Bài kiểm tra tổng hợp (Hoán vị, tập hợp, chia hết)

Multiple Choice

$$4!=...$$  

• $$4+3+2+1$$  

• $$1x2x3x4$$  

• $$4+5+6$$  

• $$4$$  

Multiple Choice

$$\frac{10!}{8!}\ =\$$  

• 80

• 9

• 10

• 90

Multiple Choice

$$\frac{20!}{21!}\ =\$$  

• 21

• 1/20

• 20

• 1/21

Multiple Choice

$$\frac{50!\times50!}{51!\times49!}\ =\$$  

• 51/49

• 1

• 50

• 50/51

Multiple Choice

$$P\left(7,2\right)\ =\$$  

• 5

• 7

• 42

• 210

Multiple Choice

How many ways can a club select a president, vice president, and a secretary from a group of 6 people?

Có bao nhiêu cách để một câu lạc bộ chọn được chủ tịch, phó chủ tịch và thư ký từ một nhóm 6 người?

• 30

• 120

• 720

• 240

Multiple Choice

How many ways ways can you arrange the letters and digit in the word FCG4?

Có bao nhiêu cách bạn có thể sắp xếp các chữ cái và chữ số trong từ FCG4?

• 12

• 4

• 24

• 15

Multiple Choice

$$Số\ thứ\ 10\ của\ dãy\ sau:\ \ \ \ 20,19,18,17,...$$  

• 9

• 10

• 11

• 12

Multiple Choice

$$Số\ thứ\ k\ của\ dãy\ số\ sau\ (k\le n):\ \ n,n-1,n-2,n-3,...$$  

• $$n-k-1$$  

• $$n-k$$  

• $$n-k+1$$  

• $$n-k+2$$  

Multiple Choice

$$20x19x18x17x16\ =\ \frac{20!}{15!}$$  

• True

• False

Multiple Choice

$$Với\ k\le n,\ Ta\ có:\ \ \ nx\left(n-1\right)x\left(n-2\right)x...\left(n-k+1\right)=\frac{n!}{\left(n-k\right)!}$$  

• True

• False

Multiple Choice

$$P\left(n,k\right)=\frac{n!}{\left(n-k\right)!}$$  

• True

• False

Multiple Choice

$$Câu\ trả\ lời\ nào\ sai?\ P\left(8,3\right)=$$  

• $$\frac{8!}{5!}$$  

• $$8x7x6$$  

• 363

• 336

Match

Match each number with the divisibility rule that corresponds.

the last digit is even or 0

the sum of the digits is divisible by 3

the last two digits are divisible by four

the last digit is cero or five

the number is divisible by both, two and three

• the last digit is even or 0

• the sum of the digits is divisible by 3

• the last two digits are divisible by four

• the last digit is cero or five

• the number is divisible by both, two and three

Match

Match each number with the divisibility rule that corresponds.

the last three digits are divisible by eight

the sum of the digits is divisible by nine

the last digit is zero

• the last three digits are divisible by eight

• the sum of the digits is divisible by nine

• the last digit is zero

Multiple Choice

What is the divisibility rule for 4?

• The last two digits form a number divisible by 4

• The last digit is a number divisible by 4

• The last digit is even

• The last digit is zero

Multiple Choice

Which of the following statements is true of this number?

• It is divisible by 3 and 9

• It is divisible by 2, 3, and 6

• It is divisible by 3

• It is prime

Multiple Choice

Which of the following statements is true of this number?

• It is divisible by 2, 6, and 9

• It is divisible by 3 and 9

• It is divisible by 3

• It is prime

Multiple Choice

What is the divisibility rule of 9?

• The sum of the digits is a number divisible by 3

• The sum of the digits is a number divisible by 9

• The last two digits form a number divisible by 3

• The last digit is zero

Multiple Choice

Any whole number is divisible by 6 if it is divisible by

• 2 and 3
• 2 and 4
• 9 and 1
• 5 and 10

Multiple Choice

Use 'Divisibility Rules' to determine which of the following numbers 237 is divisible by:

• 2

• 3

• 5

• 9

Multiple Choice

In a month, there are 3 Saturdays that are even days. What day is the 13th of that month?

• Monday

• Tuesday

• Wednesday

• Thursday

• Friday

Multiple Choice

How many senior boys play football and wrestle?

