GCSE MATHEMATICS (LINEAR) Higher Tier Paper 2. Morning (NOV H01) Materials. Instructions. Information. Advice PMT

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "GCSE MATHEMATICS (LINEAR) Higher Tier Paper 2. Morning (NOV H01) Materials. Instructions. Information. Advice PMT"

Transcript

1 Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature GCSE H MATHEMATICS (LINEAR) Higher Tier Paper 2 Friday 4 November 2016 Materials For this paper you must have: a calculator mathematical instruments. Morning Time allowed: 2 hours Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Answer all questions. You must answer the questions in the spaces provided. around each page or on blank pages. Do all rough work in this book. Information The marks for questions are shown in brackets. The maximum mark for this paper is 105. The quality of your written communication is specifically assessed in Questions 2, 6 and 20. These questions are indicated with an asterisk (*). You may ask for more answer paper, tracing paper and graph paper. These must be tagged securely to this answer book. Advice In all calculations, show clearly how you work out your answer. (NOV H01) WMP/Nov16/E5 4365/2H

2 2 Formulae Sheet: Higher Tier a 1 Area of trapezium = (a + b)h 2 h b Volume of prism = area of cross section length cross section length 4 3 Volume of sphere = πr 3 r Surface area of sphere = 4πr Volume of cone = πr 2 h Curved surface area of cone = πrl l r h In any triangle ABC 1 2 Area of triangle = ab sin C a b c Sine rule = = sin A sin B sin C A b c C a B Cosine rule a 2 = b 2 + c 2 2bc cos A The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by b ± (b 2 4ac) x = 2a (02)

3 3 Answer all questions in the spaces provided. 1 On this grid, rotate shape A by 90 clockwise about point P. [3 marks] A P Turn over for the next question 3 Turn over (03)

4 people are asked about their work. Here are some of the results. Full time Part time Not working Total Men Women Total (a) The total number working part time is the same as the total number of people not working. Complete the table. [4 marks] (04)

5 5 *2 (b) In this survey, there are 60 men and 40 women. Which is greater the percentage of the men who work full time or the percentage of the women who work full time? You must show your working. [3 marks] Answer Turn over for the next question 7 Turn over (05)

6 6 3 This hexagon has two lines of symmetry. Not drawn accurately 152 y Work out the size of angle y. [3 marks] Answer degrees (06)

7 7 4 A builder mixes sand and cement in the ratio 4 : 1 4 (a) Altogether he mixes 250 kg How much sand and cement does he use? [2 marks] Sand kg Cement kg 4 (b) Cement is sold in 25 kg bags. Work out the maximum amount of mix that the builder can make with 3 bags of cement. [3 marks] Answer kg Turn over for the next question 8 Turn over (07)

8 8 5 (a) Complete the table of values for y = x 2 5 for values of x from 3 to 3 [2 marks] x y (b) Draw the graph of y = x 2 5 for values of x from 3 to 3 [2 marks] y O x (c) Use the graph of y = x 2 5 to write down the values of x when y = 0 [1 mark] Answer and (08)

9 9 6 The table shows the proportions of left-handed and right-handed students in a school. Left-handed Right-handed Boys 15% 85% Girls 12% 88% *6 (a) 20 boys and 10 girls are chosen at random from the school. Estimate the number of left-handed students chosen. [3 marks] Answer 6 (b) There are an equal number of boys and girls in the school. A student is chosen at random. Work out the probability that the student is right-handed. [2 marks] Answer 10 Turn over (09)

10 10 7 (a) Work out the area of a circle of radius 6 cm [2 marks] Answer cm 2 7 (b) Quarter circles of radius 6 cm are cut from the corners of a rectangle as shown. [3 marks] 20 cm Not drawn accurately 50 cm Work out the shaded area. Answer cm 2 (10)

11 11 8 In 1981 the population of England was 46 million. In 2011 the population of England was 53 million. Work out the increase in population as a percentage of the 1981 figure. [3 marks] Answer % Turn over for the next question 8 Turn over (11)

12 12 9 The area of the rectangle and the area of the triangle are equal. Not drawn accurately 8 cm 6 cm 2x cm (4x + 2) cm Work out the value of x. [4 marks] x = (12)

