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Discrete Math Practice Test: printable

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Discrete Math Practice Test

Name: ______________________   Date: __________   Score: ____ / 33

33 questions. Calculator allowed. Show your working. steplyclass.com/discrete-math/practice-test/

  1. 1

    Are p -> q and q -> p equivalent
    1. A) Equivalent
    2. B) Not equivalent

  2. 2

    Are p -> q and ~p -> ~q equivalent
    1. A) Equivalent
    2. B) Not equivalent

  3. 3

    Is (p and q) -> r equivalent to (p -> r) and (q -> r)
    1. A) Equivalent
    2. B) Not equivalent

  4. 4

    Prove the sum of two even numbers is even

    Answer: ____________________

  5. 5

    Prove the product of an even number and an odd number is even

    Answer: ____________________

  6. 6

    Prove the product of two multiples of 4 is a multiple of 16

    Answer: ____________________

  7. 7

    Prove if n2 is even, then n is even

    Answer: ____________________

  8. 8

    Prove if xy is even, then x is even or y is even

    Answer: ____________________

  9. 9

    Prove if n3 + 5 is odd, then n is even

    Answer: ____________________

  10. 10

    Prove 1 + 2 + ... + n = n(n + 1)/2 by induction

    Answer: ____________________

  11. 11

    Prove 2 + 5 + 8 + ... + (3n − 1) = n(3n + 1)/2 by induction

    Answer: ____________________

  12. 12

    Prove 2 + 4 + 8 + ... + 2n = 2n + 1 − 2 by induction

    Answer: ____________________

  13. 13

    Prove 6n − 1 is divisible by 5 by induction

    Answer: ____________________

  14. 14

    Prove 32n − 1 is divisible by 8 by induction

    Answer: ____________________

  15. 15

    Prove 5n + 7 is divisible by 4 by induction

    Answer: ____________________

  16. 16

    Calculate 17 mod 5

    Answer: ____________________

  17. 17

    Calculate −20 mod 6
    1. A) −20
    2. B) −4
    3. C) 4

  18. 18

    Is −4 ≡ 11 (mod 5)
    1. A) Yes
    2. B) No

  19. 19

    Calculate 3100 mod 5
    1. A) 9
    2. B) 1
    3. C) 4
    4. D) 3

  20. 20

    Last digit of 977
    1. A) 9
    2. B) 81
    3. C) 1

  21. 21

    Last digit of 4777

    Answer: ____________________

  22. 22

    Calculate gcd(48, 18) by Euclid's algorithm
    1. A) gcd(48, 18) = 6
    2. B) gcd(48, 18) = 12
    3. C) gcd(48, 18) = 48
    4. D) gcd(48, 18) = 18

  23. 23

    Calculate gcd(210, 154) by Euclid's algorithm
    1. A) gcd(210, 154) = 154
    2. B) gcd(210, 154) = 14
    3. C) gcd(210, 154) = 210
    4. D) gcd(210, 154) = 56

  24. 24

    Write gcd(161, 28) as 161x + 28y

    Answer: ____________________

  25. 25

    Solve a_n = 5a_(n-1), a_0 = 2

    Answer: ____________________

  26. 26

    Solve a_n = 4a_(n-1) + 3, a_0 = 0

    Answer: ____________________

  27. 27

    Solve a_n = a_(n-1) − 5, a_1 = 0

    Answer: ____________________

  28. 28

    Solve a_n = 5a_(n-1) − 6a_(n-2), a_0 = 2, a_1 = 5

    Answer: ____________________

  29. 29

    Solve a_n = 8a_(n-1) − 12a_(n-2), a_0 = 2, a_1 = 8

    Answer: ____________________

  30. 30

    Solve a_n = 8a_(n-1) − 16a_(n-2), a_0 = 2, a_1 = 12

    Answer: ____________________

  31. 31

    Euler path in the graph AB, BC, CA

    Answer: ____________________

  32. 32

    Euler path in the graph AB, AC, BC, CD, CE, DE

    Answer: ____________________

  33. 33

    Does the graph AB, BC, CA, CD, DE, EC have an Euler circuit

    Answer: ____________________

Answer key

  1. B Not equivalent
  2. B Not equivalent
  3. B Not equivalent
  4. 2(a + b)
  5. 2(2ab + a)
  6. 16ab
  7. 2(2a2 + 2a) + 1
  8. 2(2ab + a + b) + 1
  9. 2(4a3 + 6a2 + 3a + 3)
  10. (k2 + 3k + 2)/2
  11. (3k2 + 7k + 4)/2
  12. 4 × 2k − 2
  13. 5(6m + 1)
  14. 8(9m + 1)
  15. 4(5m − 7)
  16. 2
  17. C 4
  18. A Yes
  19. B 1
  20. A 9
  21. 4
  22. A gcd(48, 18) = 6
  23. B gcd(210, 154) = 14
  24. gcd(161, 28) = 7
  25. a_n = 2 × 5n
  26. a_n = 4n − 1
  27. −5n + 5
  28. a_n = 2n + 3n
  29. a_n = 2n + 6n
  30. a_n = 2 × 4n + n × 4n
  31. A, B, C, A
  32. A, B, C, D, E, C, A
  33. A, B, C, D, E, C, A

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