Specialist Mathematics 2017 Sample paper
|
|
- Adam Shaw
- 5 years ago
- Views:
Transcription
1 South Australian Certificate of Education Specialist Mathematics 07 Sample paper Question Booklet Part (Questions to 9) 75 marks Answer all questions in Part Write your answers in this question booklet You may write on page 5 if you need more space Allow approximately 90 minutes Examination information Materials Question Booklet (Part ) Question Booklet (Part ) one SACE registration number label Reading time 0 minutes You may make notes on scribbling paper Writing time 3 hours Show all working in the question booklets State all answers correct to three significant figures, unless otherwise instructed Use black or blue pen You may use a sharp dark pencil for diagrams Approved calculators may be used complete the box below Total marks 50 SACE Board of South Australia 07 Graphics calculator For office use only Attach your SACE registration number label here. Brand Model Supervisor check Re-marked. Brand Model
2 This sample Specialist Mathematics paper shows the format of the examination for 07. page of 5
3 You may remove this page from the booklet by tearing along the perforations so that you can refer to it while you write your answers. LIST OF MATHEMATICAL FORMULAE FOR USE IN STAGE SPECIALIST MATHEMATICS Circular Functions sin Acos A tan cot Asec A Acosec A sina B sin Acos B cos Asin B cosa B cosacos B sin Asin B tan A tan B tana B tanatanb sin A sin Acos A cos Acos Asin A cos A sin A tan A tan A tan A sin Acos BsinABsinAB cos Acos B cosa BcosAB sin Asin BcosABcosAB sina sin B sin A Bcos A B cos Acos Bcos ABcos A B cos Acos Bsin A Bsin A B Matrices and Determinants If A a b then det A A adbc and c d A A d c b. a Quadratic Equations b b 4ac If ax + bx + c = 0 then x. a Distance from a Point to a Plane The distance from x, y, z to Ax By Cz D 0 is given by AxByC z D. A B C Derivatives f x y arcsin x arccos x arc tan x fx x x x dy dx Properties of Derivatives d dx f x g x f x g x f x g x d f x f x g x f x gx dx gx g x d dx f g x f g x g x Integration by Parts d f x g x x f x g x f x g x dx Volumes of Revolution b About x axis y dx, where y is a function of x. a d About y axis x dy, where y is a one-to-one c function of x. Mensuration Area of sector r Arc length r, where is in radians In any triangle ABC B c a A b C Area of triangle absin C a b c sin A sin B sin C a b c bccos A page 3 of 5
4 This sample Specialist Mathematics paper shows the format of the examination for 07. page 4 of 5
5 The examination questions begin on page 6. This sample Specialist Mathematics paper shows the format of the examination for 07. page 5 of 5 PLEASE TURN OVER
6 PART (Questions to 9) (75 marks) Question (8 marks) The parametric equations below describe a Bézier curve. xt 4t 4t0 3 y t 8t 4t 4 where t 0, (a) Find all points on the curve where the x-value is 0. ( marks) (b) Find the leftmost point on the curve. (3 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 6 of 5
7 (c) Find the length of the curve. (3 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 7 of 5 PLEASE TURN OVER
8 Question (8 marks) x (a) On the axes in Figure, graph the function f( x). x x Clearly show the behaviour of the function near the asymptotes. 4 f( x) x 3 Figure (6 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 8 of 5
9 (b) On the axes in Figure, graph the function f f 4 x x x 3 Figure ( marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 9 of 5 PLEASE TURN OVER
10 Question 3 (8 marks) In the following system of equations, k is a real constant. xyz x3yz k x5ykz (a) Write the system in augmented matrix form and, stating all row operations used, show that this leads to the reduced system: : 0 : k. 0 0 k 3 : k 3 (3 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 0 of 5
11 (b) (i) State the value of k for which the system has an infinite number of solutions. ( mark) (ii) Solve the system for the value of k stated in your answer to part (b)(i). (3 marks) (iii) Give a geometrical interpretation of the system of equations for this value of k. ( mark) This sample Specialist Mathematics paper shows the format of the examination for 07. page of 5 PLEASE TURN OVER
12 Question 4 (9 marks) (a) Find an approximate value for 3 3 x x d x. 3 x x x Give your answer to four significant figures. ( marks) (b) (i) Show that x x 3 x x x x x. ( marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page of 5
13 (ii) Show that 3 3 x x dx ln3 3. x x x 6 (5 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 3 of 5 PLEASE TURN OVER
14 Question 5 (8 marks) (a) Let a (i) Find a.,, 4 and b 5, 3,. ( mark) (ii) Find a b. ( mark) (iii) Verify that ab a b a b. ( marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 4 of 5
15 (b) Use the vector property cd cd c d to prove that, for any vectors c and d, cd c d c d. ( marks) (c) If c 0, d 5, and c d 5, find: (i) c d. ( mark) (ii) c d. ( mark) This sample Specialist Mathematics paper shows the format of the examination for 07. page 5 of 5 PLEASE TURN OVER
16 Question 6 (8 marks) Let v 68i and w 7i. (a) On the Argand diagram in Figure 3, plot and label the points corresponding to v and w. Im z Re z Figure 3 ( mark) (b) On the Argand diagram in Figure 3, draw the set of complex numbers z such that z 0. ( marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 6 of 5
17 (c) Verify that v is a member of the set of complex numbers that you drew in part (b). ( mark) (d) Let u be a complex number such that ui ww. Find u in Cartesian form. ( marks) (e) On the Argand diagram in Figure 3, mark the set of complex numbers z that satisfies both z 0 and zu zv. ( marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 7 of 5 PLEASE TURN OVER
18 Question 7 (8 marks) (a) Use mathematical induction to prove that n 3n n n for n, where n is an integer. (5 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 8 of 5
19 (b) (i) Show that the sum of n terms n n n Sn 3 can be written as the cubic polynomial function 3 f n3n 4. 5n. 5n. ( marks) (ii) For what value of n will S n 3065? ( mark) This sample Specialist Mathematics paper shows the format of the examination for 07. page 9 of 5 PLEASE TURN OVER
20 Question 8 (8 marks) (a) Use integration by parts to show that where c is a constant. x xsin xdx sin x cos xc 4 (4 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 0 of 5
21 (b) Figure 4 shows the graph of y xsin x, where 0 x. y x 3 Figure 4 Show that the area of one of the regions bounded by the curve and the x-axis is exactly three times the area of the other region. (4 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page of 5 PLEASE TURN OVER
22 Question 9 (0 marks) Figure 5 shows OA, the parabolic arc y x, for 0 x. Figure 6 represents the three-dimensional shape formed by rotating OA around the y-axis. y y A 4 A 3 3 y = x O x O x Figure 5 Figure 6 Figure 7 shows a thin rectangular strip of length x cm and width dy cm, drawn from a point x, y on OA. Figure 8 represents the thin disc of radius r cm and height h cm that is created when the rectangular strip is rotated around the y-axis. y y A 4 A 3 x dy 3 r = x h = dy O x O x Figure 7 Figure 8 This sample Specialist Mathematics paper shows the format of the examination for 07. page of 5
23 (a) (i) State the volume of the thin disc shown in Figure 8 in terms of x and y. ( mark) (ii) Hence write a definite integral in terms of y to represent the exact volume of the three-dimensional shape shown in Figure 6. (3 marks) (b) (i) A glass manufacturer makes drinking glasses in the three-dimensional shape shown in Figure 6. One of these glasses is filled with water to a depth of k cm, where 0 k 4. Find the volume of water in the glass in terms of k. ( marks) Question 9 continues on page 4. This sample Specialist Mathematics paper shows the format of the examination for 07. page 3 of 5 PLEASE TURN OVER
24 (ii) An empty glass is placed under a tap from which water is flowing at the rate of cm 3 s. At what rate is the depth changing when the glass is half full? (4 marks) This sample Specialist Mathematics paper shows the format of the examination for 07. page 4 of 5
25 You may write on this page if you need more space to finish your answer to any question. Make sure to label each answer carefully (e.g. Question 4(b)(ii) continued ). This sample Specialist Mathematics paper shows the format of the examination for 07. page 5 of 5 end of question booklet
26
27
28
2016 SPECIALIST MATHEMATICS
2016 SPECIALIST MATHEMATICS External Examination 2016 FOR OFFICE USE ONLY SUPERVISOR CHECK ATTACH SACE REGISTRATION NUMBER LABEL TO THIS BOX Graphics calculator Brand Model Computer software RE-MARKED
More informationDRAFT. Mathematical Methods 2017 Sample paper. Question Booklet 1
1 South Australian Certificate of Education Mathematical Methods 017 Sample paper Question Booklet 1 Part 1 Questions 1 to 10 Answer all questions in Part 1 Write your answers in this question booklet
More informationSpecialist Mathematics 2017 Sample paper
South Australian Certificate of Education The external assessment requirements of this subject are listed on page 20. Question Booklet 2 Specialist Mathematics 2017 Sample paper 2 Part 2 (Questions 10
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *5238158802* MATHEMATICS 9709/31 Paper 3 Pure Mathematics 3 (P3) October/November 2013 Additional Materials:
More informationADDITIONAL MATHEMATICS 4037/01
Cambridge O Level *0123456789* ADDITIONAL MATHEMATICS 4037/01 Paper 1 For examination from 2020 SPECIMEN PAPER 2 hours You must answer on the question paper. No additional materials are needed. INSTRUCTIONS
More informationMEI STRUCTURED MATHEMATICS CONCEPTS FOR ADVANCED MATHEMATICS, C2. Practice Paper C2-C
MEI Mathematics in Education and Industry MEI STRUCTURED MATHEMATICS CONCEPTS FOR ADVANCED MATHEMATICS, C Practice Paper C-C Additional materials: Answer booklet/paper Graph paper MEI Examination formulae
More informationMathematics (JAN12MPC201) General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core TOTAL
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 2 Friday 13 January 2012 General Certificate of Education Advanced
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *0835058084* ADDITIONAL MATHEMATICS 0606/11 Paper 1 October/November 2012 2 hours Candidates
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 08 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Monday November 08 Reading time: 3.00 pm to 3.5
More informationSec 4 Maths SET D PAPER 2
S4MA Set D Paper Sec 4 Maths Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e Answer all questions. Write your answers and working on the separate Answer Paper provided.
More information2016 MATHEMATICAL METHODS
2016 MATHEMATICAL METHODS External Examination 2016 FOR OFFICE USE ONLY SUPERVISOR CHECK ATTACH SACE REGISTRATION NUMBER LABEL TO THIS BOX Graphics calculator Brand Model Computer software RE-MARKED Friday
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *0050607792* ADDITIONAL MATHEMATICS 0606/21 Paper 2 May/June 2012 2 hours
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 06 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Monday 7 November 06 Reading time:.5 am to.00 noon
More informationabc Mathematics Pure Core General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Pure Core SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER MATHEMATICS
More informationMATHEMATICS 4722 Core Mathematics 2
ADVANCED SUBSIDIARY GCE MATHEMATICS 4722 Core Mathematics 2 QUESTION PAPER Candidates answer on the Printed Answer Book OCR Supplied Materials: Printed Answer Book 4722 List of Formulae (MF1) Other Materials
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/02 Paper 2 Examination from 2013 SPECIMEN PAPER 2 hours Candidates
More informationwww.onlineexamhelp.com www.onlineexamhelp.com * 031 674 651 3 * UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/22
More informationMathematical Methods 2018
1 Question booklet 1 Mathematical Methods 2018 Part 1 (Questions 1 to 9) 64 marks Answer all questions in Part 1 Write your answers in this question booklet You may write on pages 12 and 22 if you need
More information*P46958A0244* IAL PAPER JANUARY 2016 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA. 1. f(x) = (3 2x) 4, x 3 2
Edexcel "International A level" "C3/4" papers from 016 and 015 IAL PAPER JANUARY 016 Please use extra loose-leaf sheets of paper where you run out of space in this booklet. 1. f(x) = (3 x) 4, x 3 Find
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
PAPA CAMBRIDGE Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 1 0 4 5 3 8 9 2 1 * ADDITIONAL MATHEMATICS 0606/23 Paper 2 May/June 2014 2 hours
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 0 8 7 6 9 0 5 1 6 * ADDITIONAL MATHEMATICS 0606/11 Paper 1 October/November 016 hours Candidates
More informationInternational Advanced Level Core Mathematics C34 Advanced
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Sample Assessment Material Time: 2 hours 30 minutes Paper
More informationMathematics Extension 2
00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table
More informationCambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level * 2 2 1 1 9 6 0 6 4 7 * ADDITIONAL MATHEMATICS 4037/22 Paper 2 May/June 2016 2 hours Candidates answer on the Question Paper. No Additional
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *122414780* FURTHER MATHEMATICS 9231/01 Paper 1 October/November 2007 Additional Materials: Answer Booklet/Paper
More informationMATHEMATICAL METHODS (CAS) Written examination 1
Victorian Certificate of Education 2010 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words MATHEMATICAL METHODS (CAS) Written examination 1 Friday 5 November 2010 Reading time:
More informationMathematics Extension 2
00 HIGHER SCHOOL CERTIFICATE TRIAL EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Approved scientific calculators and templates
More informationMathematics Extension 2
Northern Beaches Secondary College Manly Selective Campus 010 HIGHER SCHOOL CERTIFICATE TRIAL EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time 3 hours Write using
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *1406924476* ADDITIONAL MATHEMATICS 0606/21 Paper 2 May/June 2010 Additional
More informationWeek beginning Videos Page
1 M Week beginning Videos Page June/July C3 Algebraic Fractions 3 June/July C3 Algebraic Division 4 June/July C3 Reciprocal Trig Functions 5 June/July C3 Pythagorean Identities 6 June/July C3 Trig Consolidation
More informationCambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level *8790810596* ADDITIONAL MATHEMATICS 4037/13 Paper 1 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials
More informationH2 MATHS SET D PAPER 1
H Maths Set D Paper H MATHS Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e b The curve y ax c x 3 points, and, H Maths Set D Paper has a stationary point at x 3. It also
More informationINNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION in preparation for General Certificate of Education Advanced Level Higher 2
INNOVA JUNIOR COLLEGE JC PRELIMINARY EXAMINATION in preparation for General Certificate of Education Advanced Level Higher CANDIDATE NAME CIVICS GROUP INDEX NUMBER Mathematics Paper Additional materials:
More informationProblems with an # after the number are the only ones that a calculator is required for in the solving process.
Instructions: Make sure all problems are numbered in order. (Level : If the problem had an *please skip that number) All work is in pencil, and is shown completely. Graphs are drawn out by hand. If you
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 2 4 2 8 1 9 0 7 2 * ADDITIONAL MATHEMATICS 0606/12 Paper 1 February/March 2016 2 hours Candidates
More informationCambridge International AS & A Level
Cambridge International AS & A Level *0123456789* FURTHER MATHEMATICS 9231/02 Paper 2 Further Pure Mathematics 2 For examination from 2020 SPECIMEN PAPER 2 hours You must answer on the question paper.
More informationPublic Assessment of the HKDSE Mathematics Examination
Public Assessment of the HKDSE Mathematics Examination. Exam Format (a) The examination consists of one paper. (b) All questions are conventional questions. (c) The duration is hours and 30 minutes. Section
More informationMATHEMATICAL METHODS
Victorian Certificate of Education 018 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER MATHEMATICAL METHODS Written examination 1 Friday 1 June 018 Reading time:.00 pm to.15 pm (15 minutes)
More informationMATHEMATICS Unit Pure Core 2
General Certificate of Education June 2008 Advanced Subsidiary Examination MATHEMATICS Unit Pure Core 2 MPC2 Thursday 15 May 2008 9.00 am to 10.30 am For this paper you must have: an 8-page answer book
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *41476759* ADDITIONAL MATHEMATICS 0606/ Paper February/March 017 hours Candidates answer on the Question
More informationCHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE TRIGONOMETRY / PRE-CALCULUS
CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE TRIGONOMETRY / PRE-CALCULUS Course Number 5121 Department Mathematics Qualification Guidelines Successful completion of both semesters of Algebra
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 07 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Monday 3 November 07 Reading time: 3.00 pm to 3.5
More informationMathematics MFP2 (JUN15MFP201) General Certificate of Education Advanced Level Examination June Unit Further Pure TOTAL
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Further Pure 2 Tuesday 16 June 2015 General Certificate of Education Advanced
More informationCore Mathematics C1 (AS) Unit C1
Core Mathematics C1 (AS) Unit C1 Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation. Graphs of functions; sketching curves defined by simple equations.
More informationADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA
GRADE 12 EXAMINATION NOVEMBER 2016 ADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA Time: 2 hours 200 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *1484530378* FURTHER MATHEMATICS 931/01 Paper 1 May/June 009 Additional Materials: Answer Booklet/Paper
More informationH I G H E R S T I L L. Extended Unit Tests Higher Still Higher Mathematics. (more demanding tests covering all levels)
M A T H E M A T I C S H I G H E R S T I L L Higher Still Higher Mathematics Extended Unit Tests 00-0 (more demanding tests covering all levels) Contents Unit Tests (at levels A, B and C) Detailed marking
More informationNATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -
More informationCore Mathematics C34
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Tuesday 20 June 2017 Afternoon Time: 2 hours 30 minutes
More informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE NORMAL ACADEMIC LEVEL (016) (Syllabus 4044) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE
More informationTIME TRIAL 4 H2 MATHEMATICS 9758 PAPER 1
TIME TRIAL H MATHEMATICS 9758 PAPER Additional Materials: Writing papers Duration: 3 Hours MF6 DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO READ THESE INSTRUCTIONS FIRST Write in dark blue or black
More informationEdexcel GCE Further Pure Mathematics (FP1) Required Knowledge Information Sheet. Daniel Hammocks
Edexcel GCE Further Pure Mathematics (FP1) Required Knowledge Information Sheet FP1 Formulae Given in Mathematical Formulae and Statistical Tables Booklet Summations o =1 2 = 1 + 12 + 1 6 o =1 3 = 1 64
More informationa Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8).
Worksheet A 1 A curve is given by the parametric equations x = t + 1, y = 4 t. a Write down the coordinates of the point on the curve where t =. b Find the value of t at the point on the curve with coordinates
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *5325132921* ADDITIONAL MATHEMATICS 0606/12 Paper 1 February/March 2018 2 hours Candidates answer
More informationSOLVING TRIGONOMETRIC EQUATIONS CONCEPT & METHODS
SOLVING TRIGONOMETRIC EQUATIONS CONCEPT & METHODS DEFINITION. A trig equation is an equation containing one or many trig functions of the variable arc x that rotates counterclockwise on the trig unit circle.
More informationMathematics (JUN11MPC301) General Certificate of Education Advanced Level Examination June Unit Pure Core TOTAL
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 3 Monday 13 June 2011 General Certificate of Education Advanced
More informationYear 2011 VCE. Mathematical Methods CAS. Trial Examination 1
Year 0 VCE Mathematical Methods CAS Trial Examination KILBAHA MULTIMEDIA PUBLISHING PO BOX 7 KEW VIC 30 AUSTRALIA TEL: (03) 908 5376 FAX: (03) 987 4334 kilbaha@gmail.com http://kilbaha.com.au IMPORTANT
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level FURTHER MATHEMATICS 9231/01 Paper 1 Additional materials: Answer Booklet/Paper Graph paper List of Formulae
More informationSec 4 Maths. SET A PAPER 2 Question
S4 Maths Set A Paper Question Sec 4 Maths Exam papers with worked solutions SET A PAPER Question Compiled by THE MATHS CAFE 1 P a g e Answer all the questions S4 Maths Set A Paper Question Write in dark
More informationCore Mathematics C34
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Tuesday 19 January 2016 Morning Time: 2 hours 30 minutes
More informationCore Mathematics C34
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Monday 16 June 2014 Morning Time: 2 hours 30 minutes You
More informationabc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Further Pure SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER
More informationMATHEMATICS EXTENSION 2
PETRUS KY COLLEGE NEW SOUTH WALES in partnership with VIETNAMESE COMMUNITY IN AUSTRALIA NSW CHAPTER JULY 006 MATHEMATICS EXTENSION PRE-TRIAL TEST HIGHER SCHOOL CERTIFICATE (HSC) Student Number: Student
More informationC4 "International A-level" (150 minute) papers: June 2014 and Specimen 1. C4 INTERNATIONAL A LEVEL PAPER JUNE 2014
C4 "International A-level" (150 minute) papers: June 2014 and Specimen 1. C4 INTERNATIONAL A LEVEL PAPER JUNE 2014 1. f(x) = 2x 3 + x 10 (a) Show that the equation f(x) = 0 has a root in the interval [1.5,
More informationCambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level * 4 5 5 1 7 0 1 0 2 8 * ADDITIONAL MATHEMATICS 4037/23 Paper 1 October/November 2016 2 hours Candidates answer on the Question Paper. No Additional
More informationU6 A Level Maths PURE MOCK Tuesday 5 th February 2019 PM Time: 2 hours Total Marks: 100
Full name: Teacher name: U6 A Level Maths PURE MOCK Tuesday 5 th February 2019 PM Time: 2 hours Total Marks: 100 You must have: Mathematical Formulae and Statistical Tables, Calculator Instructions Use
More informationIYGB. Special Extension Paper A. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas
IYGB Special Extension Paper A Time: 3 hours 30 minutes Candidates may NOT use any calculator Information for Candidates This practice paper follows the Advanced Level Mathematics Core and the Advanced
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 08 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Wednesday 6 June 08 Reading time: 0.00 am to 0.5
More informationThe number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 72.
ADVANCED SUBSIDIARY GCE UNIT 4752/0 MATHEMATICS (MEI) Concepts for Advanced Mathematics (C2) THURSDAY 7 JUNE 2007 Morning Time: hour 0 minutes Additional materials: Answer booklet (8 pages) Graph paper
More informationCambridge International Examinations Cambridge Ordinary Level
www.onlineexamhelp.com Cambridge International Examinations Cambridge Ordinary Level * 2 4 5 9 7 1 6 2 7 8 * ADDITIONAL MATHEMATICS 4037/21 Paper 2 May/June 2014 2 hours Candidates answer on the Question
More informationADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA
GRADE 1 EXAMINATION NOVEMBER 017 ADVANCED PROGRAMME MATHEMATICS: PAPER I MODULE 1: CALCULUS AND ALGEBRA Time: hours 00 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 1 1 9 9 9 9 1 * ADDITIONAL MATHEMATICS 0606/1 Paper May/June 016 hours Candidates answer on the
More informationCambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level *3621984096* ADDITIONAL MATHEMATICS 4037/23 Paper 2 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials
More informationSOLVING TRIGONOMETRIC EQUATIONS CONCEPT & METHODS (by Nghi H. Nguyen) DEFINITION.
SOLVING TRIGONOMETRIC EQUATIONS CONCEPT & METHODS (by Nghi H. Nguyen) DEFINITION. A trig equation is an equation containing one or many trig functions of the variable arc x that rotates counter clockwise
More informationCore Mathematics C12
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Monday 10 October 2016 Morning Time: 2 hours
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *5331723388* ADDITIONAL MATHEMATICS 0606/12 Paper 1 February/March 2017 2 hours Candidates answer
More information(e) (i) Prove that C(x) = C( x) for all x. (2)
Revision - chapters and 3 part two. (a) Sketch the graph of f (x) = sin 3x + sin 6x, 0 x. Write down the exact period of the function f. (Total 3 marks). (a) Sketch the graph of the function C ( x) cos
More informationSECTION A. f(x) = ln(x). Sketch the graph of y = f(x), indicating the coordinates of any points where the graph crosses the axes.
SECTION A 1. State the maximal domain and range of the function f(x) = ln(x). Sketch the graph of y = f(x), indicating the coordinates of any points where the graph crosses the axes. 2. By evaluating f(0),
More informationx n+1 = ( x n + ) converges, then it converges to α. [2]
1 A Level - Mathematics P 3 ITERATION ( With references and answers) [ Numerical Solution of Equation] Q1. The equation x 3 - x 2 6 = 0 has one real root, denoted by α. i) Find by calculation the pair
More informationTopic 1 Part 3 [483 marks]
Topic Part 3 [483 marks] The complex numbers z = i and z = 3 i are represented by the points A and B respectively on an Argand diagram Given that O is the origin, a Find AB, giving your answer in the form
More informationPearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)
Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) First teaching from September 2017 First certification from June 2018 2
More informationπ π π π Trigonometry Homework Booklet 1. Convert 5.3 radians to degrees. A B C D Determine the period of 15
Trigonometry Homework Booklet 1. Convert 5.3 radians to degrees. A. 0.09 B. 0.18 C. 151.83 D. 303.67. Determine the period of y = 6cos x + 8. 15 15 A. B. C. 15 D. 30 15 3. Determine the exact value of
More informationWJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS
Surname Centre Number Candidate Number Other Names 0 WJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS A.M. MONDAY, 22 June 2015 2 hours 30 minutes S15-9550-01 For s use ADDITIONAL MATERIALS A calculator
More informationTopic 3 Part 1 [449 marks]
Topic 3 Part [449 marks] a. Find all values of x for 0. x such that sin( x ) = 0. b. Find n n+ x sin( x )dx, showing that it takes different integer values when n is even and when n is odd. c. Evaluate
More informationwww.onlineexamhelp.com www.onlineexamhelp.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 1 0 2 2 9 5 6 0 3 3 * ADDITIONAL MATHEMATICS 4037/22 Paper
More informationPENRITH HIGH SCHOOL MATHEMATICS EXTENSION HSC Trial
PENRITH HIGH SCHOOL MATHEMATICS EXTENSION 013 Assessor: Mr Ferguson General Instructions: HSC Trial Total marks 100 Reading time 5 minutes Working time 3 hours Write using black or blue pen. Black pen
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *8262841617* ADDITIONAL MATHEMATICS 0606/13 Paper 1 May/June 2017 2 hours Candidates answer on the
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More informationPROVINCIAL EXAMINATION MINISTRY OF EDUCATION, SKILLS AND TRAINING MATHEMATICS 12 GENERAL INSTRUCTIONS
INSERT STUDENT I.D. NUMBER (PEN) STICKER IN THIS SPACE JANUARY 1997 PROVINCIAL EXAMINATION MINISTRY OF EDUCATION, SKILLS AND TRAINING MATHEMATICS 12 GENERAL INSTRUCTIONS 1. Insert the stickers with your
More informationC3 Revision Questions. (using questions from January 2006, January 2007, January 2008 and January 2009)
C3 Revision Questions (using questions from January 2006, January 2007, January 2008 and January 2009) 1 2 1. f(x) = 1 3 x 2 + 3, x 2. 2 ( x 2) (a) 2 x x 1 Show that f(x) =, x 2. 2 ( x 2) (4) (b) Show
More informationCambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level *054681477* ADDITIONAL MATHEMATICS 407/11 Paper 1 May/June 017 hours Candidates answer on the Question Paper. No Additional Materials are required.
More informationN13/5/MATHL/HP1/ENG/TZ0/XX MATHEMATICS HIGHER LEVEL PAPER 1. Candidate session number 0 0. Monday 11 November 2013 (afternoon)
883720 MATHEMATICS HIGHER LEVEL PAPER Monday November 203 (afternoon) 2 hours Candidate session number 0 0 Examination code 8 8 3 7 2 0 INSTRUCTIONS TO CANDIDATES Write your session number in the boxes
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *7292744436* ADDITIONAL MATHEMATICS 0606/23 Paper 2 May/June 2017 2 hours Candidates answer on the
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *7560400886* ADDITIONAL MATHEMATICS 0606/22 Paper 2 May/June 2011 2 hours
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 00 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words SPECIALIST MATHEMATICS Written eamination Monday November 00 Reading time:.00 pm to.5
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01 Paper 1 Additional Materials: Answer Booklet/Paper Electronic
More informationΠ xdx cos 2 x
Π 5 3 xdx 5 4 6 3 8 cos x Help Your Child with Higher Maths Introduction We ve designed this booklet so that you can use it with your child throughout the session, as he/she moves through the Higher course,
More informationThe external assessment requirements of this subject are listed on page 20. DRAFT
South Australian Certificate of Education The external assessment requirements of this subject are listed on page 20. Mathematical Methods 2017 Sample paper 2 Question Booklet 2 Part 2 Questions 11 to
More informationFurther Concepts for Advanced Mathematics (FP1) FRIDAY 11 JANUARY 2008
ADVANCED SUBSIDIARY GCE 4755/0 MATHEMATICS (MEI) Further Concepts for Advanced Mathematics (FP) FRIDAY JANUARY 008 Additional materials: Answer Booklet (8 pages) Graph paper MEI Examination Formulae and
More informationAdvanced Higher Grade
Practice Eamination A (Assessing Units & ) MATHEMATICS Advanced Higher Grade Time allowed - hours 0 minutes Read Carefully. Full credit will be given only where the solution contains appropriate working..
More information