A level mathematics books

A level mathematics books. It’s perfect for helping students put their knowledge to the test and build their skills. Written by an experienced author and teacher, this print book with Cambridge Elevate edition provides fully-worked solutions for exercises contained within the Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook. PapaCambridge provides Cambridge International AS and A Level Mathematics - Further (9231) 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 - Further (9231). 2PURE MATHEMATICS 1 the coordinates of the second point ()xy 22, . A-level math paper 2 Discrete probability distribution. This coursebook provides a complete course for developing and practising the skills required for the O Level Mathematics qualification. Student Book 1 You should be able to find the magnitude and direction of a vector. These texts provide motivation with plenty of exercises of varying difficulty, interesting examples, modern applications, and unique approaches to the Apr 12, 2018 · Cambridge International AS & A Level Mathematics: Pure Mathematics 2 & 3 matches the corresponding units of the syllabus. Jan 25, 2018 · Written for the OCR A Level Mathematics specification for first teaching from 2017, this print Student Book covers the content for the second year of A Level. 68 books based on 19 votes: Introducing Pure Mathematics by Robert Smedley, Understanding Pure Mathematics by A. It showcases the different mental processes for dissecting a problem, and discusses how one can go from a master of tricks into an actual, standalone mathematical thinker. Free accompanying ebook included. Apr 29, 2020 · About the Book. The NRICH Project aims to enrich the mathematical experiences of all learners. This title offers additional practice exercises for students following the Pure Mathematics 2 & 3 unit of the Cambridge International AS & A Level Mathematics syllabus (9709). The materials follow the same order as the corresponding coursebook and contain extra worked examples to help students understand the skills required of the syllabus. 6 %âãÏÓ 24358 0 obj > endobj 24374 0 obj >/Encrypt 24359 0 R/Filter/FlateDecode/ID[33D876A8150E9848A0A901BED9F74E1F>]/Index[24358 45]/Info 24357 0 R/Length Jul 6, 2018 · This series has been developed specifically for the Cambridge International AS & A Level Mathematics (9709) syllabus to be examined from 2020. Showing all 7 results Default sorting Sort by popularity Sort by average rating Sort by latest Sort by price: low to high Sort by price: high to low Nov 11, 2022 · Addeddate 2023-06-04 12:25:52 Identifier cambridge-international-as-a-level-pure-mathematics-1-coursebook-no-watermark-leibniz-math. They are written to introduce new mathematical skills with clear explanations and provide practice materials in order to help students consolidate their knowledge Buy Cambridge AS & A Level Math Textbooks, Workbooks, Pastpapers and Revision Guides online at BooksPlus. 7 out of 5 stars 310 ratings This huge CGP Textbook is packed with thousands of questions for both years of A-Level Maths - it’s suitable for the Edexcel, AQA, OCR and OCR MEI courses. by David S. AS and A level Mathematics New Content Resources – Pure Mathematics Modelling Questions A collection of questions taken from previous A level Mathematics Pure Mathematics papers – essentially every question with the word ‘model’ included. 2 shows this general triangle. . Now available in ActiveLearn at no extra cost! Written for the AQA AS/A Level Mathematics specifications for first teaching from 2017, this print Student Book covers the content for AS and the first year of A Level. org_ku_djvu. The Book has been written by a team of experienced teachers so that the exchange of idens is constant and vigorous. Kinematics Fundamental by Sunil Kumar: Openstax book which I used to practice the projectile motion chapter in Further Mechanics. Get it Aug 5 - 8. This book can be used alongside the Year 1 book to cover all the content needed for the Edexcel A level Pure Cambridge International AS & A Level Mathematics provides a good preparation for study of Cambridge International AS & A Level Further Mathematics (9231). J. txt download 619. 1. Price. Jun 1, 2018 · With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study. txt download A book dedicated to taking one from the mere act of exercise solving to the core of mathematics — mathematical thinking. Please note: From 2020 Cambridge International A Level Mathematics has two different routes: Pure Mathematics and Probability & Statistics only This series of resources has been developed to support teachers and students of Cambridge International AS & A Level Mathematics (9709). %PDF-1. Designed to be used alongside our popular Pearson Edexcel AS and A level Mathematics course, our Practice Books offer the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions for every Pure, Statistics and Mechanics topic. Press Option/Alt + K at any time to jump back to these sign posts, or continue tabbing Skip to main content Skip to site header Accessibility information A level maths books . Paper 1: Pure Maths (2 hrs) Paper 2: Pure Maths (2 hrs) Paper 3: Mechanics and Statistics (2 hrs) Click here for more information on the specific content in these exams. Mar 15, 2018 · Cambridge International AS & A Level Mathematics: Pure Mathematics 1 matches the corresponding unit of the syllabus, with a clear and logical progression through. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of Cambridge Mathematical Textbooks is a program of undergraduate and beginning graduate level textbooks for core courses, new courses, and interdisciplinary courses in pure and applied mathematics. Caters For The Interest and Raises Hope of The users. 24/08/2023 : CAIE A Levels, O Levels and IGCSE 2023 Past Papers of March and May /June are updated Written for the OCR AS/A Level Mathematics specifications for first teaching from 2017, this print Student Book covers the content for AS and the first year of A Level. Review: Serious math learners will be thrilled by the rigorous conciseness of this textbook. 61 $ 38. 79: Edexcel AS and A level Mathematics Pure Mathematics Year 2 Practice Workbook: 9781292274676: £8. 100 marks, 3 hours Section A (Pure Maths): 40 marks Section B (Probability & Statistics): 60 marks. Sep 16, 2020 · on October 5, 2022 at 5:37 am [PDF/ePub] Download Hodder Cambridge International AS and A Level Psychology. These books are based on the highly successful series for the Mathematics in Title. 61. 3 million copies sold of the previous edition, Pearson’s textbooks are the market-leading and most trusted resources for AS and A level Mathematics. 1. | Michele Conway, Nathan Barker, Paul Fannon, Ben Woolley, Janet Such, Jess Barker Examinations syllabus for Cambridge International AS and A Level Mathematics 9709. 3 AS Further Mathematics Students sitting an AS Level Further Mathematics paper may also require those formulae listed for A Level Mathematics in Section 2. 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 May 25, 2017 · Exam Edexcel A level Mathematics First September 2017 First Summer 2018 With over 1. Teachers should be aware that there are recommended combinations of components to study in Cambridge International AS & A Level Mathematics (9709) to support progression to Cambridge A Level Mathematics for AQA | New 2017 Cambridge A Level Maths resources help students with learning and revision. See more ideas about mathematics, levels, advanced mathematics. The book has been planned in such a way that each topic begins with precise introductory notes, followed by worked examples, sample questions with their solutions. Book (60) Online & Online Blended (28) Mixed Media (5) Cambridge International AS & A Level Further Mathematics supports students following the 9231 syllabus. 59 Multiple items Jan 31, 2018 · A-level Mathematics. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for This is the first of a series of books for the University of Cambridge International Examinations syllabus for Cambridge International A & AS Level Mathematics 9709. The book is designed both as a complete AS Mathematics course, and as the first year of the full A level Mathematics. Free Download all MATHEMATICS notes in PDF for O & A level, Form one,two,three,four,five and six for Zimbabwe,Tanzania,Cameroon, Kenya,Zambia,South Africa, Nigeria Section Topic Sheet 1 (From OCR) Sheet 2 (From Edexcel) Full Lessons And Worksheets; Yr1 Pure – Algebra: Proof: Sheet 1 (From OCR) Sheet 2 (From Edexcel) Written by an experienced author and teacher, this print book with Cambridge Elevate edition provides fully-worked solutions for exercises contained within the Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook. Book 1 You should be able to link displacement vectors to coordinates and perform operations with vectors. New & used copies available with free delivery in the UK. 79 Feb 25, 2018 - Find the Advanced Level Mathematics Books you need here. Apr 22, 2019 · Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Practice Book (A level Maths and Further Maths 2017) by Harry Smith (Author) 4. AQA books are another Maths revision and practice series – because, after all, you can’t have TOO much of either, can you? We find this one especially useful Jul 18, 2017 · Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Textbook + e-book (A level Maths and Further Maths 2017) $38. Let AB ˜˚˜˜ p = and ˜˚˜˜ q = BC. 3 million copies sold of the previous edition), Pearson's own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics May 29, 2023 · A-level Mathematics. Pearson Edexcel International A Level Mathematics Further Pure 1 Student Book: Print Product - Student Textbook (1 copy), includes 3-year digital access to an ActiveBook (digital version of the book) A Vast Reserve of E-Books for IGCSE/O/AS/A level Subjects CIEnotes provides a variety of Cambridge International Examination e-books (coursebooks, revision guides, calculation books and workbooks) Directory