0 ( - sin 60 ) ( - ) - - sin 60. cs0.. OR OR sin 60 cs0 - cs 0 sin 0 - sin (8) [] QUESTION 6 6. tan θ 6 tan θ θ ,9, 6. sin x 0 r cs x - x k x k r x k x k cs x - where k ε Z x k r x k tan θ reference angle ,9 () sin x 0 r cs x - x k x k x k x k x k x k k ε Z (9)
7 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) p () 6.. x -90 ; 0 ; 90 ; 80 mark per values () 6.. Minimum value f f(x) - () [7] QUESTION 7 7. PR S 80 -,,9 and RP S,7 In PRS: PS RS sin,9 sin,7 RS.sin,9 PS sin,7,7.sin,9 sin,7 0,9 km 7. Height f the muntain is PQ PQ sin, PS PQ PS.sin, 7. 0,9.sin,,7 km Area f PRS. RS. PS.sin, 7 (,7)(0,9) sin,7 7,8km,9 and,7 applying sine rule () PQ sin, PS area rule () () []
8 8 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION 8 8. Slant height: H h + r H 98, mm Using Pythagras therem () 8. Exterir surface area r + rh x 9 x 9 + x 9 x, 9,6mm Ttal exterir surface area x 9,6 79mm using frmula 9,6mm () 8. Vlume f the cne π r h frmula π 9 9 0,7mm Vlume f sand after minutes,7mm 66,7mm,7mm divisin by () []
9 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) 9 QUESTION Mde 9 () 9.. Arithmetic mean ,8 0 () rder Median , 9.. Lwer quartile(q ) 9 Upper quartile (Q ) () Range , 8 Skewed t right / mre spread ut n right bx whiskers cmment () () () []
10 0 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION 0 0. MARKS TALLY FREQUENCY CUM. FREQ. 0-9 //// 0-9 //// //// //// /// //// //// 0 Tally Frequency Cumm. Frequency () 0. Ogive representing marks Cummulative frequency axes Pltting pints shape () Marks 0. x x 90 9 n 0 x x - x (x - x ) Variance n i ( x x) 0 0 Standard deviatin,9 {Answer nly (using calculatr) Full marks} i n 90 x (x - x ) frmula fr variance S.D var iance (6) []
11 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) QUESTION. Gals Scatter plt Match axes and labels pltting pints (). Linear (). See graph drawing (). 9 accrding t candidate s graph () [6] Ttal: 0
MEMORANDUM ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT
MLIT MEMANDUM ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT IIMVIWO ZEBANGA LESHUMI ELINANYE GRADE 11 EXAMINATIONS GRAAD 11-EKSAMEN NOVEMBER 008 MATHEMATICAL
More informationISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT
MATH ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT IIMVIWO ZEBANGA LESHUMI ELINANYE GRADE 11 EXAMINATIONS GRAAD 11-EKSAMEN NOVEMBER 2008 MATHEMATICS FIRST
More informationNOVEMBER 2008 MATHEMATICS THIRD PAPER
MATH ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT IIMVIWO ZEBANGA LESHUMI ELINANYE GRADE 11-EXAMINATIONS GRAAD 11-EKSAMEN NOVEMBER 2008 MATHEMATICS THIRD
More informationBasic Education MATHEMATICS P2 PREPARATORY EXAMINATION SEPTEMBER 2015 MEMORANDUM NATIONAL SENIOR CERTIFICATE GRADE 12
Basic Educatin KwaZulu-Natal Department f Educatin REPUBLIC OF SOUTH AFRICA MATHEMATICS P PREPARATORY EXAMINATION SEPTEMBER 05 MEMORANDUM NATIONAL SENIOR CERTIFICATE GRADE N.B. This memrandum cnsists f
