Tutorial Letter 101/3/2022 Pre-Calculus (Engineering) MAT1514 Semesters 1 and 2 Department of Mathematical Sciences

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Tutorial Letter 101/3/2022 Pre-Calculus (Engineering) MAT1514 Semesters 1 and 2 Department of Mathematical Sciences Note: This is a fully online module. It is, therefore, only available on myUnis ... a. 2 Page 1 INTRODUCTION ..........................................................................................................................3 1.1 Getting started ..............................................................................................................................3 2 OVERVIEW OF MAT1514 ............................................................................................................3 2.1 Purpose ........................................................................................................................................3 2.2 Outcomes .....................................................................................................................................3 3 CURRICULUM TRANSFORMATION...........................................................................................4 4 LECTURER(S) AND CONTACT DETAILS...................................................................................5 4.1 Lecturer(s) ....................................................................................................................................5 4.2 Department...................................................................................................................................5 4.3 University......................................................................................................................................5 5 RESOURCES...............................................................................................................................5 5.1 Joining myUnisa............................................................................................................................5 5.2 Prescribed book(s)........................................................................................................................6 5.3 Recommended book(s).................................................................................................................6 5.4 Electronic reserves (e-reserves) ...................................................................................................6 5.5 Library services and resources .....................................................................................................6 6 STUDENT SUPPORT SERVICES................................................................................................7 6.1 First-Year Experience Programme @ Unisa ...................................................................................7 6.2 Students with disabilities.................................................................................................................8 7. HOW TO STUDY ONLINE............................................................................................................8 7.1 What does it mean to study fully online? .......................................................................................8 7.2 myUnisa tools ...............................................................................................................................8 8. STUDY PLAN...............................................................................................................................9 9. ASSESSMENT ...........................................................................................................................11 9.1 Submission of assignments ........................................................................................................11 9.1.1 Written assignments ...................................................................................................................11 9.1.2 Multiple - Choice assignments ...................................................................................................12 9.2 Examination................................................................................................................................12 10. CONCLUSION............................................................................................................................12 CONTENTS MAT1514/101/3/2022 3 1 INTRODUCTION Dear Student Welcome to MAT1514 Pre-Calculus (Engineering). In MAT1514 you have to work independently and motivate yourself to do so regularly to be successful. See an example of a study plan further on in this letter. The amount of time you study is not important, but how efficient you use that time is very important. Because this is a fully online module, you will need to use myUnisa to study and complete the learning activities for this module. Visit the website for MAT1514 on myUnisa frequently. The website for your module is MAT1514-22-S1 or MAT1514-22-S2 depending on the semester you are registered for. This module is not a continuous assessment module as modules offered by the School of Engineering are. You will write an examination and not tests. If you are registered for semester 1 you will write your final examination in May/June 2022 and if you are registered for semester 2 you will write your final examination in Oct/Nov 2022. 1.1 Getting started Owing to the nature of this module, you can read about the module and find your study material online. Go to the website at https://my.unisa.ac.za and log in using your student number and password. Click on "myModules" at the top of the web page and then on "Sites" in the top right corner. In the new window, click on the grey Star icon next to the modules you want displayed on your navigation bar. Close the window in the top right corner. Then select the option "Reload to see your updated favourite sites". Now go to your navigation bar and click on the module you want to open. 2 OVERVIEW OF MAT1514 2.1 Purpose This module will be useful to students in developing basic skills which can be applied in the natural sciences and engineering sciences. The focus is on building strong algebraic and trigonometric skills that will support the development of analytical skills that are crucial in problem solving in more advanced mathematics and related subjects. This module will support students in their studies in the field of engineering and the physical sciences as part of a diploma. 2.2 Outcomes For this module, you will have to master several outcomes: 4 Specific outcomes and assessment criteria Specific outcomes Assessment criteria 1 Manipulate algebraic expressions and solve algebraic equations 1. Recognition and use of the absolute value of numbers. 2. Factorizing expressions with rational (fractional) exponents. 3. Simplifying compound fractions. 4. Rationalizing denominator or numerator containing a surd. 5.Solving an equation containing terms in which fractional exponents occur. 6. Solving exponential and logarithmic equations. 2 Draw and interpret graphs of linear, absolute value, quadratic, exponential, logarithmic and trigonometric functions. 1. Sketching the graph of an absolute value, a reciprocal, a piece-wise, an exponential and a logarithmic function. 2. Deducing the following information from the graph: - Domain and range of a function. - Increasing and decreasing function - Maximum and minimum values of a function. - The average rate of the function. 3. Transformation of functions. 4. Combining and composition of functions. 5. One-to-one functions and their inverses. 6. Combination of graphs. 7. Modelling with functions (word problems). 3 Define and draw graphs of trigonometric functions and inverse trigonometric functions. 1. Define trigonometric ratios using the unit circle and the right-angled approach. 2. Define trigonometric functions and inverses. 3. Graph trigonometric functions and inverse trigonometric functions. 4. Formulate the concept of a periodic function. 4 Solve trigonometric equations 1. Solve trigonometric equations by using: - quadratic identities - sum- and -difference identities - double angle, half-angle and reduction formulas - sum-to-product and product-to-sum formulas 5 Apply definitions and properties of functions and rules related to these functions, to solve real-life problems. 1. Modelling with algebraic equations (word problems). 2. Modelling with exponential and logarithmic functions (word problems). 3. Apply the concept of average rate of change to reallife situations. 4. Construct models using variation. 3 CURRICULUM TRANSFORMATION Unisa has placed curriculum transformation high on the teaching and learning agenda. Curriculum transformation includes the following pillars: student-centred scholarship, the pedagogical renewal of teaching and assessment practices, the scholarship of teaching and MAT1514/101/3/2022 5 learning, and the infusion of African epistemologies and philosophies. These pillars and their principles will be integrated at both programme and module levels as a phased-in approach. You will notice a marked change in the teaching and learning strategy implemented by Unisa, together with how the content is conceptualised in your modules. We encourage you to embrace these changes during your studies at Unisa in a responsive way. 4 LECTURER(S) AND CONTACT DETAILS 4.1 Lecturer(s) The primary lecturer for this module is Ms L E Greyling at the time of compiling this tutorial letter (September 2021): Department: Mathematical Sciences If you experience any problems with the mathematical content you are welcome to contact the lecturer: CONTINUES... [Show More]

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