13 13 10 A ladder of length 31 feet is leaning against a wall as shown. The foot of the ladder is 8 feet from the wall. The wall is 35 feet tall. Not drawn accurately 31 feet 35 feet 8 feet Work out the distance from the top of the ladder to the top of the wall. [4 marks] Answer feet 8 Turn over (13)

14 14 11 Bag A contains 3 red balls and 7 blue balls. Bag B contains 8 red balls and 2 blue balls. Bag A Bag B A ball is picked at random from each bag. 11 (a) Complete the tree diagram to show all the probabilities. [3 marks] Bag A Bag B... Red... Red... Blue... Blue... Red... Blue (14)

15 15 11 (b) Work out the probability of picking a red ball from Bag A and a blue ball from Bag B. [2 marks] Answer Turn over for the next question 5 Turn over (15)

16 16 12 The straight line passes through points (0, 2) and (2, 8) y x 12 (a) Work out the equation of the straight line. [3 marks] Answer (16)

17 12 (b) On this grid the line y = x is shown y x On the same grid, draw the line x + y = 9 for values of x from 0 to 9 [2 marks] 12 (c) Solve the simultaneous equations 1 2 y = x and x + y = 9 [2 marks] Answer 7 Turn over (17)

18 18 13 (a) Simplify fully 5x 2 3y 4 2x y 3 [2 marks] Answer 13 (b) Expand and simplify (x + 7)(x 3) [2 marks] Answer 13 (c) Solve (x 8)(x + 2) = 0 [1 mark] Answer 13 (d) Factorise 8x 2 y + 6xy 2 [2 mark] Answer (18)

19 19 14 In a sale the normal price of a dress is reduced by 25% The sale price is then reduced by 10 The dress is now priced at 80 The manager says, The price is now one-third less than the normal price. Show that he is correct. [5 marks] Turn over for the next question 12 Turn over (19)

20 20 15 A train company records the number of minutes, t, some trains were late in one month. The histogram summarises the results. 6 5 Frequency density Number of minutes, t 15 (a) How many trains were more than 15 minutes late? [3 marks] Answer (20)

21 21 15 (b) Which is the modal class? Circle your answer. [1 mark] 0 t 5 15 t t t Which of these when converted to decimals are recurring decimals? Circle your answers. [2 marks] π Turn over for the next question 6 Turn over (21)

22 22 17 The surface area of a solid cylinder is given by the formula S = 2πrh + 2πr 2 17 (a) Rearrange the formula to make h the subject. [2 marks] Answer 17 (b) Work out the value of h when S = 95π cm 2 and r = 5.3 cm Give your answer to a suitable degree of accuracy. [4 marks] Answer cm (22)

23 23 18 y is inversely proportional to x 2 where x 0 When x = 2, y = (a) Form an equation for y in terms of x. [3 marks] Answer 18 (b) Work out the value of x when y = 5 [2 marks] Answer 11 Turn over (23)

24 24 19 (a) Work out the length x. [3 marks] Not drawn accurately x cm Answer cm 19 (b) Circle the statements that are true. [2 marks] sin 123 = sin 57 sin 123 = cos 57 cos 123 = cos 57 cos 123 = cos 57 (24)

25 25 19 (c) Work out the length y. [1 mark] Not drawn accurately 57 y 19 8 cm Answer cm Turn over for the next question 6 Turn over (25)

26 26 *20 A rectangle of card, 20 cm by 10 cm, is used to make a cylindrical tube A, as shown. The card does not overlap. 10 cm 10 cm A Not drawn accurately 20 cm Another rectangle of card, 20 cm by 10 cm, is used to make a cylindrical tube B, as shown. The card does not overlap. 20 cm 20 cm B Not drawn accurately 10 cm 10 cm (26)

27 27 The tubes are filled with clay. Which tube uses more clay? You must show your working. [4 marks] Answer Turn over for the next question 4 Turn over (27)

28 28 21 Use algebra to work out the x-coordinates of the points of intersection of y = 3x 2 and y = 4x + 2 Give your answers to 1 decimal place. [5 marks] Answer (28)

