Study better. Learn faster. Get the grade you want.
Discover why millions of students use us to learn better.

- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Mathematics
- Mathematics 114
- Camacho
- Terms, Concepts and Things to Remember

Sign up now and start studying these cards for FREE

when you're given the slope of a line and one point, what formula do you use?

Point-Slope Form: y-y1=m(x-x1)

When you're given only two points , find the equation of the line by:

1.) first, finding m: y2-y1/x2-x1

2.) then, plug m in to the point-slope form equation and use either set of points.

2.) then, plug m in to the point-slope form equation and use either set of points.

if two lines are perpendicular, their slopes will be:

Reciprocal and opposite (if one is +, the other will be -)

to find a common intersection between three lines, you must:

1.) set two of them equal to each other and solve for x

2.) plug x and either m value into the equation to get y

3.) plug x and y back into the equation with no numerical values and solve for m

2.) plug x and either m value into the equation to get y

3.) plug x and y back into the equation with no numerical values and solve for m

given g(x) = f(x+b) +c. where in this function can you find the shifts?

f= stretched or shrunk by this value

(x+b) = shifted to the left or right by this value

c= shifted up or down by this value

- or + (f) = denotes the direction the parabola will open

(x+b) = shifted to the left or right by this value

c= shifted up or down by this value

- or + (f) = denotes the direction the parabola will open

how do you find the vertex from an equation in the form (x+t)^{2} + c

t(f(t)) is the vertex.

or, (t,c)

or, (t,c)

X^{m}X^{n}=?

X^{m+n}

(X^{m})^{n}

X^{mn}

(xy)^{m}

x^{m}y^{m}

x^{0}x^{n}

x^{n}

x^{-n}

1/x^{n}

x^{m}x^{-m}

1

how do you find the degree of a polynomial?

find the highest power in the polynomial; this is the degree

for |x| very large, the numerator and denominator (largest terms excluded):

are approximately 1

what is a rational function?

a function of the form r(x) = p(x) / q(x) where p and q are polynomials, and q can't equal 0.

How do you divide polynomials?

use standard long division

i^{2} = ?

1

define a sum and difference of two complex numbers

(a+bi) + (c+di) = (a+c) +(b+d)i

(a+bi)-(c+di) = (a-c) + (b-d) i

What is the complex conjugate?

if the expression is (a + bi), its complex conjugate is (a-bi)

Define multiplication of complex numbers

(a+bi)(c+di) = (ac-bd) + (ad-bc)i

Define division of complex numbers

(a+bi) / (c+di) = (ac + bd/c^{2}+d^{2}) + (bc-ad/c^{2}+d^{2}) i

What are the three ways to solve systems of linear equations?

substitution, standard elimination, and gaussian elimination with matrices

log_{b}y= x is the inverse of?

b^{x}=y

x^{logxy}=

y

log_{x}x^{t}=

t

log_{b}1 =

0

Log_{b}b=

1

log_{b}y=

logy/logb

log_{b}(xy)=

log_{b}x+log_{b}y

log_{b }(x/y) =

log_{b}x-log_{b}y

log_{b}y^{t} =

tlog_{b}y

Describe the expression B(t) = Pe^{rt}

B(t) = final amount

P= initial amount

r = growth/decay rate

t =time

what is the equation for the distance between two points?

√( (x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2})

What is the equation for the midpoint of a line?

(x_{1}+x_{2}/2 ), (y_{1}+y_{2}/2)

What is the equation of a circle?

(x-h)^{2 }+(y-k)^{2} = r^{2}

Area of a trapezoid

1/2 (b1+b2)h

Area of an ellipse/ equation in ellipse form

area = πab when the equation is in x^{2}/a^{2}+y^{2}/b^{2}=1 form

Area Stretch Theorem

The area of R' = cd times the original area (R)

what is the definition of *e*?

e is the number such that area(1/x,1,e) =1

lnx is a shorthand way of writing what?

log_{e}x

e^{0}=?

=1

lne^{x}=?

x

e^{lny}=?

y

What is the equation for the doubling time of a system?

70/R, where r = growth rate

What is the equation for the doubling rate of a system?

70/t, where t=time in years

how do you find the center, r, and area of a circle given in x^{2}+hx+y^{2}+ky=c form?

you complete the square, yielding the form (x-h)^{2}+(y-k)^{2}=r^{2}. from here you can find the center (h,k) and radius (r). area = πr^{2}

Cos(any ø)^{2} +sin(any ø)^{2} always equals...

1

any point in the region from π/2-->π is...

negative

what is the equation to find arc length?

L=øπ/180

what is the equation to find the area of a slice?

s=1/2ør^{2}

How do you convert from degrees to radians?

øπ/180

how do you convert from radians to degrees?

180/π

how do you find the 4 smallest + numbers ø such that sin or cosø = 0,-1 or 1?

go around the unit circle counterclockwise, stopping each time sin or cos= given integer x. do this 4 times. find the 1st one, add 2π to it to get the next one, etc...

how do you find the 4 smallest + numbers ø such that sin or cosø = 1/2 or √3/2?

find the first ø. (ex 30º). find the next ø in line on the unit circle (ex 150º). these are your 1st two numbers. Then, add your original ø to 360º, which yields the 3rd number. finally, add your second ø to 360 to get the 4th number.

secantø=

1/cosø

cosecantø=

1/sinø

cotangentø=

cosø/sinø

what is another way to write cotangent?

1/tanø

Cos^{2}ø+Sin^{2}ø =?

1

write tanø in terms of cosø

tanø= √(1-cos^{2}ø)/cosø

write secant in terms of tanø

1+tan^{2}ø=sec^{2}ø

what are the 3 trig identities with (π/2-ø)?

cos(π/2-ø) = sinø

sin(π/2-ø) = cosø

tan(π/2-ø) = 1/tanø

What are the 3 trig identities with (90-ø)?

cos(90-ø)= sinø

sin(90-ø)= cosø

tan(90-ø)= 1/tanø

What are the 3 trig identities with (ø+π)?

cos(ø+π) = -cosø

sin(ø+π) = -sinø

tan(ø+π) = tan ø

what are the 3 trig identities with (ø+2π)?

cos(ø+2π) = cosø

sin(ø+2π) = sinø

tan(ø+2π) = tanø

About this deck

Author: Melanie S.

Textbook: Precalculus: A Prelude to Calculus

Created: 2010-10-21

Updated: 2011-07-02

Size: 65 flashcards

Keywords: flash card flashcards digital flashcards note sharing notes textbook wiki college dorm class classroom exam homework test quiz university college education learn student teachers tutors share, study blue studyblue studyblu

Views: 79

Textbook: Precalculus: A Prelude to Calculus

Created: 2010-10-21

Updated: 2011-07-02

Size: 65 flashcards

Keywords: flash card flashcards digital flashcards note sharing notes textbook wiki college dorm class classroom exam homework test quiz university college education learn student teachers tutors share, study blue studyblue studyblu

Views: 79

Simply amazing. The flashcards are smooth, there are
many different types of
studying tools, and there is
a great search engine. I praise
you on the awesomeness.
- Dennis

I have been getting MUCH
better grades on all my tests
for school. Flash cards, notes,
and quizzes are great on here.
Thanks!
- Kathy

I was destroying whole rain forests with my flashcard production, but YOU, StudyBlue, have saved the ozone layer. The earth thanks you.
- Lindsey

This is the greatest app on my phone!! Thanks so much for making it easier to study. This has helped me a lot!
- Tyson

© 2014 StudyBlue Inc. All rights reserved.