More informationMathematics P2 1 Preparatory Examination September 2016 NSC-MEMORANDUM. Education. KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA
Mathematics P Preparatry Examinatin September 06 Educatin KwaZulu-Natal Department f Educatin REPUBLIC OF SOUTH AFRICA MATHEMATICS P PREPARATORY EXAMINATION SEPTEMBER 06 MEMORANDUM NATIONAL SENIOR CERTIFICATE
More informationGRADE 12 LEARNER SUPPORT PROGRAMME
Province of the EASTERN CAPE EDUCATION Steve Vukile Tshwete Education Complex Zone 6 Zwelitsha 5608 Private Bag X00 Bhisho 5605 REPUBLIC OF SOUTH AFRICA CHIEF DIRECTORATE CURRICULUM MANAGEMENT GRADE LEARNER
More informationSOLUTIONS SET 1 MATHEMATICS CLASS X
Tp Careers & Yu SOLUTIONS SET MTHEMTICS CLSS X. 84 7 Prime factrs f 84 are, and 7.. Sum f zeres 5 + 4 Prduct f zeres 5 4 0 Required plynmial x ( )x + ( 0) x + x 0. Given equatin is x + y 0 Fr x, y L.H.S
More informationANSWER KEY FOR MATH 10 SAMPLE EXAMINATION. Instructions: If asked to label the axes please use real world (contextual) labels
ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION Instructins: If asked t label the axes please use real wrld (cntextual) labels Multiple Chice Answers: 0 questins x 1.5 = 30 Pints ttal Questin Answer Number 1
More informationM thematics. National 5 Practice Paper B. Paper 1. Duration 1 hour. Total marks 40
M thematics Natinal 5 Practice Paper B Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationM thematics. National 5 Practice Paper E. Paper 1. Duration 1 hour. Total marks 40
N5 M thematics Natinal 5 Practice Paper E Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationPAST EXAM PAPER & MEMO N3 ABOUT THE QUESTION PAPERS:
EKURHULENI TECH COLLEGE. N. 3 Mgale Square, Krugersdrp. Website: www. ekurhulenitech.c.za Email: inf@ekurhulenitech.c.za TEL: 0 040 7343 CELL: 073 770 308/060 75 459 PAST EXAM PAPER & MEMO N3 ABOUT THE
More informationM thematics. National 5 Practice Paper C. Paper 1. Duration 1 hour. Total marks 40
N5 M thematics Natinal 5 Practice Paper C Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationM thematics. National 5 Practice Paper D. Paper 1. Duration 1 hour. Total marks 40
N5 M thematics Natinal 5 Practice Paper D Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationCop yri ht 2006, Barr Mabillard.
Trignmetry II Cpyright Trignmetry II Standards 006, Test Barry ANSWERS Mabillard. 0 www.math0s.cm . If csα, where sinα > 0, and 5 cs α + β value f sin β, where tan β > 0, determine the exact 9 First determine
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENI CERTIFICATE GRADE MATHEMATICS P NOVEMBER 009 MEMANDUM MARKS: 50 This memorandum consists of 5 pages. Mathematics/P DoE/November 009 QUESTION B( ; 5) y O // M A(5 ; ) // C ( ; 5) D(9 ; 7).