29 29 22 Work out the height h of the triangle ABC. C Not drawn accurately 12 cm h 10 cm A 15 cm B [5 marks] Answer cm END OF QUESTIONS 10 (29)

30 30 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED (30)

31 31 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED (31)

32 32 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright Information For confidentiality purposes, from the November 2015 examination series, acknowledgements of third party copyright material will be published in a separate booklet rather than including them on the examination paper or support materials. This booklet is published after each examination series and is available for free download from after the live examination series. Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team, AQA, Stag Hill House, Guildford, GU2 7XJ. Copyright 2016 AQA and its licensors. All rights reserved. (02) (32)

43603H. (NOV1243603H01) WMP/Nov12/43603H. General Certificate of Secondary Education Higher Tier November 2012. Unit 3 10 11 H

43603H. (NOV1243603H01) WMP/Nov12/43603H. General Certificate of Secondary Education Higher Tier November 2012. Unit 3 10 11 H Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier November 2012 Pages 3 4 5 Mark Mathematics

Διαβάστε περισσότερα

Candidate Number. General Certificate of Secondary Education Higher Tier November 2013

Candidate Number. General Certificate of Secondary Education Higher Tier November 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark General Certificate of Secondary Education Higher Tier November 2013 3 4 5 Mathematics

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae

Διαβάστε περισσότερα

General Certificate of Secondary Education Higher Tier

General Certificate of Secondary Education Higher Tier Version 1.0 Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature Pages Mark General Certificate of Secondary Education Higher Tier 3 4 5 Mathematics

Διαβάστε περισσότερα

Mathematics (Linear) 43652H. General Certificate of Secondary Education Higher Tier June 2012. Paper 2. Wednesday 13 June 2012 9.00 am to 11.

Mathematics (Linear) 43652H. General Certificate of Secondary Education Higher Tier June 2012. Paper 2. Wednesday 13 June 2012 9.00 am to 11. Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier June 2012 Pages 2 3 4 5 Mark Mathematics

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 6 3 1 7 7 7 6 4 0 6 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 October/November 2013 Candidates answer

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference

Διαβάστε περισσότερα

physicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes

physicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6666/01 Edexcel GCE Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes Materials required for examination Mathematical

Διαβάστε περισσότερα

Core Mathematics C12

Core Mathematics C12 Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Wednesday 25 May 2016 Morning Time: 2 hours

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 0 5 1 0 3 4 8 7 8 5 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 May/June 2013 Candidates answer on the

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *4358398658* GREEK 0543/04 Paper 4 Writing May/June 2015 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

Core Mathematics C34

Core Mathematics C34 Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Tuesday 21 June 2016 Morning Time: 2 hours 30 minutes

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *2517291414* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2013 1 hour 30 minutes

Διαβάστε περισσότερα

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *8175930111* GREEK 0543/04 Paper 4 Writing May/June 2017 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *1880009435* GREEK 0543/04 Paper 4 Writing May/June 2018 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education *3148288373* GREEK 0543/04 Paper 4 Writing May/June 2016 1 hour Candidates answer on the Question

Διαβάστε περισσότερα

*2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009

*2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009 1 hour 30 minutes

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education GREEK 0543/04 Paper 4 Writing For Examination from 2015 SPECIMEN PAPER Candidates answer on the Question

Διαβάστε περισσότερα

Paper Reference R. Statistics S1 Advanced/Advanced Subsidiary. Tuesday 10 June 2014 Morning Time: 1 hour 30 minutes

Paper Reference R. Statistics S1 Advanced/Advanced Subsidiary. Tuesday 10 June 2014 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6683/01R Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Tuesday 10 June 2014 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical

Διαβάστε περισσότερα

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

Wednesday 20 May 2015 Afternoon

Wednesday 20 May 2015 Afternoon Oxford Cambridge and RSA Wednesday 20 May 2015 Afternoon LEVEL 3 CERTIFICATE ENGINEERING H865/01 Mathematical Techniques and Applications for Engineers * 5 1 0 8 5 0 0 8 2 4 * Candidates answer on the

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Friday 18 June 2010 Morning Time: 45 minutes

