Algebra Review

Question 0

Coefficient

Answer 0

Number that is multiplied by a variable (ex. 2 in 2x)

Question 1

Constant

Answer 1

Term with no variable

Question 2

Identity

Answer 2

Statement of equality between two algebraic expressions that is true for all possible variables involved

Question 3

Equation

Answer 3

Statement of equality between two algebraic expressions that is true for only certain values of the variables involved

Question 4

x^-a

Answer 4

1/(x^a)

Question 5

(x^a)(x^b) =

Answer 5

x^(a+b)

Question 6

(x^a)/(x^b) =

Answer 6

x^(a-b)

Question 7

x^0 =

Answer 7

1

Question 8

(x^a)(y^a) =

Answer 8

(xy)^a

Question 9

(x/y)^a =

Answer 9

(x^a)/(y^a)

Question 10

(x^a)^b =

Answer 10

x^ab

Question 11

(x+y)/a =

Answer 11

(x/a) + (y/a)

Question 12

When dividing an inequality by a negative number, the direction of the inequality is…

Answer 12

Reversed.

Question 13

When dividing an inequality by a positive number, the direction of the inequality is…

Answer 13

Preserved.

Question 14

Domain (function)

Answer 14

Set of all permissible inputs of that function

Question 15

Simple interest

Answer 15

Based on the initial deposit, or principal (which serves as the amount on which interest is computed)

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

Where r is the interest rate (ex 6%, r=0.06) and t is time in years (ex 6 months, t=0.5)

Question 16

Compound interest

Answer 16

Interest added to the principal (initial deposit) at some time interval (annually, quarterly, or monthly). Interest is then earned on each new principal
V = P (1+(r/100))^t

Question 17

Compound interest at an annual interest rate of r percent, compounded n times per year

Answer 17

V = P ( 1 + (r/100n))^nt

Question 18

To find the distance between two points on a graph…

Answer 18

Construct a right triangle and use Pythagorean theory to find hypotenuse

Question 19

Linear equation (graphing)

Answer 19

y = mx + b 
m = slope
b = y-intercept

Question 20

Slope

Answer 20

Rise over run

X2-X1

Question 21

Two lines are perpendicular if…

Answer 21

Slopes are negative reciprocal of one another

Ex. y=2x+5 and y=-1/2x +9

Question 22

Finding y-intercept

Answer 22

Insert (x,y) point into equation if you know slope. Then solve for b

Question 23

Equation system solution result:

Answer 23

Point at which the two lines intersect

Question 24

Reflection of point (a,b) across the line y=x

Answer 24

Point (b,a)

Question 25

Reflection of any line across the line y=x is also found by…

Answer 25

Interchanging x and y.
Ex. y=2x+5
Change to x= 2y + 5 and solve for y to find reflection line.

Question 26

Solutions of the equation ax^2+bx+c are the ________ of the parabola

Answer 26

X-intercepts

Question 27

To solve for x intercepts of parabola,

Answer 27

Set equation so that y=0, then solve.

Question 28

To solve for y-intercept of parabola,

Answer 28

Set equation so that x=0, then solve.

Question 29

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

Answer 29

Circle with a center of (a,b) and radius r

Question 30

To find intersection points of the function of a line and a parabolic function,

Answer 30

Set them equal to one another, then move everything to one side (set equal to 0). Then use a, b, and c values to solve with quadratic equation. Will yield x-coordinates of the two solutions. Then insert both x coordinates into simpler function and solve. Will yield y-coordinates.

Question 31

Reflection of function y= h(x) about the x-axis is always…

Answer 31

y= -h(x)

Question 32

Graph of h(x)+c is the graph of h(x)

Answer 32

Shifted upward by c units

Question 33

Graph of h(x)-c is the graph of h(x)

Answer 33

Shifted downward by c units

Question 34

Graph of h(x+c) is the graph of h(x)

Answer 34

Shifted to the left by c units

Question 35

Graph of h(x-c) is the graph of h(x)

Answer 35

Shifted to the right by c units