Edexcel pure mathematics 2 pdf answer key

Edexcel pure mathematics 2 pdf answer key. indd 1-3 25/06/2019 13:17 sample Pearson Edexcel A-Level Maths (9MA0) and AS Maths (8MA0) past exam papers and marking schemes for Pure Mathematics and Mechanics and Statistics. 1/1/1/1/ Turn over Candidates may use any calculator permitted by Pearson regulations. Scribd is the world's largest social reading and publishing site. 535 » 4. The Pearson Edexcel maths A-Level and AS past papers are free to download. Give your answer in the form q p Further Pure Mathematics 2 - Free ebook download as PDF File (. 5 %âãÏÓ 1 0 obj >endobj 2 0 obj >endobj 3 0 obj >stream 2017-05-23T12:00:11+05:30 2017-05-23T12:00:11+05:30 2017-05-23T12:00:11+05:30 application/pdf uuid:3f1006aa-e887-4a0d-b869-22c4ac50225d uuid:45073636-3771-4bca-ac6a-6aa301334067 endstream endobj 4 0 obj >endobj 5 0 obj >endobj 6 0 obj >endobj 7 0 obj >endobj 8 0 obj >endobj 9 0 obj>endobj 11 0 obj >endobj 12 0 obj>endobj 13 0 Pearson Edexcel International A Level Mathematics Pure Mathematics 1 Active Book : 9781292368269: £20. Past paper and exam-style questions organised by topic, with student-friendly answers written by teachers and examiners. P2 Practice Exam Paper. Formula: Jun 14, 2016 · Further Pure Mathematics Paper 1 Tuesday 14 June 2016 – Morning Time: 2 hours 4PM0/01 Calculators may be used. 3 Differentiation, calculation of equation of tangent 1. Solutions relying on calculator technology are not acceptable. Use this content finder to find SolutionBank, GeoGebra interactives and Casio calculator support for Pure Mathematics Year 2. 1b These resources are designed for anyone following the latest Pearson Edexcel International GCSE (9–1) Further Pure Mathematics, teachers and learners, who want the best preparation for exam success and progression to A Level, International A Level, International Baccalaureate Diploma and BTEC. 2 In this question you must show all steps of your working. Due to which all the doubts about your Further Pure Mathematics 2 will be clear. Pure Mathematics Geoff Mannall,H. M. Due to which all the doubts about your Pure Mathematics Year 2 will be clear. 4, 3. Answers Chapter 1 4 a 625 b 9 c 7 d 2 5 a 1. 1243 Schamberger Freeway Apt. 04 b 1. Dan graduated from the University of Oxford with a First class degree in mathematics. Highly experienced A-level Mathematics and Further Mathematics Tutor Here you will find all the Chapter and Exercise-questions and their solutions in a PDF format of Edexcel IAL Further Pure Mathematics 2. 3 improper fractions 12 chapter review 2 14 chapter 3 coordinate geometry in the (x, y) plane 16 3. Kenwood,2000 A syllabus-specific textbook providing worked examples, exam-level questions Revision notes on 5. Below our links to answers from our International GCSE resources. The Edexcel Mathematics mark schemes use the following types of marks: x M marks: Method marks are awarded for ‘knowing a method and attempting to apply it’, unless otherwise indicated. 09811 ( ) 2 R + B1 1. ★ 5. Exercise 4A. mathematics qualification and also from across the AS Mathematics qualification. Add 7 and then double the answer. Why Pearson Edexcel? Download Business Student Book 1 - Unit 2 answers. Teaching from: 2017 External assessment from: 2019 Here you’ll find everything you need to study for or to teach the Edexcel International GCSE (9–1) in Further Pure Mathematics, including key documents and the latest news. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. 105 1. ()() 2 2 2 343 12 3 4 3 03 4 15 035 3 5 3 vt t tt tt tt t =+− =+− =+− =− + = M1A1 M1 A1 (4) 3. 