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Question 1

What is the formula for sum of consecutive integers

Answer 1

Sum=average*number of terms

Average=(first+last)/2

Number of terms=last-first+1

Question 2

How would you solve how many integers are there from 14 to 765, inclusive?

Answer 2

(Last-first+1)

765-14+1

Question 3

How would you solve all the even integers between 12 and 24, inclusive?

Answer 3

((Last-first)/increment)+1

((24-12)/2)+1

Question 4

How would you solve how many multiples of 7 are there between 10 and 40?

Answer 4

Could find least multiple of 7 and highest multiple of 7 then solve.

((35-14)/7)+1

Question 5

An integer is divisible by 2 if…

Answer 5

The integer is even

Question 6

An integer is divisible by 3 if…

Answer 6

The sum of the integer’s digits is divisible by 3

Question 7

An integer is divisible by 4 if

Answer 7

The integer is divisible by 2 twice or if the last two digits are divisible by 4

Question 8

An integer is divisible by 5 if

Answer 8

The integer ends in 0 or 5

Question 9

An integer is divisible by 6 if

Answer 9

The integer is divisible by 2 and 3

Question 10

An integer is divisible by 8 if

Answer 10

The integer is divisible by 2 three times or if the last three digits are divisible by 8

Question 11

An integer is divisible by 9 if

Answer 11

The sum of the integer’s digits is divisible by 9

Question 12

The first 17 prime numbers are…

Answer 12

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

Question 13

The product of k consecutive integers is always divisible by…

Answer 13

k factorial (k!)

Example a product of set of 4 consecutive numbers will be divisible by 4!—4x3x2x1=24

Question 14

Odd+odd=

Answer 14

Even

Question 15

Even+even=

Answer 15

Even

Question 16

Even+odd=

Answer 16

Odd

Question 17

Odd-odd=

Answer 17

Even

Question 18

Even-even=

Answer 18

Even

Question 19

Even x even=

Answer 19

Even

Question 20

Even x odd=

Answer 20

Even

Question 21

Odd x even=

Answer 21

Even

Question 22

Odd x odd=

Answer 22

Odd

Question 23

Even/odd=

Answer 23

Even

Question 24

Odd/odd=

Answer 24

Odd

Question 25

Even/even=

Answer 25

Even or odd

Question 26

Patterns of units digits for powers of 0 is…

Answer 26

end in 0

Question 27

Patterns of units digits for powers of 2 is…

Answer 27

Follow the four number pattern 2-4-8-6

Question 28

Patterns of units digits for powers of 3

Answer 28

Follows the four number pattern 3-9-7-1

Question 29

Patterns of units digits for powers of 4

Answer 29

Two number patter 4-6. All positive odd powers of 4 end in 4. All positive even powers of 4 end in 6.

Question 30

Patterns of units digits for powers of 5

Answer 30

End in 5

Question 31

Patterns of units digits for powers of 6

Answer 31

End in 6

Question 32

Patterns of units digits for powers of 7

Answer 32

Follow the four-number pattern 7-9–3-1

Question 33

Patterns of units digits for powers of 8

Answer 33

Follow the four number pattern 8-4-2-6

Question 34

Any factorial >=5! will always have its unit digit

Answer 34

As zero

Question 35

m=2k+1 where k is an integer. Is this odd or even?

Answer 35

Always odd

Question 36

If the sum of two prime will always be… and except for…

Answer 36

Even…unless one of those primes is 2

Question 37

2^1

Answer 37

2

Question 38

2^2

Answer 38

4

Question 39

2^3

Answer 39

8

Question 40

2^4

Answer 40

16

Question 41

2^5

Answer 41

32

Question 42

2^6

Answer 42

64

Question 43

2^7

Answer 43

128

Question 44

2^8

Answer 44

256

Question 45

2^9

Answer 45

512

Question 46

3^4

Answer 46

81

Question 47

4^3

Answer 47

64

Question 48

4^4

Answer 48

256

Question 49

5^3

Answer 49

125

Question 50

5^4

Answer 50

625

Question 51

6^3

Answer 51

216

Question 52

7^3

Answer 52

343

Question 53

8^3

Answer 53

512

Question 54

9^3

Answer 54

729

Question 55

Right triangle triplets are

Answer 55

3, 4, 5
6, 8, 10
5, 12, 13
7, 24, 25

Question 56

(a+b)^2

Answer 56

a^2 + 2ab + b^2

Question 57

(a-b)^2

Answer 57

a^2 - 2ab + b^2

Question 58

a^2 - b^2

Answer 58

(a+b)(a-b)