AS and A level E-Books (Physics, Chemistry, Biology, Pure Mathematics. May 2, 2024 · Abstract Algebra. Write in column vector form: pq − pq ˜˚˜˜ a bc 4 d AC. Apr 15, 2018 · Cambridge International AS & A Level Mathematics: Pure Mathematics 1 matches the corresponding unit of the syllabus, with a clear and logical progression through. Teachers should be aware that there are recommended combinations of components to study in Cambridge International AS & A Level Mathematics (9709) to support progression to Cambridge Written for the AQA A Level Mathematics specification for first teaching from 2017, this print Student Book covers the content for the second year of A Level. Mar 24, 2023 · Cambridge International AS and A Level Mathematics - Further (9231) Ebooks. Click on the buttons below for books and complete course. They are written to introduce new mathematical skills with clear explanations and provide practice materials in order to help students consolidate their knowledge Cambridge International AS and A Level Mathematics has been written especially for the Cambridge International Examinations syllabus 9709. Mar 24, 2023 · 📑 Update(s): 11/01/2024 : May / June 2023 and Oct / Nov 2023 past papers are updated. New comments cannot be posted. It clearly indicates materials required for P3 study only, and contains materials on topics such as logarithmic and exponential functions, trigonometry, differentiation, integration, numerical solutions of equations, vectors Analysis is a branch of mathematics focused on the study of real numbers, complex numbers, and their representation. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for Buy A-Level Maths Textbook: Year 1 & 2: thousands of practice questions for the full course (CGP A-Level Maths) by CGP Books, CGP Books (ISBN: 9781782947233) from Amazon's Book Store. Dummit and Richard M. It should be useful as a revision guide or to find alternative explanations to the ones in your textbook. The eight chapters of this book cover the pure mathematics in AS level. Jul 6, 2018 · This title offers additional practice exercises for students following the Pure Mathematics 1 unit of the Cambridge International AS & A Level Mathematics syllabus (9709). com] Authors: David Bowles, Brian Jefferson, Eddie Mullan, John Rayneau, Mark Rowland, Robert Wagner, Paul Williams, Garry Wiseman and Katie Wood. From Wikibooks, open books for an open world This book covers A-level mathematics with chapters each focusing on the requirements for each Cambridge International AS & A Level Mathematics provides a good preparation for study of Cambridge International AS & A Level Further Mathematics (9231). It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for Practice Books. E Sue Pemberton Series Editor: Julian Gilbey PL Cambridge International AS & A Level Mathematics: SA M Pure Mathematics 1 Coursebook Original material © Cambridge University Press 2017 Contents Contents Series introduction vi How to use this book viii 1 Quadratics E x Acknowledgements 1 1. A-level math paper 2 Probability theory. In Stock. These include the skill of working with mathematical information, as well as the ability to think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings. This book is written for the revised GCE Advanced level (A level) Mathematics specifications for first teaching in 2017. Buy A-Level Maths Textbook: Year 1 & 2 By CGP Books. With over 900,000 copies sold (plus 1. The H1 Maths paper consists of two sections, namely Section A (focusing on Pure Maths topics) and Section B (focusing on Probability and Statistics). Jul 6, 2018 · This series has been developed specifically for the Cambridge International AS & A Level Mathematics (9709) syllabus to be examined from 2020. Feb 10, 2023 · Access-restricted-item true Addeddate 2023-02-10 14:12:41 Associated-names Porkess, Roger Autocrop_version The book assumes a knowledge of mathematics up to Ordinary Level and covers all the pure mathematics necessary for the Advanced Level examination in mathematics (A26), of the Northern Universities Joint Matriculation Board, together with the great majority of the work required for the Advanced Level examinations of the Southern Universities This Book provides a thorough treatment of Advanced Level Mathematics (P425/1&2). Mar 24, 2023 · Cambridge IGCSE Mathematics (0580) Ebooks. Written for the AQA AS/A Level Mathematics specifications for first teaching from 2017, this Digital Student Book covers the content for AS and the first year of A Level. The series also contains a more advanced book for pure mathematics and one each for mechanics and statistics. Fig. Student Books with comprehensive and supportive explanations and plenty of practice to prepare A level students. Everyday low prices and free delivery on eligible orders. 