Free Printable DISCRETE MATH CHALLENGE

1.

State the degree of vertex G

a)

2

b)

4

c)

5

d)

3

2.

Is G-F-D-F-B a path?

a)

No

b)

Yes

3.

Determine whether the following graphs are isomorphic or not.

a)

Yes

b)

No

4.

Does Euler circuit exist in this graph?

a)

Yes

b)

No

5.

Does Hamilton circuit exist in this graph?

a)

Yes

b)

No

6.

What is the ancestor of Q?

a)

Q,T,A,B

b)

P,T,A,B

c)

T,A,B

d)

R,A,B

7.

What is the descendent of S?

a)

N,M,K

b)

B

c)

T,P,Q

d)

N,M,K,L

8.

Find the shortest path .

a)

11

b)

10

c)

12

d)

13

9.

Draw a binary search tree from the word FRUIT.

a)

b)

c)

d)

10.

Draw a binary search tree from the sentence “I like to dance and drawing”.

a)

b)

c)

d)

11.

Draw a binary search tree from The sequence number 21, 7, 5, 11, 8, 15

a)

b)

c)

d)

12.

Find the pre order for the following tree.

a)

A,B,D,E,I,H,C,F,G,J,K

b)

A,B,D,E,H,I,C,F,G,J,K

c)

A,B,,C,D,E,F,G,H,I,J,K

d)

A,B,D,E,H,I,C,F,G,K,J

13.

Find the in order for the following tree.

a)

D,B,H,E,I,A,F,C,J,K,G

b)

B,D,H,E,I,A,F,C,J,G,K

c)

D,B,H,E,I,A,F,C,J,G,K

d)

D,B,H,E,I,A,C,F,J,G,K

14.

Find the post order for the following tree.

a)

D,H,I,E,B,F,J,K,G,A,C

b)

H,I,E,D,B,F,J,K,G,C,A

c)

D,H,I,E,B,F,J,K,G,C,A

d)

D,H,I,E,B,J,F,K,G,C,A

15.

Find the pre order for the following tree.

a)

G,R,K,N,W,M,F,T

b)

G,R,K,N,W,M,T,F

c)

G,R,N,K,W,M,F,T

d)

G,R,K,N,W,M,T,F

16.

Given $\xi=\left\{x:5\le x\le20\ and\ x\ is\ an\ integer\right\}$
P = {6,8,10,12,14,16,18,20}

Q = {5,6,7,8,9,10,11}
R= {5,7,9,11,13,15,17,19}

Find R-Q

a)

{6,8,10}

b)

{6,8,10,13,15,17,19}

c)

{13,15,17,19}

d)

{11,13,17,19}

17.

Given $\xi=\left\{x:5\le x\le20\ and\ \ x\ is\ an\ integer\right\}$
P = {6,8,10,12,14,16,18,20}

Q = {5,6,7,8,9,10,11}

R= {5,7,9,11,13,15,17,19}

Find $P\cap Q$

a)

{5,6,8,10}

b)

{6,8,10}

c)

{5,7,11}

d)

{12,14,16,18,20}

18.

Given $\xi$ = {1,2,3,4,5,6,7,8,9,10}
F = { x : x is an odd number}

M = (x : x is a prime number}

Find

\left(F\cup M\right)'

a)

{4,5,6,7,9}

b)

{2,4,6,8,10}

c)

{2,3,4,5,6}

d)

{4,6,8,10}

19.

a)

{g,i,k,m}

b)

{b,d}

c)

{b,d,g,I,k,m}

d)

{a,c,e}

20.

The number of elements in sets P, Q and R are shown in the Venn diagram above. Given that $n\left(R\right)=n\left(P\cap Q\right)$ , find the value of x.

a)

-3

b)

4

c)

1

d)

-1

21.

Consider the following directed graph, determine whether these relations are reflexive, symmetric and/or transitive.

a)

Not Reflexive, Not symmetric, Transitive

b)

Not Reflexive, symmetric, Not Transitive

c)

Not Reflexive, Not symmetric, Not Transitive

d)

Not Reflexive, symmetric, Transitive

22.

Consider the following directed graph, determine whether these relations are reflexive, symmetric and/or transitive.

a)

Reflexive, Not symmetric, Transitive

b)

Reflexive, symmetric, Transitive

c)

Reflexive, Not symmetric, Not Transitive

d)

Reflexive, symmetric, Not Transitive

23.

