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      This forum is available for everyone to post questions, answers and comments related to this module.

      We will monitor it and post answers, but you are most welcome (and encouraged!) to answer each others' questions and comment on each others' queries. 

      You will also get all posts by e-mail. 
      Subscription to these posts can be cancelled, but we strongly suggest keeping active in the forum!

  • Module Description

    This module is designed to strengthen your mathematical skills in elementary arithmetic and algebra, including integers, fractions, decimal representations, estimation, polynomials, rational functions, square roots, inequalities, linear and quadratic equations.

    • The content of the module is based on the webbook: Essential Mathematics by Franco Vivaldi , which explains methods and provides examples that you are expected to work through . 
    • We shall have one lecture per week  (Thursdays, 17:00-18:00), in which we will cover respective sections of the book.
      You are then expected to spend at least two hours per week  studying the corresponding section of the book, doing all relevant questions and self-marking them against the answers shown in the book (answers are in the book next to the exercises). 
      Some questions in the webbook have a * (star) or ** (two stars) next to them. * indicates a slightly more difficult question and ** a significantly more difficult question, respectively, than no star. The * and ** questions are similar to those in the tests and exam. 
    • During the tutorials (

      one tutorial per week for each group, Mondays), we will solve together some questions selected from the webbook.
      In the tutorials you can also discuss with us any problems with the lecture material or with the webbook.  

    • There is weekly online coursework.
      Almost every week, 15 questions will be made available in the form of an online quiz.
      The quizzes are designed to help you prepare for the module Assessments (please see the "Assessment information" Tab for more info) and they will NOT contribute to your final mark. You are still expected to take them independently and without copying each other's work, but of course if there are any questions, please ask during the workshops.
      We will not enforce that you do the quizzes, but you will not be able to score well in the actual Assessments without solving all courseworks.
    • Every week, make sure you: 
      ✓ Read the relevant webbook pages.
      ✓ Do and self-mark the webbook exercises.
      To prepare for the module Assessments, you should attempt as many exercises as possible in the webbook. As mentioned above, solutions are provided there for your immediate feedback.
      ✓ Do the coursework (online quiz).  

  • Syllabus

    • Module Syllabus

      Lecture 1: Divisibility and primes

      Lecture 2: GCD and LCM

      Lecture 3: Fractions

      Lecture 4: Square roots

      Lecture 5: Estimation

      Lecture 6: Monomials and polynomials

      Lecture 7: Polynomial factorisation and rational expressions

      Lecture 8: Substitutions and algebra with square roots

      Lecture 9: Linear equations, inequalities and quadratic equations (part 1)

      Lecture 10: Linear equations, inequalities and quadratic equations (part 2)

  • Module aims and learning outcomes

    At the end of this module, you should be able to:

    • Solve linear (simultaneous) equations.
    • Make simple estimations (to the nearest integer, ten, hundred, thousand, etc.).
    • Sort decimals and fractions in order, convert numbers between different forms (including scientific form).
    • Round numbers to a given number of decimal places or significant figures.
    • Carry out mixed arithmetical operations in the correct order.
    • Calculate the GCD and LCM of pairs of rational numbers.
    • Simplify expressions involving rational numbers and square roots.
    • Manipulate simple algebraic expressions.
    • Multiply and divide polynomials in one indeterminate.
    • Simplify rational expressions in polynomials with one indeterminate.
    • Use simple properties of inequalities.

  • Teaching team

    • Dr. Argyro Mainou: Teaching Fellow, School of Mathematical Sciences, Queen Mary University of London.

    email: a.mainou@qmul.ac.uk 

    office: MB-202 

    learning support hours: Mondays 14:00 - 15:00 @MB-202  (please prefer this slot for SEF026-related discussions)
                                                       Thursdays 14:00 - 15:00 @School's Social Hub (MB-B11) (Learning Café)


    • Dr. John Bray: Lecturer in Pure Mathematics, School of Mathematical Sciences, Queen Mary University of London.

    email: j.n.bray@qmul.ac.uk

    office: 

    learning support hour: 


  • Hints and Tips

    • QMplus Help for Students URL

      This link has information to help you get the best out of QM+, including helpful guides and videos.

