Level 1A

Question 1

What is the divisibility rule for 3?

Answer 1

If the sum of the digits of the number are divisible by 3, then the number is divisible by 3.

Question 2

What is the sum of the first n odd natural numbers?

Answer 2

The sum of the first n odd natural numbers is n^2. This is easy to see and leads to some cool insights: 1 = 1 + 3 = 4 (2^2) 1 + 3 + 5 = 9 (3^2) 1 + 3 + 5 +7 = 16 (4^2) This pattern explains why the difference between n^2 and (n+1)^2 is (2n+1). Note: the formula 2n - 1 can tell you which odd number you are on. For example, 9 is the 5th odd number because when you solve the problem 2n - 1 = 9 you get n = 5.

Question 3

Evaluate 26²

Answer 3

676

Question 4

What is the decimal equivalent of 11/16?

Answer 4

0.6875

Question 5

What is the divisibility rule for 8?

Answer 5

If the last three digits is a three-digit number that is divisible by 8, then the number is divisible by 8.

Question 6

Evaluate 2⁹

Answer 6

512

Question 7

What is the decimal equivalent of 5/6?

Answer 7

0.83333333 (The 3 is repeating)

Question 8

Evaluate 14²

Answer 8

196

Question 9

What is the divisibility rule for 2?

Answer 9

The number is an even number.

Question 10

Evaluate 23²

Answer 10

529

Question 11

What is the divisibility rule for 4?

Answer 11

If the tens digit and ones digit form a two-digit number that is divisible by 4, then the number is divisible by 4.

Question 12

What is the decimal equivalent of 5/16?

Answer 12

0.3125

Question 13

What is the divisibility rule for 10?

Answer 13

If the last digit is a 0, then the number is divisible by 10.

Question 14

What is the divisibility rule for 5?

Answer 14

If the final digit is 0 or 5, then the number is divisible by 5.

Question 15

What is the divisibility rule for 9?

Answer 15

If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

Question 16

Evaluate 2³

Answer 16

8

Question 17

Evaluate 17²

Answer 17

289

Question 18

What is the decimal equivalent of 3/8?

Answer 18

0.375

Question 19

What is the decimal equivalent of 7/16?

Answer 19

0.4375

Question 20

Lis all the prime numbers greater than 40 but less than 60.

Answer 20

41, 43, 47, 53, 59

Question 21

Evaluate 2¹²

Answer 21

4096

Question 22

List all the prime numbers less than 20.

Answer 22

2, 3, 5, 7, 11, 13, 17, 19

Question 23

Evaluate 45²

Answer 23

2025 The key is to multiple the tens digit times one more than the tens digit and then appened a 25. So 4*5 = 12 then append 25 and you get 2025. The reason for this is because of the differnece of squares. (45+5)(45-5) = (50)(40) but also 45^2 -25. Thus (50)(40) is 25 less than 45^2.

Question 24

What is the divisibility rule for 7?

Answer 24

This requires an algorithm to follow. Here are the steps: 1) Remove the ones digit - which effectively shortens the number by 1 digit. 2) Multiply the number removed by 2. 3) Subtract that from the new number. 4) If the result is divisible by 7, then the number is divisible by 7. 5) If you are not sure, then repeat steps 1 - 4 until you get a number you know is divisible by 4. Example 1 - 224 Remove 4 and multiply it by 2 to get 8. Subtract this from 22 to get 14. Since 14 is divisible by 7, then 224 is divisible by 7. Example 2 - 1288 Remove the 8 and multiply it by 2 and then subtract from 128 - 16 = 112. If you aren’t sure about 112 then remove 2 and multiply by 2 and then subtact 4 from 11 to get 7. Since 7 is divisible by 7, then 1288 is divisible by 7.

Question 25

Evaluate 2⁶

Answer 25

64

Question 26

What is the decimal equivalent of 15/16?

Answer 26

0.9375

Question 27

List all the numbers less than or equal to 100 that have an odd number of factors.

Answer 27

1, 4, 9, 16, 25, 36, 49, 64, 81, 100. \*\*Perfect squares have an odd number of factors because you can list all factors as factor pairs, except for the square root which only counts once.