• 9
• 12
• 18
• 39

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Multiple Choice

Numbers like -3, -2, -1, 0, 1, 2, 3 are called

• whole numbers
• integers
• rational numbers
• natural numbers

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Multiple Choice

Set A' is the complement of a set A

What statement does the shaded region represent?

• A' ∩ B
• A ∩ B'
• A ∩ B
• A' ∩ B'

Multiple Choice

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

• Union
• Intersection
• Disjointed
• Subset

Multiple Choice

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

• Union

• Intersection

• Disjointed

• Subset

Multiple Choice

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

• Union
• Intersection
• Disjointed
• Subset

Multiple Choice

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

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

Multiple Choice

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

• {3, 5, 7}

• {2, 3, 5, 7}

• {2, 3, 5, 7, 9}

• {1, 2, 3, 5, 7, 9}

Multiple Choice

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

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

Multiple Choice

How many subsets will this set have? S = {a,b,c,d} ?

• 8

• 15

• 16

• 24

• 32

Multiple Choice

From the above Venn diagram, what is the set S∩T?

• {casey, drew, jade, glen}

• {alex, casey, drew,hunter}

• {casey, drew}

• {drew, jade}

Multiple Choice

Set of factors of 12 is

• { 1,2,3,4,5}

• {2,3,4}

• {1,2,3,4,6,12}

• {1,3,5,7}

Multiple Choice

Two sets A and B are said to be equal, written A = B, if and only if A and B contain

exactly the same elements. Determine whether the stated equality is true or false:

{1, 2, 3} = {3, 2, 1}

• True

• False

Multiple Choice

Two sets A and B are said to be equal, written A = B, if and only if A and B contain

exactly the same elements. Determine whether the stated equality is true or false:

{2, 3, 4} = {4, 3, 2, 1}

• True

• False

Multiple Choice

Determine whether the stated equality is true or false:

N ∈ Z.

• True

• False

Multiple Choice

There are 100 students at a class: 50 take math; 40 take English; 30 take history; 15 take English and math; 10 take English and history; 10 take math and history; 5 take all three subjects. How many students are there taking math but not the other two subjects?

Có 100 học sinh trong một lớp: 50 học sinh học toán; 40 học sinh học tiếng Anh; 30 học sinh học lịch sử; 15 học sinh học tiếng Anh và toán; 10 học sinh học tiếng Anh và lịch sử; 10 học sinh học toán và lịch sử; 5 học sinh học cả ba môn. Có bao nhiêu học sinh học toán nhưng không học hai môn còn lại?

• 30

• 60

• 10

• 100

Fill in the Blanks

How many 4 digit numbers start or end with even digit?

Multiple Choice

How many arrangements are there of the letters of BANANA such that no two N's appear in adjacent positions? 
Có bao nhiêu cách sắp xếp các chữ cái của chữ BANANA sao cho không có hai chữ N nào đứng cạnh nhau?

• $$40$$  

• $$60$$  

• $$80$$  

• $$30$$  

Multiple Choice

There are 6 books of Math, Physics, Chemistry, Biology, English, and France are arranged on 1 row of bookshelf. How many ways are there to arrange the Math book on the left side of the Biology book?

Có 6 quyển sách Toán, Lý, Hóa, Sinh, Anh, Pháp được xếp trên 1 hàng giá sách. Có bao nhiêu cách sắp xếp quyển Toán ở bên trái quyển Sinh? (2 cuốn Toán và Sinh không nhất thiết phải cạnh nhau)

• $$240$$  

• $$360$$  

• $$120$$  

• $$720$$   

Multiple Choice

How many 8 digit numbers are there, such that they are divisible by 9 and all of the digits are distinct?

Có bao nhiêu số có 8 chữ số chia hết cho 9 và tất cả các chữ số đều khác nhau?

• $$4x8!$$   

• $$5x8!$$   

• $$36x7!$$   

• $$9!$$    

Fill in the Blanks

FCG3 club has 25 members, of which 5 students have no siblings, 15 have a brother, 12 have a sister. How many FCG3 members have both brother and sister?

FCG3 club có 25 thành viên, trong đó có 5 bạn là con một trong gia đình, 15 bạn có anh trai, 12 bạn có chị gái. Hỏi có bao nhiêu bạn FCG3 có cả anh trai và chị gái?

Fill in the Blanks

How many positive integers less than 1000 are divisible by neither 2,3 nor 5?

Có bao nhiêu số nguyên dương nhỏ hơn 1000 mà không chia hết cho cả ba số 2,3 và 5?