Discrete Math Practice Test
33 questions from 11 lessons · 100 minutes · percent score and grade · step-by-step answers
How it works
- 33 questions, about 100 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 9 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise these lessons next: the lessons of the questions you got wrong, with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
Formulas: the Discrete Math formula sheet.
1 Question 1
Are p -> q and q -> p equivalent- A) Equivalent
- B) Not equivalent
2 Question 2
Are p -> q and ~p -> ~q equivalent- A) Equivalent
- B) Not equivalent
3 Question 3
Is (p and q) -> r equivalent to (p -> r) and (q -> r)- A) Equivalent
- B) Not equivalent
4 Question 4
Prove the sum of two even numbers is evenType the answer.
5 Question 5
Prove the product of an even number and an odd number is evenType the answer.
6 Question 6
Prove the product of two multiples of 4 is a multiple of 16Type the answer.
7 Question 7
Prove if n2 is even, then n is evenType the answer.
8 Question 8
Prove if xy is even, then x is even or y is evenType the answer.
9 Question 9
Prove if n3 + 5 is odd, then n is evenType the answer.
10 Question 10
Prove 1 + 2 + ... + n = n(n + 1)/2 by inductionType the answer.
11 Question 11
Prove 2 + 5 + 8 + ... + (3n − 1) = n(3n + 1)/2 by inductionType the answer.
12 Question 12
Prove 2 + 4 + 8 + ... + 2n = 2n + 1 − 2 by inductionType the answer.
13 Question 13
Prove 6n − 1 is divisible by 5 by inductionType the answer.
14 Question 14
Prove 32n − 1 is divisible by 8 by inductionType the answer.
15 Question 15
Prove 5n + 7 is divisible by 4 by inductionType the answer.
16 Question 16
Calculate 17 mod 5Type the answer.
17 Question 17
Calculate −20 mod 6- A) −20
- B) −4
- C) 4
18 Question 18
Is −4 ≡ 11 (mod 5)- A) Yes
- B) No
19 Question 19
Calculate 3100 mod 5- A) 9
- B) 1
- C) 4
- D) 3
20 Question 20
Last digit of 977- A) 9
- B) 81
- C) 1
21 Question 21
Last digit of 4777Type the answer.
22 Question 22
Calculate gcd(48, 18) by Euclid's algorithm- A) gcd(48, 18) = 6
- B) gcd(48, 18) = 12
- C) gcd(48, 18) = 48
- D) gcd(48, 18) = 18
23 Question 23
Calculate gcd(210, 154) by Euclid's algorithm- A) gcd(210, 154) = 154
- B) gcd(210, 154) = 14
- C) gcd(210, 154) = 210
- D) gcd(210, 154) = 56
24 Question 24
Write gcd(161, 28) as 161x + 28yType the answer.
25 Question 25
Solve a_n = 5a_(n-1), a_0 = 2Type the answer.
26 Question 26
Solve a_n = 4a_(n-1) + 3, a_0 = 0Type the answer.
27 Question 27
Solve a_n = a_(n-1) − 5, a_1 = 0Type the answer.
28 Question 28
Solve a_n = 5a_(n-1) − 6a_(n-2), a_0 = 2, a_1 = 5Type the answer.
29 Question 29
Solve a_n = 8a_(n-1) − 12a_(n-2), a_0 = 2, a_1 = 8Type the answer.
30 Question 30
Solve a_n = 8a_(n-1) − 16a_(n-2), a_0 = 2, a_1 = 12Type the answer.
31 Question 31
Euler path in the graph AB, BC, CAType the answer.
32 Question 32
Euler path in the graph AB, AC, BC, CD, CE, DEType the answer.
33 Question 33
Does the graph AB, BC, CA, CD, DE, EC have an Euler circuitType the answer.