  • Where to get help

    Struggling?

    If you are finding any aspect of the course challenging or have any other difficulty, we are here to help. 

    But note that we cannot help unless we know there is a problem, so make sure you contact the module organisers (or any other lecturer or the program director or the maths office) if there is an issue of concern.


  • Module handbook

  • Week 1: Divisibility and primes

    Welcome to Week 1!


    To do:

    1.  Participate in the lecture; we will go through Section 1.1 of the webbook (p.5-7). 

    2. After the lecture, try to solve the problems on p.7-9 of the webbook. If needed, read through p.1-7 of the webbook.

    3.  After the lecture, solve the problems from online coursework 1. The coursework will be available from Thursday, 28 September, 18:00 and the deadline for submission will be on Thursday, 5 October, 17:00.


    • Lecture_1 File
      2.5 MB
    • Coursework 1 Quiz

    • Tutorial 1 

      During Tutorial 1, we will solve together some questions selected from the webbook (p. 7-9). 

      You can also discuss with us any questions about the lecture material or the webbook.  



  • Week 2 : GCD and LCM

    Welcome to Week 2!


    To do:

    1.  Participate in the lecture; please read page 10 of the webbook. 

    2. After the lecture, try to solve the problems on p.10-11 of the webbook. During the 9 October tutorial on Monday, we shall discuss some of these problems. 

    3.  After the lecture, solve the problems from online coursework 2. The coursework will be available from Thursday, 5 October, 18:00 and the deadline for submission will be on Thursday, 12 October, 17:00.


    • Lecture_2 File
      794.2 KB
    • Coursework 2 Quiz

    • Tutorial 2 

      During Tutorial 2, we will solve together some questions selected from the webbook (p. 10-11). 

      You can also discuss with us any questions about the lecture material or the webbook.  



  • Week 3: Fractions

    Welcome to Week 3!


    To do:

    1.  Participate in the lecture; please read pages 12 - 13 and 17 of the webbook.  

    2. After the lecture, try to solve the problems on p.13-16 and 18-20 of the webbook. 

    3.  After the lecture, solve the problems from online coursework 3 . The coursework will be available from Thursday, 12 October, 18:00 and the deadline for submission will be on Thursday, 19 October, 17:00.


    • Lecture_3 File
      264.2 KB
    • Coursework 3 Quiz

    • Tutorial 3 

      During Tutorial 3, we will solve together some questions selected from the webbook (p. 13-16 and 18-20). 

      You can also discuss with us any questions about the lecture material or the webbook.  



  • Week 4: Square roots

    Welcome to Week 4!


    To do:

    1.  Participate in the lecture; please read pages 25-26 of the webbook.  

    2. After the lecture, try to solve the problems on p. 26-30 of the webbook. 

    3.  After the lecture, solve the problems from online coursework 4. The coursework will be available from Thursday, 19 October, 18:00 and the deadline for submission will be on Thursday, 26 October, 17:00.


    • Lecture_4 File
      439.5 KB
    • Coursework 4 Quiz

    • Tutorial 4 

      During Tutorial 4, we will solve together some questions selected from the webbook (p. 26-30). 

      You can also discuss with us any questions about the lecture material or the webbook.  



  • Week 5: Estimation

    Welcome to Week 5!


    To do:

    1.  Participate in the lecture; please read pages 31-33 of the webbook.  

    2. After the lecture, try to solve the problems on p. 33-36 of the webbook.  

    3.  After the lecture, solve the problems from online coursework 5. The coursework will be available from Thursday, 26 October, 18:00 and the deadline for submission will be on Thursday, 2 November, 17:00.


    • Lecture_5 File
      1.1 MB
    • Coursework 5 Quiz

    • Tutorial 5 

      During Tutorial 5, we will solve together some questions selected from the webbook (p. 33-36). 

      You can also discuss with us any questions about the lecture material or the webbook.  



