math review

Question 1

Real Number

Answer 1

Any number found in the real world, both rational and irrational

Question 2

Why? |x+ y| <= |x|+|y|

Answer 2

Because y could be a negative number resulting in subtraction in the first half and a higher number on the right. Proof using x=10 and y=-2 vs 2

Question 3

Composite Number

Answer 3

Any integer greater than 1 that isn’t a prime number

Question 4

Sq Rt + Number

Answer 4

every positive number has two square roots but generally we refer to the pos sq root only

Question 5

Square x, x>1

Answer 5

Will result in a bigger number

Question 6

Square x, x<1

Answer 6

Will result in a smaller number ie squaring a decimal- helps to think in fractions cuz we are increasing the denominator

Question 7

Sq Rt of - #

Answer 7

Will result in imaginary number, i

Question 8

i^2

Answer 8

-1

Question 9

231 in scientific notation

Answer 9

2.31 * 10^2

Question 10

0.0231 in scientific notation

Answer 10

2.31 * 10^-2

Question 11

Dividing Decimals

Answer 11

move decimal in dividend and divisor until divisor is an integer (698.12/12.4) becomes (6981.2/124)

Question 12

x/0 =

Answer 12

undefined

Question 13

x isnt 0 & y isn’t 0, x/y

Answer 13

i/(y/x)

Question 14

x isnt 0, x^-1

Answer 14

1/x

Question 15

x isnt 0, (x^y)^z

Answer 15

x^yz

Question 16

x isnt 0, (xz)^y

Answer 16

z^yz^y

Question 17

z isnt 0, (x/z)^y

Answer 17

x^y/z^y

Question 18

z isnt 0, x^(y/z)

Answer 18

(xy)^1/2 = (x^1/2)^y

Question 19

2.310^14(1/3.910^4)

Question 20

Ratio of x to y

Answer 20

x/y

Question 21

How many solutions do two linear equations that are not equivalent have?

Answer 21

One at most

Question 21

How many solutions do two linear equations have if they are equivalent?

Answer 21

2
ex: 3x-y=6 & 6x-2y=12

Question 21

x^3-2x^2+x=-5(x-1)^2

Answer 21

x^3-2x^2+x+5(x-1)^2=0
x^3-2x^2+x+5(x-1)^2=0
x(x^2-2x+1)+5(x-1)^2=0
(x+5)(x-1)^2=0
x=-5 x=1

Question 22

a^2-b^2 factors to???

Answer 22

(a-b)(a+b)
ex: (9x^2-25) -> (3x-5)(3x+5)

Question 23

Quadratic Formula

Answer 23

x=[-b+-sqrt(b^2-4ac)]/2a

*roots are going to be 2 distinct numbers unless sqrt(b^2-4ac) <= 0 which means our only rot will be -b/2a

Question 24

Multiplying or dividing inequality by a negative number

Answer 24

This will recers the order or chang the direction of the inequality

i.e. 6>2
*-1 *-1
-6<-2