QR - Key rules and Formulas

Question 1

Order of operations for solving a math problem - Please Excuse My Dear Aunt Sally [PEMDAS]

Answer 1

Parentheses
Exponents
Mulitplication
Division
Addition
Substraction

Question 2

What is the sum of the inside angles of a triangle

Answer 2

180 degrees

Question 3

What is an even number that is neither a positive nor negative number

Answer 3

0

Question 4

Prime numbers (at least the first 15)

Answer 4

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
53 59 61 71 73 79 83 89 97

Question 5

Perfect squares through 15^2, as well as 20^2 and 25^2

Answer 5

1^2= 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
11^2 = 121
12^2 = 144
13^2 - 169
14^2 = 196
15^2 = 225
20^2 = 400
25^2 = 625

Question 6

The first ten powers of 2

Answer 6

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024

Question 7

The fraction to decimal equivalents

1. 1/2
2. 1/3
3. 1/4
4. 1/5
5. 1/6
6. 1/8
7. 1/12

Answer 7

1. 0.50
2. 0.33
3. 0.25
4. 0.20
5. 0.17
6. 0.125
7. 0.08

Question 8

Square root of

1. 2
2. 3

Answer 8

1. 1.4 - remembering 2/14 is the valentine’s day might help

2. 1.7 - remembering 3/17 is the St Patrick’s Day

Question 9

The divisibility rule for 2

Answer 9

Rule: divisible if it ends with 0,2,4,6, or 8

Question 10

Divisibility rule for 3

Answer 10

Rule: divisibility if the sum of the digits is a multiple of 3

Question 11

The divisibility rule for 4

Answer 11

Rule: divisible if the last two digits are a multiple of 4 (or if the last two digits are 00)

Question 12

The divisibility rule for 5

Answer 12

Rule: divisible if it ends with a 5 or 0

Question 13

The divisibility rule for 6

Answer 13

Rule: divisible if it is divisible by 2 and 3

Question 14

The divisibility rule for 9

Answer 14

Rule: divisible if the sum of the digits are a multiple of 9

Question 15

The divisibility rule for 10

Answer 15

Rule: divisible if the last digit is 0

Question 16

Exponent rule - Rule of 1

Answer 16

1. Any number raised to the power of one (^1) = to the number itself
2. One raised to any power = 1

Question 17

Exponent rule - Power Rule

Answer 17

When multiplying two power that have the same base, you can add the exponents

Question 18

Exponent rule - Power Rule

Answer 18

To raise a power to a power, just multiply the exponents

Ex: 5^2 raised to the 3rd power (5^2)3 = 5^6

Question 19

Exponent rule - Quotient Rule

Answer 19

We can divide 2 power with the same base by subtracting the exponents
Ex: 4^5 / 4^2 = 4^3

Question 20

Exponent rule = Zero Rule

Answer 20

Any non zero number raised to the power of zero = 1

Question 21

Exponent rule - Negative Exponents

Answer 21

Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power

Ex: 4^-2 = 1/(4^2)

Question 22

Prime factorization tips

Answer 22

Prime factorization is finding which prime numbers multiply together to make the original number

1. It’s best to start working from the smallest prime number
2. Break a number down into any factors you can, then work those factor down to primes

Ex: 90 - broken into 9 and 10
Prime factors of 9 = 33
Prime factors of 10 - 25

Question 23

Difference of square patterns

Answer 23

(X+y) (x-y)

X^2 - y^2

Question 24

Formulas involving rate

Rate problems fall into one of the 2 patterns

1. Investigating an overall average rate when two different rates are given for specified distances
2. Calculating the rate or time needed to accomplish a certain distances or amount of work

Answer 24

Rate * Time = Distance

Question 25

Work problems

Answer 25

The rates at which certain persons or machines work alone are usually given, and it is necessary to compute the rate at which they work together (or vice versa)
Basic formula
1/r + 1/s = 1/h

Question 26

Interest problems

1. Annual interest
2. Compound interest

Answer 26

1. Annual interest = principal * interest rate * time
2. The concept of compound interest is that interest is added back to the principal sum so that interest is earned on that added interest during the next compounding period.
   Compound interest =
   A = P [ [1 + (r/n)]^ (nt) ], where

A = amount
P = principal
R = interest rate (decimal)
N = number of times interest is compounded per year
T = time (years)

Question 27

Discount

Answer 27

If a price is discounted by n %, the the price = (100-n) * original price

Question 28

Gross profit

Answer 28

1. Gross profit = revenues - expenses or selling price - cost