Free Printable Mock Test_6-2

1.

Which of the following numbers is/are rational number(s)

a)

18

b)

$\sqrt[]{21}$

c)

6/5

d)

2.625

2.

0.523666... is a/an

a)

integer

b)

natural number

c)

rational number

d)

irrational number

3.

2, 2x4, 8x4, 32x4, 128x4 ........ is a geometric sequence with a common ratio of 4.

a)

$U_n=U_1.\left(n+1\right)^d$

b)

$U_n=U_{n-1}+d$

c)

$U_n=U_1.\left(r\right)^n$

d)

$U_n=U_1.\left(r\right)^{n-1}$

4.

2, 4, 8, 16, 32, ....... is ?

a)

an arithmetico-geometric sequence

b)

a geometric sequence

c)

an arithmetic sequence

d)

a protomeric sequence

5.

What is the meaning of 'r' in a geometric sequence?

a)

It is the 'rational'

b)

It is the 'ration'

c)

It is the 'ratio'

d)

It is the 'relation'

6.

What is the sum formula (Sn) of a finite arithmetic sequence?

a)

$Something\ in\ between\ U_1\ and\ U_n$

b)

$Sn\ =\ n\ \left(U_1+U_n\right)$

c)

$Sn\ =\ \frac{n}{2\ }\ \left(U_1+\left(n-1\right)d\right)$

d)

$Sn\ =\ \frac{n}{2\ }\ \left(2U_1+\left(n-1\right)d\right)$

7.

U: 2, 4, 6, 8, 10.... is an arithmetic sequence with a common difference d=2. The $n^{th}-term$ formula is:

a)

$U_n=U_1-\left(n+1\right)d$

b)

$U_n=U_1+\left(n-1\right)^d$

c)

$U_n=U_1+\left(n-1\right)d$

d)

$U_n=U_p+\left(p-n\right)d$

8.

Is the sequence geometric? If so, identify the common ratio.

6, 12, 24, 48

a)

yes, 2

b)

yes, -2

c)

yes, 4

d)

no

9.

Find the next four terms of the arithmetic sequence 16, 24, 32,...

a)

40, 48, 56, 64

b)

36, 40, 44, 48

c)

35, 40, 45, 50

d)

40, 44, 50, 56

10.

What are the next four terms of the arithmetic sequence 122, 111, 100, ...?

a)

89, 78, 67, 56

b)

95, 90, 85, 80

c)

92, 88, 84, 80

d)

99, 88, 77, 66

11.

What type of sequence is this?

5, 9/2, 4, 7/2, 3, 5/2, 2

a)

Arithmetic sequence

b)

Arithmetic series

c)

Harmonic sequence

d)

Geometric sequence

12.

The sum of the first n terms of an arithmetic series is -85.5. The first term of the series is -27/3 and the common difference is 1/2. How many terms are in the series?

a)

16

b)

17

c)

18

d)

20

13.

What is the sum of the first 35 terms in an arithmetic series with the first term 18, common difference -12?

a)

770

b)

775

c)

870

d)

875

14.

Find the sum of the first 105 terms in an arithmetic series with the first term 95876 is 7, 271, 880. Find the last term?

a)

6998

b)

6754

c)

7168

d)

72636

15.

Find the sum of the first 15 terms in a geometric series with the first term 81, 920 and the ratio 1/2.

a)

32/3

b)

5

c)

18

d)

1589/3

16.

Find the sum of the first 20 terms in a geometric series with the first term 9 and the common ratio -1.

a)

-20

b)

20

c)

15

d)

415/2

17.

Find the sum of the the following series

2+6+18+54+....

a)

-1

b)

1

c)

infinity

d)

No sum

18.

Find the sum of the following sequence

9, 13.5, 20.25, 30.375, ...

a)

-18

b)

18

c)

No sum

19.

Find the sum of the following series

2+4/3+8/9+16/27+ ...

a)

So sum

b)

6

c)

-6

20.

Expand the summation.

a)

-1800

b)

-1818

c)

-1825

d)

-1795

21.

Expand and simplify

a)

802

b)

1002

c)

1396

d)

1755

22.

Expand and simplify if possible.

a)

b)

c)

d)

23.

Write the expression in sigma notation

a)

b)

c)

d)

24.

Expand the expression

a)

b)

c)

d)

25.

Expand the expression

a)

b)

c)

d)

26.

a)

b)

c)

d)

27.