More informationMOCK CBSE BOARD EXAM MATHEMATICS. CLASS X (Paper 1) (AS PER THE GUIDELINES OF CBSE)
MOCK CSE ORD EXM MTHEMTICS CLSS X (Paper 1) (S PER THE GUIDELINES OF CSE) Time: 3 Hurs Max. Marks: 80 General Instructins 1. ll the questins are cmpulsry. 2. The questin paper cnsists f 30 questins divided
More informationBEAULIEU COLLEGE PRELIMINARY EXAMINATIONS 2016 MATHEMATICS GRADE 12 PAPER 2
BEAULIEU COLLEGE PRELIMINARY EXAMINATIONS 2016 MATHEMATICS GRADE 12 PAPER 2 Examiner: Mr J Ruiz Mesa Ttal marks: 150 Date: 25 July 2016 Instructins: Mderatr: Ms A Smith Time: 3hrs This questin paper cnsists
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 06 MARKS: 50 TIME: 3 hours This question paper consists of 3 pages and a -page answer book. Mathematics/P DBE/November 06 INSTRUCTIONS AND INFORMATION
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationLEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot
Mathematics DM 05 Tpic : Trignmetric Functins LECTURE OF 5 TOPIC :.0 TRIGONOMETRIC FUNCTIONS SUBTOPIC :. Trignmetric Ratis and Identities LEARNING : At the end f the lessn, students shuld be able t: OUTCOMES
More information7 TH GRADE MATH STANDARDS
ALGEBRA STANDARDS Gal 1: Students will use the language f algebra t explre, describe, represent, and analyze number expressins and relatins 7 TH GRADE MATH STANDARDS 7.M.1.1: (Cmprehensin) Select, use,
More informationUGANDA ADVANCED CERTIFICATE OF EDUCATION INTERNAL MOCK 2016 PURE MATHEMATICS. 3 hours
P/ PURE MATHEMATICS PAPER JULY 0 HOURS UGANDA ADVANCED CERTIFICATE OF EDUCATION INTERNAL MOCK 0 PURE MATHEMATICS hurs INSTRUCTIONS TO CANDIDATES: Attempt ALL the EIGHT questins in sectin A and any FIVE
More informationTrigonometric Ratios Unit 5 Tentative TEST date
1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
Mathematics/P DoE/November 008 NSC Memorandum NATIONAL SENI CERTIFICATE GRADE MATHEMATICS P NOVEMBER 008 MARKS: 0 This memorandum consists of ages. Coyright reserved Mathematics/P DoE/November 008 Continued
More informationPLEASURE TEST SERIES (XI) - 07 By O.P. Gupta (For stuffs on Math, click at theopgupta.com)
A Cmpilatin By : OP Gupta (WhatsApp @ +9-9650 50 80) Fr mre stuffs n Maths, please visit : wwwtheopguptacm Time Allwed : 80 Minutes Max Marks : 00 SECTION A Questin numbers 0 t 0 carry mark each x x 5
More informationMATHEMATICS SYLLABUS SECONDARY 5th YEAR
Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE
More informationSAFE HANDS & IIT-ian's PACE EDT-04 (JEE) Solutions
ED- (JEE) Slutins Answer : Optin () ass f the remved part will be / I Answer : Optin () r L m (u csθ) (H) Answer : Optin () P 5 rad/s ms - because f translatin ωr ms - because f rtatin Cnsider a thin shell
More informationIndividual Events 5 I3 a 6 I4 a 8 I5 A Group Events
Answers: (993-94 HKMO Final Events) Created by: Mr. Francis Hung Last updated: 8 August 08 SI a I a 6 I A Individual Events I3 a 6 I4 a 8 I A 6 b 4 b B 60 b *9 see the remarks b 0 B 36 c c 0 C c 6 c 3
More information( ) ( ) Pre-Calculus Team Florida Regional Competition March Pre-Calculus Team Florida Regional Competition March α = for 0 < α <, and
Flrida Reginal Cmpetitin March 08 Given: sin ( ) sin π α = fr 0 < α
More informationPre-Calculus Individual Test 2017 February Regional
The abbreviatin NOTA means Nne f the Abve answers and shuld be chsen if chices A, B, C and D are nt crrect. N calculatr is allwed n this test. Arcfunctins (such as y = Arcsin( ) ) have traditinal restricted
More information1 PreCalculus AP Unit G Rotational Trig (MCR) Name:
1 PreCalculus AP Unit G Rtatinal Trig (MCR) Name: Big idea In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin will invlve the unit circle which will
More informationLHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers
LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the
More informationCambridge Assessment International Education Cambridge Ordinary Level. Published
Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid
More informationCalculus Placement Review. x x. =. Find each of the following. 9 = 4 ( )
Calculus Placement Review I. Finding dmain, intercepts, and asympttes f ratinal functins 9 Eample Cnsider the functin f ( ). Find each f the fllwing. (a) What is the dmain f f ( )? Write yur answer in
More informationJune Core Mathematics C3 Mark Scheme
June 009 666 Cre Mathematics C Mark Questin. (a) Iterative frmula: n + +, 0. ( ) n + (.)..78....97....6069... An attempt t substitute 0. int the iterative frmula. Can be implied by. r.0 Bth.(0) and awrt.7
More informationENGI 4430 Parametric Vector Functions Page 2-01
ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr
More informationFunction notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property
Functin ntatin & cmpsite functins Factring Dividing plynmials Remainder therem & factr prperty Can d s by gruping r by: Always lk fr a cmmn factr first 2 numbers that ADD t give yu middle term and MULTIPLY
More informationHigher. Specimen NAB Assessment
hsn.uk.net Higher Mathematics UNIT Specimen NAB Assessment HSN50 This dcument was prduced speciall fr the HSN.uk.net website, and we require that an cpies r derivative wrks attribute the wrk t Higher Still
More informationMATHEMATICS Higher Grade - Paper I
Higher Mathematics - Practice Eaminatin B Please nte the frmat f this practice eaminatin is different frm the current frmat. The paper timings are different and calculatrs can be used thrughut. MATHEMATICS
More informationNUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
More informationRoots and Coefficients Polynomials Preliminary Maths Extension 1
Preliminary Maths Extension Question If, and are the roots of x 5x x 0, find the following. (d) (e) Question If p, q and r are the roots of x x x 4 0, evaluate the following. pq r pq qr rp p q q r r p
More informationCBSE QUESTION PAPER CLASS-X MATHS
CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1: In figure, AB = 5 3 cm, DC = 4cm, BD = 3cm, then tan θ is (a) (b) (c) (d) 1 3 2 3 4 3 5 3 Question 2: In figure, what values of x will make DE
More informationST MARY S DSG, KLOOF MATHEMATICS PAPER II GRADE 11 NOVEMBER 2016
P a g e ST MARY S DSG, KLOOF MATHEMATICS PAPER II GRADE NOVEMBER 06 TIME: ½ HOURS TOTAL: 5 MARKS EXAMINER : S.THOMPSON MODERATORS: : Mrs van ROOYEN : Mrs DREW NAME: MATHS TEACHER: INSTRUCTIONS ) Read all
More informationNATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 10
NATIONAL ENIOR CERTIFICATE/ NAIONALE ENIOR ERTIFIKAAT GRADE/GRAAD 0 MATHEMATIC P/WIKUNDE V NOVEMBER 07 MARKING GUIDELINE/NAIENRIGLYNE MARK/PUNTE: 00 These marking guidelines cnsist f 0 pages. Hierdie nasienriglyne
More informationPRE-CALCULUS B FINAL REVIEW NAME Work out problems in your notebook or on a separate piece of paper.
PRE-CALCULUS B FINAL REVIEW NAME Wrk ut prblems in yur ntebk r n a separate piece f paper. CHAPTER 5 Simplify each t ne trig wrd r a number: tan (1) sec sec () sin ct + 1 + cs + ( sin cs ) () sin - cs
More informationGrade 11 November Examination 2015 Mathematics: Paper 2 Time: 3 hours Marks: 150
Grade 11 November Examination 2015 Mathematics: Paper 2 Time: 3 hours Marks: 150 Instructions and Information: Read the following instructions carefully before answering the questions. 1. This question
More informationChapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
More informationGrade 11 November Examination 2016 Mathematics: Paper 2 Time: 3 hours Marks: 150