  • Week 6: Monomials and polynomials

    Welcome to Week 6!


    To do:

    1.  Participate in the lecture; please read page 37 of the webbook.  

    2. After the lecture, try to solve the problems on pages 38-40 of the webbook.   

    3.  After the lecture, solve the problems from online coursework 6. The coursework will be available from Thursday, 2 November, 18:00 and the deadline for submission will be on Thursday, 9 November, 17:00.

    • Lecture_6 File
      951.7 KB
    • Coursework 6 Quiz

    • Tutorial 6 

      During Tutorial 6, we will solve together some questions selected from the webbook (p. 38-40 and p. 42, up to problem 18). 

      You can also discuss with us any questions about the lecture material or the webbook.  



  • Week 7: Mock Test 1 online

    There are no lectures or tutorials and there is no coursework during Week 7.


    Please use the link below to access the MOCK Test 1, which is last year's Test 1 (academic year 2022-2023).

    • MOCK Test 1 Quiz
      Please note that this MOCK test will remain open for you to practice and will not have a limit for the number of attempts.


      The actual test on Monday, Week 8, will have a time limit of 2 hours and you will only be allowed one submission attempt - more details will follow about Monday's test soon.
    • MOCK Test 1 solutions File

      Solutions of MOCK Test 1 in pdf.

      94.5 KB

  • Week 8: ~~~~~~~~~~~~~~~~~~~~~~~~~~Test 1 online~~~~~~~~~~~~~~~~~~~~~~~~~~~~ new material on Thursday: Polynomial factorization and rational expressions

    Welcome to Week 8!


    To do:

    1. Take the online Test 1 on Monday, 13 Nov 2023, at 11:00-13:00 . 

    Please read the following information before taking the test and then use the link below to access the test.

    • Test 1 will be in the form of an online quiz, similar to the weekly coursework quizzes. It will consist of 20 multiple-choice questions.
    • Only ONE attempt will be allowed for submitting your answers.
    • The test is based on all material discussed during the first 5 weeks in lectures, tutorials and webbook. 
    • Its contribution towards the final mark of this module is 25%.
    • You will be able to access the quiz from 11:00 to 13:00 on Monday, 13 Nov 2023.
    • You will have exactly 2 hours to solve all problems and to submit your answers. You won't be able to submit your answers after the 2 hours have expired (after 13:00 on November 13th) . If your attempt is still in progress after the2 hours, any work you have accomplished so far will be automatically submitted.
    • Test 1 Quiz

    • 2. Participate in the lecture; please read pages 41 and 46 of the webbook.

      3. After the lecture, try to solve the problems on p. 42-54 of the book.

      4. After the lecture, solve the problems from online coursework 7. The coursework will be available from Thursday, 16 November, 18:00 and the deadline for submission will be on Thursday, 23 November, 17:00. 


    • Coursework 7 Quiz

    • Tutorial 8 

      During Tutorial 8, we will solve together some questions selected from the webbook (p. 42-54). 

      You can also discuss with us any questions about the lecture material or the webbook.  



    • Test 1 (EC) Quiz

        → This test consists of 20 multiple-choice questions. 
        The test will be available for 24 hours (Tue 28 Nov 00:00 - 24:00). Once you open the test, you will have exactly 2 hours to solve all problems  and to submit your answers. You won't be able to submit your answers after the 2 hours have expired . If your attempt is still in progress after the 2 hours, any work you have accomplished so far will be automatically submitted.
        Only ONE attempt is allowed         for submitting your answers.

        → The test's contribution towards the final mark of this module is 25% .

        → You will be able to access this quiz from 00:00 to 24:00 on Tuesday, 28 Nov 2023.

        Please contact maths@qmul.ac.uk if you experience any issues when submitting your work on QMplus.

        Please do not leave your submission to the last minute , sincethere is a risk of your attempt timing out - try submitting enough time before and if there is any issue, send your answers to  maths@qmul.ac.uk   before  the closing time of the quiz and within 2 hours since you first accessed it.


