Math Review - Algebra

Question 1

(a - b)³ =

Answer 1

a³ - 3a²b +3ab² - b³

Question 1

4²4³ =

Answer 1

4⁵

Question 2

Two lines are ______ if their slopes are negative reciprocals of each other

Answer 2

perpendicular

EX: y = 2x + 5 and y = -1/2x +9

Question 4

(4²)³ =

Answer 4

4⁶

Question 5

10³z³ =

Answer 5

1,000z³

Question 6

a² - b² =

Answer 6

(a + b)(a - b)

Question 6

(x^a)(y^a) =

Answer 6

(xy)^a

Question 7

Distance =

Answer 7

Rate x Time

Question 7

What is the slope of a horizontal line?

Answer 7

0, since the rise is 0 for any two points on the line

Question 8

x² - 9 =

Answer 8

(x + 3)(x - 3)

Question 9

(-3)⁰ =

Answer 9

1

Question 10

y = mx + b

Answer 10

m = slope

b = y-intercept

Question 10

What is the equation for a circle

Answer 10

(x-a)² + (y-b)² = r²

With its center at the point (a,b) and with radius r

Question 12

(x^a)^b =

Answer 12

x^ab

Question 13

(a + b)² =

Answer 13

a² + 2ab + b²

Question 14

Two lines are ______ if their slopes are equal

Answer 14

Parallel

Question 15

What is the slope of a vertical line?

Answer 15

Is not defined, since the run is 0

Question 17

(x^a)(x^b) =

Note: x and y are nonzero real numbers and the exponents a and b are integers

Answer 17

X^a+b

Question 18

1

____

2^-a

Note: x and y are nonzero real numbers and the exponents a and b are integers

Answer 18

2^a

Question 20

x^ax^b =

Answer 20

x^a+b

Question 21

The slope of a line passing through two points (x₁,y₁), and (x₂,y₂) where x₁ does not equal x₂, is defined as

Answer 21

y₂ - y₁

_______

x₂ - x₁

AKA: Rise / Run

Question 22

x^a

____ =

x^b

Note: x and y are nonzero real numbers and the exponents a and b are integers

Answer 22

x^a-b =

   =    1

      \_\_\_\_

        x<sup>b-a</sup>

Question 23

(y³)(y^-1) =

Note: x and y are nonzero real numbers and the exponents a and b are integers

Answer 23

y²