Grade November Examination 06 Mathematics: Paper Time: 3 hours Marks: 50 Instructions and Information: Read the following instructions carefully before answering the questions.. This question paper consists
More informationFinding the Earth s magnetic field
Labratry #6 Name: Phys 1402 - Dr. Cristian Bahrim Finding the Earth s magnetic field The thery accepted tday fr the rigin f the Earth s magnetic field is based n the mtin f the plasma (a miture f electrns
More informationA1 for 25 2 B2 for all 4 correct
1 2x + 2(x + 9) < 200 2x + 2x + 18 < 200 4x + 18 < 200 4x < 182 x < 45.5 45 4 B1 for x + 9 oe seen (it could just be on a diagram) or any rectangle with length 9 cm greater than width M1 for 2x + 2(x +
More informationY10 Foundation SOW Term 1
Y10 Fundatin SOW Term 1 Algebra Fcus Students shuld be cmpletely familiar with all the rules f algebra Plt straight line graphs f functins by setting up a table f x and y pints as crdinate pairs (by use
More informationKING DAVID HIGH SCHOOL LINKSFIELD GRADE 11 MATHEMATICS PAPER 2 NOVEMBER Writing Time: 2½ hours Total: 120 marks
KING DAVID HIGH SCHOOL LINKSFIELD GRADE 11 MATHEMATICS PAPER 2 NOVEMBER 2017 Writing Time: 2½ hours Total: 120 marks NAME: INSTRUCTIONS AND INFORMATION Read the following instructions carefully before
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 05 MARKS: 50 TIME: 3 hours This question paper consists of 5 pages and a 4-page answer book. Mathematics/P DBE/November 05 CAPS Grade INSTRUCTIONS
More informationPrecalculus A. Semester Exam Review
Precalculus A 015-016 MCPS 015 016 1 The semester A eaminatin fr Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr
More informationMATHEMATICS Higher Grade - Paper I
Higher Mathematics - Practice Eaminatin D Please nte the frmat f this practice eaminatin is different frm the current frmat. The paper timings are different and calculatrs can be used thrughut. MATHEMATICS
More informationAlgebra2/Trig: Trig Unit 2 Packet
Algebra2/Trig: Trig Unit 2 Packet In this unit, students will be able t: Learn and apply c-functin relatinships between trig functins Learn and apply the sum and difference identities Learn and apply the
More informationMATHEMATIC PAPER II Page 1 of 21 MATHEMATICS PAPER 2
MATHEMATIC PAPER II Page 1 of 21 GRADE 11 EXAMINATION NOVEMBER 2015 MATHEMATICS PAPER 2 Time: 3 hours Examiners: Miss Eastes, 150 marks Moderators:Mrs. Jacobsz, Mrs. Rixon, Mrs. Thorne PLEASE READ THE
More informationQUESTION x = 15 answer (3) For drawing the radius vector in the correct quadrant 1/3. sin α > 0 in second quadrant
Mathematics/P 7 DoE/Novemer 009() QUESTION 8 8. sin α 8 7 ( 5 ; 8) sin α > 0 in second quadrant y 8 r 7 α α 5 tanα α 8 5 ( Pythagoras) 7 α 5 For drawing the radius vector in the correct quadrant /3 8.
More informationCHAPTER 8b Static Equilibrium Units
CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but
More informationLondon Examinations IGCSE
Centre No. Candidate No. Surname Signature Initial(s) Paper Reference(s) 4400/4H London Examinations IGCSE Mathematics Paper 4H Higher Tier Thursday 4 November 2004 Morning Time: 2 hours Examiner s use
More informationDepartment of Mathematics
Department of Mathematics TIME: 3 Hours Setter: DS DATE: 03 August 2015 GRADE 12 PRELIM EXAMINATION MATHEMATICS: PAPER II Total marks: 150 Moderator: AM Name of student: PLEASE READ THE FOLLOWING INSTRUCTIONS
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More information39th International Physics Olympiad - Hanoi - Vietnam Theoretical Problem No. 1 /Solution. Solution
39th Internatinal Physics Olympiad - Hani - Vietnam - 8 Theretical Prblem N. /Slutin Slutin. The structure f the mrtar.. Calculating the distance TG The vlume f water in the bucket is V = = 3 3 3 cm m.
