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MATH 2201

INFORMATION ABOUT EXAM 1

SPRING 2023

Exam 1 is on Thursday, February 2, during class, and covers Lectures 1-8: from the start of classes through Babylonian Mathematics [NOT Egyptian Mathematics]

PLAN FOR TAKING THE EXAM

We will meet on Zoom, with me proctoring. Kindly keep your camera on. I will email everyone the typed white Exam sheet as an attachment around 1 :25 PM and start the Zoom meeting at 1:30 PM. Please DO NOT BEGIN until I say it's time to do so. We'll start the Exam promptly at 1:35 PM.

Use your own blank paper (preferably white or a very light color) for your solutions. Print your FULL NAME in the TOP RIGHT CORNER of the FIRST PAGE. When done, SIGN your NAME at the END of the LAST PAGE to attest that you have honored the Exam Pledge below.

Don't leave any information on the white typed Exam sheet that you want graded!

The Exam will officially end at 2:30 PM, to give you time to take photos of your solutions and send them to me by email. IF YOU HAVE AN APP THAT CONVERTS YOUR PHOTOS INTO ONE BLACK

os(W)s(H)i(I)b(T)le(E)a(P)n(D)d(F) e(F)m(IL)ai(E),l them(THAT)all(W)to(OU)m(L)e(D) .BE IDEAL. If not, take each photo with as much illumination

HOW TO WRITE UP YOUR SOLUTIONS THANK YOU IN ADVANCE !!!

(1) SHOW WORK TO JUSTIFY YOUR ANSWERS, unless it is explicitly state otherwise.

Yes, points will be taken off if you only put down an answer you figured out in your head and you don't show the necessary computations or steps showing how you found it. To receive full credit, write solutions neatly and logically, without skipping steps.

(2) LEAVE SPACE BETWEEN EACH SOLUTION (I'm begging you!), so your work is easy to read and allows me to be generous in grading. CROSS OFF WORK YOU DON'T WANT COUNTED.

(3) BOX YOUR ANSWERS, when applicable, so I can easily identify them.

(4) DON'T WRITE CLOSE TO THE EDGE OF THE PAPER (leave ample margins), so your photos will be able to capture everything on the pages.

(5) IF USING A PENCIL, PLEASE WRITE DARKLY ENOUGH to produce readable photos.

ACADEMIC INTEGRITY WARNING

YOU ARE NOT ALLOWED TO USE ANY ASSISTANCE ON THE EXAM. That means NO BOOKS, NOTES, DRAWING TOOLS, CALCULATORS, OR ANY ELECTRONIC DEVICES, and absolutely no communication with others (texting, messaging, etc.) ANY VIOLATIONS WILL HAVE VERY SERIOUS CONSEQUENCES, as described on the Syllabus regarding Academic Integrity.

EXAM PLEDGE YOU MUST SIGN YOUR HANDWRITTEN SOLUTIONS at the end of the last page AFTER you finish the Exam. WITH YOUR SIGNATURE YOU ARE PLEDGING THAT YOU HAVE

NEITHER GIVEN NOR RECEIVED NOR USED ASSISTANCE ON THE EXAM.

STUDY GUIDELINES

THE SAMPLE QUESTIONS on the next 2 pages ARE NOT COMPREHENSIVE.

Their purpose is to give you some idea of the TYPES of questions and problems to expect and the level of historical and mathematical detail. [ULM students, see note below.]

You need to learn: (1) the material in the Lecture Notes and in the accompanying Reading (see exceptions below about the Reading) and (2) how to do ALL of the HW.

Not to worry, the exam will be shorter than the list of Sample Questions!

FOR MATERIAL IN THE ASSIGNED READING THAT WAS NOT COVERED IN

CLASS, use the following guideline, as stated on the Syllabus: you do NOT need to know isolated facts and dates mentioned in passing; however, IF A TOPIC IS DISCUSSED IN AT

LEAST ONE PARAGRAPH OR MORE, YOU SHOULD BE ABLE TO STATE, IN A SENTENCE

OR TWO, THE KEY FACT(S) AND SUMMARIZE THE MAIN IDEA(S).

***Any Babylonian tables (Multiplication, Reciprocal, etc.) will be provided, as well as any Babylonian recipes for solving quadratic equations. However, make sure to memorize our modern Quadratic Formula.***

ULM STUDENTS: all the information above applies, but you are ALSO responsible for knowing how to do problems like the ULM HW problems and may be asked to do computations that are more difficult than those in this guide (but they will be doable by hand, since NO calculators are allowed).

ADVICE ABOUT STUDYING THE HW PROBLEMS and THE MATHEMATICAL EXAMPLES IN THE LECTURE NOTES and IN THESE SAMPLE QUESTIONS

First, try your best to do a problem without any help. If you need help, consult your notes or books or share ideas with others (or ask me!). Only then should you look up the Solution and make sure you understand it. After that, continue to practice doing the

problem more quickly and efficiently, so you will not hesitate if you find a similar one on the Exam.

SAMPLE QUESTIONS FOR EXAM 1

(1) (a) Does the trapezoid problem on Aaboe p.26 tell us about Babylonian Mathematics before Pythagoras?

(b) Which civilization in South America used knotted cords to keep accounts?

sticks, or tying knots in strings . On which one of these objects was tallying found in the Nile region,

dating back almost 20,000 years ago?

(2) Write the decimal number 14,601 in: (a) Roman Numerals, (b) Mayan Numerals, (c) Sexagesimal Notation, and (d) Cuneiform.

(3) (a) Multiply the two binary numbers 1111 and 11 using binary multiplication.

(b) Check your solution to part (a) by converting all the numbers into our number system.

(4) Briefly describe Henry Rawlinson's dramatic role in copying cuneiform inscriptions.

(5) TRUE or FALSE [ PLEASE write out the entire word, since handwritten letters "T" and "F" can be hard to distinguish. ]

(a) The Babylonians used a symbol for zero, when needed, at the end of a number to indicate its size. (b) The decipherment key for both Grotefend and Rawlinson was to start with Persian cuneiform.

(d) The Peruvian Quipus displayed a base 20 system that was not place-value.

(6) Convert the decimal 0.0075 into sexagesimal notation.

(7) (a) Find the fractions and as the Babylonians would, using Aaboe p.10 and Xerox 2. Supply the modern sexagesimal point wherever necessary for mathematical correctness.

(b) Why is it not possible to express the fraction

as a finite decimal?

(8) What is the general historical significance of both the Beam Problem and the Triangle in a Circle Problem?

(9) The Babylonians would solve x2 + px = q using the recipe x = 2 + q − . Write the following

as a modern equation in x and show how the Babylonians would solve it: "I have added the area and ten

times the side of my square and it is 56. Find the side of the square ." Identify p and q and do the

computations in our number system. Then, in our modern way, find the solution not found by them.

(10) Express the following problem as an equation of the form x2 − px = q : "I have subtracted the side of a square from the area and it is 8;45." Identify p and q and then solve for x using the recipe

x = 2 + q + . Do all your computations in the sexagesimal system. [Hint: 2 = .]

(11) (a) In problems (9) and (10) above, the Babylonians considered two types (or categories) of quadratic

equations and then used the appropriate recipe to solve each type (where p and q are always

positive numbers). What do these two types of equations have in common?

(b) In class and on the HW we looked at a third type of quadratic equation that was stated very

differently from these two. How did they state this third type and what is the special name that historians have given to this type? How many positive solutions does this type produce?