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GRE Quantitative > Algebra > Flashcards

Algebra Flashcards

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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
Q

equation for a line

A

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

26
Q

y-intercept

A

where it crosses the y axis

27
Q

x-intercept

A

where it crosses the x axis

28
Q

slope formula

A

x2-x1

“rise” (y) over “run” (x)

29
Q

slope of a horizontal line

A

0

30
Q

slope of a vertical line

A

undefined

31
Q

equation for a horizontal line

A

y = b

b=y-intercept

32
Q

equation for a vertical line

A

x = a

a=x-intercept

33
Q

Two lines are parallel if their slopes are…

A

equal

y=2x + 5
y=2x + 2

34
Q

Two lines are perpendicular if their slopes are…

A

negative reciprocals

y=2x + 5
y= -1/2 x + 9

35
Q

equation for a parabola

A

y = axˆ2 + bx + c

x-intercepts are the solutions of the equation

36
Q

In a parabola, if a is positive, the parabola…

A

opens upward, vertex is lowest point

37
Q

In a parabola, if a is negative, the parabola…

A

opens downward, vertex is the highest point

38
Q

equation for a graph of a circle

A

(x-a)ˆ2 + (y-b)ˆ2 = rˆ2

center at point (a, b), radius r (take the square root!) greater than 0

39
Q

The absolute value graph forms a…

A

V

40
Q

For any function f, the graph of y = -f(x) flips the graph over the…

A

x-axis

ex: y = √x ; y= - √x

41
Q

The graph of f(x) + c is the graph of f(x)…

A

shifted UPWARD by c units

42
Q

The graph of f(x) - c is the graph of f(x)…

A

shifted DOWNWARD by c units

43
Q

The graph of f(x + c) is the graph of f(x)…

A

shifted to the LEFT by c units

44
Q

The graph of f(x - c) is the graph of f(x)…

A

shifted to the RIGHT by c units

45
Q

Quadratic formula

for solving equations that can’t be factored

A

-b +/- √ (bˆ2 - 4ac)
_______________
2a

46
Q

Simple interest

A

interest payments are separate from the principle

calculate the interest, multiply it by the time, add it to the principle

47
Q

Compound interest

A

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
Q

General rate formula

A

time = quantity / rate

49
Q

Work formula

A

1/T = 1/a + 1/b + 1/c

GRE Quantitative (5 decks)

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