How many terms are there in the expansion

a)

100

b)

97

c)

99

d)

101

28.

a)

b)

c)

d)

29.

Which number is next in the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 21...

a)

55

b)

34

c)

8

d)

1.62

30.

Which of the following is NOT an example of Fibonacci numbers found in nature?

a)

spirals on a sunflower

b)

pinecone spirals

c)

the number of petals on a daisy

d)

a mountain range

31.

What is the 20th number in the Fibonacci Sequence?

a)

1,234

b)

4,625

c)

5,765

d)

6,765

32.

What is one way to decide if two numbers follow a Fibonacci sequence?

a)

if their sum is the same as their difference

b)

if their ratio is approximately the golden ration

c)

if each number is prime

d)

if their product is approximately the golden ratio

33.

The length of a golden rectangle is approximately 8 cm. Which of the following measures could be the width of the rectangle?

a)

4cm

b)

10cm

c)

5cm

d)

16cm

34.

Find Fib 30

a)

832,240

b)

832,040

c)

562,823

d)

2,879

35.

Part of the Fibonacci Sequence is 1 , 1, 2 , 3, 5 8. Why is the five where it is in the sequence?

a)

Because 1+1+1+2=5

b)

Because 8-3=5

c)

Because 2+3=5

d)

Because 5 is after 4

36.

In a Fibonacci sequence, that is the next term of 610?

a)

987

b)

847

c)

653

d)

547

37.

What is the sum of the first 15 terms of Fibonacci sequence where the first term is 1?

a)

1,497

b)

1,597

c)

1,596

d)

1,237

38.

In the Fibonacci sequence ___, 55, 89, 144,... What is the missing term?

a)

34

b)

21

c)

13

d)

8

39.

What is the sum of Fib 20?

a)

16,011

b)

17,710

c)

17,711

d)

14,110

40.

What is the missing term 34,55, 89, 144, ____

a)

203

b)

233

c)

250

d)

345

41.

What is the sum of Fib 12?

a)

346

b)

356

c)

366

d)

376

42.

What is the approximate number for the Golden Ratio?

a)

1.1

b)

0.000465

c)

1.61913398875…

d)

1.61803398875…

43.

What is the 25th term of Fibonacci sequence if the first term is 1?

a)

55,025

b)

65,725

c)

75,025

d)

85,345

44.

Identify the prime numbers from the following list: 7, 12, 19, 25, 31

a)

2, 3, 5

b)

12, 25, 31

c)

11, 13, 17

d)

7, 19, 31

45.

Determine if 53 is a prime number or not

a)

No

b)

Maybe

c)

Yes

d)

Not sure

46.

Find the greatest common divisor of 24 and 36

a)

30

b)

12

c)

6

d)

18

47.

Calculate the greatest common divisor of 56 and 84

a)

14

b)

28

c)

42

d)

70

48.

Use prime factorization to find the GCD of 30 and 45

a)

20

b)

15

c)

10

d)

25

49.

Apply prime factorization to find the GCD of 72 and 90

a)

The GCD of 72 and 90 is 12.

b)

The GCD of 72 and 90 is 24.

c)

The GCD of 72 and 90 is 36.

d)

The GCD of 72 and 90 is 18.

50.

Apply the Euclidean algorithm to find the GCD of 48 and 60

a)

12

b)

24

c)

6

d)

36

51.

Use the Euclidean algorithm to find the GCD of 81 and 99

a)

9

b)

18

c)

27

d)

36

52.

Perform prime factorization of the number 120

a)

2^2 * 3 * 5

b)

2^4 * 3 * 5

c)

2^3 * 3^2 * 5^2

d)

2^3 * 3 * 5

53.

Find the prime factorization of the number 150

a)

3 * 3 * 5 * 5

b)

2 * 2 * 3 * 5

c)

2 * 2 * 2 * 3 * 3 * 5

d)

2 * 3 * 5 * 5

54.

Find the GCF for 40 and 48.

a)

2

b)

4

c)

8

d)

16

55.

Use a number tree to find the prime factorization of 105

a)

7x5x3

b)

11x5x3

c)

7x5x2x1

d)

7x5x3x2

56.

Sum of all composite numbers between 25 and 30.

a)

81

b)

78

c)

62

d)

87

57.

The common method used prime factorization method.

a)

Factor Tree Method

b)

Family Tree Method

c)

Exponential Method

d)

Multiplication Method

58.

Find the HCF of 50 and 70 using factor tree method

a)

5

b)

7

c)

10

d)

2

59.

