Algebra Flashcards
Gcf
Id prime factors, stack by number
Id factors in common in each column
Eg
54=2^1×3^3
72=2^3×3^2
90=2^1×3^2×5^1
GCF=2^1×3^2
Gcf=18
Lcm
Stack factora, id'd the largest factors in each column Eg 54=2^1×3^3 72=2^3×3^2 90=2^1×3^2×5^1
Lcm=2^3×3^3×5^1
2^4
16
2^5
32
2^6
64
3^3
27
3^4
81
3^5
243
4^3
64
4^4
256
6^3
216
Exponents-raising a power to a power
(X^3)^4
Multiply exponents
X^12
(2x^2)^3
2^3 x^6
Multiply exponents same base
3^4×3^2
Add the exponents
3^6
Divide exponents with the same base
3^4/3^2
Subtract exponents
3^2
Negative exponents
5^-3
(2/3)^-2
1/5^3
(3/2)^2
N^0
1
-2^0
-1 (negative sign is a coefficient unless it’s in a parenthesis)
Combinations
Order does not matter (words like selected, picked , choose)
Factorial of the total group/factorial of selected group
Want to select 5 kittens from a litter of 7.
7!/5!2!
42/2
Permutation
Order matters (arrange, place in order)
No duplicates then just factorial
How many unique ways are there to arrange letters in pillow?
Duplicates so you divide out
6!/2!
How many unique ways to arrange peppers
7!/3!2! (Because 3 ps and 2 es)
An integer is divisible by 4 if
The last 2 digits can be cut in half twice
An integer is divisible by 8 if
The last 3 digits can be cut in half 3 times
An integer is divisible by 3 if
The sum of its digits is divisible by 3
An integer is divisible by 9 if
The sum of its digits is divisible by 9
An integer is divisible by 9 if
The sum of its digits is divisible by 9
An integer is divisible by 6 if
Its divisible by 2 and 3
If an integer is divisible by a number not mentioned
Consider chunking ( eg. 224 is divisible by 7 because 210.and 14 are both divisible)
An integer is divisible by 7 if
Cross off the last digit, double it and subtract
203
3×2=6
20-6=14
An integer is divisible by 11 if
Subtract the last digit from the number formed by the first digits. If divisible by 11 …121=12-1=1
Or take alternating sum of digits =
2728=2-7+2-8=-111
Difference of squares
(X^2-Y^2)=(x+y)(x-y)
Solving equally spaces number sets algebraically
Eg. If the sum of 4 consecutive integers=334
4x+6=334
2 properties of equally spaced number sets
Average always equals median
Average of first last terms =average of the entire set
Variance
Square of standard deviation
Distance/sd=
Number of deviations
Normal distribution
0-1 sd: 34%
1-2 sd: 14%
2+:2%
Counting and adding equally spaced numbers
Diff of first and last terms /interveral +1
Sum=number of terms times set average
Properties of 0
Division by 0 is impossible
O is an integer
0 is neither positive nor negative
It is considered even
Multiply 2 numbers with a diff of
Take the number between them, square it and subtract 1
Eg. 199×201=399
Separate pools
A pet store has 6cats and 5 dogs. If 2 c ans 3 d are chosen at random hoe many ways can 5 animals be selected
6!/2!4! × 5!/3!2!
Fundamental counting principle
If there are m ways to do one 5hing and n ways to do another there are m×n ways to do bothe
