SEF041 - Mathematics B - 2024/25
Topic outline
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View all general news and announcements.
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Forum Description: This forum is available for everyone to post messages to. Students can raise questions or discuss issues related to the module. Students are encouraged to post to this forum and it will be checked daily by the module leaders. Students should feel free to reply to other students if they are able to.
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SCIENCE AND ENGINEERING FOUNDATION PROGRAMME
SEF041 MATHEMATICS B (Semester 1)
TEACHING SCHEME ACADEMIC YEAR 2024/25
Source References
Course Notes
Mathematics B workbook is the main set of notes (containing all the lecture notes, examples and worked examples)and each chapter [MB - Chapter X] will be available each week. This workbook is designed for your independent study. It contains the lecture notes, related to the given week's learning outcomes.
This material is a main source for your learning for this module with plenty of examples and exercises for independent learning and contains FULL Learning Outcomes summarised after each chapter (which you can use as a checklist for the course).
We will refer to these in the live webinar sessions as well.
Course textbooks (recommended but not obligatory)
Textbook 1 [J.Olive Survival Guide]: Maths: A Student's Survival Guide, A Self-Help Workbook for Science and Engineering Students by Jenny Olive, published by Cambridge University Press, 2nd Edition February 2005, ISBN: 9780511074257. Note: e-book is available for this textbook.
Textbook 2 [Bostock,Chandler Core Maths]: Core Maths for Advanced Level, L. Bostock F.S. Chandler, published by Nelson Thornes, revised 3rd Edition 2013, ISBN: 978-1408522288. There is no e-book available.
Below the relevant chapters from the workbook and textbooks for each week will be listed together with suggested exercises for practice and revision.
Chapter 1 [4.5hrs] Logarithms and the Exponential Function
Powers
Logarithms
The Exponential Function
Logarithmic and Exponential Equations
[J.Olive Survival Guide], Chapter 1, Section 1D, Chapter 3, Section 3C(c,d)
[Bostock,Chandler Core Maths] Ch 2: Surds, Indices and Logarithmics: Ex 2G, Ch 4: Equations 2: Ex 4B, Ch 17: Exponential and Logarithmic Functions: Ex 17B
Chapter 2 [4hrs] Polynomials
Roots of quadratic Equations
Polynomials - Factor and Remainder Theorems
[J.Olive Survival Guide], Chapter 1, Section 1B(c) and Chapter 2, Section 2D, Section 2E
[Bostock,Chandler Core Maths] Ch 1 Algebra 1 : Ex 1J,K,L,M; Ch 30 Algebra 2: Ex 30A,B,C,D,E, F & G
Chapter 3 [7hrs] Coordinate Geometry,
Introduction to geometry of straight lines
[J.Olive Survival Guide], Chapter 2, Section 2B(a-h)]
[Bostock,Chandler Core Maths] Ch 6 Coordinate Geometry 1: Ex 6C;
Ch 28 Coordinate Geometry 3: Ex 28 A,B,C,D
Chapter 4 [4hrs] Functions 1
Domain and Range
Composite Functions
Inverse Functions
Odd and Even Functions
[J.Olive Survival Guide], Chapter
[Bostock,Chandler Core Maths]
Chapter 5 [4hrs] Functions 2
Curve Sketching
The Modulus of a Function, Modulus Inequalities
Rational Functions, Limits and Asymptotes
[Bostock,Chandler Core Maths] Ch 11 Functions 1: Ex 11 D; Ch 18 Functions 2: Ex 18C,D,E,F
Week 7 READING WEEK
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MID-TERM TEST
Assessment 1: Mid-term assessment on topics covered in weeks 1- 5.
