A2Tslideshowreview2010x
Download
Report
Transcript A2Tslideshowreview2010x
tan
sin
cos
sec
1
cos
csc
1
sin
cot
cos
sin
sin cos
2
2
sin
2
1 cos
2
cos
2
1 sin
2
1 tan
2
sec
2
1 cot
2
csc
2
sin 2
cos 2
tan 2
Use your FORMULA
SHEET!!!!!
We use law of cosines when we have
______s.a.s._________ or
______s.s.s.____________.
r e g 2egCosR
2
2
2
Use law of sines when asked
to find the number of
triangles
that can be constructed.
j
a
sin J sin A
Axis of symmetry
equation: Turning point
b
x
2a
Plug in to find y!
Sum of the roots:
b
a
Product of the roots:
c
a
Quadratic formula:
b b 4ac
x
2a
2
Use this when asked for:
a+bi, simplest radical form
or to a decimal place.
i i
1 i
i i
(Divide exp. By 4)
2
3
1 i
0
Completing the square:
1. Subtract/add over the constant.
2. Factor out the coefficient of the x^2
and x term, if there is one.
3. Take half of the coefficient of the x
term and square it and add it to that
side, and also add it to the other
side.
4. Factor the trinomial you made.
5. Solve for y (or x), whichever they ask
for.
ex. y 3x 12x 7
2
Discriminant is used
to determine the
types of roots:
Rational, irrational,
equal or imaginary
b 4ac
2
If:
b2 4ac 0, roots are rational and equal
b 4ac 0, imaginary roots.
2
b 2 4ac 0, roots are real, unequal and
rational (if it's a perfect square)
b 4ac 0, real, irrational, unequal (if it's
not a perfect square)
2
Conic sections:
1. circle
3. hyperbola
4. parabola
ax ay r
2
2
2
ax 2 by 2 c or
xy k
2
y ax bx c
Distance Formula:
d
x1 x2 y1 y2
2
*used to find lengths of
line segments*
2
Midpoint formula:
x1 x2 y1 y2
,
2
2
*used to find the midpoint*
y
y
1
2
Slope:
x1 x2
s r
Theta must be in radians.
Inequalities: # line, use
test points.
If <, then shade between
endpoints.
If >, then shade outside
endpoints.
To find the inverse of a
Function:
1.Switch the x and y
2.Solve for y
3. If graphing, go to table
and switch the x and y.
Inverse variation:
Multiply, do not set up a
proportion!
Products
equal.
xy=xy
Direct variation:
x x
y y
Exponential growth and
decay.
amount after time t=initial amount(1 rate)
y ab
Remember to change
y a(1 r) or
t
time
x
percents by moving decimal
to the left 2 places.
Don’t forget to keep the “e”:
y Pe
rt
This is used when there is
Continuous growth.
You can only solve
exponential equations, log
equations must be written
Exponential form first!
Find a common base or log
Both sides to solve!
log b x p b x
p
Log form to:
exponent
form
log ab log a log b
a
log log a log b
b
log a n log a
1
log x log x
2
n
Fractional exponents:
3
2
x
x
3
Power over root!!!
Bottom number in the notch!
COfunctions: angles add
up to 90. complementary
sin 30 = cos 60
tan 14 = cot 76
sec 3 = csc 87
y asinb(x c) d
d is the midline Vert.shift
a is the amplitude
b is the Number of
curves from 0
to 2
c is the Phase shift
2
p
b
Period is the length of one
curve.
1
arcsin x is the same as sin x
We are looking for the
angle!!, 2nd calc sin
…..etc….
Remember when solving trig
Equations, find all quadrants.
Force problems –
remember to find the
top angle.
And no, the resultant
does not bisect the angle,
only in a rhombus!!
Area of a non-right triangle
Formula sheet!!!!!
1
k ab sin c
2
Must have 2 sides and the
Included angle!
If you see any of these, use
your FORMULA SHEET.
Binomial expansion:
st
nCr(1 term)
n r
nd
(2 term)
r
Plug in the
numbers and add
them all up!
Statistics and the Bell
Curve:
Use your formula sheet!
Mean, median, mode and
standard deviation, use
stats and 1-var stats in
your calculator.
X
For populations
Sx
For samples
If you are asked to find the
normal approximation and
not given the mean or s.d.
use these formulas and
your calculator:
mean np and std.dev.= npq
normalcdf (low #, upper #, mean, std .dev.)
X
X
is the mean
is the population
standard deviation
S x is the sample
standard deviation
All of these are found in
1 var-stat L1,L2
when asked to graph a
complex number: a+bi,
graph it as you would the
point (a,b) and then draw
an arrow from the origin to
the point.
Ex. Find the sum of 3+4i
and -2+i, then graph the sum.
If asked to find the length
of a + bi:
a b
2
2
Y=sin x
Y=cos x
You must know the domain
and range for the inverse
trig. functions:
1
y sin x, D : 1 x 1
R:
1
2
y
2
y cos x, D : 1 x 1
R: 0 y
1
y tan x, D : all reals
R:
2
y
2
Laws of Exponents:
x x x
a
b
ab
a
x
ab
x
b
x
a b
ab
(x ) x
1
a
x a
x
Remember,
anything
raised to the
zero power
is one.
Fractional Exponents:
r
b b
p
p
r
Fractional Equations:
Find where denom. =0.
Multiply through by the
Least common denominator
Getting rid of the fraction.
These values go on # line!
Fractional inequalities:
You must test on the number
line and see what interval
works for your inequality.
Sequences and series:
Arithmetic – separated by a
common difference.
an a1 (n 1)d
S
Oh yeah, it’s on
your formula sheet!
Geometric- each term is
multiplied by some number
to get to the next one. Divide
any term by the previous one
to find r, the common ratio.
an
r
an 1
an a1r
Sum=
n1
on your formula
sheet!
If you are given a
recursive formula, plug in
the first term to get the next
term and then plug in that
term to get the next one and
so on……… an 2an1 1
Probability:
r
C
(
p
)
(
q
)
n r
nr
At least r: r and up to n.
At most r: r and down to 0.
Probability:
Use permutations when
order is important. n
Pr
Use combinations when
order is NOT important.
C
n r
Probabilities based on
Geometric figures are the
ratio of areas.
Area formulas:
circle : a r
rectangle: a=bh
2
Radical equations
isolate the radical
square both sides
solve for x
check your solutions
Factoring:
GCF
Difference of squares
Trinomial
By grouping
Absolute Value equations:
isolate the abs. value
set up two equations
solve for x
check your solutions
Inequalities - # line!
Functions:
Vertical line test or no
x’s repeat.
one-to-one: no x’s or
y’s repeat, horizontal
and vert. line test.
onto- all x’s and y’s
are used, a line.