Algebra Flashcards
Identify the parts of each of the terms in the following polynomial:
7xˆ5 + 2
7=coefficient
x=variable
5=degree
2=constant (its degree is 0)
Multiplying two algebraic expressions:
x+2)(3x-7
FOIL First (3xˆ2) Outside (-7x) Inside (6x) Last (-14)
3xˆ2-1x-14
Identity 1
ca+cb=
c(a+b)
Identity 2
ca-cb=
c(a-b)
Identity 3
(a+b)ˆ2=
aˆ2+2ab+bˆ2
Identity 4
(a-b)ˆ2=
aˆ2-2ab+bˆ2
Identity 5
aˆ2-bˆ2=
(a+b)(a-b)
Identity 6
(a+b)ˆ3=
aˆ3+3aˆ2b+3abˆ2+bˆ3
Identity 7
(a-b)ˆ3=
aˆ3-3aˆ2b+3abˆ2-bˆ3
Rule 1
xˆ-1=
4ˆ-3=
1/x^a
1/(4ˆ3)=1/64
Rule 2
(x^a)(xˆb) =
(3ˆ2)(3ˆ4)=
xˆ(a+b)
3^(2+4) = 3^6 = 729
Rule 3
x^a / x^b =
5ˆ7 / 5ˆ4 =
x^a-b
5ˆ7-4 = 5ˆ3 = 125
Rule 4
xˆ0 =
(-3)ˆ0=
0ˆ0=
1
1
undefined
Rule 5
(x^a)(y^a)=
(2ˆ3)(3ˆ3)=
(xy)^a
6ˆ3=216
Rule 6
(x/y)^a=
(3/4)ˆ2=
x^a/y^a
3ˆ2/4ˆ2= 9/16
Rule 7
(x^a)ˆb=
(2ˆ5)ˆ2=
x^ab
2ˆ10= 1024
(-x)ˆ2 does NOT =
(-3)ˆ2=
-3ˆ2=
-xˆ2
9
-9
When solving an inequality, when you multiply or divide by a negative number you need to…
flip the inequality sign
Function
Takes input (x) and gives output (f(x)=3x+5), etc.
Solved like equations
More than one value of x can give the same output (i.e. the function has more than one “answer”)
g(x) = x^2-2x+3
g(0)=3 and g(2)=3
Domain
The set of permissible inputs for a function
What is the domain for f(x) = 2x / x-6?
All real numbers EXCEPT 6, b/c that would be 12/0 and would be undefined.
Rate formula
d=rt
distance = rate(time)
*make sure units of measurement are equal, i.e. minutes = parts of an hour if rate is miles per hour, etc.
Simple interest formula
V = P(1+ (rt/100)) V=value P=principal r=rate of interest t=time (in years)
Compound interest formula
V=P(1+ (r/100n))ˆnt P=principle r=rate n=# of times per year compounded t=time (# of years)
equation for a line
y=mx+b
m=slope
b=y-intercept
y-intercept
where it crosses the y axis
x-intercept
where it crosses the x axis
slope formula
x2-x1
“rise” (y) over “run” (x)
slope of a horizontal line
0
slope of a vertical line
undefined
equation for a horizontal line
y = b
b=y-intercept
equation for a vertical line
x = a
a=x-intercept
Two lines are parallel if their slopes are…
equal
y=2x + 5
y=2x + 2
Two lines are perpendicular if their slopes are…
negative reciprocals
y=2x + 5
y= -1/2 x + 9
equation for a parabola
y = axˆ2 + bx + c
x-intercepts are the solutions of the equation
In a parabola, if a is positive, the parabola…
opens upward, vertex is lowest point
In a parabola, if a is negative, the parabola…
opens downward, vertex is the highest point
equation for a graph of a circle
(x-a)ˆ2 + (y-b)ˆ2 = rˆ2
center at point (a, b), radius r (take the square root!) greater than 0
The absolute value graph forms a…
V
For any function f, the graph of y = -f(x) flips the graph over the…
x-axis
ex: y = √x ; y= - √x
The graph of f(x) + c is the graph of f(x)…
shifted UPWARD by c units
The graph of f(x) - c is the graph of f(x)…
shifted DOWNWARD by c units
The graph of f(x + c) is the graph of f(x)…
shifted to the LEFT by c units
The graph of f(x - c) is the graph of f(x)…
shifted to the RIGHT by c units
Quadratic formula
for solving equations that can’t be factored
-b +/- √ (bˆ2 - 4ac)
_______________
2a
Simple interest
interest payments are separate from the principle
calculate the interest, multiply it by the time, add it to the principle
Compound interest
interest payments are reinvested; the principle amount grows after each period of time
(multi-step interest, calculate it for 1st period and add, recalculate for 2nd period based on addition, etc.)
General rate formula
time = quantity / rate
Work formula
1/T = 1/a + 1/b + 1/c
