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Discrete Math Practice Test: answer key

Every answer, with a link to its step-by-step solution

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#AnswerLessonSolution
1B Not equivalentEquivalent statementsSolved step by step
2B Not equivalentEquivalent statementsSolved step by step
3B Not equivalentEquivalent statementsSolved step by step
42(a + b)Direct proofSolved step by step
52(2ab + a)Direct proofSolved step by step
616abDirect proofSolved step by step
72(2a2 + 2a) + 1Proof by contrapositiveSolved step by step
82(2ab + a + b) + 1Proof by contrapositiveSolved step by step
92(4a3 + 6a2 + 3a + 3)Proof by contrapositiveSolved step by step
10(k2 + 3k + 2)/2Proof by inductionSolved step by step
11(3k2 + 7k + 4)/2Proof by inductionSolved step by step
124 × 2k − 2Proof by inductionSolved step by step
135(6m + 1)InductionSolved step by step
148(9m + 1)InductionSolved step by step
154(5m − 7)InductionSolved step by step
162RemaindersSolved step by step
17C 4RemaindersSolved step by step
18A YesRemaindersSolved step by step
19B 1Powers mod n, last digitsSolved step by step
20A 9Powers mod n, last digitsSolved step by step
214Powers mod n, last digitsSolved step by step
22A gcd(48, 18) = 6Euclid's algorithmSolved step by step
23B gcd(210, 154) = 14Euclid's algorithmSolved step by step
24gcd(161, 28) = 7Euclid's algorithmSolved step by step
25a_n = 2 × 5nSolving recurrencesSolved step by step
26a_n = 4n − 1Solving recurrencesSolved step by step
27−5n + 5Solving recurrencesSolved step by step
28a_n = 2n + 3nSecond-order recurrencesSolved step by step
29a_n = 2n + 6nSecond-order recurrencesSolved step by step
30a_n = 2 × 4n + n × 4nSecond-order recurrencesSolved step by step
31A, B, C, AEuler pathsSolved step by step
32A, B, C, D, E, C, AEuler pathsSolved step by step
33A, B, C, D, E, C, AEuler pathsSolved step by step

Grade

Count your right answers and divide by the number of questions: A 90% or more, B 80%, C 70%, D 60%, F below 60%.