Consider the following directed graph. Which of the following is a correct ordered pair?

a)

({1,1}, {1,2}, {3,4}, {3,2}, {3,3}, {4,1}, {4,3}, {4,4})

b)

({1,1}, {1,2}, {2,1}, {2,2}, {3,4}, {3,2}, {3,3}, {4,1})

c)

({1,1}, {1,2}, {1,3}, {2,4}, {3,2}, {4,1}, {4,2}, {4,4})

d)

({1,1}, {1,2}, {1,3}, {2,4}, {3,2}, {3,4}, {4,1}, {4,4})

24.

Consider the following directed graph, determine whether these relations are Equivalent Relation or not.

a)

Yes

b)

I don’t know

c)

I am not sure

d)

No

25.

What is the definition of SYMMETRIC?

a)

A relation R on a set A is called symmetric if (a,b) ∈ R and (b,c) ∈ R then (a,c) ∈ R

b)

A relation R on a set A is called symmetric if (a,b) ∈ R, then (b,a) ∈ R

c)

A relation R on a set A is called symmetric if (a,a) ∈ R for all a ∈ A

d)

A relation R on a set A is called symmetric if (a,b) ∈ R

26.

A function is defined as a relation in which every element in the domain has a unique image. In other words, a function is….?

a)

Many to One and One to Many relations.

b)

Many to Many and Many to One relations.

c)

One to one and One to Many relations.

d)

One to One and Many to One relations.

27.

Given that $f\left(x\right)=-3x$ and $g\left(x\right)=x^2$ , find the answer for $gf\left(x\right)$

a)

$-9x^2$

b)

$9x^2$

c)

$-3x^2$

d)

$-6x^2$

28.

Given that $h\left(x\right)=-2x+1$ find the answer for $h^{-1}\left(3\right)$

a)

-1

b)

1

c)

4

d)

0

29.

Find the value of $\lfloor\lceil-3.2\rceil+\lfloor4.05\rfloor-1.1\rfloor$

a)

-2

b)

1

c)

0

d)

-1

30.

Find the range for this function.

a)

{2,3,5}

b)

{-2,2,3,5}

c)

{4,9,25}

d)

{4,9,10,25}

31.

All of Richard’s juices are either made by Orange flavor or Mango flavor, and he has 48 bottles of Orange juice and 24 bottles of Mango juice. If he wants to drink only one bottle of juice, how many choices does Richard have all together?

a)

1152

b)

336

c)

72

d)

48

32.

There are 21 novels and 18 volumes of poetry on a reading list for a college English course. How many different ways can a student select one novel and one volume of poetry to read?

a)

378

b)

143640

c)

39

d)

7560

33.

Syukor wants to go to Pulai. He can choose from 3 bus services or 2 train services to head from his home to Johor Bahru. From there, he can choose from another 2 bus services or 3 train services to head to Pulai. How many ways are there for Syukor to get to Pulai?

a)

36

b)

25

c)

12

d)

10

34.

Calculate the number of permutations of 6 different objects, taken 2 at a time.

a)

12

b)

15

c)

30

d)

50

35.

Calculate the number of arrangements of any three letters from the word “FRAGMENT”.

a)

40320

b)

336

c)

6

d)

512

36.

Four-digit odd numbers less than 7000 are to be formed from the digits 2, 4, 6, 7, 8 and 9, without repetitions. How many numbers that can be formed?

a)

72

b)

48

c)

18

d)

180

37.

7 boys and 3 girls are to be seated in a row. Calculate the number of ways they can be seated if the 3 girls want to be seated together.

a)

720

b)

30240

c)

210

d)

241920

38.

A committee that consists of 6 teachers is to be chosen from 7 male teachers and 5 female teachers. Find the number of different committees that can be formed if there is no restriction.

a)

924

b)

720

c)

665280

d)

462

39.

A tennis team that consists of 8 students is to be chosen from a group of 8 Form Four students and 6 Form Five students. Calculate the number of teams that can be formed if the team must consist of exactly 5 Form Four students.

a)

56

b)

336

c)

840

d)

1120

40.

Jack wants to choose 7 CDs from 5 local CDs and 9 foreign CDs. Calculate the number of different choices if his choices must have at least 3 local CDs.

a)

2940

b)

1716

c)

2976

d)

1723

DISCRETE MATH CHALLENGE

Total questions: 40

Worksheet time: 40mins

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