Question 28

What is the decimal equivalent of 5/8?

Answer 28

0.625

Question 29

What is the decimal equivalent of 1/8?

Answer 29

0.125

Question 30

What is the decimal equivalent of 1/6?

Answer 30

0.16666666 (The 6 is repeating)

Question 31

What is the divisibility rule for 6?

Answer 31

If the number is divisible by 2 and 3, then the number is divisible by 6.

Question 32

What is the decimal equivalent of 13/16?

Answer 32

0.8125

Question 33

What is the divisibility rule for 11?

Answer 33

This requires an algorithm to follow: 1) Start with the first digit and add every other digit to get a sum. 2) Add together the other digits. 3) Subtract the two sums. If the difference is a multiple 11 (including 0), then the number is divisible by 0. Example 1 - Is 132,649 divisibly be 11. Starting with the first digit 1 + 2 + 4 = 7 The other digits sum is 3 + 6 + 9 = 18. 18 - 7 = 11 thus 132,649 is divisibly by 11.

Question 34

What is the divisibility rule for 12?

Answer 34

If the number is divisible by 3 and by 4, then the number is divisible by 12.

Question 35

List all the prime numbers greater than 20 but less than 40.

Answer 35

23, 29, 31, 37

Question 36

Evaluate 20²

Answer 36

400

Question 37

Evaluate 29^2

Answer 37

841

Question 38

What is the decimal equivalent of 9/16?

Answer 38

0.5625

Question 39

What is the decimal equivalent of 1/16?

Answer 39

0.0625

Question 40

List the fibonacci sequence for numbers less than 150?

Answer 40

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 - you should only select a 5 if you can list these out without having to do the sums.

Question 41

What is the decimal equivalent of 3/16?

Answer 41

.1875

Question 42

What is the decimal equivalent of 7/8?

Answer 42

0.875

Question 43

Evaluate 32²

Answer 43

1024

Question 44

Evaluate 11².

Answer 44

121

Question 45

Evaluate 35²

Answer 45

1225 The key is to multiple the tens digit times one more than the tens digit and then appened a 25. So 3\*4 = 12 then append 25 and you get 1225. The reason for this is because of the differnece of squares. (35+5)(35-5) = (40)(30) but also 35^2 -25. Thus (40)(30) is 25 less than 35^2.

Question 46

What is the sum of the first "n" positive integers? (i.e. what is the sum of 1 + 2 + 3 + 4 + ...+ n)

Answer 46

The sum of the first "n" positive integers is n(n+1)/2.

Question 47

What are the three versions of the formula that connects distance (d), rate (r), and time (t)?

Answer 47

d = rt r = d/t t = d/r` It is important to be flexible with all three of these formulas.

Question 48

What is the area of a circle with radius r?

Answer 48

A = pi\*r²

Question 49

What is the circumference of a circle with radius r?

Answer 49

C = 2(pi)\*r

Question 50

What is the area of a square with side length x?

Answer 50

x²

Question 51

What is the area of a rectangle with sides b and h?

Answer 51

A = b\*h

Question 52

What is the perimeter of a rectangle with sides b and h?

Answer 52

P = 2\*b + 2\*h

Question 53

What is the area of a parallelogram?

Answer 53

The area of a parallelogram the length of one of the sides, referred to as the base times the distance between that side and the side opposite call the height. Note that the height is perpendicular to both sides.

Question 54

How do you convert a repeating decimal to a fraction?

Answer 54

For how many places after the decimals that are repeated you put that many 9's under the number (not as a decimal) that is repeated and then simplify. Here are some basic examples:

Question 55

What are the three ways that distance, rate and time are related?

Answer 55

If we let d = distance, r = rate, and t = time then the formula can be expressed to equal each of them as follows.

Question 56

Evaluate 2!

Answer 56

2! = 2\*1 = 2

Question 57

Evaluate 4!

Answer 57

4! = 4\*3\*2\*1 = 24

Question 58

Evaluate 6!

Answer 58

720