More informationMathematics GCSE Higher Tier Taster Pages
Question 14 (June 2011 4306/1H) a) on the cumulative frequency diagram you can work out the lower quartile, median and upper quartile. These have been got by using the dashed red lines. Draw them across
More informationA - LEVEL MATHEMATICS 2018/2019
A - LEVEL MATHEMATICS 2018/2019 STRUCTURE OF THE COURSE Yur maths A-Level Maths curse cvers Pure Mathematics, Mechanics and Statistics. Yu will be eamined at the end f the tw-year curse. The assessment
More informationChapter 9 Vector Differential Calculus, Grad, Div, Curl
Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields
More informationLondon Examinations IGCSE. Wednesday 7 November 2007 Afternoon
Centre No. Candidate No. Surname Signature: Mr.Demerdash Initial(s) Paper Reference(s) 4400/4H London Examinations IGCSE Mathematics Paper 4H Higher Tier Wednesday 7 November 2007 Afternoon Time: 2 hours
More informationCHM112 Lab Graphing with Excel Grading Rubric
Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline
More informationExperiment #3. Graphing with Excel
Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-
More informationMATHEMATICS: PAPER II TRIAL EXAMINATION 11 SEPTEMBER 2015 MEMO
MATHEMATICS: PAPER II TRIAL EXAMINATION 11 SEPTEMBER 2015 TIME: 3 HOURS TOTAL: 150 MARKS MEMO PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. Write your examination number on the paper. 2. This question
More informationGEOMETRY Transformation Project
GEOMETRY Transfrmatin Prject T bring tgether the unit f transfrmatins, yu will be making a Gemetry Transfrmatins Prject based n yur interest. This prject is meant t give yu an pprtunity t explre hw transfrmatins
More informationToday is Monday 2/5/18
D Nw: -Take calculatr -Take ut HW -Cpy tnight's HW Tday is Mnday 2/5/18 -Study fr midterm! -Part 1 tmrw, part 2 Wednesday -Extra help tmrw. @ 6:50AM 1) Use the diagram t answer the fllwing 2 3 4 5 1 6
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationMEMO MATHEMATICS: PAPER II
MEMO CLUSTER PAPER 2016 MATHEMATICS: PAPER II Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 28 pages and an Information Sheet of 2 pages(i-ii).
More informationGrade 11 Assessment Exemplars
Grade Assessment Eemplars Learning Outcomes and. Assignment : Functions - Memo. Investigation: Ratios - Guideline 6. Control Test: Equations, Inequalities, Eponents - Memo 8. Project: Finance - Memo.5
More informationSolving Inequalities: Multiplying or Dividing by a Negative Number
11 Slving Inequalities: Multiplying r Dividing by a Negative Number We slve inequalities the same way we slve equatins, with ne exceptin. When we divide r multiply bth sides f an inequality by a negative
More informationHere is a link to the formula booklet:
IB MATH SL2 SUMMER ASSIGNMENT review of topics from year 1. We will be quizzing on this when you return to school. This review is optional but you will earn bonus points if you complete it. Questions?
More informationxfyy.sny E gyef Lars g 8 2 s Zs yr Yao x ao X Axe B X'lo AtB tair z2schhyescosh's 2C scoshyesukh 8 gosh E si Eire 3AtB o X g o I
Math 418, Fall 2018, Midterm Prf. Sherman Name nstructins: This is a 50 minute exam. Fr credit yu must shw all relevant wrk n each prblem. Yu may nt use any calculatrs, phnes, bks, ntes, etc. There are
More informationTrigonometric Functions. Concept Category 3
Trignmetric Functins Cncept Categry 3 Gals 6 basic trig functins (gemetry) Special triangles Inverse trig functins (t find the angles) Unit Circle: Trig identities a b c 2 2 2 The Six Basic Trig functins
More informationCONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS
CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS Objectives To introduce students to a number of topics which are fundamental to the advanced study of mathematics. Assessment Examination (72 marks) 1 hour
More informationSpecial Maths Exam Paper 2 November 2013 Solutions
Special Maths Eam Paper 2 November 2013 Solutions Question One 1.1 sin θ = 4/5 > 0, 270 o < θ 360 o. If 4 and 5 are the lengths of sides of a right-angled triangle, with 5 the hpotenuse, then the third
More informationConcept Category 2. Trigonometry & The Unit Circle
Cncept Categry 2 Trignmetry & The Unit Circle Skill Checklist Use special right triangles t express values f fr the six trig functins Evaluate sine csine and tangent using the unit circle Slve tw-step
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More information5 th grade Common Core Standards
5 th grade Cmmn Cre Standards In Grade 5, instructinal time shuld fcus n three critical areas: (1) develping fluency with additin and subtractin f fractins, and develping understanding f the multiplicatin
More informationSolutionbank C1 Edexcel Modular Mathematics for AS and A-Level
Heinemann Solutionbank: Core Maths C Page of Solutionbank C Exercise A, Question Find the values of x for which f ( x ) = x x is a decreasing function. f ( x ) = x x f ( x ) = x x Find f ( x ) and put
More informationM thematics. National 5 Practice Paper A. Paper 1. Duration 1 hour. Total marks 40
N5 M thematics Natinal 5 Practice Paper A Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationReview exercise 2. 1 The equation of the line is: = 5 a The gradient of l1 is 3. y y x x. So the gradient of l2 is. The equation of line l2 is: y =
Review exercise The equation of the line is: y y x x y y x x y 8 x+ 6 8 + y 8 x+ 6 y x x + y 0 y ( ) ( x 9) y+ ( x 9) y+ x 9 x y 0 a, b, c Using points A and B: y y x x y y x x y x 0 k 0 y x k ky k x a
More informationPages with the symbol indicate that a student should be prepared to complete items like these with or without a calculator. tan 2.
