Algebra

Question 1

Gcf

Answer 1

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

Question 2

Lcm

Answer 2

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

Question 3

2^4

Answer 3

16

Question 4

2^5

Answer 4

32

Question 5

2^6

Answer 5

64

Question 6

3^3

Answer 6

27

Question 7

3^4

Answer 7

81

Question 8

3^5

Answer 8

243

Question 9

4^3

Answer 9

64

Question 10

4^4

Answer 10

256

Question 11

6^3

Answer 11

216

Question 12

Exponents-raising a power to a power

(X^3)^4

Answer 12

Multiply exponents

X^12

Question 13

(2x^2)^3

Answer 13

2^3 x^6

Question 14

Multiply exponents same base

3^4×3^2

Answer 14

Add the exponents

3^6

Question 15

Divide exponents with the same base

3^4/3^2

Answer 15

Subtract exponents

3^2

Question 16

Negative exponents

5^-3

(2/3)^-2

Answer 16

1/5^3

(3/2)^2

Question 17

N^0

Answer 17

1

Question 18

-2^0

Answer 18

-1 (negative sign is a coefficient unless it’s in a parenthesis)

Question 19

Combinations

Answer 19

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

Question 20

Permutation

Answer 20

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)

Question 21

An integer is divisible by 4 if

Answer 21

The last 2 digits can be cut in half twice

Question 22

An integer is divisible by 8 if

Answer 22

The last 3 digits can be cut in half 3 times

Question 23

An integer is divisible by 3 if

Answer 23

The sum of its digits is divisible by 3

Question 24

An integer is divisible by 9 if

Answer 24

The sum of its digits is divisible by 9

Question 24

An integer is divisible by 9 if

Answer 24

The sum of its digits is divisible by 9

Question 25

An integer is divisible by 6 if

Answer 25

Its divisible by 2 and 3

Question 26

If an integer is divisible by a number not mentioned

Answer 26

Consider chunking ( eg. 224 is divisible by 7 because 210.and 14 are both divisible)

Question 27

An integer is divisible by 7 if

Answer 27

Cross off the last digit, double it and subtract

203

3×2=6

20-6=14

Question 28

An integer is divisible by 11 if

Answer 28

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

Question 29

Difference of squares

Answer 29

(X^2-Y^2)=(x+y)(x-y)

Question 30

Solving equally spaces number sets algebraically

Eg. If the sum of 4 consecutive integers=334

Answer 30

4x+6=334

Question 31

2 properties of equally spaced number sets

Answer 31

Average always equals median

Average of first last terms =average of the entire set

Question 32

Variance

Answer 32

Square of standard deviation

Question 33

Distance/sd=

Answer 33

Number of deviations

Question 34

Normal distribution

Answer 34

0-1 sd: 34%
1-2 sd: 14%
2+:2%

Question 35

Counting and adding equally spaced numbers

Answer 35

Diff of first and last terms /interveral +1

Sum=number of terms times set average

Question 36

Properties of 0

Answer 36

Division by 0 is impossible
O is an integer
0 is neither positive nor negative
It is considered even

Question 37

Multiply 2 numbers with a diff of

Answer 37

Take the number between them, square it and subtract 1

Eg. 199×201=399

Question 38

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

Answer 38

6!/2!4! × 5!/3!2!

Question 39

Fundamental counting principle

Answer 39

If there are m ways to do one 5hing and n ways to do another there are m×n ways to do bothe