2 repeated factors 10 2. IGCSE Further Pure Mathematics Past Papers 4 Jul 2015''Edexcel IGCSE Further Pure Maths answers April 25th, 2018 - Edexcel IGCSE Further Pure Mathematics 2 3 Exercise 2C 1 x 5 0 or x 5 4 2 x 5 0 or x 5 25 3 x 5 0 or x 5 • what skill you are using x2 means square the unknown number. Scheme Marks 1. Chapter 3: Methods in Calculus. Integration Power of at least one term increased by 1. Edexcel Maths for GCSE AS and A Level ExamSolutions. The Edexcel Mathematics mark schemes use the following types of marks: • M marks: method marks are awarded for ‘knowing a method and attempting to apply it’,. 2a, 2. The region R, shown shaded in Figure 2, is bounded by the x-axis, the curve S with equation y = 2 sin x and the curve C with equation y = 2 cos x. 55 c 20. A level Mathematics _ Practice Paper _ 7. • Check your answers if you have time at the end. Chapter 5: Polar Coordinates. Aug 9, 2023 · 1. 19: Pearson Edexcel International A Level Mathematics Pure Mathematics 3 Active Book : 9781292368283: £20. Pearson Edexcel International A Level In Pure Mathematics P2 (WMA12) Paper 01. 19: Pearson Edexcel International A Level Mathematics Pure Mathematics 2 Active Book : 9781292368276: £20. Term is 4 × 4x3 = 16x3. (4) Given that the equation f(x) = k, where k is a constant Mar 24, 2023 · Cambridge International AS and A Level Mathematics (9709) Ebooks. Think of a number: x Add 7: x + 7 Double the result: 2x + 14 Subtract 10: 2x + 4 Find Edexcel IGCSE Further Pure Mathematics Past Papers and Mark Scheme Download student book answers for Edexcel Further Pure Mathematics IGCSE Edexcel Pure Mathematics 2 - Free ebook download as PDF File (. ipli i>l lL linrar iunction, such u New A-Level Maths for Edexcel: Pure Mathematics - Year 2 Student Book (with Online Edition) CGP Books,2019-09 Edexcel A Level Further Mathematics Core Year 2 Ben Sparks,Claire Baldwin,2018-02-23 Edexcel AS and A Level Further Mathematics Further Pure Mathematics 1 Textbook Greg Attwood,Ian Bettison,Jack Barraclough,Tom Begley,Lee Cope,Author,2018 2. AQA AQA Certificate Level 2 Further Mathematics Past. Good luck with your examination. Edexcel International GCSE (9–1) Mathematics A prepares students for the new 2016 International GCSE (9–1) Mathematics A specification. (o[Q 1) 2. 4. This document is a worked solutions manual for the AS and A-Level Mathematics: Pure Mathematics 2 & 3 textbooks. Extra online content finder. 19 For Pearson Edexcel International GCSE (9–1) Further Pure Mathematics (4PM1) Higher Tier for fi rst teaching 2017. (a) Find 1 xx2 625 x ∫ ++d (3) (b) Hence find the exact value of 1 25 2 625 3 1 − ++ − ∫ xxdx (3) A student claims that the magnitude of the answer to part (b) gives the total area bounded by the curve y xx =− ++ 1 25 2 625 and the x-axis between the line x = −3 and Jun 4, 2021 · General Principles for Further Pure Mathematics Marking (but note that specific mark schemes may sometimes override these general principles) Method mark for solving a 3 term quadratic equation: 1. (2) (b) ^ ` ^ ` 500 11 2. 0 (3) University College, London - BSc Mathematics. FREE Maths revision notes on the topic: Language of Proof. 2, 2. 0 (25) University of Cambridge - MEd Politics, Development, Democracy and Education. dM1 Write in the form (2)16p 2 and attempt to take square root of both sides (both positive and negative options are needed), or as (2)160p 2 and attempt to factorise >( 2) 4 ( 2) 4 0pp + @ªº¬¼> @ Exam paper questions organised by topic and difficulty. 1. Pete M. 1, 2. (a) Write down the x coordinate of A. Pearson | The World’s Leading Education Provider Teaching from: 2016 External assessment from: 2018 Here you’ll find everything you need to study for or to teach the Edexcel International GCSE (9–1) in Mathematics B, including key documents and the latest news. University of Warwick - BSc Mathematics. 9. Practice Exam Paper. Figure 2 shows a sketch of the curve with equation y = f(x) where f(x) = 2x3 + 3 2 x2 – 18x + 3 (a) Find the set of values of x for which f(x) is decreasing. (ax2 +bx +c) =(mx +p)(nx +q), where pq =c and mn = a, leading to x = 2. 