7 4. Pure Mathematics Summations r r n 2 =1 ∑ = 1 6 n(n + 1)(2n + 1) r r n 3 =1 ∑ = 1 4 n 2(n + 1)2 Matrix transformations Anticlockwise rotation through θ about O: coss in sinc os θθ Jan 1, 2017 · Exam Board: Edexcel Level: AS and A level Subject: Mathematics First teaching: September 2017 First exams: Summer 2018 With over 1. Best Prices & Express Shipping across Pakistan. PapaCambridge provides Cambridge IGCSE Mathematics (0580) Ebooks and resources which includes all the recommended ebooks of this subject and a many other books related to Cambridge IGCSE Mathematics (0580). Cambridge International AS & A Level Further Mathematics: Further Mechanics helps learners improve confidence as mathematicians with clear explanations, worked examples, diverse activities and engaging discussion points. This series of resources has been developed to support teachers and students of Cambridge International AS & A Level Mathematics (9709). The step up from GCSE to A-level can be challenging. There are fifteen chapters in this book; the first nine cover Mechanics 1 and the remaining six Mechanics 2. There is one book corresponding to each syllabus unit, except for this book which covers two units, t he second and third Pure Mathematics units, P2 and P3. The series also includes two books for pure mathematics and one for statistics. ISBN: 9781782947233. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing Cambridge AS and A Level Mathematics Roots Millennium School, City School, Beaconhouse school, aspire college lyceum college, lgs, lahore grammar school, allied school Cambridge international CAIE hodder AS A level Cambridge Books school books pakistan ADVANCED LEVEL PURE MATHEMATICS. 1 Consider the points A(2,5), B(1− ,3 ) and C(7 ,2− ). Thus, for example, x 1 stands for ‘the x-coordinate of the first point’. 24/08/2023 : CAIE A Levels, O Levels and IGCSE 2023 Past Papers of March and May /June are updated The A-Level Maths in its current form has been taught in schools and colleges since September 2017. This manual is designed to help save you time with over 1,000 readily-available solutions. 59 Multiple items Edexcel A level Mathematics Statistics & Mechanics Year 2 Practice Book: 9781292274652: £5. Pure Mathematics 4 (P4) is a compulsory unit in the following qualifications: International Advanced Level in Mathematics International Advanced Level in Pure Mathematics Assessment overview The following table gives an overview of the assessment for this unit. Foote. Jun 11, 2019 · Cambridge International AS and A Level Mathematics Pure Mathematics 1_djvu. 1 Solving quadratic equations by factorisation 1. Books that cover that sort of spec but in a deeper way with perhaps harder more fundamental questions Locked post. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing Pearson Edexcel A level Mathematics Pure Mathematics Year 2 Textbook + e-book Greg Attwood In stock online £25. Specification Planning resources Teaching resources Assessment resources Key dates Sep 28, 2023 · Edexcel A Level Mathematics Statistics and Mechanics Year 2 Textbook + E-Book by Greg Attwood, Ian Bettison, Alan Clegg, Gill Dyer, Jane Dyer, Keith Gallick, Susan Hooker, Michael Jennings, Mohammed Ladak, Jean Littlewood, Bronwen Moran, Su Nicholson, Laurence Pateman, Keith Pledge, Harry Smith Cambridge AS & A Level Further Mathematics Full book: I used this book extensively for mechanics and statistics. A-level math paper 2 Statistics, mode, mean, median, cumulative frequency, orgive, histograms. Jun 8, 2021 · 3. 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 A level Mathematics Pure Mathematics Year 2 Textbook + e-book Greg Attwood In stock online £25. It assumes you have already done GCSE Mathematics. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. 7357. If you're finding the transition up difficult, the 'Bridging GCSE and A-level Maths Student Book' by Collins might be a helpful book to have close by, alongside the specific study guides Collins produces for each A-level awarding body. Cambridge International AS and A Level Mathematics has been written especially for the Cambridge International Examinations syllabus 9709. Cambridge International AS & A Level Mathematics: Pure Mathematics 1 matches the corresponding unit of the syllabus, with a clear and logical progression through. It covered my Further Maths syllabus (9231) entirely. Mathematical analysis is usually based on specific theories, such as limits, integration, sequences, differentiation, functions, and analytic series. The books are quite light-hearted and funny too – which perhaps isn’t what you’d expect from a Maths text book! AS/A Level Maths for AQA – Core 1 & 2. Cambridge International AS & A Level Mathematics: Cambridge Elevate Teacher's Resource contains detailed lesson notes for each section of all five coursebooks in this series as well as additional guidance on the Explore activities within the books, PowerPoint slides with links to further resources and answers to Mar 24, 2023 · At A Level, teachers can also choose from different routes to Cambridge International A Level Mathematics depending on the choice of applied mathematics (Mechanics and/or Probability and Statistics). 