---------------------------Chapter 6 [6hr+] Trigonometry - part 1
Elementary trigonometry [own review] [2hr+]
Radians, Relationships between sin, cos and tan, Periodic Functions
[Bostock,Chandler Core Maths] (Ch 10 Circular Measure: Ex 10A, Ch 15 Trigonometric Functions: Ex 15A,B,C,D, Ch 18 Functions 2: Ex 18B)
Reciprocal trigonometric functions [4hrs]
Trigonometric Identities
Solving trigonometric equations
[Bostock,Chandler Core Maths] Ch 22 Trigonometry 2: Ex A,B,C ; Ch 23 Trigonometry 3: Ex 23B
Chapter 7 [4hrs] Trigonometry - part 2
General Trigonometric Identities
Double Angle Identities
Inverse Angle Identities
[Bostock,Chandler Core Maths] Ch 23 Trigonometry 3: Ex 23 A, Mixed Exercises 23
Chapter 8 [4hrs] Calculus 1
Derivative of product and function of a function and compound functions
Stationary points
[Bostock,Chandler Core Maths] Ch 13 Differentiation 1: Ex 13E,F, Mixed Exercises 13; Ch14 Tangents, Normals and Stationary Values: Ex 14A,Ex 14B,14C,14D; Ch21 Differentiation 2: Ex 21A,B,C,D.E; Ch24 Differentiation 3: Ex 24C, Mixed Exercises 24; Ch25 Differentiation 4: Ex 25A,B
Chapter 9 [4hrs] Calculus 2
Integration
Definite Integration
Techniques of Integration
[Bostock,Chandler Core Maths] Ch20 Integration 1: Ex 20B,C,D,E,F,G; Ch29 Integration 2: Ex 21A,B,C,D.E; Ch31 Integration 3: Ex 31A,B,C
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Assessment 2: on topics covered in weeks 6 - 12 (chapters 5 - 9) - week 0 of Semester B
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(i) Algebra:
Review theory of indices, logarithms, quadratic equations and quadratic functions, factorisation, logarithmic and exponential equations. Polynomials: the remainder theorem and factor theorem, identical polynomials. Inequalities and equations involving the modulus sign. Equation of a straight line: various forms of equation of a line. Gradients, mid-points, distances, orthogonal lines.
(ii) Functions:
The set-theoretical definition of a function; composite functions; inverse functions. The modulus of a function. Determination of the range or image set of a function. Odd and even functions; periodic functions, rational functions. Limits and asymptotes of functions. The algebraically defined exponential and logarithmic functions.
(iii) Coordinate geometry:
Equation of a straight line: various forms of equation of a line, Gradients, mid points, distances.
(iv) Trigonometry:
Definition of the functions for an acute angle and extension to any angle. Graphical representation of the functions. Basic relationships between trigonometric functions. Inverse trigonometric functions. Compound angle, multiple- and half-angle formulas. Trigonometric identities. The solution of trigonometric equations and equations involving factor formulae over a restricted domain of the angle. Graphical and general solutions of trigonometric equations.
(v) Calculus (differentiation):
Fundamental elements of differential calculus; the derivative of a function, gradient at a point on a curve, the general gradient function, instantaneous rate of change. Second and higher order derivatives. Methods of differentiation: differentiation of powers, function of functions, products, quotients and trigonometric functions. Application of differentiation: maximum, minimum and turning points. Differentiation techniques for parametric and inverse trigonometric functions, implicit differentiation. Differentials: small increments and comparative rates of change.
(vi) Calculus (integration):
Elements of integral calculus: standard integrals; differentiation reversed. Definite integrals; area under the curve involving standard integrals. Methods of integration: exponential and logarithmic functions, trigonometric functions, integration by recognition, substitution, integration by parts. Integration by computer, both symbolic and numerical. Physical examples of calculus including position, velocity and acceleration. Applications of integral calculus: determining plane area; approaches to determining the volume of solids; volumes of revolution. Numerical Methods: locating roots of equations - change of sign method; interval bisection method; the Newton–Raphson method.
(vii) Complex Number Theory:
the algebra of complex numbers: Cartesian form; the modulus and argument of a complex number; the modulus-argument form; polar form; conjugate complex numbers. Graphical representation of complex numbers; the Argand plane, the vector association. Representation of addition, subtraction, multiplication and division.
(viii) Sequence and Series:
Binomial theorem and applications. Summation of finite series; the method of difference for polynomial terms; the natural number series; application of partial fractions. Infinite series and their convergence. The expansion of a function: Maclaurin's series; the expansions of the logarithmic, exponential and trigonometric functions. Other methods of expansion. Applications of power series expansions. Approximations.
(ix) Vectors:
2 and 3 dimensional vectors. Vector algebra: basic concepts; angle between two vectors; multiplication and division of a vector by a real number. Scalar product of vectors. Position vectors; position vector of a point; resolution of a vector in two and three dimensions. Equation of a line and a plane in three dimensions.
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At the end of this module, students should be able to:
- Solve a wide variety of logarithm, exponential, quadratic, polynomial and trigonometric equations.
- Solve simple problems in 3 dimensional coordinate geometry including using vectors.
- Apply the remainder and factor theorem to polynomials.
- Deal with inequalities and equations involving the modulus sign.
- Determine functions of functions and find the inverse of a function.
- Differentiate and integrate a wide range of functions including using a computer.
