Math Test Three! - Math 1ZA3 1st Sample Test #3 Name:_...

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Math 1ZA3 1st Sample Test #3 Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test consists of 24 multiple choice questions worth 1 mark each (no part marks), and 1 question worth 1 mark (no part marks) on proper computer card filling. All questions must be answered on the COMPUTER CARD with an HB PENCIL. Marks will not be deducted for wrong answers (i.e., there is no penalty for guessing). You are responsible for ensuring that your copy of the test is complete. Bring any discrepancy to the attention of the invigilator. Calculators are NOT allowed. 1. Find if , , . 0Ð"Ñ 0 Ð>Ñ œ $Î > 0Ð%Ñ œ #! 0 Ð%Ñ œ ( ww w (a) (b) (c) (d) (e) &'()* 2. Find if 0Ð Ñ 0 ÐBÑ œ B B 1 $ w sec tan B 0 Ð ! Ñ œ # sec # , . (a) (b) (c) (d) (e) # # " # $ $ $  " $ 3. Evaluate lim 8Ä∞ 3œ" 8 #$ 3 & 3 88 8 $    # (a) (b) (c) (d) (e) %& & "& %& %& %# 4. If you were to use use Mathematical Induction to show that , which of the 3œ" 8 # 8Ð8"ÑÐ#8"Ñ ' following would be the second step? (a) Assume  3œ" 3œ" 55 ## 5Ð5"ÑÐ#5"Ñ Ð5"ÑÐ5#ÑÐ#5$Ñ '' Ð 3" Ñœ , and show that (b) Assume 3œ" 3œ" " 5Ð5"ÑÐ#5"Ñ Ð5"Ñ5Ð#5"Ñ , and show that (c) Assume 3œ" 3œ" " 5Ð5"ÑÐ#5"Ñ Ð5"Ñ5Ð#5"Ñ , and show that (d) Assume 3œ" 3œ" " 5Ð5"ÑÐ#5"Ñ Ð5"ÑÐ5#ÑÐ#5$Ñ , and show that (e) Assume 3œ" 3œ" " 5Ð5"ÑÐ#5"Ñ Ð5"ÑÐ5#ÑÐ#5$Ñ , and show that 5. Write the following sum in sigma notation: . $& ( " ( %*" ' ) "  â (a) (b) (c) (d) (e)  3œ" 3œ" 3œ! 3œ" 3œ" ())) 8 Ð#3"Ñ Ð#3"Ñ Ð#3"Ñ Ð#3"Ñ Ð3"Ñ Ð3"Ñ Ð3"Ñ Ð3"Ñ Ð3"Ñ #3 #####
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6. Scientists can determine the age of ancient objects by a method called . Radiocarbon dating The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, carbon-14, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates carbon-14 through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of carbon- 14 begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 74% as much carbon-14 radioactivity as does plant material on earth today. Estimate the age of the parchment. (a) (b) (c) years years years  "# # # $(ÎÐ&!†&($!Ñ &($! &($! ln ln ln ln $( $( &! &! (d) (e) years years &($! &($! ln ln ln ln $( $( &! &! ## 7. Consider the sequence defined by . To show that this sequence is +œ" ß+ œ "8 " " $+ 8 monotonic using induction, which of the following would be the second step?
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Math Test Three! - Math 1ZA3 1st Sample Test #3 Name:_...

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