What mathematical concept did Euclid prove in what is now known as the Fundamental Theorem of Arithmetic?

a)

The existence of prime numbers

b)

The uniqueness of prime factorization

c)

The sum of perfect numbers

d)

The properties of geometric series

60.

Steps in finding the LCM using Prime Factorization Method, except

a)

Find the quotient of these numbers with the highest powers is the LCM of the given numbers.

b)

Find the prime factors of the given numbers by repeated division method.

c)

Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power

d)

The product of these factors with the highest powers is the LCM of the given numbers.

61.

The following are the steps in finding the LCM using listing method, except

a)

List the first few multiples of A and B

b)

Mark the common multiples from the multiples of both numbers

c)

Select the Smallest common multiple, that lowest common multiple is the LCM of the numbers

d)

Select the Largest common multiple, that lowest common multiple is the LCM of the numbers

62.

Relatively prime integers, also known as coprime or mutually prime integers, are numbers that share a common divisor.

a)

True

b)

False

c)

true more than 1 common divisor

d)

False, no common divisor other than itself

63.

Smallest Prime number

a)

0

b)

1

c)

2

d)

3

64.

According to Euler's Circuit Theorem, an Euler Circuit will occur if EVERY vertex has an even degree

a)

True

b)

False

65.

According to Euler's Path Theorem, an Euler Path will occur if there are exactly two odd vertices.

a)

True

b)

False

66.

The following graph has

a)

Euler Circuit

b)

Euler Path

c)

Neither

67.

The following graph has

a)

Euler Circuit

b)

Euler Path

c)

Neither

68.

The following graph has

a)

Euler Circuit

b)

Euler Path

c)

Neither

69.

The following graph has

a)

Euler Circuit

b)

Euler Path

c)

Neither

70.

The following graph has

a)

Euler Circuit

b)

Euler Path

c)

Neither

71.

The following graph has

a)

Euler Circuit

b)

Euler Path

c)

Neither

72.

What was the goal of Woodrow Wilson's 14 points?

a)

to achieve world peace

b)

to punish germany

c)

to start WW2

d)

to reward Russia

73.

What did Wilson believe about world diplomacy?

a)

It should be discussed only with allies

b)

It should be secretive

c)

It should be open and transparent

d)

It should not be discussed

74.

What did Wilson believe about navigation of seas

a)

the US should dominate navigation

b)

there should be freedom of the seas

c)

the allies should have free access

d)

there should be a number of trade barriers

75.

What did Wilson say should be done with Belgium?

a)

Given freedom from tariffs

b)

Become an American protectorate

c)

Become a British colony

d)

Given it's independence

76.

What organization did Wilson want to establish?

a)

United Nations

b)

European Union

c)

League of Nations

d)

NAFTA

77.

What was the point of the League of Nations according to Wilson?

a)

to grant independence to nations

b)

to resolve international disagreements

c)

to sue Germany

d)

establish new governments

78.

Whose chancellor sent a letter to Wilson after reading the 14 points?

a)

England

b)

France

c)

Austria Hungary

d)

Germany

79.

What treaty officially ended the war?

a)

Treaty of Versailles

b)

Woodrow Wilson's 14 Points

c)

League of Nations

d)

Hague Accords

80.

What country opposed the 14 points because they wanted reparations from Germany?

a)

United States

b)

Italy

c)

Belgium

d)

France

81.

How quickly did America join the League of Nations?

a)

Never

b)

Immediately

c)

At the start of WWII

d)

1918

82.

Which was NOT a part of Wilson's 14 Points?

a)

Eliminating Militraism

b)

Eliminating Imperialism

c)

Punishing Germany

d)

Creating an international peace keeping organization

83.

What phrase describes Wilson's philosophy for peace after WWI?

a)

"Peace with honor"

b)

"Peace without victory"

c)

"Make the world safe for democracy"

d)

"What do you mean I can't get Chic-fil-a breakfast at four in the afternoon?!"

84.

What does the tau function (τ(n)) represent?

a)

Sum of all prime factors of n

b)

Number of positive divisors of n

c)

Product of all divisors of n

d)

Largest divisor of n

85.

Which of the following is true about the sigma function (σ(n))?

a)

It counts the number of prime numbers less than n

b)

It gives the number of divisors of n

c)

It gives the sum of all positive divisors of n

d)

It gives the average of the factors of n

Mock Test_6-2_Number Theory

Total questions: 85

Worksheet time: 4hrs 15mins

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