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Chapter 6 Discrete Functions Assignment Knowledge and Understanding Communication Thinking Application Total / 10 / 10 / 10 /10 /40 Multiple Choice [Knowledge and Understanding 10 marks--1 mark each] Identify the choice that best completes the statement or answers the question. Use only Capital Letters. 1. Which of the following functions can be used to generate the terms in the sequence 3, 5, 7, 9, ...? A. An) = 2n+1 C. An) = 3n B. An) = 1+ 2 D. An) = 372 - 1 2. The 20th term in the sequence defined by x = 272 - 30 72 - 272 A. 30 C. 40 B. 36 D. 44 Which term in the sequence defined by , = (n+ 1) (n -1) has a value of 99? A. 8 C. 10 B. 9 D. 11 4. The value, V, of an antique is modelled by the equation V(x) = 4000(1.02) ", where n represents the numb of years after it was purchased. How much was the purchase value? A. $4000 C. $80 B. $4080 D. $3920 5. Which of the following recursion formulas produces the sequence 1, 3, 13, 63, ...? A. 1 = 1, tx = x-1 + 2 C. 1 = 1, tx = 61x-1-5 B. $1 = 1, t = 5x-1 -2 D. $1 = 1, t = 21x_1 - 8 6. Which term in the same row of Pascal's triangle as $6. 2 has the same value as $6 2? A. $6. 3 C. $6.5 B. $6.4 D. $6.6 7. How many terms are in the sequence 0.2, 0.6, 1.0, 1.4, ..., 5.8? A. 12 C. 14 B. 13 D. 15 8. The sum of a geometric series where a = 4, r = 2, and n = 5 is A. C. -124 B. 62 D. 128 9. The sum of a geometric series 6 + 3 + 1.5 + ..- + 0.023 437 5 is A. 11.976 562 5 C. 125 B. 11.87 D. 5.988 28 Page 1 of 4Full Name: Date: MCRBUT 10. The sum of an arithmetic series where a = >, d = -3, and n = 40 is A. -2320 C. 2340 B. 2320 D. -4640 Matching [Communication 10 marks--1 mark each] Use only Capital Letters on the spaces provided. Match the correct term to its description below. A. arithmetic series F. recursion formula B. geometric sequence G. discrete function C. Pascal's triangle H. continuous function D. arithmetic sequence I. sequence E. explicit formula J. geometric series 1 1. an ordered list of numbers identified by a rule or pattern 12. a formula that represents any term in a sequence 13. a function that maps real numbers to real numbers 14. a function whose graph is made up of separate points that are not connected 15. a formula by which each term of a sequence is generated from the preceding term or terms 16. a triangular arrangement of numbers with rows starting and ending with ones and all interior numbers derived by adding two values from the row above 17. a sequence where there is a common difference between consecutive terms 18. a sequence where there is a common ratio between consecutive terms 19. the sum of the terms of a sequence in which the terms have a common difference 20. the sum of the terms of a sequence in which the terms have a common ratio Short Answer [Thinking 10 marks] Show all calculations using proper mathematical notations. Simplify and justify your solutions. 21. Find the value of a given Sg = -3280 and r= -3. Be sure to show all of your work. [2 marks] Page 2 of 423. For the arithmetic sequence -8, -5, -2, 1, ..., determine i) the value of a and d [2 marks] ii) an explicit formula for the general term [1 mark] iii) $20 [1 mark] Page 3 of 4Full Name: Date: MCR3U1 Problem Solving [Application 10 marks] Show all calculations in organized manner using proper mathematical notations. Simplify and justify your solutions whenever possible. 24. The first prize in a lottery is $250 000. Each winner chosen after the first is paid 20% as much as the winner before them. a) Determine a and r for a geometric sequence that represents this situation. [2 marks] b) Determine an explicit formula for the general term. [1 mark] c) Determine a formula for the sum of n terms of the geometric sequence. [1 mark] d) If 5 winning numbers are chosen, how much will i) the last person chosen be paid? [2 marks] ii) have been paid out in the lottery? [2 marks] 1 15 73 25. For the sequence,, 3' 11 ' 13' 5' , ... , determine i) an explicit formula for the nth term, using function notation [1 mark] i) $1 [1 mark]