PRECALCULUS
WORKSHEET 1 ON VECTORS & NAVIGATION
Draw a figure for each problem, and show all work. Give your answers correct to three decimal
places.
1. A ship sails 100 miles east and then 40 miles o
PRECALCULUS GT/HONORS
WORKSHEET 1 ON 5.5-5.6
Draw a figure for each problem. Show all work, and give your answers correct to three decimal
places.
1.
.
c 36, d 22, C 90 D
_
_
2.
A 44, B 61, b 70.
a
Ann and Sue both verified the same trig identity.
Anns Work
cos
sec tan
1 sin
1
sin
cos cos
1 sin 1 sin
cos 1 sin
1 sin 2
cos (1 sin )
Sues Work
cos
sec tan
1 sin
cos 1 sin
1 sin 1 sin
PRECALCULUS GT/HONORS
WORKSHEET ON 6.1
For each of the following:
Ex. For each of the following:
(a) Draw the vectors represented and the resultant.
(b) Find the magnitude of the resultant.
(c) Find t
finding limits
graphically and
numerically (1.2)
September 6th, 2016
I. An Introduction to Limits
Informal Definition: The limit of f(x), as x
approaches c from either side is the number L that
It is
PRECALCULUS GT/HONORS
WORKSHEET ON 5.5-5.6
Determine the number of triangles. Answer one, two, or none. Draw a figure and show your
work.
1. A 125, a 14, b 18
2. A 61, a 85, b 52
3. A 72, a 68, b 76
4
PRECALCULUS ADVANCED
WORKSHEET 2 ON VECTORS AND NAVIGATION
1. An airplane is traveling in the direction 50 with an airspeed of 300 mi/h. There is a
40 mi-per-hour wind with a direction 120. Find the p
AP EXAM FREE-RESPONSE QUESTIONS - THE MEAN VALUE THEOREM
What do MVT questions look like on the AP Free-Response Questions?
All of the Free-Response Questions in the table below have one or more parts
PLTW POE - Mid Term Review 2017 - VEX
1. In a certain country last year a total of 500 million tons of trash was recycled. The chart below shows the
distribution, in millions of tons, for the differen
Polynomial Functions
I. Polynomial functions:
A) Is any function whose first term is axn where n is a
positive whole number.
1) The exponent is called the power (or degree).
B) A polynomial function c
Radian and Degree Measure (part 2)
V. Arc Length.
A) An arc is a part of the circle (part of the circumference).
B) Formula: s = r
1) s is the arc length, r is the radius of the circle and
is the cen
Graphing y = ebx Functions
I. The Natural Base e.
A) e 2.72
B) e occurs in nature and in math/science formulas.
1
C) e = 1
n
n
as n approaches + .
D) y = Aebx+C + D is the natural base exponential f
Intro to Conics Parabolas
I. Parabolas.
A) Quadratic form: y = ax2 + bx + c
B) Directions parabolas open.
1) y = ax2 + bx + c
2)
y = ax2 + bx + c
or
x = ay2 + by + c.
x = ay2 + by + c
x = ay2 + by + c
Graphs of Cosine Functions (part 2)
I. Graphing the cosine function f(x) = cos .
A) Use the unit circle to find cos (width values).
1) cosine is the width, x, when is the angle.
2) = 0
= / 2
=
= 3/2
Radian and Degree Measure (part 2)
V. Arc Length.
A) An arc is a part of the circle (part of the circumference).
B) Formula: s = r
1) s is the arc length, r is the radius of the circle and
is the cen
Radian and Degree Measure
I. Angles (2 rays: an Initial side & a Terminal side).
A) Initial side = the starting ray of the angle.
1) It is on the + x-axis (from the origin).
B) Terminal side = the end
Sinusoidal Modeling
I. Getting the trig equation from data points.
Standard formula: y = D + A trig B(x + C).
A) A = Amplitude (the height [y values] of the graph).
1) A = the distance between the hig
Properties of Logarithms
I. Properties of Logarithms (Expand & Condense Logs).
A) Expansion of logs (you write the word log many times).
1) log b mn log b m + log b n
(add the logs)
2) log b m/n log b
Solving Exponential Equations
I. Relationship between Exponential and Logarithmic Equations.
A) Logs and Exponentials are INVERSES of each other.
1) That means they cancel each other out.
B) To solve
Compound Interest
I. Compound Interest: A = P ( 1 + r/n)nt
A = Account balance after time has passed.
P = Principal: $ you put in the bank.
r = interest rate (written as a decimal).
n = number of time
Logarithmic Functions and Their Graphs
I. Logarithm = another way of writing exponential expressions.
A) log base# x = y
B) Converting log expressions into exponent form (vice-versa).
1) log b y = x
b
Graphing Sine Functions (part 1)
I. Graphing the sine function f(x) = sin .
A) Use the unit circle to find sin (height values).
1) sine is the height when is the angle (x , y)
2) = 0
= / 2
=
= 3/2
Solving Exponential Equations
I. Relationship between Exponential and Logarithmic Equations.
A) Logs and Exponentials are INVERSES of each other.
1) That means they cancel each other out.
B) To solve
Modeling Exponential Functions
I. Writing Exponential Growth/Decay Equations from Stories.
A) Basic function: y = a(1 r)t
1) a = the initial amount.
2) r = the % increase or decrease (written as a dec
Radian and Degree Measure
I. Angles (2 rays: an Initial side & a Terminal side).
A) Initial side = the starting ray of the angle.
1) It is on the + x-axis (from the origin).
B) Terminal side = the end
Right Triangle Trigonometry
I. Definitions of Right Triangle Trigonometric Functions.
A)
opp
sin
hyp
adj
cos
hyp
opp
tan
adj
1) opp = opposite side, adj = adjacent side, hyp = hypotenuse
2) SOH CAH