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sample test3

# sample test3 - Math 1ZZ5 1st Sample Test#3 Name(Last...

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Math 1ZZ5 1st Sample Test #3 Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test consists of 16 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. Solve the initial value problem ÐB BÑC  C œ B / CÐ/Ñ œ " ln w# B (a) (b) B/ "/ BB / ÐB"Ñ"/ Ð/"Ñ B/ " ln (c) (d) B/ ÐB"Ñ"/ Ð/"Ñ / ÐB"Ñ"/ Ð/"Ñ " ln ln (e) / ÐB "Ñ"/ Ð/ "Ñ B B# /# ln 2. Find an equation of the curve that passes through the point and whose slope at any Ð"ß "Ñ point on the curve is . ÐBßCÑ \$C#B'BC" (a) (b) Cœ Ð#/ "Ñ \$Ñ "" \$& \$ÐBB Ñ' \$ÐBB Ñ' ## (c) (d) Cœ Ð\$/ %\$ \$ÐBB Ñ' \$ÐBB Ñ (e) " \$ ÐBB Ñ# # 3. Find the orthogonal trajectories of the family of curves " ÐB  5Ñ \$ (a) (b) (c) BG ˆ‰ (* ( \$( * *Î( (Î\$ (Î\$ (d) (e) *( \$Î( \$Î( 4. Convert the polar equation to Cartesian coordinates. < œ #Ð"  Ñ cos ) " (a) (b) (c) (d) (e) BœC # B C œ# Cœ%B\$ Bœ ÐC %Ñ Bœ%C% # # " % 5. Find a set of polar coordinates for with negative . Ð#ß #Ñ < (a) (b) (c) (d) Ð# #ß Ñ Ð# Ñ Ð# #ß  Ñ Ð# #ß  Ñ ÈÈ È È 11 1 1 %% % % \$\$ (e) Ð# #ß  Ñ È \$ # 1

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6. Sketch the polar curve . <œ # ß !Ÿ Ÿ% )1
7. Sketch the graph of the function . 0ÐBß CÑ œ ÐB  %B  %C  %C  &Ñ " # ## ln

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8. Draw a contour plot of . 0ÐBßCÑ œ ÐC"# ln sin
9. Sketch the parametric curve . B œ >ß C œ >ß ! Ÿ > Ÿ # È sin 1 10 20 30 1.0 0.5 0 0.5 1.0 0.5 1.0 1.5 2.0 2.5 1.0 0.5 0 0.5 1.0 10 20 30 1.0 0.5 0 0.5 1.0 (a) (b) (c) 0.5 1.0 1.5 2.0 2.5 1.0 0.5 0 0.5 1.0 50 100 150 200 1.0 0.5 0 0.5 1.0 (d) (e) 10. Find the cartesian equation of the parametric curve .

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sample test3 - Math 1ZZ5 1st Sample Test#3 Name(Last...

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