Algebra

Question 0

Term

Answer 0

A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables

Question 1

Variable

Answer 1

A letter used to represent a quantity whose value is unknown

Question 2

Expression

Answer 2

An algebraic expression is a combinatiin of one or more terms.

Terms in an expression are separated by either addition or subtraction signs

Question 3

Coefficient

Answer 3

In the term 3xy, 3 is called a coefficient.

In a single term, such as z, 1 is the coefficient

Question 4

Constant

Answer 4

A value that does not change

Question 5

Monomial

Answer 5

A single term

Question 6

Polynomial

Answer 6

Expression with more than one term

Question 7

Binomial

Answer 7

A polynomial with exactly two terms

Question 9

Trinomial

Answer 9

A polynomial with exactly three terms

Question 10

(a + b)^2

Answer 10

a^2 + 2ab + b^2

Question 11

(a - b)^3

Answer 11

a^3 - 3a^2b + 3ab^2 - b^3

Question 12

a^2 - b^2

Answer 12

(a + b)(a - b)

Question 13

Quadratic formula

ax^2 + bx + c = 0

Answer 13

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

if the expression under the square root is 0, then there is only one solution, if negative there is no (real number) solution.

Question 14

Domain of a function

Answer 14

the set of all permissible inputs

Question 15

A mixture of 12 ounces of vinegar and oil is 40% vinegar. How many ounces of oil must be added to produce a mixture that is only 25%?

Answer 15

x = number of ounces of oil to be added
new mixture = 12 + x ounces
ounces of vinegar = 0.4 * 12 = 4.8
new mixture must be 25% vinegar, so:

amount vinegar / amount new mixture = 0.25
4.8 / (12 + x) = 0.25
4.8 = 3 + 0.25x
x = 1.8/0.25 = 7.2

Question 16

Jeff and Dennis drove the same course at average speeds of 51mph and 54mph, respectively. It took Jeff 40 minutes to drive the course, how long did it take Dennis?

Answer 16

The distance d is equal to the rate r, in mph, and the time t, in hours: d = rt

51*(40/60) = 54*(x/60)
51*40 = 54x

Question 17

Radio costs $30 to make. 500 radios are produced and sold. What must be the selling price per radio to ensure that the profit (revenue from sales minus production cost) is greater than $8200?

Answer 17

y is revenue from sales
500( y - 30) > 8200
y > 46.4

Question 18

Quadrants

Answer 18

Counterclockwise I, II, III, IV

Question 19

Reflection of a graph about the line y = x

Answer 19

Interchange the x and y in the equation of any graph.

y = 2x + 5 reflected about the line x = y
x = 2y + 5 => y = (1/2)x - (5/2)

Question 20

x-intercepts of a parabola

Answer 20

The solutions of the equations are the x-intercepts.

The y-intercept is the equation when x=0.

Question 21

Equation of a circle

Answer 21

A circle with a center point (a,b) and radius r.

(x - a)^2 + (x - b)^2 = r^2

Question 22

For any function h(x) and any positive number c:

h(x) + c

Answer 22

h(x) shifted UP c units

Question 23

For any function h(x) and any positive number c:

h(x) - c

Answer 23

h(x) shifted DOWN c units

Question 24

For any function h(x) and any positive number c:

h(x + c)

Answer 24

h(x) shifted to the LEFT c units

Question 25

For any function h(x) and any positive number c:

h(x - c)

Answer 25

h(x) shifted to the RIGHT c units

Question 26

For any function h(x) and any positive number c:

c*h(x)

Answer 26

h(x) stretched vertically by a factor of c if c > 1.

h(x) shrunk vertically by a factor of c if 0 < c < 1.