- Apply differentiation to locate maxima and minima, and sketch simple polynomials.
- Solve problems involving simple rates of change.
- Evaluate definite integrals, calculate the area under a curve and the volume, or surface of revolution.
- Represent and manipulate complex numbers in various forms.
- Solve problem involving comparative rates of change.
- Find roots of equations using numerical approximation.
- Solve problems involving finite, infinite power series.
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Group No Day Time Location Tutor name 1 Friday 12:00 - 13:00 Engineering: 216 Muhammad Sufiyan Sadiq 2 Friday 12:00 - 13:00 iQ East Court (scape): 1.04 Tayyab Ahmad Ansari 3 Friday 12:00 - 13:00 iQ East Court (Scape): 2.01 Runyue Wang 4 Friday 11:00 - 12:00 Bancroft: 1.01.2 Muhammad Sufiyan Sadiq 5 Friday 11:00 - 12:00 Queens: LG3 Tayyab Ahmad Ansari 6 Friday 11:00 - 12:00 Queens: LG2 Runyue Wang -
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SCHEDULE - SEMESTER 1
WEEK
DATE TOPIC ACTIVITY (links in relevant week) 1
Group 1: 23 Sep (Monday)
Group 2: 26 Sep
(Thursday)
27 Sep
(Friday)Powers & Logarithms Asynchronous
Task 1, Task 2, Task 3
Synchronous
Lecture (MME) Week 1
Synchronous
Feedback and Support Session2
Group 1: 30 Sep (Monday)
Group 2: 3 Sep (Thursday)
4 Oct (Friday)
4 Oct( Friday)Polynomials & Quadratics Asynchronous
Task 1, Task 2
Synchronous
Lecture (MME) Week 2
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups3
Group 1: 7th Oct
(Monday)
Group 2: 10 Oct (Thursday)
11 Oct
(Friday)
11 Oct
(Friday)Coordinate Geometry Introduction Asynchronous
Task 1, Task 2, Task 3, Task 4
Synchronous
Lecture (MME) Week 3
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups4
Group 1: 14 Oct (Monday)
Group 2: 17 Oct
(Thursday)
18 Oct
(Friday)
18 Oct
(Friday)Translations, Parametric equations &
CirclesAsynchronous
Task 1, Task 2, Task 3
Synchronous
Lecture (MME) Week 4
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups5
Group 1: 21 Oct (Monday)
Group 2: 24 Oct
(Thursday)
25 Oct
(Friday)
25 Oct
(Friday)Mappings and Functions Asynchronous
Task 1, Task 2, Task 3, Task 4
Synchronous
Lecture (MME) Week 5
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups6
Group 1: 28 Oct (Monday)
Group 2: 31 Oct
(Thursday)
1 Nov
(Friday)
1 Nov
(Friday)Graphs, Asymptotes, Inequalities & Modulus Asynchronous
Task 1, Task 2, Task 3, Task 4
Synchronous
Lecture (MME) Week 6
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups
Asynchronous
Revision before the Assessment 17 Reading Week No classes Revision of material covered in weeks 1 - 6.
Preparation for Assessment 1.8 17th Nov
(Fri)
Group 1: 11 Nov
(Monday)
Group 2: 14 Nov
(Thursday)
15 Nov
(Friday)
15 Nov
(Friday)Functions/Intro to Trigonometry Summative Assessment 1
(no tutorials)
Synchronous
Lecture (MME) Week 8
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups9
Group 1: 18 Nov (Monday)
Group 2: 21 Nov
(Thursday)
22 Nov
(Friday)
22 Nov
(Friday)Trigonometry (I) Asynchronous
Task 1, Task 2, Task 3 and Task 4
Synchronous
Lecture (MME) Week 9
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups10
Group 1: 25 Nov (Monday)
Group 2: 28 Nov
(Thursday)
39 Nov
(Friday)
29 No
(Friday)Trigonometry (II) Asynchronous
Task 1, Task 2, Task 3 and Task 4
Synchronous
Lecture (MME) Week 10
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups11
Group 1: 02 Dec (Monday)
Group 2: 05 Dec
(Thursday)
6 Dec
(Friday)
6 Dec
(Friday)Differentiation Asynchronous
Task 1, Task 2
Synchronous
Lecture (MME) Week 11
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups12
Group 1: 09 Dec (Monday)
Group 2: 12 Dec
(Thursday)
13 Dec
(Friday)
13 Dec
(Friday)Integration Asynchronous
Task 1, Task 2
Synchronous
Lecture (MME) Week 12
Synchronous
Feedback and Support Session
Synchronous
Tutorial class-different groups -
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This week we want to welcome you to the course and show you how to get the best out of it.