        → In completing this assessment:

        • You may use books and notes.
        • The use of calculators is not allowed.
        • You may use the Internet as a resource, but not to ask for the solution to a test question or to copy any solution you find.
        • You must not seek or obtain help from anyone else. 

        You will be able to see your marks and the correct answers after the Quiz closes, that is on Tuesday 28 Nov, 24:00.
        Not available unless: You belong to EC Students - Test 1 Week 8

    • Week 9: Substitutions and algebra with square roots

      Welcome to Week 9!


      To do:

      1.  Participate in the lecture; please read pages 55 and 59 of the webbook.  

      2. After the lecture, try to solve the problems on p. 55-58 and 59-62 of the webbook.   

      3.  After the lecture, solve the problems from online coursework 8. The coursework will be available from Thursday, 23 November, 18:00 and the deadline for submission will be on Thursday, 30 November, 17:00.

      • Coursework 8 Quiz

      • Tutorial 8 

        During Tutorial 8, we will solve together some questions selected from the webbook (p. 55-58 and p. 59-62). 

        You can also discuss with us any questions about the lecture material or the webbook.  



    • Week 10: Linear equations, inequalities and quadratic equations (part 1)

      Welcome to Week 10!


      To do:

      1.  Participate in the lecture; please read page 63 of the webbook. 

      2. After the lecture, try to solve the problems on p. 64-67 of the webbook.   

      3.  After the lecture, solve the problems from online coursework 9. The coursework will be available from Thursday, 30 November, 18:00 and the deadline for submission will be on Thursday, 7 December, 17:00. 

      • Coursework 9 Quiz

      • Tutorial 9 

        During Tutorial 9, we will solve together some questions selected from the webbook (p. 64-67). 

        You can also discuss with us any questions about the lecture material or the webbook.  



    • Week 11: Quadratic equations (part 2)

      Welcome to Week 11!


      To do:

      1.  Participate in the lecture; please read pages 68-70 of the webbook.  

      2. After the lecture, try to solve the problems on p. 70-74 of the webbook.   

      3.  Please note that this week there is no online coursework, as it would clash with your preparations for online Test 2 (Week 12, Monday 11 Dec, 11:00-13:00 ). 

      4. Instead, please prepare for Test 2 next week by doing the two sample Week 12 tests that you can find below.
      →The sample tests can also be found under the "Assessment information" Tab, in the "Exam papers" Topic.

      • Week 12 Test 2018 Quiz

        Please note that this MOCK test will remain open for you to practice and will not have a limit for the number of attempts.

      • Week 12 Test 2019 Quiz

        Please note that this MOCK test will remain open for you to practice and will not have a limit for the number of attempts.

      • No tutorial next week - online Test 2 instead

        Please check "Week 12" Tab below for more details on Week 12's schedule and activities.

        Don't forget the revision session that will take place on Thursday of Week 12.

    • Week 12: ~~~~~~~~~~~~~~~~~~~~Test 2 online~~~~~~~~~~~~~~~~~~~~~ Revision session on Thursday: MOCK final exam

      Welcome to Week 12!


      To do:

      1. Take the online Test 2 on Monday, 11 Dec 2023, at 11:00-13:00 . 

      Please read the following information before taking the test and then use the link below to access the test.

      • Test 2 will be in the form of an online quiz, similar to Test 1. It will consist of 20 multiple-choice questions.
      • Only ONE attempt will be allowed for submitting your answers.
      • The test is based on all material discussed during  Weeks 6-11 in lectures, tutorials and webbook. 
      • Its contribution towards the final mark of this module is 25%.
      • You will be able to access the quiz from 11:00 to 13:00 on Monday, 11 Dec 2023.
      • You will have exactly 2 hours to solve all problems and to submit your answers. You won't be able to submit your answers after the 2 hours have expired (after 13:00 on November 13th) . If your attempt is still in progress after the2 hours, any work you have accomplished so far will be automatically submitted.

      IMPORTANT!!!
      Please submit your rough work related to Test 2 as a single PDF file under the link you can find below (Rough work for Test 2). Please provide a brief explanation in your rough work about how you solved each question.
      If you do not submit your rough work, the mark for your test will be 0.

      • Test 2 Quiz

      • 2. Participate in the lecture; mini final MOCK exam session, followed by solutions and Q&A.


      • mini MOCK final exam File
        81.8 KB
      • IMPORTANT!!!
        Please submit your rough work related to Test 2 (EC) as a single PDF file under the link you can find below (Rough work for Test 2 (EC)). Please provide a brief explanation in your rough work about how you solved each question.
        If you do not submit your rough work, the mark for your test will be 0.

      • Test 2 (EC) Quiz

          → This test consists of 20 multiple-choice questions. 
          The test will be available for 24 hours (Fri 19 Jan 00:00 - 24:00). Once you open the test, you will have exactly 2 hours to solve all problems  and to submit your answers. You won't be able to submit your answers after the 2 hours have expired . If your attempt is still in progress after the 2 hours, any work you have accomplished so far will be automatically submitted.
          Only ONE attempt is allowed for submitting your answers.

          Please submit your rough work related to Test 2 (EC) as a single PDF file under the link you can find below (Rough work for Test 2 (EC)). If you do not submit your rough work, the mark for your test will be 0.


          → The test's contribution towards the final mark of this module is 25% .

          → You will be able to access this quiz from 00:00 to 24:00 on Friday, 19 Jan 2024.

          Please contact maths@qmul.ac.uk if you experience any issues when submitting your work on QMplus.

          Please do not leave your submission to the last minute , since there is a risk of your attempt timing out - try submitting enough time before and if there is any issue, send your answers to  maths@qmul.ac.uk   before  the closing time of the quiz and within 2 hours since you first accessed it.


          → In completing this assessment:

          • You may use books and notes.
          • The use of calculators is not allowed.
          • You may use the Internet as a resource, but not to ask for the solution to a test question or to copy any solution you find.
          • You must not seek or obtain help from anyone else. 

          Not available unless: You belong to EC Students - Test 2 Week 12
        • Rough work for Test 2 (EC) Assignment

          Please upload here your rough work on the 2024 Week 12 Test (EC) as a single pdf file.

          Not available unless: You belong to EC Students - Test 2 Week 12

      • Q-Review

      • Assessment description

        • In-term tests will take place online in Week 6 or 8 and in Week 12.
          Final exam will take place in person in January 2024.

          Assessment pattern -  In-term test 1 (Week 6 or 8) – 25% of your total mark
                                                         In-term test 2 (Week 12) – 25% of your total mark
                                                         Final exam (January 2024) – 50% of your total mark

          Format for in-term assessments - There are two in-term tests in Week 6 or 8 (exact Week TBA) and in Week 12, each contributing 25% towards your final mark for this module. The tests are based on material discussed in lectures, tutorials and the webbook, up to the test date.  Each test will consist of 20 questions, to be done within 2 hours. In-term assessments will be held online.

          Format of final assessment - The final exam for this module will take place in January 2024 (exact date TBA).  The exam is based on all material discussed in lectures, tutorials and the webbook, throughout the term.  It contributes 50% towards your final mark for this module. The final exam will be in-person and more details on its format will be announced soon.

          Link to past papers - Will be added later.

          Description of feedback - Will be added later.



      • Coursework

        → Please note that the weekly coursework does not contribute to your final mark; more details in the "Module Description" Section, under the "IMPORTANT Module Information" Tab.

        → Find the link to the weekly coursework in the relevant Week's Section, under the         "Module Content" Tab.

      • Exam papers

        • Week 12 Test 2018 Quiz

          Please note that this MOCK test will remain open for you to practice and will not have a limit for the number of attempts.

        • Week 12 Test 2019 Quiz

          Please note that this MOCK test will remain open for you to practice and will not have a limit for the number of attempts.

        • final exam 2015 File
          1.2 MB
        • final exam 2017 File
          85.3 KB

      • Reading List Online

        • Webbook File

          We will closely follow the webbook written by Prof. Franco Vivaldi.

          398.6 KB

      • Early feedback questionnaire