Number Properties

Question 1

First Prime Numbers to 100

Answer 1

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Question 2

Divisibility Test for 3

Answer 2

Sum of all digits is divisible by 3, then divisible by 3

Question 3

Divisibility Test for 4

Answer 3

if last two digits are divisible by 4, then divisible by 4

Question 4

Divisibility Test for 5

Answer 4

Last digit is 0 or 5, divisible by 5

Question 5

Divisibility Test for 6

Answer 5

If both divisibilty tests for 2 and 3 apply, then this does

Question 6

Divisibility Test for 7

Answer 6

Long Division

Question 7

Divisibility Test for 8

Answer 7

If last three digits are divisible by 8, then divisible by 8

Question 8

Divisibility Test for 9

Answer 8

If sum of all the digits in the given number is divisible by 9, that number is divisible by 9

Question 9

Divisibility Test for 2

Answer 9

last digit is a multiple of 2 or is 0

Question 10

Divisibility Test for 10

Answer 10

last two digits are an integer multiple of 10

Question 11

x^2

Answer 11

0

Question 12

xy>0 means, xy

Answer 12

both positive, both negative (xy>0)

one positive, one negative (xy

Question 13

Critical rule for inequality manipulation - divide or multiply by negative number…

Answer 13

flip the sign

Question 14

Do not multiply or divide by variable in inequality unless…

Answer 14

you know the sign for sure

Question 15

Square root of variable in inequality leads to…

Answer 15

absolute value

Question 16

use conjugate to (example: x + sqrt5)

Answer 16

simplify denominator (x-sqrt5)/(x-sqrt5)

Question 17

Direct Proportionality

Answer 17

y=kx or y/x = k

Question 18

Indirect proportionality

Answer 18

y = k/x or yx = k

Question 19

Inequalities and Reciprocals, if x

Answer 19

1) If both x and y are positive, flip sign with reciprocal (1/x>1/y)
2) If both x and y are negative, flip sign with reciprocal (1/x>1/y)
3) If x is negative and y is positive, do not flip sign (1/x

Question 20

Inequalities and squaring

Answer 20

1) If both are positive, don’t flip sign
2) if both are negative, flip sign
3) if one is negative, one positive, can’t square
4) if don’t know signs, can’t square

Question 21

Combining inequalities (do and do not)

Answer 21

Do multiply and add

Do not subtract and divide

Question 22

Quadratic Formula

Answer 22

x = -b +- sqrt(b^2 - 4ac)

all over 2a

Question 23

Discriminant and what it tells us

Answer 23

b^2 - 4ac

tells us how many solutions - positive, 2 solutions,0, 1 solution, negative, no solutions

Question 24

Quadratics, 3 special products

Answer 24

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

(x+y)^2 = (x+y) (x+y) = x^2 + 2xy + y^2

(x-y)^2 = (x-y) (x-y) = x^2 - 2xy + y^2

Question 25

Divisibility & Addition/Subtraction (Multiples of Integer)

Answer 25

Add or subtract multiples of an integer, get a different multiple of that integer

Question 26

Divisibility & Addition/Subtraction (Non-Multiples of Integer)

Answer 26

Multiple + or - Non-Multiple = Non-Multiple

Non Multiple + or - Non-Multiple = Sometimes Yes, Sometimes no, except when integer is 2 (always yes)

Question 27

Advanced GCF & LCM

Answer 27

GCF - find by multiplying the shared primes (take the smallest count, including 0) in any of the columns

LCM - find by multiplying the largest count in any column - LCM is formed out of all the primes, less shared primes

Question 28

of Factors in a Perfect Square, Cube

Answer 28

Odd # of factors in perfect square

An even # of factors can never be a perfect square

Perfect squares’ prime factorization contains only even powers of primes!

Perfect cubes’ prime factorization contains only powers of primes that are multiples of 3