ICS 6D Gassko Final Exam

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May 7, 2024

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ICS 6D Gassko Final Exam TOTAL POINTS 57 / 71 QUESTION 1 1 Question 1 (a-b) 0 / 4 - 0 pts Correct ✓ - 2 pts for a), answer is incorrect. ✓ - 2 pts for b), answer is incorrect. QUESTION 2 2 Question 1 (c-e) 0 / 6 - 0 pts Correct ✓ - 2 pts for c), answer is incorrect. ✓ - 2 pts for d), answer is incorrect. ✓ - 2 pts for e), answer is incorrect. QUESTION 3 3 Question 2 2 / 4 - 0 pts Correct - 2 pts for the first question, the answer is incorrect. ✓ - 2 pts for the second question, the answer is incorrect. QUESTION 4 4 Question 3 3 / 3 ✓ - 0 pts Correct - 1 pts for the first blank, the answer is wrong. - 1 pts for the second blank, the answer is wrong. - 1 pts for the third blank, the answer is wrong. - 0.5 pts half points for the first blank QUESTION 5 5 Question 4 3 / 4 - 0 pts Correct ✓ - 1 pts for a), the answer is wrong - 1 pts for b), the answer is wrong - 1 pts for c), the answer is wrong - 1 pts for d), the answer is wrong QUESTION 6 6 Question 5 6 / 6 ✓ - 0 pts Correct - 1 pts In c), approach is correct, but there is calculation mistakes which leads to incorrect results. - 1 pts In d), approach is correct, but there is calculation mistakes which leads to incorrect results. - 2 pts In c), both approach and result is not correct. - 2 pts In d), both approach and result is not correct. - 1 pts In b), answer is not correct. - 1 pts In a), answer is not correct. QUESTION 7 7 Question 6 4 / 4 ✓ - 0 pts Correct - 1 pts a) is incorrect. - 1 pts b) is incorrect. - 1 pts c) is not correct. - 1 pts d) is incorrect. - 0.5 pts c): should simplify it. - 0.5 pts d): should simplify it. - 0.5 pts d): Should not include primes with zero exponents. - 0.5 pts a): Should not contain zero exponents. QUESTION 8 8 Question 7 3 / 3 ✓ - 0 pts Correct - 1 pts a) is not correct. - 1 pts b) is not correct. - 1 pts c) is not correct. - 0.5 pts a): approach is correct though calculation result is not correct. - 0.5 pts b): approach is correct though calculation result is not correct. - 0.5 pts c): approach is correct though calculation

result is not correct. QUESTION 9 9 Question 8 2 / 2 ✓ - 0 pts Graded by Preston - 0 pts Correct - 0.5 pts Algebra Error - 1 pts Minor conceptual error - 2 pts Completely incorrect QUESTION 10 10 Question 9 (a) 2 / 2 ✓ - 0 pts Graded by Casey - 1 pts N Incorrect - 1 pts Phi Incorrect QUESTION 11 11 Question 9 (b) 4.5 / 5 ✓ - 0 pts Graded by Preston - 0.5 pts Algebra Error/Minor error in EA - 1 pts EA completely incorrect - 0.5 pts One Equation Wrong - 1 pts Both equations Wrong - 1 pts Process Incorrect for 3 ✓ - 0.5 pts algebra error in 3 - 2 pts Process and Answers Incorrect for 3 - 0.5 pts Choose wrong coefficient for 4 - 1 pts Completely Incorrect for 4 QUESTION 12 12 Question 9 (c) 5 / 5 ✓ - 0 pts Graded by Casey - 1 pts Binary Representation Incorrect - 2 pts Terms Incorrect - 1 pts Terms Incorrect, but correct approach - 2 pts Final Value Inccorect - 1 pts Final Value Incorrect, but used correct terms QUESTION 13 13 Question 10 10 / 10 ✓ - 0 pts Graded by Casey - 0.5 pts Base Case Insufficient (i.e. didn't clearly evaluate left- and right-hand side) OR Started at n=1 instead of n=0 - 2 pts Base Case Incorrect - 0.5 pts Incorrect bounds on k in Inductive Hypothesis (e.g. missing k>=0). Note: "all positive integers" => k>= 1. - 2 pts Inductive Hypothesis Incorrect - 1 pts Trying to Prove Incorrect (k+1) - 2 pts Inductive Hypothesis Applied Inccorectly - 2 pts Insufficient Work Shown - 1 pts Did Not Arrive At Correct Final Answer - 0.5 pts Algebra Mistake - 2 pts Incorrectly Expanded Sum QUESTION 14 14 Question 11 3 / 3 ✓ - 0 pts Graded by Casey - 1 pts Bases Cases Incorrect - 0.5 pts Base Cases Partially Incorrect - 1 pts Recursive Call Coefficients Incorrect - 0.5 pts Wrong Sign on Recursive Call Coefficient - 1 pts Recursive Call Arguments Incorrect QUESTION 15 15 Question 12 9.5 / 10 ✓ - 0 pts Graded by Preston - 1 pts Only 1 Base Case or two wrong base cases - 2 pts No base cases correctly proven ✓ - 0.5 pts small error in IS - 1 pts Not strong induction IH, or IH incorrect - 1 pts Trying to Prove Incorrect - 3 pts IS completely Incorrect - 2 pts IH incorrectly applied - 2 pts Insufficient work shown in proof - 1 pts Didn't arrive at correct solution Page 2

Seat Assignment: Name (student to the left): Name (student to the right): Student ID Number: Name: _ Final Exam ICS 6D Winter 2018 March 19, 2018 Instructor: Irene Gassko Instructions • Wait until instructed to turn over the cover page. • Please print the names of the students to your immediate left and right on the provided lines. If your are at the end of a row you may leave the corresponding line blank. • There are questions on both sides. of the page. The back of the last page can be used for scratch work but will not be graded. • Special Instructions for this exam (please read carefully): - You can use any standard notation in your final answer, including P(n, k), C(n, k), (�), the factorial func- tion (n!), or standard arithmetic. You will get full credit as long as the expression evaluates to the correct answer. - Write your final answer on the provided line. You should have only one expression on the line for each question. We will score the question based only on the value of the expression on the line. - In all of the questions, the word "or" means the inclusive "or•;:

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