QR - Key rules and Formulas Flashcards
Order of operations for solving a math problem - Please Excuse My Dear Aunt Sally [PEMDAS]
Parentheses Exponents Mulitplication Division Addition Substraction
What is the sum of the inside angles of a triangle
180 degrees
What is an even number that is neither a positive nor negative number
0
Prime numbers (at least the first 15)
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
Perfect squares through 15^2, as well as 20^2 and 25^2
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
The first ten powers of 2
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
The fraction to decimal equivalents
- 1/2
- 1/3
- 1/4
- 1/5
- 1/6
- 1/8
- 1/12
- 0.50
- 0.33
- 0.25
- 0.20
- 0.17
- 0.125
- 0.08
Square root of
- 2
- 3
- 1.4 - remembering 2/14 is the valentine’s day might help
2. 1.7 - remembering 3/17 is the St Patrick’s Day
The divisibility rule for 2
Rule: divisible if it ends with 0,2,4,6, or 8
Divisibility rule for 3
Rule: divisibility if the sum of the digits is a multiple of 3
The divisibility rule for 4
Rule: divisible if the last two digits are a multiple of 4 (or if the last two digits are 00)
The divisibility rule for 5
Rule: divisible if it ends with a 5 or 0
The divisibility rule for 6
Rule: divisible if it is divisible by 2 and 3
The divisibility rule for 9
Rule: divisible if the sum of the digits are a multiple of 9
The divisibility rule for 10
Rule: divisible if the last digit is 0
Exponent rule - Rule of 1
- Any number raised to the power of one (^1) = to the number itself
- One raised to any power = 1
Exponent rule - Power Rule
When multiplying two power that have the same base, you can add the exponents
Exponent rule - Power Rule
To raise a power to a power, just multiply the exponents
Ex: 5^2 raised to the 3rd power (5^2)3 = 5^6
Exponent rule - Quotient Rule
We can divide 2 power with the same base by subtracting the exponents
Ex: 4^5 / 4^2 = 4^3
Exponent rule = Zero Rule
Any non zero number raised to the power of zero = 1
Exponent rule - Negative Exponents
Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power
Ex: 4^-2 = 1/(4^2)
Prime factorization tips
Prime factorization is finding which prime numbers multiply together to make the original number
- It’s best to start working from the smallest prime number
- 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
Difference of square patterns
(X+y) (x-y)
X^2 - y^2
Formulas involving rate
Rate problems fall into one of the 2 patterns
- Investigating an overall average rate when two different rates are given for specified distances
- Calculating the rate or time needed to accomplish a certain distances or amount of work
Rate * Time = Distance
Work problems
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
Interest problems
- Annual interest
- Compound interest
- Annual interest = principal * interest rate * time
- 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)
Discount
If a price is discounted by n %, the the price = (100-n) * original price
Gross profit
- Gross profit = revenues - expenses or selling price - cost