In SEF041 Mahtematics B momdule, in the first semester, we will cover mathematical topics such as algebra, functions, geometry, trigonometry and calculus. In the second semester, module provides students with a more extensive knowledge of calculus (especially in techniques of integration) and an introduction to complex numbers, numerical methods, vector analysis and power series. In this module you are going to learn by working on tasks. To complete the tasks, you will need to find information and understand ideas. On this QMPlus page are resources that will help you do that.
This week, we are going to work on few tasks together that will introduce you to this way of learning and we will look at rules for powers and logaritms and we will learn to solve various equations involving exponentials and logarithms.
THIS WEEK'S LEARNING OUTCOMES
By the end of this week, you will be able to Apply the rules for powers and logarithms to a variety of problems and solve exponential and logarithmic equations, namely you will be able:
1. Simplify expressions involving powers with the same and different bases.
2. Understand the relationship between exponential and logarithmic expressions.
3. Transform exponential expressions into logarithmic ones, and vice versa.
4. Know and apply the rules for logarithms, including the rule for the change of base for logarithms and simplify logarithmic expressions.
5. Understand and applying the methods for solving different kinds of problems involving exponentials or logarithms.
You will achieve them by using the online content below (Mathematics B workbook, videos and chosen sections from the recommended textbooks), and consolidate them by attending the live session.
Mathematics B workbook is the main set of notes (containing all the lecture notes, examples and worked examples) and each chapter [Mathematics B workbook - Chapter X] will be available each week. This workbook is designed for your independent study. It contains the notes, related to the given week's learning outcomes. This material is a main source for your learning for this module with plenty of examples and exercises for independent learning and contains FULL Learning Outcomes summarised after each chapter (which you can use as a checklist for the course). We will refer to these Chapters and Worked Examples in the live webinar sessions as well.
Note: On the bottom of each TASK’s resources there are also EXTRA PRACTICE links (do them if you fell that you need extra practice) and ADDITIONAL MATERIAL. Both of these resources are not obligatory (they won't be required for the live sessions or tutorials) but you may wish to use these, for example if you feel that extra practice would be helpful for you – they are carefully chosen to match the topics of the given TASK. You may wish to use these, but they won't be required for the live sessions or tutorials.Recommended textbooks (for extra reading/practice) - not obligatory) Textbook 1 [J.Olive Survival Guide]:Maths: A Student's Survival Guide, A Self-Help Workbook for Science and Engineering Students by Jenny Olive, published by Cambridge University Press, 2nd Edition; February 2005, ISBN: 9780511074257. Note: e-book is available. Textbook 2 [Bostock,Chandler Core Maths]: Core Maths for Advanced Level, L. Bostock F.S. Chandler, published by Nelson Thornes, revised 3rd Edition 2013, ISBN: 978-1408522288. There is no e-book for this textbook.
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Mathematics B workbook is the main set of notes for this module (containing all the lecture notes, examples and worked examples) and each chapter will be available each week.
Below the specific TASKS basing on this workbook are outlined. Follow the steps outlined in each TASK.85.3 KB -
The lecturer will tailor your live sessions depending on your answers
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The lecturer will tailor your live sessions depending on your answers
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If enough people tick yes, lecturer may decide to do something on it in the live session
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A side-by-side table of the power laws and rules for logarithms.
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ADDITIONAL MATERIAL is not obligatory. You may wish to use these resources, but they won't be required for the live sessions or tutorials.
If you feel that algebra and numeracy refreshers would be helpful to you (for example if you haven't done any maths since a while) please take the time to go through these refreshes on algebra, numeracy this week and make sure that you are fully familiar with the methods and the terminology used as we will need this in the course.
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This video will help you to understand that the only numbers you can plug into a logarithm argument are positive numbers. Negative numbers, and the number 0, aren’t acceptable arguments to plug into a logarithm function, but why?
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This link has information to help students to get the best out of QMplus - with helpful guides and videos...
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THIS WEEK'S LEARNING OUTCOMES
By the end of this week, you will be able to Solve quadratic equations and use Factorisation and Remainder theorems for polynomials, namely:
1. Solving problems related to the number of roots of a quadratic.
2. Factorising quadratics.
3. Understanding that the roots do not completely determine a quadratic.
4. Finding quadratics whose roots are related to a given polynomial without finding the roots explicitly.
5. Applying the Factorisation Theorem to factorise polynomials.
6. Applying the method of polynomial division.
7. Applying the Remainder Theorem to problems involving polynomials.
You will achieve 1., 2., 3. And 4. by completing TASK 1 [QUADRATICS], 5. - 7. with TASK 2 [POLYNOMIALS] and you will consolidate your knowledge by attending the live session.
