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Math 1050-5 Babenko V. September, 2014 Practice Test 1 Name: UID#: This is a closed book Test. No books, laptops, or messaging are permitted. NO calculators are allowed. You have 12 problems, they are equal in weight. The entire exam is worth 12 points. For full credits show all work! Box your answer so it is easy to locate. You have 50 minutes. GOOD LUCK!!! 1 1. Decide whether the given sequence is arithmetic, geometric, or neither. a) 2, 8, 10, 12, ... b) 3, 7, 12, 18, ... c) 2, −4, −10, −16, ... 2. Find a) 3 ? i2 = i=1 b) 50 ? 3= i=1 c) 50 ? i= i=1 3. a) Is the picture below the graph of a function? 2 3. b) Does this function have an inverse or not? 3. c) Describe the transformations compared to the base graph. g(x) = 5(x − 1)3 + 5 3 4. a) What is the 53rd term in the sequence 3, 12, 48, 192, ... ? 4. b) What is the 15th term in the sequence 3, 13, 23, 33, ...? 5. a) What is the sum of the ﬁrst 20 terms of the sequence 0, 2, 4, 6, ...? 5. b) What does the following series equal: 7 + 4 7 4 + 7 16 + 7 64 + ...? 6. a) A library wants to choose 30 of its 8,000 books to put on a summer reading list. How many ways could the library choose 30 of its books? 6. b) A library has 8,000 books, and it wants to rank its 20 best books, from ﬁrst to twentieth. How many diﬀerent rankings are possible? 7. A library wants to buy three books: an adventure book, a nonﬁction book, and a pamphlet on health issues. The library staﬀ has narrowed its options down to four diﬀerent choices for which adventure book to buy, ﬁve choices for which nonﬁction book to buy, and three options for which pamphlet on health issues to buy. How many diﬀerent combinations of three books could they buy? 8. a) A library wants to arrange their 8,000 books in an order One option is to order the books alphabetically, but how many diﬀerent ways could they order their books? 9 8. b) What is ( )? (Your answer should be a natural number in standard form.) 6 5 9. If f (x) = x200 + 3 and g(x) = x300 + 2, then what is (f ◦ g)(x)? 10. a) What is the implied domain of f (x) = 5x5 − 35x? 10. b) What is the implied domain of g(x) = 10. c) Simplify the expression: 11. f (x) = 3x+1 . x−5 √ 48 Find inverse function. 6 2x2 +3x−7 ? 5x−7 12. Below is the graph of a function f (x). Use this graph to answer questions. a) What is f(5)? b) What is the domain of f ? c) What is the range of f ? d) What are the x-intercepts of the graph of f ? e) What is the y-intercept of the graph of f ? 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Total 7 /10 /10 /10 /10 /10 /10 /10 /10 /10 /10 /10 /10 /120 /12