Algebra Flashcards

1
Q

Identify the parts of each of the terms in the following polynomial:
7xˆ5 + 2

A

7=coefficient
x=variable
5=degree
2=constant (its degree is 0)

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2
Q

Multiplying two algebraic expressions:

x+2)(3x-7

A
FOIL
First (3xˆ2)
Outside (-7x)
Inside (6x)
Last (-14)

3xˆ2-1x-14

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3
Q

Identity 1

ca+cb=

A

c(a+b)

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4
Q

Identity 2

ca-cb=

A

c(a-b)

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5
Q

Identity 3

(a+b)ˆ2=

A

aˆ2+2ab+bˆ2

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6
Q

Identity 4

(a-b)ˆ2=

A

aˆ2-2ab+bˆ2

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7
Q

Identity 5

aˆ2-bˆ2=

A

(a+b)(a-b)

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8
Q

Identity 6

(a+b)ˆ3=

A

aˆ3+3aˆ2b+3abˆ2+bˆ3

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9
Q

Identity 7

(a-b)ˆ3=

A

aˆ3-3aˆ2b+3abˆ2-bˆ3

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10
Q

Rule 1
xˆ-1=

4ˆ-3=

A

1/x^a

1/(4ˆ3)=1/64

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11
Q

Rule 2
(x^a)(xˆb) =

(3ˆ2)(3ˆ4)=

A

xˆ(a+b)

3^(2+4) = 3^6 = 729

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12
Q

Rule 3
x^a / x^b =

5ˆ7 / 5ˆ4 =

A

x^a-b

5ˆ7-4 = 5ˆ3 = 125

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13
Q

Rule 4

xˆ0 =

(-3)ˆ0=

0ˆ0=

A

1

1

undefined

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14
Q

Rule 5
(x^a)(y^a)=

(2ˆ3)(3ˆ3)=

A

(xy)^a

6ˆ3=216

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15
Q

Rule 6
(x/y)^a=

(3/4)ˆ2=

A

x^a/y^a

3ˆ2/4ˆ2= 9/16

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16
Q

Rule 7
(x^a)ˆb=

(2ˆ5)ˆ2=

A

x^ab

2ˆ10= 1024

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17
Q

(-x)ˆ2 does NOT =

(-3)ˆ2=

-3ˆ2=

A

-xˆ2

9

-9

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18
Q

When solving an inequality, when you multiply or divide by a negative number you need to…

A

flip the inequality sign

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19
Q

Function

A

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

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20
Q

Domain

A

The set of permissible inputs for a function

21
Q

What is the domain for f(x) = 2x / x-6?

A

All real numbers EXCEPT 6, b/c that would be 12/0 and would be undefined.

22
Q

Rate formula

A

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.

23
Q

Simple interest formula

A
V = P(1+ (rt/100))
V=value
P=principal
r=rate of interest
t=time (in years)
24
Q

Compound interest formula

A
V=P(1+ (r/100n))ˆnt
P=principle
r=rate
n=# of times per year compounded
t=time (# of years)
25
equation for a line
y=mx+b m=slope b=y-intercept
26
y-intercept
where it crosses the y axis
27
x-intercept
where it crosses the x axis
28
slope formula
y2-y1 -------- x2-x1 "rise" (y) over "run" (x)
29
slope of a horizontal line
0
30
slope of a vertical line
undefined
31
equation for a horizontal line
y = b | b=y-intercept
32
equation for a vertical line
x = a | a=x-intercept
33
Two lines are parallel if their slopes are...
equal y=2x + 5 y=2x + 2
34
Two lines are perpendicular if their slopes are...
negative reciprocals y=2x + 5 y= -1/2 x + 9
35
equation for a parabola
y = axˆ2 + bx + c | x-intercepts are the solutions of the equation
36
In a parabola, if a is positive, the parabola...
opens upward, vertex is lowest point
37
In a parabola, if a is negative, the parabola...
opens downward, vertex is the highest point
38
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
39
The absolute value graph forms a...
V
40
For any function f, the graph of y = -f(x) flips the graph over the...
x-axis | ex: y = √x ; y= - √x
41
The graph of f(x) + c is the graph of f(x)...
shifted UPWARD by c units
42
The graph of f(x) - c is the graph of f(x)...
shifted DOWNWARD by c units
43
The graph of f(x + c) is the graph of f(x)...
shifted to the LEFT by c units
44
The graph of f(x - c) is the graph of f(x)...
shifted to the RIGHT by c units
45
Quadratic formula | for solving equations that can't be factored
-b +/- √ (bˆ2 - 4ac) _______________ 2a
46
Simple interest
interest payments are separate from the principle | calculate the interest, multiply it by the time, add it to the principle
47
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.)
48
General rate formula
time = quantity / rate
49
Work formula
1/T = 1/a + 1/b + 1/c