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Math 1050 Practice Exam 1 February 10, 2012 Answer all questions below. Every question is worth the same number of points. You may use the available space for work, but must write ALL answers on the answer sheet. No cell phones, calculators, or notes are allowed during the exam. These rules will be strictly enforced. Name: Number: For #1-3 decide whether the statement is true or false. 1. π ∈ /Q 2. (4, 6] ⊆ [4, 7) 3. Z ⊆ Q For #4-6, decide whether the given sequence is arithmetic, geometric, or neither. 4. 4, 1, −2, −5, . . . 5. 7, 11, 22, 15, . . . 6. 7, 21, 63, 189, . . . 7. Find 15 ! 3 i=1 8. Find 70 ! i i=1 9. Find 5 ! i=1 (i2 − i) 10. What is the 52nd term in the sequence 4, 8, 16, 32, . . .? 11. What is the 101st term in the sequence 6, 10, 14, 18, . . .? 12. What is the sum of the first 35 terms of the sequence 20, 25, 30, 35, . . .? 13. What does the following series equal: 18 + 6 + 2 + 23 + . . .? Page 2 14. You are choosing a class council. Out of 32 students, you must select a president, vice president, secretary, and treasurer. How many diﬀerent class councils are possible? 15. You’re buying a car. You know which model you want to buy, but you are given the option of 2 interior colors, 5 exterior colors, and 3 sound systems. How many diﬀerent types of car could you buy? 16. The faculty needs to nominate a panel of three members for a special committee. If there are 132 faculty members, how many diﬀerent committees are possible? 17. There are 150 students in this class. How many diﬀerent ways are there to assign seats for the first exam? ! " 8 18. What is ? (Your answer should be a natural number in standard form.) 6 Page 3 19. If f (x) = x + 1 and g(x) = x3 , what is f ◦ g(x)? 20. What is the implied domain of f (x) = 21x2 + 7? 1 ? x−4 21. What is the implied domain of g(x) = Below is the graph of a function f (x). Use this graph to answer questions #22-27. 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 22. What is f (2)? 23. What is the domain of f ? 24. What is the range of f ? 25. What are the x-intercepts of the graph of f ? 26. What is the y-intercept of the graph of f ? Page 4 1 2 3 4 5 27. Is the picture below the graph of a function? 6 28. Write out! the " product (x − 2y) so that your final answer doesn’t include numbers that n look like k . 29. Graph id. 30. Graph f (x) = 4. 31. Graph x2 . 32. Graph x3 . 33. Graph x1 . 34. Graph 1 . x2 35. Graph g : [−2, 1) → R where g(x) = x. 36. Graph h : {2, 3, 4} → R where h(x) = x2 − 3. Page 5 Name: Number: 1. 14. 2. 15. 3. 16. 4. 17. 5. 18. 6. 19. 7. 20. 8. 21. 9. 22. 10. 23. 11. 24. 12. 25. 13. 26. 27. Page 6 28. ******************************************************************************** 29. id 30. f (x) = 4 32. x3 33. 35. g(x) 36. h(x) 1 x 31. x2 32. Page 7 1 x2