© Scarborough, June 2006 Math 365 Summer I Math 365-100 NEATLY PRINT NAME: ____________________________ Exam 1 STUDENT ID: _________________________ Summer 2006 DATE: _______________________________ Scarborough PHONE: _____________________________ EMAIL: ______________________________ "On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work." ________________________________ Signature of student Academic Integrity Task Force, 2004 http://www.tamu.edu/aggiehonor/FinalTaskForceReport.pdf WRITE ALL SOLUTIONS IN THE SPACE PROVIDED; FULL CREDIT WILL NOT BE GIVEN WITHOUT CORRECT ACCOMPANYING WORK. FULLY SIMPLIFY ALL ANSWERS AND GIVE EXACT ANSWERS UNLESS OTHERWISE STATED. WHERE PROVIDED, PUT YOUR FINAL ANSWER IN THE BLANK PROVIDED. POINTS WILL BE DEDUCTED FOR SPELLING ERRORS. REMEMBER YOUR UNITS!© Scarborough, June 2006 Math 365 Exam I 2 (3pts) 1. True or False. Circle the correct answer. a. True or False If ac = bc, then a = b, for all real numbers a, b and c. b. True or False {8, a, *, L, Φ, µ} has 64 proper subsets. c. True or False Function composition is not commutative. Each blank is worth 2 points. a4 = __________________________ 2. If a1 = 5, a2 = 11, and an = 2 * an – 1 + 3 * an – 2 for n > 2, find a4. ______________________________ 3. If m and n are natural numbers, demonstrate the closure property of multiplication of the natural numbers. __________________________________________________________ 4. What is the inverse to the conditional statement “If Natalie is my daughter, then she will visit me.” an = ___________________________ 5. Given the sequence 4, 20, 100, 500, . . . , what is an for all n? ()()g f x=o ___________________________ 6. Given f(x) = x – 5 and g(x) = –x2 + 9. Find and simplify()()g f xo.© Scarborough, June 2006 Math 365 Exam I 3 __________________________________ 7. What is the next figure in the sequence? ____________________________________________ 8. Which step of Polya’s 4-step Problem Solving Model is expressed in the following statement? ”Instead of solving the problem for n = 60, let me see if I can solve the problem for n = 5.” 9. Let H = {s, a, w}, A = {g, i, r, a, f, e}, and P = {s, u, n}. Given U H A P= ∪ ∪, find the following. a. _______________________________ = (){ , , }n H P w e s ∪ ∩  b. __________________________________ = P A∩ c. __________________________________ = H A∪ d. _____________________________________________________________ = P x H ____________________________ 10. What is the number preceding 1000three?© Scarborough, June 2006 Math 365 Exam I 4 ______________________________ 11. 9T8eleven – 7T9eleven = _____________________________ 12. What set is represented by the shaded area? H AT _________________________________________________________________ 13. Negate “No unicorn is real and some dreams come true.“ _________________________ 14. If n(S) = n(T) = 4 , how many 1 – 1 correspondences are there between the sets S and T? ______________________________ 15. Name two properties the Roman numeration system has? ______________________________ _________________________________ 16. Give a counterexample to the conjecture: “If p is prime, then 6p + 1 is prime.”© Scarborough, June 2006 Math 365 Exam I 5 ______________________________ 17. Write 159 in Roman numerals. _______________________________ 18. Twenty-five and 7 are whole numbers but 257 is not a whole number. Use the Division Algorithm to put this problem into the form a = bq + r where a, b, q, and r are whole numbers. (3pts) 19. Give an example thoroughly illustrating the associative property of addition of whole numbers. (4pts) 20. Explain the relationships that exist between the four operations: addition, subtraction, multiplication and division. (3pts) 21. Give an example of a logical statement. (3pts) 22. Is the following argument valid or invalid? Why or why not? Draw a Venn diagram to support your answer. Some sasas are memes. All fifis, memes, and sasas are blings. Some fifis are sasas. Therefore some fifis are memes.© Scarborough, June 2006 Math 365 Exam I 6 (4pts) 23. Using scratch addition, compute 144five + 223 five + 34 five + 324 five. (3pts) 24. Use the set definition of less than to show 3 < 5. (4pts) 25. Make a truth table for ~p q∨. Hint: There will be 4 columns.© Scarborough, June 2006 Math 365 Exam I 7 (5pts) 26. Find the sum of the first 33 terms of an arithmetic sequence in which the 9th term is 58 and a21 = 142. (2pts) 27. Model 10 ÷ 2.© Scarborough, June 2006 Math 365 Exam I 8 (3pts) 28. Explain, as you would to a student, why you cannot divide zero by zero. (4pts)29. What is 78nine in base four? (2pts) 30. Model 7 – 4, other than using base-ten blocks.© Scarborough, June 2006 Math 365 Exam I 9 (2pts) 31. Model 2 + 6 on the number line. 0 1 2 3 4 5 6 7 8-1-2-3-4-5-6-7-8 (2pts) 32. Model 3 * 4. (2pts) 33. Define place value.© Scarborough, June 2006 Math 365 Exam I 10 (3pts) 34. Model 23 – 16 using illustrations of base-ten blocks clearly showing any regrouping/trading and the difference. (2pts) 35. Compute 495 + 372 using the expanded algorithm. (4pts) 36. The sum of three consecutive odd numbers is 213. What is the largest of the three