Note: On the bottom of each TASK’s resources there are also EXTRA PRACTICE links (do them if you fell that you need extra practice) and ADDITIONAL MATERIAL. Both of these resources are not obligatory (they won't be required for the live sessions or tutorials) but you may wish to use these, for example if you feel that extra practice would be helpful for you – they are carefully chosen to match the topics of the given TASK.
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The lecturer will tailor your live sessions depending on your answers
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If enough people tick no, lecturer may decide to do something on it in the live session
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Tick yes if you agree with the above statement.
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Read this page to know:
- when the assessments take place,
- what topics each one covers,
- and how much they are worth.
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Coursework (3 in person midterms tests): 50 % of final grade
Examination: 50 % of final grade
See 'ASSESSMENT Profile' for more details
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Online Quizes: There will be eleven Quizzes in Sem A in the form of online quizzes. There are no Quiz in Weeks 7. Each Quiz consists of 5-10 questions. All Quizzes are Important. These Quizzes do NOT contribute to your final mark for this module.
Weekly homework sheets: Provide exam-like Questions related to the topics of the given week.
You should revise the corresponding notes and related workbook chapter and the tutorial sheet solutions prior to attempting the problems from the homework sheet.
Then work through these exam-like questions, write down your solutions and submit them to your tutor or lecturer.
Homework and online Quizzes are optional (does not count towards your module mark) however tutors or lecturer will check your solutions and provide detailed comments on scripts. Homework does not contribute to the final mark, but it will be checked and corrected.
This is the only way you can get feedback on your individual work throughout the whole semester on this module.
Even though the submission of homework is optional understanding the solutions to these problems will be required for the mid- and end-term tests and the exam. The problems set in Homework Sheets are based on past exams, so it is really good preparation!
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Here you will find the information about the ASSESSMENT 1 for this module.
Mathematics B Semester 1 - Assessment 1/in Week 7: This is a summative assessment and your mark from Assessment 1 will contribute 10% to your final module mark. Make sure that you understand the Assessment Profile [LINK CORRECTED] for the module.
Assessment Pattern - 10% of final marks
Format and dates for the first in-term assessments -
The first in person assessment will be set in week 7:
Wednesday 6th Nov, 9:00--10:00am at Bancroft Room no's 1.13 and 1.13a
Format of assessment 1- The first assessment will be a one hour handwritten exam on campus. You will need a non-programmable calculator.
Link to past papers -
Past papers and solutions have been added to the Assessment section of the module content page.
Description of Feedback -
In term assessment will be marked with written feedback provided. In addition Assessments with solutions will be available the following week on QM Plus.
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ASSESSMENT 1 TEST RULES:
1. All questions will need to be answered correctly to get the highest mark 100%. No answer and incorrect answer give 0 marks.
2. For each question there is a single correct answer. Record each answer in the corresponding place.
3. You will be provided with Questions and answers papers, where spaces will be available to record you answers.
4. And you MUST REMEMBER to SUBMIT the Questions and Answers Sheets before 1 hours period has elapsed. This assessment is scheduled only once and cannot be rescheduled. Any student who fails to attend an assessment (and who does not have a valid reason for applying for exemption due to extenuating circumstances) will be awarded 0 marks.
The topics included in the test are covering Mathematics B workbook - Chapters 1 - 4 (inclusive), i.e. WEEKS 1 - 5 TASKS (all included).
REVISION:
To prepare for this assessment, I suggest you go over your lecture slides, revise all the weekly TASKS, completing questions on corresponding Mathematics B workbook chapters, the Weekly Homework Worksheets, and any related material you have found, as you normally would for a written exam.
Revise your own notes, QReview recordings and do extra examples suggested under the links in each of the TASKS and from the recommended textbooks. Don't forget to review the Tutorial sheets solutions.
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These quizzes don't count towards your final mark - they're just to help you learn. They all have multiple-choice or numerical answers which are marked automatically, and you can attempt them as many times as you want. So please keep trying until you get all the questions right!
Some of the questions are deliberately tough, because you're allowed several attempts, so don't get disheartened if you find it difficult - the best way to learn is to struggle with difficult tasks.
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This quiz will test you on the concepts taught during week 1. It will become available at the end of the week.
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