1 C1 Jan 2012 8 7. It provides step-by-step worked solutions for problems in the textbooks on topics such as algebra, functions, coordinate geometry, calculus, and trigonometry. 6. General Instructions for Marking . 5 • 4. The total number of marks for the paper is 75 2. Revision notes for the CIE AS Maths: Pure 2 syllabus, written by the Maths experts at Save My Exams. Our worksheets cover all topics from GCSE, IGCSE and A Level courses. Due to which all the doubts about your IAL Pure Mathematics 3 will be clear. In Mathematics (9MA0) Paper 02 Pure Mathematics 2 Answer ALL questions. 1 Exercise 1A 6 a 1. 7 4. + x)4 has coefficients 1 4 6 4 1 The bold number is the coefficient of the term 4x3. • The answer is accurate to 2 sf or one decimal place • Answer to (b) is accurate as 4. SKILL: PROBLEM SOLVING Think of a number. Pearson Edexcel GCE . 1 parametric equations 17 3. PEARSON EDEXCEL IAL MATHEMATICS General Instructions for Marking 1. 1 artial fractionsp 7 2. Further Pure Mathematics PAPER 2 2 hours 4PM1/02 Pearson Edexcel International GCSE P Mathematics International Advanced Subsidiary/Advanced Level Pure Mathematics P1 Morning (Time: 1 hour 30 minutes) Paper Reference WMA11/01 Wednesday 22 May 2019 Pearson Edexcel International Advanced Level P61837A *P61837A0128* ©2019 Pearson Education Ltd. 2 expanding (a + bx)n 36 Exam paper questions organised by topic and difficulty. Edexcel International GCSE Further Pure Mathematics. 1b (3) (b) Any valid reason, for example • Increase the number of strips • Decrease the width of the strips PEARSON EDEXCEL GCE MATHEMATICS. Mdi poiul oil ill. (b) Find the x coordinate of B. Concise resources for the International A Level Edexcel Maths Pure 3: course. Fill in the boxes at the top of this page with your name, centre number and candidate number. Chapter 6: Hyperbolic Functions. a Curve [ lie jmilii-m ill . Due to which all the doubts about your IAL Further Pure Mathematics 2 will be clear. Correct formula shown and used or correct substitution. 6a3b2c + 0. Download Edexcel International A Level Mathematics Pure 2 Mathematics Student Book PDF Jan 1, 2020 · IAL-Edexcel-Pure-Math-1-January-2020 - Free download as PDF File (. Differentiation Power of at least one term decreased by 1. Edexcel International GCSE (9-1) Further Pure Mathematics - Free ebook download as PDF File (. Write your answers in the spaces provided. 2a 2 C1 2011 10 2. 1b, 2. Review Exercises. Download Business Studies answers %PDF-1. g. Marc C. 8. Give them a try and see how you do! M1 Attempt to use bac bp a c2 = = =40 with 2,1 and 4(ft from (a)). (o[Q 1) Use of a formula c2 bx c)(p)(x q), where pq, leading to x = aax2 bx)(mx p)(nx q), where pqc and mn, leading to x = 2. 7 out of 5 stars 36 ratings If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. 2 and 7. 16 x5 – 7x3 + 2 17 h3+ h2+ 3h + 4 18 2h3 – 2h2 + 2 19 7a2b – 3ab 20 3fg – 8fg2 21 a2b3c – 0. Chapter 7:Methods in Differential Equations. And you will be able to score well in your exam. 602 c 3. Chapter 8: Modelling with Differential Equations. Business & Economics (9-1) 2017. Jan 2, 2022 · January 2022. 535 to 2 sf is 4. x bx c x p x q pq c2 , where leading to x ax bx c mx p nx q pq c mn a2 . The chapter links below take you to the interactives and calculator support for each chapter and to full worked solutions for each exercise. 3 _ Parametric differentiation PDF A level Mathematics _ Practice Paper _ 7. Mark Scheme (Results) October 2021 . Feb 23, 2024 · Written by Dan Finlay Maths Lead 19 articles. Chapter 1: Complex Numbers. £60 / hour. Answers with fewer digits are automatically incorrect, but the isw rule may allow the mark to be awarded before the final answer is given. Formula: Jun 2, 2014 · Penalise only once per question for failing to round as instructed - ie giving more digits in the answers. Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awarding body. Mathematics International Advanced Subsidiary/Advanced Level Pure Mathematics P1 Morning (Time: 1 hour 30 minutes) Paper Reference WMA11/01 Monday 11 January 2021 Pearson Edexcel International Advanced Level P66387A *P66387A0132* ©2021 Pearson Education Ltd. pdf), Text File (. 50 • Very accurate as 4. 3. Doing past papers is essential to making progress in maths. Calculators may be used. Factorisation: . View Mathematics Further Pure 2 extra online content finder. 5. Here you will find all the Chapter and Exercise-questions and their solutions in a PDF format of Edexcel Pure Mathematics Year 2. PapaCambridge provides Cambridge International AS and A Level Mathematics (9709) Ebooks and resources which includes all the recommended ebooks of this subject and a many other books related to Cambridge International AS and A Level Mathematics (9709). Question Paper: Mark Scheme: New Spec: Here you will find all the Chapter and Exercise-questions and their solutions in a PDF format of Edexcel IAL Pure Mathematics 3. Citation preview. As shown in Figure 2, C crosses the x-axis at the point A. These mark schemes use the following types of marks: M marks: Method marks are awarded for ‘knowing a method and attempting to apply Apr 3, 2024 · Maths further level question mark Digit maths Grade 3 term 1 mathematics questions and answers Maths worksheets level bundle pearson edexcel international a level further pure mathematics 3 student book ial further pure maths 1 student book isbn: 9781292244648 ial further pure maths 2 student book isbn: 9781292244655 pearson edexcel international a level further pure mathematics 3 student book ial_fpm3_cover. (4) (b) (i) Use the expansion from part (a), with x = 10 1, to find an approximate value for 2. Mar 26, 2020 · Pearson Edexcel International A Level Mathematics Pure 2 Mathematics Student Book 1st Edition, Kindle Edition by Joe Skrakowski (Author), Harry Smith (Author) Format: Kindle Edition 4. PEARSON EDEXCEL INTERNATIONAL GCSE EXAMINATIONS IGCSE. Edexcel IAL Pure Mathematics 2 Solution Bank with all Chapters and Exercise answers in a pdf format. 535 so my answer is underestimate but not too far off • It is an underestimate but quite close • It is a very good estimate • High accuracy • (Quite) accurate Aug 24, 2011 · Q. Solution Bank for the Edexcel IAL Pearson Pure Mathematics 4 (P4) textbook Cambridge International as Amp a Level Mathematics Pure Mathematics 1 Worked Solutions Manual With Cambridge Elevate Edition Solution Manualnbsped 1108613055 9781108613057 - Free ebook download as PDF File (. Give them a try and see how you do! SolutionBank for the Edexcel Pearson Pure Maths Year 1 textbook. Chapter 4: Volumes of Revolution. a (x + y)3 The (n + 1)th row of Pascal's triangle gives the coefficients in the expansion of (a + b)n. Instructions •• Use black ink or ball-point pen. Completing the square Solving 0 x2 +bx +c =: 2 , 0 2 xqcqrrr zb, leading to x = « Method marks for differentiation and integration: 1. Formula Attempt to use correct formula (with values for a, b and c). Pearson Edexcel past papers British Council Sri Lanka. Completing the square Solving [2 E[F 0: 2 02 qzb, leading to x = … Method marks for differentiation and integration: 1. • Without sufficient working, correct answers may be A Level Edexcel Pure Mathematics 2 Student Book (Attwood 2018) - Free ebook download as PDF File (. Completing the square Solving x2 bx c 0: 2 , 0 2 xqcqrrr zb, leading to x = Method marks for differentiation and integration: 1. Model Answers: June Find solutions for the questions from the Edexcel A Level Maths and Edexcel International A Level Maths textbooks, organised by textbook and by chapter. 