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MAC 1140

MAC 1140. Test 4 Review and Practice Solutions. MAC 1140 Test 4 Review 12.1 – 12.5 . You will need to have your own graphing calculator for the test. You may not share calculators or use any type of communication device in place of a calculator.

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MAC 1140

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  1. MAC 1140 Test 4 Review and Practice Solutions

  2. MAC 1140 Test 4Review 12.1 – 12.5 • You will need to have your own graphing calculator for the test. • You may not share calculators or use any type of communication device in place of a calculator. • Tests cannot be made up for any reason other than an NWFSC event for which you must miss class. • If you miss one test, your final exam score will be substituted. A second missed test is a zero.

  3. Exam Topics

  4. To Study for the Test • Complete all assigned homework. Remember that a score of at least 70% on each assignment gives you 10 bonus points on the test. • Complete the practice test and check your solutions. • Set up a study system (note cards for example) for each of the 10 objectives in the chart above. • Review your notes and applicable problem set questions for each of the 10 objectives in the chart above. • Work the suggested text problems for each of the 12 objectives in the chart above.

  5. Things to Know Summation Formulas

  6. Arithmetic Sequences

  7. Geometric Sequences

  8. Geometric Series Converges if with sum

  9. Mathematical Induction 1) Show that the statement is true for 2) Show that if the statement is true for , then it’s true for 3) Conclude that the statement is true for all natural numbers

  10. Binomial Theorem Start with The exponents of subsequent terms go up with the constant and down with the variable.

  11. 1) Find the first five terms of a)

  12. b)

  13. 2) Find each suma)

  14. b)

  15. 3) Find the 120th term of

  16. 4) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 7th term is 4 and the 22nd term is 34.

  17. 4) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 7th term is 4 and the 22nd term is 34. OR

  18. 5) When Eric started work as an orange picker, he picked 10 oranges in the first minute, 12 in the second minute, 14 in the third minute, and so on. How many oranges did Eric pick in the first 30 minutes?

  19. 6) a) Find the sixth term of

  20. b) Find the seventh term of

  21. Find the nth term of

  22. 7) Determine whether each series converges or diverges. If it converges, find its sum.a)

  23. b)

  24. 8) a) Answer the following questions to prove by mathematical induction that • Show that the statement is true for • What is the right hand side if (in factored form)? 3) What is the right hand side if (in factored form)? 4) Use the information in number 2 to show that the statement in number 3 is true.

  25. b) Answer the following questions to prove by mathematical induction that • Show that the statement is true for • What is the right hand side if (in factored form)? • What is the right hand side if (in factored form)? • Use the information in number 2 to show that the statement in number 3 is true

  26. 9) Expand each binomial using the binomial theorem. You may use your calculator to compute the combinations. a) + +++ 1

  27. b) + ++ 1

  28. 10) Use the binomial theorem to answer each question. You may use your calculator to compute the combinations. • What is the coefficient of in The two exponents must add up to 12.

  29. b) What is the third tem of The third term has an exponent on the constant term of one less than the term. Since the term is the third, it’s an exponent of 2. OR The exponent on the variable counts down → 8, 7, 6. The exponent on the variable is 6. In either case, the term is:

  30. Test 4 Extra Practice

  31. 1) Find the sum:

  32. 1) Find the sum:

  33. 2) Find the 90thterm of

  34. 2) Find the 90thterm of

  35. 3)A brick driveway has 50 rows of bricks. The first row has 16 bricks and the fiftieth row has 65 bricks. Assuming that the number of bricks in each row forms an arithmetic sequence, what is total number of bricks?

  36. 3)A brick driveway has 50 rows of bricks. The first row has 16 bricks and the fiftieth row has 65 bricks. Assuming that the number of bricks in each row forms an arithmetic sequence, what is total number of bricks?

  37. 4) Determine whether the series converges or diverges. If it converges, find its sum.a)

  38. 4) Determine whether the series converges or diverges. If it converges, find its sum.a)

  39. 5) Use the binomial theorem to answer the question. You may use your calculator to compute the combinations. What is the coefficient of in

  40. 5) Use the binomial theorem to answer the question. You may use your calculator to compute the combinations. What is the coefficient of in The two exponents must add up to 12.

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