3 The quadratic Download PDF files of A-levels Mathematics 9709 books in reasonable pricing. Mechanics, Statistics, Core Maths, Further Mathematics, Business Studies, Accounting, Economics, Computing, Psychology Cambridge O Level Mathematics is a resource to accompany the revised 4024 syllabus. This book provides in-depth coverage of Pure Mathematics 1 for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. Vast collection of Textbooks, Helping Books, Notes, Past Papers, Pairing Schemes, Test Papers, O/A Level Books, Entry Test, CSS and other exams resources. Description: ISBN. It aims to fit in with the OCR New GCE A-level Mathematics syllabus but is not endorsed by OCR. This title offers additional practice exercises for students following the Mechanics unit of the Cambridge International AS & A Level Mathematics syllabus (9709). It contains materials on topics such as velocity and acceleration, force and motion, friction, connected particles, motion in a straight line, momentum, and work and energy. This book covers the rst Pure Mathematics unit, P1. There were a number of significant changes made to the syllabus and to the way the A-Level Maths course is examined. It contains materials on topics such as quadratics, functions, coordinate geometry, circular measure, series, differentiation and integration. 3 days ago · Bridging GCSE and A-level Maths Student Book by Collins. In preparing the manuscript, the writers have been guided by the Uganda National Examination Board syllabus and National Curriculum Development Centre. This title has been endorsed by Cambridge Assessment International Education Thoroughly explore the Cambridge International updated AS & A Level Psychology syllabus with this brand-new Student Book that embeds psychological theories, perspectives and applications within real-world First teaching: 2017 First assessment: 2018 Here you'll find everything you need to prepare for teaching A level Mathematics, including our flexible specification which gives you separate papers for pure and applied maths, plus a wide range of free exam practice to prepare students, and the opportunity to either specialise or broaden your area of study. Dense with information on every page and presented in a relaxed, open manner, Dummit and Foote’s Abstract Algebra effectively works to usher the reader into a realm of sophisticated algebraic concepts and theories. A-level math paper 2 Binomial distribution Jan 5, 2021 · Access-restricted-item true Addeddate 2021-01-05 21:03:07 Boxid IA40027921 Camera Sony Alpha-A6300 (Control) 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 Cambridge International AS & A Level Mathematics: Mechanics matches the corresponding unit of the syllabus, with clear and logical progression through. H1 Maths. 2 Completing the square 3 6 1. There is one book corresponding to each syllabus unit, except that units P2 and P3 are contained in a single book. 3 million copies sold of the previous edition, Pearson's textbooks are the market-leading and most trusted resources for AS and A level Mathematics. Description: Provides teacher support for the syllabus for examination from 2020. org The Cambridge International AS and A Level Mathematics syllabus builds on the skills acquired at Cambridge IGCSE (or equivalent) level. The syllabus allows teachers to choose from three different routes to Cambridge International AS Level Mathematics: Pure Mathematics only, Pure Mathematics and Mechanics or Pure Mathematics and Probability and Statistics. They are written to introduce new mathematical skills with clear explanations and provide practice materials in order to help students consolidate their knowledge Aug 31, 2021 · AQA A Level Mathematics A Level Year 1 / AS Level Bridging version [global. A-level math paper 2 Correlation and scatter diagrams. Sadler, Further Pure Mathematics by Br Cambridge International A Level Mathematics develops a set of transferable skills. 39: Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Practice Book: 9781292274683: £8. A-level math paper 2 Index numbers. oup. Firstly, current A-Level Maths is described as being a “linear” course. Published by CGP Books. Description: Provides full support for Paper 3 of the syllabus for examination from 2020. ISBN-10: 178294723X Mathematics contents for AS and A level Mathematics qualifications. PURE MATHEMATICS Mensuration Volume of sphere = 4 3 3 πr Surface area of sphere = 4πr2 Volume of cone or pyramid = 1 3 ××base area height Area of curved surface of cone = πr×slant height Arc length of circle =rθ (θin radians) Area of sector of circle 12 2 = r θ (θin radians) Algebra For the quadratic equation ax bx c2 ++=0: 2 4 2 bb May 8, 2017 · The UK's most trusted A level Mathematics resources. 1K Download_pdf_ebooks. Exam Cambridge Assessment International EducationFirst 2018 First 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge Jun 6, 2024 · This is a book about AS (advanced subsidiary) and A (advanced) level Mathematics. smbs yrkex czvou klfkya oor ovinm bcrvrpe sqohk aptsxt puogrq