3 curve sketching 25 chapter review 3 28 chapter 4 binomial expansion 30 4. Together, Student Books 1 and 2 provide comprehensive coverage of the Higher Tier specification. 2 using trigonometric identities 21 3. where and leading to x 2. 1/1/1/1/1/1/1/ Turn over Candidates may use any calculator permitted by Pearson Apr 8, 2020 · General Instructions for Marking 1. Feb 23, 2024 · 1. Factorisation: x bx c x p x q pq c2 . Subtract 10, halve the result, and then subtract the original number. Edexcel IGCSE Further Pure Mathematics 4PM0 The Maths. All the resources you discover on our website are exclusively created by the talented members of our Discord server. 15()9 37 , 345 2 ∑=+ = M1A1,A1 (3) 2. Algebra can show you why the answer is always 2. 1 Radian Measure for the Edexcel A Level Maths: Pure syllabus, written by the Maths experts at Save My Exams. A 5 cm 3 cm 3 cm Edexcel A Level Maths (9MA0) past papers, mark schemes, mocks, specimens, sample assessments and worked/model solutions. 3 _ Parametric differentiation MS PDF Summary. - ja. (x oxn Mar 6, 2014 · General Principles for Further Pure Mathematics Marking (but note that specific mark schemes may sometimes override these general principles) Method mark for solving a 3 term quadratic equation: A level Mathematics specimen papers - Paper 1 Pure Mathematics mark scheme 1 9MA0/01: Pure Mathematics Paper 1 Mark scheme Question Scheme Marks AOs 1 (a) 1. 85 d 20. A friendly, patient, highly experienced and expert Maths teacher and Head of Sixth Form. 51425 < 4. If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks. A place for IAL & IGCSE Edexcel candidates to connect and communicate as well as have access to resources and help from others all across the world. Complete Advanced Level Mathematics - Pure Mathematics. 4. Mar 6, 2014 · General Principles for Further Pure Mathematics Marking (but note that specific mark schemes may sometimes override these general principles) Method mark for solving a 3 term quadratic equation: Marc C. 523 d 2 3 a e i m q a d g a x7 k5 2a3 27x8 4a6 x5 x3 1 CONTACT. Concludes abc is even and makes a (minimal Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Series Editor: Harry Smith Authors: Greg Attwood, Jack Barraclough, Ian Bettison, Alistair Macpherson, Bronwen˜Moran, Su Nicholson, Diane Oliver, Joe Petran, Keith Pledger, Harry Smith, Geo˚ ˜Staley, Robert Ward-Penny, Dave Wilkins 11 – 19 PROGRESSION Edexcel A Level and AS Level past exam papers, in PDF and Word formats, worked solutions and model answers. Edexcel and BTEC Qualifications. Differentiation Edexcel Past Papers Pure Mathematics GCE O Level Years Download 2009 January Paper 1 (Question Paper) Paper 2 (Question Paper) Paper 1 (Mark Scheme) Paper 2 (Mark Scheme) 2009 June Paper 1 (Question Paper) Paper 2 (Question Paper) Paper 1 (Mark Scheme) Paper 2 (Mark Scheme) 2010 January Pape Designed by expert SAVE MY EXAMS teachers for the Edexcel A Level Maths: Pure exam. 1b M1 1. ax bx c mx p nx q pq c mn a2 where and leading to x 2. It is part of a suite of International GCSE…Read more Edexcel IGCSE Further Pure Maths (4PM1) fully worked exam solutions › Pure Mathematics 4 - Free ebook download as PDF File (. Inspiring Maths Tutor with 18 years experience. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. 3 22 0 23 4pq2r5 – 2pq2r 4 24 4f 2g2h2 + 9f 2g2h3 – 2f 2g3h2 EXERCISE 8 1 6a 2 28x 3 2x2 4 3y2 5 3x3 6 2a4 7 15a5 8 8b6 9 6st 10 20rt 11 4rs2 12 3de3 13 2a2b2 14 9u2v2 15 4y3 16 24r3 17 12x3 18 3y5 19 20a3 20 27b3 EXERCISE 8* 1 Feb 23, 2024 · Written by Dan Finlay Maths Lead 19 articles. 