Free Printable MTH 322

1.

When using mathematical induction to prove : $\sum_{i=1}^ni^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ . In step #2, after you have made your assumption, what are you trying to prove? (What is your goal?)

a)

$\sum_{i=1}^{k+1}i^2=\frac{\left(k\right)\left(k+1\right)\left(2k+1\right)}{6}+\left(k+1\right)^2$

b)

$S_{k+1}=\frac{k\left(k+1\right)\left(2k+1\right)}{6}$

c)

$\sum_{i=1}^{k+1}i^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$

d)

$S_{k+1}=\left(k+1\right)^2$

2.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²
On the basis of this assumption,
[The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]
What must we show?

a)

The statement is true for n = 1:
2x1 − 1 = 1²

b)

The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

c)

The statement is true for n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

3.

The sum of the first n odd numbers is equal to the n^th square.
1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

To prove this by mathematical induction, what will be the induction assumption?

a)

The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

b)

The statement is true for n = 1:
2x1 − 1 = 1²

c)

The statement is true for n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

4.

The second part (If the statement is true for n = k, then it will be true for its successor, k + 1) contains the induction assumption. What is it?

a)

If the statement is true for n = k, then it will be true for its successor, k + 1.

b)

The statement is true for n = k.

c)

The statement is true for n = k+1.

5.

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the second?

a)

The statement is true for n = k+1.

b)

If the statement is true for n = k, then it will be true for its successor, k + 1.

c)

The statement is true for n = 1.

d)

The statement is true for n = k.

6.

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the first?

a)

The statement is true for n = 1.

b)

The statement is true for n = k.

c)

The statement is true for n = k+1.

7.

What property is this?
15 ⋅ 1

a)

Identity

b)

Distributive

c)

Associative

d)

Communitive

8.

What property is this?
3 x 8 x 5b = 5b x 3 x 8

a)

Identity

b)

Distributive

c)

Associative

d)

Communitive

9.

True Or False:
This is Communitive Property
(4x + 2x) + 7x = 4x + (2x + 7x)

a)

True

b)

False

10.

What property is this?
2x²(3y) = 3y(2x²)

a)

Identity

b)

Distributive

c)

Associative

d)

Communitive

11.

What property is this?
2x(5 + y) = 10x + 2xy

a)

Identity

b)

Distributive

c)

Associative

d)

Communitive

12.

True Or False:
This is Distributive Property
2x(5 + y) = 10x + 2xy

a)

True

b)

False

13.

True Or False:
This is Identity Property
(4x + 2x) + 7x = 4x + (2x + 7x)

a)

True

b)

False

14.

Which one of these is Identity Property

a)

13 x 1

b)

2x(5 + y) = 10x + 2xy

c)

2x(191 + y) = 13x + 2xy

d)

3

15.

Which one of these is communitive Property

a)

13 x 1

b)

2x(5 + y) = 10x + 2xy

c)

3 x 8 x 5b = 5b x 3 x 8

d)

3

16.

Which one of these is Distributive Property

a)

13 x 1

b)

2x(5 + y) = 10x + 2xy

c)

2x(191 + y) = 13x + 2xy

d)

2x(5 + y) = 10x + 2xy

17.

Statement 1: Mango is a fruit.

Statement 2: The box is full of fruits.

Conclusion: The box is full of mangoes.

a)

Inductive reasoning

b)

Deductive reasoning

c)

Inductivity

d)

Deductivity

18.

Statement 1: All mangoes are a fruits.

Statement 2: All fruits have seeds.

Conclusion: Mangoes have seeds.

a)

Inductive reasoning

b)

Deductive reasoning

c)

Inductivity

d)

Deductivity

19.

Inductive Reasoning means...

a)

Guessing

b)

Testing and observing patterns to make conjectures

c)

Explaining why

d)

Ura nok seblu!

20.

A process that includes looking for patterns and making conjectures is called _______________________.

a)

Inductive Reasoning

b)

Deductive Reasoning

c)

Conjecture

d)

Conditional Statement

21.

A process that uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

a)

Deductive Reasoning

b)

Inductive Reasoning

c)

Conjecture

d)

Proof

22.

Which equation shows an example of the Multiplicative Inverse Property?

a)

89 x 0 = 0

b)

89 x 1/89 = 1

c)

8 + -8 = 0

d)

8 x 1 = 8

23.

Which equation is NOT an example of the Additive Inverse Property?

a)

0 = 5 + -5

b)

w + -w = 0

c)

6 x 1/6 = 1

d)

6 + -6 = 0

24.

Which equation is an example of the Commutative Property of Addition?

a)

4 + 5 + 6 = ( 4 + 5 ) + 6

b)

4( 5 + 6 ) = 4(5) + 4 (6)

c)

4 + 5 + 6 = 5 + 4 + 6

d)

( 4 + 5 ) + 6 = 4 + ( 5 + 6 )

25.

What is the property shown in this equation?
8(5 + 3) = 8(5) + 8(3)

a)

Associative Property of Addition

b)

Commutative Property of Addition

c)

Additive Identity Property

d)

Distributive Property

26.

Are these two expressions equivalent?
2 • (3 • 7) and (2 • 3) • 7

a)

Yes, because of the associative property

b)

Yes, because of the commutative property

c)

Yes, because of the distributive property

d)

No, these two expressions are not exquivalent

27.

Are these two expressions equivalent?
40 ÷ 10 and 10 ÷ 40

a)

Yes, because of the associative property

b)

Yes, because of the commutative property

c)

Yes, because of the distributive property

d)

No, these two expressions are not equivalent

28.

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

a)

{-4, -3, -2, -1, 0, 1, 2, 3}

b)

{-3, -2, -1, 1, 2, 3}

c)

{-4, -3, -2, -1, 1, 2, 3, 4}

d)

{-4, -3, -2, -1, 1, 2, 3}

29.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

30.