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding

Paper Reference. Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Thursday 24 May 2007 Morning Time: 45 minutes

Διαβάστε περισσότερα

Core Mathematics C34

Core Mathematics C34 Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C34 Advanced Friday 12 June 2015 Morning Time: 2 hours 30 minutes You

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

Date Morning/Afternoon Time allowed: 1 hour 30 minutes

Date Morning/Afternoon Time allowed: 1 hour 30 minutes *0000000000* GCSE (9 1) Mathematics J560/06 Paper 6 (Higher Tier) Practice Paper Date Morning/Afternoon Time allowed: 1 hour 30 minutes You may use: A scientific or graphical calculator Geometrical instruments

Διαβάστε περισσότερα

Paper Reference. Advanced/Advanced Subsidiary. Thursday 9 June 2005 Morning Time: 1 hour 30 minutes

Paper Reference. Advanced/Advanced Subsidiary. Thursday 9 June 2005 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference 6 6 8 3 0 1 Paper Reference(s) 6683/01 Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Thursday 9 June 2005 Morning Time: 1 hour 30 minutes Surname Signature

Διαβάστε περισσότερα

Homework 8 Model Solution Section

Homework 8 Model Solution Section MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx

Διαβάστε περισσότερα

PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity

PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

Paper Reference. Modern Greek Paper 1 Listening and Responding. Friday 15 May 2009 Afternoon Time: 45 minutes (+5 minutes reading time)

Paper Reference. Modern Greek Paper 1 Listening and Responding. Friday 15 May 2009 Afternoon Time: 45 minutes (+5 minutes reading time) Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Friday 15 May 2009 Afternoon Time: 45 minutes

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Advanced Unit 2: Understanding, Written Response and Research

Advanced Unit 2: Understanding, Written Response and Research Write your name here Surname Other names Edexcel GCE Centre Number Candidate Number Greek Advanced Unit 2: Understanding, Written Response and Research Thursday 9 June 2011 Morning Time: 3 hours Paper

Διαβάστε περισσότερα

*H31123A0228* 1. (a) Find the value of at the point where x = 2 on the curve with equation. y = x 2 (5x 1). (6)

*H31123A0228* 1. (a) Find the value of at the point where x = 2 on the curve with equation. y = x 2 (5x 1). (6) C3 past papers 009 to 01 physicsandmathstutor.comthis paper: January 009 If you don't find enough space in this booklet for your working for a question, then pleasecuse some loose-leaf paper and glue it

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 7615/01 London Examinations GCE Modern Greek Ordinary Level. Friday 14 May 2010 Afternoon Time: 3 hours

Paper Reference. Paper Reference(s) 7615/01 London Examinations GCE Modern Greek Ordinary Level. Friday 14 May 2010 Afternoon Time: 3 hours Centre No. Candidate No. Paper Reference 7 6 1 5 0 1 Surname Signature Paper Reference(s) 7615/01 London Examinations GCE Modern Greek Ordinary Level Friday 14 May 2010 Afternoon Time: 3 hours Initial(s)

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

Διαβάστε περισσότερα

1999 MODERN GREEK 2 UNIT Z

1999 MODERN GREEK 2 UNIT Z STUDENT NUMBER CENTRE NUMBER HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MODERN GREEK 2 UNIT Z (55 Marks) Time allowed Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Write your Student

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY GRADE TRIALS EXAMINATION AUGUST 05 MATHEMATICS PAPER Time: 3 hours Examiners: Miss Eastes, Mrs. Jacobsz, Mrs. Dwyer 50 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY. Read the questions carefully.