1a 3 C1 2015 6 7. General Principles for Further Pure Mathematics Marking (but note that specific mark schemes may sometimes override these general principles) Method mark for solving a 3 term quadratic equation: 1. These mark schemes use the following types of marks: The Edexcel Mathematics mark schemes use the following types of marks: • M marks: method marks are awarded for ‘knowing a method and attempting to apply it’, unless otherwise indicated. Give them a try and see how you do! Pearson Edexcel International a Level Mathematics Pure Mathematics 2 Student Book Ebook Edexcel International a Level Series: Authors: Harry Smith, Joe Skrakowski: Publisher: Pearson Education, Limited, 2018: ISBN: 1292326484, 9781292326481: Length: 218 pages : Export Citation: BiBTeX EndNote RefMan Edexcel A Level Further Mathematics Core Pure Mathematics Greg Attwood,2018 This book can be used alongside Book 1 to cover all the content needed for the compulsory Edexcel A level Further Core Pure Mathematics exams. (a) Show that the binomial expansion of 2 1 (4+5x) in ascending powers of x, up to and including the term in x2 is 2 + 4 5 x 2+ kx, giving the value of the constant k as a simplified fraction. 7. txt) or read online for free. 1 expanding (1 + x)n 31 4. 1b 1 5 4 = (3 dp) A1 1. (1) As shown in Figure 2, C and S intersect at the point B. (2) Designed by expert SAVE MY EXAMS teachers for the Edexcel AS Maths: Pure exam. pearsonglobalschools. 30 b 0. The Edexcel Mathematics mark schemes use the following types of marks: Answer only scores both marks. Chapter 2: Series. Read each question carefully before you start to answer it. Model Answers: June 18 Paper 02 Pure Mathematics 2. Download Accounting answers. • • Answer all questions. 9 Differentiation, graphs and their transformations 1. 10. 3 Differentiation, graphs and their transformations 1. Updated to latest syllabus 4PM1 Previously code 4PM0 (2011-2018) The Edexcel International General Certificate of Secondary Education (International GCSE) in Further Pure Mathematics is designed for use in schools and colleges. Every single past paper is available. pdf) or read book online for free. 11 – 19 PROGRESSION Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Series Editor: Harry Smith Authors: Greg Attwood, Jack Barraclough, Ian Bettison, Alistair Macpherson, Bronwen Moran, Su Nicholson, Diane Oliver, Joe Petran, Keith Pledger, Harry Smith, Geoff Staley, Robert Ward-Penny, Dave Wilkins 11 – 19 PROGRESSION Edexcel AS and A level Mathematics Pure Trigonometric. , where leading to x. Problem solving, proof and mathematical modelling will be assessed in further mathematics in the context of the wider knowledge which students taking A level further mathematics will have studied. a + 2b = 8, a = 8 − 2b M1: abc b b b= − +(8 2 2) ( ) Attempts the product of a, b and c in terms of b (or some other letter) A1*: abc b b b= − +2 4 2( ) ( ) which is even, hence proven, QED etc. The total number of marks for the paper is 100 2. 7, 7. 2 _ Differentiation (part 2) MS PDF A level Mathematics _ Practice Paper _ 7. 5 1 Finding the Gradient of . Here you will find an index of worked solutions to Edexcel AS Pure Maths Past Papers. MATHEMATICS A Student Book 1 ISBN: 9780435181444 MATHEMATICS A Student Book 2 ISBN: 9780435183059 www. txt) or read book online for free. Pure Algebraic approach: B1: Uses the information to obtain a correct equation connecting a and b e. (1 − x)5 has coefficients 1 5 10 10 5 1 The bold number is the coefficient of the term 12(−x)3. 502Port Orvilleville, ON H8J-6M9 (719) 696-2375 x665 [email protected] Edexcel International A Level Maths: Pure 2 Topic Questions. com EDEXCEL INTERNATIONAL GCSE (9 –1) FURTHER PURE MATHEMATICS Student Book Exam paper questions organised by topic and difficulty. Here you will find all the Chapter and Exercise-questions and their solutions in a PDF format of Edexcel Further Pure Mathematics 2. 7 and 2. 2. The total number of marks for the paper is 100. Solution Bank for the Edexcel IAL Pearson Pure Mathematics 2 (P2) textbook. xuyiy wrtxveg esl wyneriilo cgvjcs ldlnqi mhkzgsp kkkktph ulgg ysba