Semester Eam Review The semester A eaminatin fr Hnrs Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr will be allwed.
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationSUBJECT Mathematics PAPER 2 GRADE 11 DATE 21 NOV 2017 EXAMINER Mrs Sillman MARKS 150 NAME MODERATOR Gr 11 Teachers TEACHER DURATION 3 hours
SUBJECT Mathematics PAPER 2 GRADE 11 DATE 21 NOV 2017 EXAMINER Mrs Sillman MARKS 150 NAME MODERATOR Gr 11 Teachers TEACHER DURATION 3 hours QUESTION NO DESCRIPTION MAXIMUM MARK ACTUAL MARK 1-3 Analytical
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 0 MARKS: 50 TIME: hours This question paper consists of pages and diagram sheets. Mathematics/P DBE/0 NSC Grade Exemplar INSTRUCTIONS AND INFORMATION
More informationAnswer ALL the questions in the SPECIAL ANSWER BOOK provided.
Mathematics/P DBE/November 04 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions... 3. 4. 5. 6. 7. This question paper consists of 0 questions. Answer
More informationNew SAT Math Diagnostic Test
New SAT Math Diagnstic Test Answer Key Slve and Graph Linear Equatins 1. Slve fr z: 4 + z (+ z) z (5 ) = 6 7 1. z = 61. Given the table f values: x -9 0 9 y 11 8 7?. y = 5 If the values in the table represent
More information2009 GCE A Level Solution Paper 1
2009 GCE A Level Solution Paper i) Let u n = an 2 + bn + c. u = a + b + c = 0 u 2 = 4a + 2b + c = 6 u 3 = 9a + 3b + c = 5 Using GC, a =.5, b = 8.5, c = 7. u n =.5n 2 8.5n + 7. (ii) Let y =.5n 2 8.5n +
More informationFigure 1a. A planar mechanism.
ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,
More informationKansas City Area Teachers of Mathematics 2011 KCATM Math Competition GEOMETRY GRADES 7-8
Kansas City Area Teachers f Mathematics 2011 KCATM Math Cmpetitin GEOMETRY GRADES 7-8 INSTRUCTIONS D nt pen this bklet until instructed t d s. Time limit: 20 minutes Yu may use calculatrs. Mark yur answer
More informationMATHEMATICS: PAPER II
NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 2014 MATHEMATICS: PAPER II EXAMINATION NUMBER Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of
More informationCalculus first semester exam information and practice problems
Calculus first semester exam information and practice problems As I ve been promising for the past year, the first semester exam in this course encompasses all three semesters of Math SL thus far. It is
More informationSet 2 Paper (a) (i) (ii) (b) The coordinates of R = ( 5, (a) Range = 8 2 (3) (b) New Mean. New variance
Section A( ( + + + +. ( ( ( M M 7 A 7 (. (a.8 A (b 00 (c A A (. (a x + xy (x ( x + y A (b. (a x x xy + y (x (x ( x + y M ( x ( x A x x + y ( x + y x x + y x M ( x y A (b If the value of y is increased
More information