Διαβάστε περισσότερα

Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education

Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education *7662998175* MATHEMATICS 0580/13 Paper 1 (Core) May/June 2014 Candidates answer on the Question

Διαβάστε περισσότερα

Aquinas College. Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET

Aquinas College. Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET Aquinas College Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical

Διαβάστε περισσότερα

Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary

Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Centre No. Candidate No. Paper Reference(s) 6683/01 Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Friday 20 May 2011 Afternoon Time: 1 hour 30 minutes Materials required for examination Mathematical

Διαβάστε περισσότερα

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1 Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the

Διαβάστε περισσότερα

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations //.: Measures of Angles and Rotations I. Vocabulary A A. Angle the union of two rays with a common endpoint B. BA and BC C. B is the vertex. B C D. You can think of BA as the rotation of (clockwise) with

Διαβάστε περισσότερα

Physics (Specification A & B) PHY6T/Q11/test

Physics (Specification A & B) PHY6T/Q11/test Centre Number Surname Candidate Signature Candidate Number Other Names Notice to Candidate. The work you submit for assessment must be your own. If you copy from someone else or allow another candidate

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

Modern Greek *P40075A0112* P40075A. Edexcel International GCSE. Monday 3 June 2013 Morning Time: 3 hours. Instructions. Information.

Modern Greek *P40075A0112* P40075A. Edexcel International GCSE. Monday 3 June 2013 Morning Time: 3 hours. Instructions. Information. Write your name here Surname Other names Edexcel International GCSE Centre Number Modern Greek Candidate Number Monday 3 June 2013 Morning Time: 3 hours You do not need any other materials. Paper Reference

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

Διαβάστε περισσότερα

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- ----------------- Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin

Διαβάστε περισσότερα

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education GREEK 0543/03 Paper 3 Speaking and Listening Role Play Booklet One For Examination from 2011

Διαβάστε περισσότερα

CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES,

CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES, CHAPTER : PERIMETER, AREA, CIRCUMFERENCE, AND SIGNED FRACTIONS. INTRODUCTION TO GEOMETRIC MEASUREMENTS p. -3. PERIMETER: SQUARES, RECTANGLES, TRIANGLES p. 4-5.3 AREA: SQUARES, RECTANGLES, TRIANGLES p.

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

Mock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) =

Mock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) = Mock Eam 7 Mock Eam 7 Section A. Reference: HKDSE Math M 0 Q (a) ( + k) n nn ( )( k) + nk ( ) + + nn ( ) k + nk + + + A nk... () nn ( ) k... () From (), k...() n Substituting () into (), nn ( ) n 76n 76n

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

Spherical Coordinates

Spherical Coordinates Spherical Coordinates MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Spherical Coordinates Another means of locating points in three-dimensional space is known as the spherical

Διαβάστε περισσότερα

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -

Διαβάστε περισσότερα

Advanced Unit 2: Understanding, Written Response and Research

Advanced Unit 2: Understanding, Written Response and Research Write your name here Surname Other names Edexcel GCE Centre Number Candidate Number Greek Advanced Unit 2: Understanding, Written Response and Research Tuesday 18 June 2013 Afternoon Time: 3 hours Paper

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Advanced Unit 2: Understanding, Written Response and Research

Advanced Unit 2: Understanding, Written Response and Research Write your name here Surname Other names Pearson Edexcel GCE Centre Number Candidate Number Greek Advanced Unit 2: Understanding, Written Response and Research Thursday 11 June 2015 Afternoon Time: 3 hours

Διαβάστε περισσότερα

PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =? Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least

Διαβάστε περισσότερα

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.

Διαβάστε περισσότερα

is like multiplying by the conversion factor of. Dividing by 2π gives you the

is like multiplying by the conversion factor of. Dividing by 2π gives you the Chapter Graphs of Trigonometric Functions Answer Ke. Radian Measure Answers. π. π. π. π. 7π. π 7. 70 8. 9. 0 0. 0. 00. 80. Multipling b π π is like multipling b the conversion factor of. Dividing b 0 gives

Διαβάστε περισσότερα

Read each question carefully before you start to answer it. Try to answer every question. Check your answers if you have time at the end.

Read each question carefully before you start to answer it. Try to answer every question. Check your answers if you have time at the end. Write your name here Surname Other names Pearson Edexcel International GCSE Centre Number Modern Greek Candidate Number Monday 22 June 2015 Morning Time: 3 hours You do not need any other materials. Paper

Διαβάστε περισσότερα

Modern Greek *P40074A0112* P40074A. Edexcel International GCSE. Thursday 31 May 2012 Morning Time: 3 hours. Instructions. Information.

