Algebra

Question 1

A letter that represents a quantity whose value is unknown

Answer 1

variable

Question 2

an expression that has one or more variables and can be written as a single term or a sum of terms

Answer 2

algebraic expression examples: 2x y- (1/4) (8)/(n+p)

Question 3

terms that have the same variable

Answer 3

like terms example: 5z + -z —> 4z

Question 4

a number that is in front of a variable

Answer 4

coefficient example: 3z —>coefficient is 3

Question 5

Combine ______ to simplify an expression

Answer 5

like terms example: 2x + 5x= 7 7x = 7

Question 6

1x and 1x^2 are NOT like terms

Answer 6

true

Question 7

1x * 1x =

Answer 7

1x^2

Question 8

Simplify: (x+2)(3x-7)

Answer 8

x(3x) + x(-7) + 2(3x) + 2(-7)= 3x^2 + (-7x) + 6x + (-14)

Question 9

Simplify: (a + b)^2

Answer 9

(a + b)(a + b) a^2 + ab + ba + b^2 a^2 + 2ab + b^2

Question 10

Simplify: (a^2 - b^2)

Answer 10

(a + b)(a - b)

Question 11

Statement of equality between two algebraic expressions

Answer 11

equation

Question 12

3x + 5= -2 is an example of a _____ equation

Answer 12

linear with one variable

Question 13

x- 3y= 10 is an example of a ______ equation

Answer 13

linear with two variables

Question 14

20y^2 + 6y -17 is an example of a _____ equation

Answer 14

quadratic equation with one variable

Question 15

If x^a = x^b, then

Answer 15

a=b (except if x=1)

Question 16

If 2^y = 64, what is y?

Answer 16

2^y=64 2^6=64 2^y=2^6 (rule x^a=x^b) then y=6

Question 17

x^-a is equal to

Answer 17

(1)/(x^a) example: 4^(-3)= (1)/(4^3)

Question 18

(x^a)(x^b) is equal to

Answer 18

x^(a+b)

Question 19

x^0 is equal to

Answer 19

1

Question 20

(x^a)(y^a) is equal to

Answer 20

(xy)^a

Question 21

(x/y)^a is equal to

Answer 21

(x^a)/(y^a)

Question 22

(x^a)^b is equal to

Answer 22

x^ab

Question 23

A linear equation with two variables can be written in the form…

Answer 23

ax + by= c

Question 24

You can solve equations with two variables in two ways: _______ or _______

Answer 24

substitution or elimination

Question 25

Substitution method of solving an equation with two variables

Answer 25

one equation is manipulated to express one variable in terms of the other example: 4x + 3y= 13 and x + 2y=2 x= 2-2y, then substitute this in first equation 4(2-2y) + 3y=13 8- 8y + 3y=13 -8y + 3y=5 -5y=5 y=-1; then substitute y in original equation

Question 26

ax^2 + bx + c is an example of ______

Answer 26

quadratic equation

Question 27

Quadratic equation must be solved using _____

Answer 27

the quadratic formula

Question 28

What is the quadratic equation?

Answer 28

Question 29

A mathematical statement that uses less than, greater than, less than or equal to, greater than or equal to, is

Answer 29

an inequality

Question 30

An inequality can be solved by…

Answer 30

simplifying the inequality by isolating the variable on one side of the inequality

example:

• 3x + 5 < 17
• 3x < 12 ***

x > -4

****dividing by a NEGATIVE in an inequality reverses the direction of the symbol

Question 31

Dividing/multiplying in an inequality by a negative number ________

Answer 31

reverses the direction of the inequality

example: -3x > 12 (divide each side by 3)

x < -4

Question 32

Solve the inequality:

(4x + 9)/(11) < 5

Answer 32

(4x + 9)/ (11) < 5

4x + 9 < 55

4x < 46

x < 11.5

All real numbers less than 11.5

Question 33

An algebraic expression in one variable can be used to define the ______ of that variable

Answer 33

function f (x)

Question 34

f (x) = 3x + 5 is an example of

Answer 34

a function

Question 35

Solve the function f (x) = 3x + 5

x = 1

Answer 35

f (1) = 3(1) + 5

f (1) = 8

Question 36

The set of all permissible inputs related to a function is…

Answer 36

the domain

Question 37

V= P (1 + (rt/100) )

P= amount in dollars

r= interest rate in percent

t= time in years

Answer 37

Simple interest equation

Question 38

Compound interest equation

Answer 38

V= P(1 + (r/100) )^t

P= amount invested in dollars

r= annual interest rate

t= time in years