What does this symbol ( ∪ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

31.

Let A = {3, 6, 9, 12, 15} and B = {4, 8, 12, 16}. Which of the following is true about the two sets?

a)

A\cup B=\left\{12\right\}

b)

$A\cap B=\left\{3,\ 4,\ 6,\ 8,\ 9,\ 12,\ 15,\ 16\right\}$

c)

$A-B=\left\{3,\ 6,\ 9,\ 15\right\}$

d)

$A-B=\left\{4,\ 8,\ 16\right\}$

32.

The set S = {fever, dry cough, tiredness} list the common symptoms of COVID-19. What is the cardinality of this set?

a)

3

b)

4

c)

5

d)

6

33.

What is the cardinality of $\phi$ ?

a)

0

b)

1

c)

Empty set

d)

None

34.

If T = {different types of triangles} and Q = {different type of quadrilaterals}, then which of the following is the most suitable for Universal set?

a)

U = {x | x is a plane figure}

b)

U = { x | x is a shape}

c)

U = { x | x is a polygon}

d)

U = { x | x is a figure}

35.

Let K be the set of the letters in the sentence 'Keep safe'. How do you write this set correctly using the Roster Method?

a)

K = {k, e, e, p, s, a, f, e}

b)

K = {k, e, p, s, e, f}

c)

K = {k, e, e, p, s, a, f}

d)

K = {k, e, p, s, a, f}

36.

Which of the following cannot be considered a subset of H = {h, e, a, l, t, h, y}?

a)

W = {h, e, a, l, t, h, y}

b)

M = { }

c)

F = {h, e, a, t}

d)

R = {h, e, a, r, t}

37.

Let O = {1, 3, 5, 7, 9, 11, 13, 15} and P = {1, 2, 3, 5, 7, 11, 13}. Find $O-P$ .

a)

$O-P=\left\{1,\ 2,\ 3,\ 5,\ 7,\ 9,\ 11,\ 13,\ 15\right\}$

b)

$O-P=\left\{1,\ 3,\ 5,\ 7,\ 11,\ 13\right\}$

c)

$O-P=\left\{9,\ 15\right\}$

d)

$O-P=\left\{2\right\}$

38.

Which of the following is a well-defined set?

a)

A set of delicious dishes.

b)

A set of world continents.

c)

A set of male president.

d)

A set of tall classmates.

39.

Which of the following describes the set M = {8, 16, 24, 32,40}

a)

A set of numbers between 8 to 40.

b)

A set of even numbers from 8 to 40.

c)

A set of numbers divisible by 8.

d)

A set of multiples of 8 from 8 to 40.

40.

Which of the following is not an example of One-to-one function?

a)

Relationship of husband and wife.

b)

Students to teachers.

c)

Flag to countries.

d)

individual to his fingerprints

41.

Which of the following is an example of One-to-one function?

a)

Student to his LRN.

b)

Cookbook to menu.

c)

Cellphone to Sim Card

d)

Tree to its leaves.

42.

which of the following is a graph of one-to-one function?

a)

b)

c)

d)

43.

Determine whether the following function is one-to-one.

f = {(1, 2), (3, 4), (5, 6), (8, 6), (10, -1) (11, 9) (12, -2)}

a)

The function is one-to-one because one unique element from its domain is assigned to an exactly one element in the co-domain.

b)

The function is one-to-one since the ordered pairs (5, 6) and (8, 6) have different first coordinates and the same second coordinate.

c)

The function is not one-to-one since the ordered pairs (5, 6) and (8, 6) have different first coordinates but has the same second coordinate.

d)

The function is not one-to-one because for every y, there is a unique x.

44.

Check if the function g : R → R defined by g(x) = x² is an onto function or not.

a)

The function is onto function because every element in the co-domain is assigned to an element in the domain.

b)

The function is onto function because the range of the function is equal to the co-domain.

c)

The function is not onto function because not all elements of the co-domain is assigned to an element in the domain.

d)

The function is not onto function because there are elements in the domain that is assigned to more than one element in the co-domain.

45.

Given that y: N→N, y(x)= x+3 . Determine whether the following function is One-to-one and onto, One-to-one but not onto, Onto but not one-to-one, or Neither one-to-one nor onto function.

a)

One-to-one and onto, because every element x that is a natural number has a corresponding unique natural number y-value.

b)

One-to-one but not onto, because it does not have any element x such that equal to 2.

c)

Onto but not one-to-one, because if y(x)= y(-3) and y(0), they have the same value.

d)

Neither one-to-one nor onto, because every element x that is a natural number has multiple natural number values. Also, it does not have any element x such that equal to 2

46.

Choose the correct statement(s)

A. If the horizontal line test intersects the graph of the function more than once, then the function is not one-to-one.

B. If the horizontal line test intersects the graph of the function once, then the function is one-to-one.

C. An onto function is a function whose image is equal to its codomain. Also, the range and domain of an onto function are equal.

D. An onto function is a function whose image is equal to its codomain. Also, the range and codomain of an onto function are equal.

a)

C only

b)

D only

c)

A,B and D

d)

A,B and C

47.

Which of the following shows an onto function?

a)

b)

48.

In using the Cayley Table, what is the identity element if you are working with group operation addition for a group of integers?

a)

0

b)

1

c)

i

d)

-1

49.

What type of set is denoted as either { } or ∅?

a)

Universal Set

b)

Empty (or Null) Set

c)

Disjointed Set

d)

Complement of a Set

50.

Given that a and b are in set S, then the property stating a b = b a is called as ____________.

a)

commutative

b)

associative

c)

binary operation

d)

isomorphic

MTH 322

Total questions: 50

Worksheet time: 4hrs 10mins

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