Modern Greek *P40074A0112* P40074A. Edexcel International GCSE. Thursday 31 May 2012 Morning Time: 3 hours. Instructions. Information. Write your name here Surname Other names Edexcel International GCSE Centre Number Modern Greek Candidate Number Thursday 31 May 2012 Morning Time: 3 hours You do not need any other materials. Paper Reference

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

CRASH COURSE IN PRECALCULUS

CRASH COURSE IN PRECALCULUS CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter

Διαβάστε περισσότερα

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2010 Question 1 2 Mark Physics

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

Advanced Subsidiary Paper 1: Understanding and Written Response. Wednesday 24 January 2018 Morning Time: 2 hours 30 minutes

Advanced Subsidiary Paper 1: Understanding and Written Response. Wednesday 24 January 2018 Morning Time: 2 hours 30 minutes Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Greek Advanced Subsidiary Paper 1: Understanding and Written Response Wednesday 24 January

Διαβάστε περισσότερα

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0. DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec

Διαβάστε περισσότερα

1. Πόσοι αριθμοί μικρότεροι του διαιρούνται με όλους τους μονοψήφιους αριθμούς;

1. Πόσοι αριθμοί μικρότεροι του διαιρούνται με όλους τους μονοψήφιους αριθμούς; ΚΥΠΡΙΚΗ ΜΘΗΜΤΙΚΗ ΤΙΡΙ ΠΡΧΙΚΟΣ ΙΩΝΙΣΜΟΣ 7//2009 ΩΡ 0:00-2:00 ΟΗΙΣ. Να λύσετε όλα τα θέματα. Κάθε θέμα βαθμολογείται με 0 μονάδες. 2. Να γράφετε με μπλε ή μαύρο μελάνι (επιτρέπεται η χρήση μολυβιού για τα

Διαβάστε περισσότερα

PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 PhysicsAndMathsTutor.com 1 Q1. The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil. What is the maximum value

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΕΤΑΙΡΕΙΑ IΔ ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΟΛΥΜΠΙΑΔΑ 2013 21 ΑΠΡΙΛΙΟΥ 2013 Β & Γ ΛΥΚΕΙΟΥ. www.cms.org.cy

ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΕΤΑΙΡΕΙΑ IΔ ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΟΛΥΜΠΙΑΔΑ 2013 21 ΑΠΡΙΛΙΟΥ 2013 Β & Γ ΛΥΚΕΙΟΥ. www.cms.org.cy ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΕΤΑΙΡΕΙΑ IΔ ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΟΛΥΜΠΙΑΔΑ 2013 21 ΑΠΡΙΛΙΟΥ 2013 Β & Γ ΛΥΚΕΙΟΥ www.cms.org.cy ΘΕΜΑΤΑ ΣΤΑ ΕΛΛΗΝΙΚΑ ΚΑΙ ΑΓΓΛΙΚΑ PAPERS IN BOTH GREEK AND ENGLISH ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΟΛΥΜΠΙΑΔΑ

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Rectangular Polar Parametric

Rectangular Polar Parametric Harold s Precalculus Rectangular Polar Parametric Cheat Sheet 15 October 2017 Point Line Rectangular Polar Parametric f(x) = y (x, y) (a, b) Slope-Intercept Form: y = mx + b Point-Slope Form: y y 0 = m

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

Διαβάστε περισσότερα

PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Γ ΓΥΜΝΑΣΙΟΥ & Α ΛΥΚΕΙΟΥ

Γ ΓΥΜΝΑΣΙΟΥ & Α ΛΥΚΕΙΟΥ ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΕΤΑΙΡΕΙΑ IΘ ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ ΟΛΥΜΠΙΑΔΑ 2018 22 ΑΠΡΙΛΙΟΥ 2018 Γ ΓΥΜΝΑΣΙΟΥ & Α ΛΥΚΕΙΟΥ www.cms.org.cy ΘΕΜΑΤΑ ΣΤΑ ΕΛΛΗΝΙΚΑ ΚΑΙ ΑΓΓΛΙΚΑ PAPERS IN BOTH GREEK AND ENGLISH ΚΥΠΡΙΑΚΗ ΜΑΘΗΜΑΤΙΚΗ

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα