Mathematics Magazine for Grades 112 



122004 



Grade 11
Theory:Graphs
Solutions from the Previous Issue:1. Find the tenth term of the arithmetic sequence 2,5,8,.. Solution: The nth term of an arithmetic sequence is given by: a_{n} = a_{1} + (n  1)∙d By subtracting any given term from the following term we find that the common difference is d = 3. From the terms given, we know that the first term is a_{1 }= 2. From the statement of the problem the desired term is the tenth, or n = 10 Thus we find that the tenth term is: a_{10} = 2 + (10 
1)∙3 = 29 2. Find the common difference between successive terms of the arithmetic sequence for which the first term is 5 and the 32^{nd} term is –119. Solution: The nth term of an arithmetic sequence is given by: a_{n} = a_{1} + (n  1)∙d (1) We are to find d given that a_{1} = 5 and a_{32} =  119, and n = 32. Substitution in (1) gives: 119 = 5 + (32 –1) d d =  4 3. How many numbers between 10 and 1000 are divisible by 6? Solution: We must first find the smallest and tle largest numbers in this range that are divisible by 6. These numbers are 12 and 996. The common difference between one multiple of 6 and the next is 6. Thus we can solve this as and arithmetic sequence a_{n} = a_{1} + (n  1)∙d (1) with a_{1} = 12 and a_{n} = 966 and d = 6. Substituting in equation (1) we have: 996 = 12 + (n  1) ∙ 6; 996 = 12 + 6n  6; 996 = 6 + 6n; 990 = 6n n =165 4. Find the sum of the first 1000 positive integers. Solution: The sum of the first n terms of an arithmetic sequence is:
a_{1000 }= 1000; n = 1000; d = 1 = 500500 Proposed Problems:
1. The cost of a longdistance phone call from Toronto to New York City is 69 cents for the first minute and 58 cents for each additional minute (or part of a minute). Draw the graph of the cost C (in dollars) of the phone call as a function of the time t ( in minutes). 2. If and find the function f + g, f – g 3. If f(x) = x^{2 }and g(x) =x – 3 find the composite functions f ^{o} g and g ^{o} f and their domains 4. If and find the function F= f ^{o} g


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