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Z - AP Calculus > PRO Algebra > Flashcards

PRO Algebra Flashcards

1
Q

x^m * x^n

A

x^(m+n)

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2
Q

(x^m)^n

A

x^(m*n)

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3
Q

x^0

A

1

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4
Q

x^-m

A

1/x^m

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5
Q

x^m / x^n

A

x^(m-n)

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6
Q

What is the midpoint formula?

A

(x1+x2)/2, (y1+y2)/2

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7
Q

What is the distance formula?

A

d=Square root of (x2-x1)^2 + (y2-y1)^2

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8
Q

What is the quadratic formula?

A

-b +/- the square root of b^2 minus 4ac all over 2a

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9
Q

(a^3 + b^3)

A

(a+b)(a^2-ab+b^2)

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10
Q

(a^3 - b^3)

A

(a-b)(a^2+ab+b^2)

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11
Q

a^2-b^2

A

(a-b)(a+b)

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12
Q

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

A

(a+b)^3

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13
Q

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

A

(a-b)^3

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14
Q

What is the HA if the degree of the numerator is less than the degree of the denominator?

A

0

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15
Q

What is the HA if the degree of the numerator is greater than the degree of the denominator?

A

DNE

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16
Q

What is the HA if the degree of the numerator is equal to the degree of the denominator?

A

Ratio of leading coefficients

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17
Q

What kind of symmetry exists if f(-x) is equal to f(x)?

A

Y-axis

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18
Q

What kind of symmetry exists if f(-x) is equal to -f(x)?

A

Origin

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19
Q

How do you find y-intercepts?

A

x=0

20
Q

How do you find x-intercepts?

A

y=0, only pay attention to numerator

21
Q

How do you find VA’s?

A

When the numerator equals a number, but the denominator is equal to 0

22
Q

How do you find slant asymptotes and how do you know if there will be one?

A

If the degree of the numerator is one more than the degree of the denominator, you can find a slant asymptote by dividing the numerator by the denominator (the remainder does not count)

23
Q

What is Ln a + Ln b?

A

Ln ab

24
Q

What is Ln a - Ln b?

A

Ln a/b

25
Q

Simplify Ln a^P

A

P times Ln a

26
Q

What is another form of logb(x)=C?

A

b^c=x

27
Q

Change logb(x) to natural logs

A

Ln x / Ln b

28
Q

What is the formula for continuously compounding interest?

A

P*e^rt

29
Q

What is the formula for interest compounded less than continuously?

A

P * (1+r/n)^nt

30
Q

Y is directly proportional to z

A

Y=kx

31
Q

Y is inversely proportional to x

A

Y=k/x

32
Q

Y is jointly proportional to x and n

A

Y=kxn

33
Q

What is the formula for a parabola?

A

Ax^2+Dx+Ey=0
or y=ax^2+bx+c
change to y=a(x-h)^2+k, where vertex is (h,k) and 1/4a is the distance between the vertex and the focus or directrix
In the regular form the x of the vertex is -b/2a

34
Q

What is the formula for a circle?

A

x^2+y^2+Dx+Ey+F
or (x-h)^2+(y-k)^2=r^2
(h,k) is center, r is radius

35
Q

What is the formula for a ellipse?

A

Ax^2+Cy^2+Dx+Ey+F=0
Wide:(x-h)^2/a^2+(y-k)^2/b^2=1
Tall:(y-k)^2/a^2+(x-h)^2/b^2=1
The center is at (h,k), the a is distance right, the b is distance left, and the foci is c (a^2-c^2=b^2) units on the sides of the center

36
Q

What is the formula for a hyperbola?

A 
Ax^2-Cy^2+Dx+Ey+F=0
Cupping y-axis:(x-h)^2/a^2-(y-k)^2/b^2=1
Cupping x-axis:(y-k)^2/a^2-(x-h)^2/b^2=1
Center:(h,k)
Vertex is a from center
Foci are c from center (c^2-a^2=b^2)
Asymptotes are +/- b/a(x-h)+k or  +/- a/b(x-h)+k
37
Q

How do you find the inverse of a function?

A

Switch the x and y

38
Q

What is the relationship between the domain and range of f^-1 related to f?

A

They switch

39
Q

If f and g are inverses what are f(g(x)) and g(f(x))?

A

x

40
Q

How do the graphs of f and its inverse relate?

A

The inverse is a reflection over y=x

41
Q

What is the requirement for a function to have an inverse?

A

It must be one to one, (passing both the vertical and horizontal line tests)

42
Q

What is i^2?

A

-1

43
Q

For an imaginary number a+bi, what is the real part and what is the imaginary part?

A

a,b

44
Q

What is the limit on “log”ing numbers?

A

You cannot log 0 or a negative number

45
Q

x^m/n

A

The n root of x^m

46
Q

What is the average rate of change of a function between two x-values?

A

The slope of the line connecting them, or Y2-Y1 over X2-X1

47
Q

What is gof?

A

The function f inserted as the x in function g

Z - AP Calculus (12 decks)

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