Click HERE for Semester 1.
what you believe you understand regarding parametric
of parametric equations. Note the context of the
problem to determine if angles are in degrees or radians!
JR: Why are these equations called parametric? What makes them that way?
Write parametric equations for the scenario:
The world's latest golfing sensation, Cheetah Forest, selects his sand wedge (56° loft) and will strike the ball at 88 feet per second.
Determine how far the ball will travel horizontally and vertically.2. An object moves along the path defined by y = x3 + 3. The x-coordinate satisfies the equation x(t) = -t + 1.
a) In what direction is the object moving?
b) What is the corresponding y(t)?
the Course syllabus
and save it to your computer's desktop. Scan through
each page and take particular note of required materials,
assessment procedures, and assignment requirements
Defined by Parametric Equations. Skim pp. 660-665.
Name That Parametrization activity.
JR: Explain in simple language how to convert a set of parametric equations into an equivalent Cartesian equation.
665 #7, 13, 15. Graph by hand and provide a table of
values you used for the sketch.
object moves according to the equation y = x2 +
3. The x-coordinate, x(t), satisfies the equation x = -t + 1.
with Parametric Curves.
JR: Explain in simple language how to take the first and second derivatives of a pair of parametric equations.
675 #7, 11, 17.
x(t) = t3 + t, y(t)
= t. Compute d2y/dx2
at the point (2, 1). What does it mean?
Coordinates. Picture Pages
Areas and Lengths in Polar Coordinates. Polar Propellers activity.
JR: Why does the parametric curve x = f(t), y = g(t) have a horizontal tangent line when dy/dt = 0 and dx/dt ≠ 0, and not the other way around? Include diagrams.
|pp. 686-687 #1, 3, 5, 11; pp. 692-693 #1, 5, 9, 21.|
the point (10, π/6) from polar to rectangular coordinates.
JR: Prove ∫ dx/(1 + x2) ≠ ln(x2 + 1) + C.
|Chapter10 AP AB/BC Review Questions; AP10-1, 2 (following p. 712). Do them all and show all work!|
||Write the polar equation of a circle with radius 3. Write the parametric equations for a circle with radius 3 centered at 1, 2).||Problem
JR: Explain in simple language how to convert polar to Cartesian and Cartesian to polar.
for the test.
||Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.||Test
10.1: Free response. NO graphing calculator or note
card! Expect questions on
everything you can about vectors (previous notes,
homework, etc. along with Websites giving background
information). This is an actual homework assignment
you are expected to do!
a formula to compute the distance between the given two
points in space A and B, for A(a, b, c)
and B(d, e, f). Explain why
this formula works.
dimensional coordinate system. Working With Surfaces in Three Dimensional
Space activity. When finished, please
JR: Explain why y = x is the equation of a plane, not a line, in 3-space. Sketch the situation.
814-815 #3, 5, 10, 11, 27.
are "basis vectors" and how are they used?
diagrammatic representations, relationships (e.g. why is i + j not a unit vector
even though i and
j are unit
Position Vector activity.
JR: In what ways is arithmetic with vectors like that with real numbers? In what ways does it differ?
822-823 #1, 5, 9, 15, 17.
does it mean to "multiply vectors?" What result
would you expect from the product?
Product. The Regular Hexagon
activity. HERE are
Edge's notes on Dot Product and HERE are Miss Welch's
notes from last year. Consider these online
830 #3, 5, 9, 15.
||What must be
true about the dot product of vectors a and b
for them to be orthogonal? for them to be
||pp. 830-831 #19,
23, 33, 35, 39, 41.
JR: Compute the angle between the vectors <1, 0, -1> and 1, 1, 0>. Explain the process and the meaning of the result in simple language.
vector product provides the following?
Product. Messing with the Cross
Product activity. HERE are Edge's notes on
Cross Product. Consider these online resources
838 #3, 13, 15.
||Review the linked online resources for Cross Product (see yesterday's activity).||pp. 838-839 #19,
27, 29, 33, 35, 39.
JR: Are the Dot Product and the Cross Product commutative in any non-trivial way? Explain.
|Finish the assigned problems.|
||A line contains
the points (-8, 1, 4) and (3, -2, 4). express the
line in each of the following forms.
and surfaces. The
Match Game activity: You will be handed four
index cards, each with equations of four different lines.
Your task is, by clever trading with other groups, to wind
up with four different descriptions of the same line.
JR: Explain the relationship between determining the equation of a line based upon
|p. 848 #1, 3, 7,
vertical traces of z = 4x2 + y2.
JR: Describe and sketch the surface resulting from x2/a2 + y2/b2 + z2/c2 = 1 if a, b, and c are different.
|pp. 856-857 #3, 11, 15, 19.|
859-860 #2,10, 7, 13, 14, 15, 18.
Chapter 12 AP AB/BC Review Questions; AP12-1 (following page 862).
JR: Explain in simple language why the Cross Product is a vector rather than a scalar, like the result of a Dot Product.
|Finish the review problems.|
||A constant force
of 3i + 5j + 10k moves a particle
from (1, 0, 2) to (5, 3, 8). Compute the work done
on the particle if the force is in Newtons and the
distance is in meters.
JR: Suppose u * (v x w) = 2. Compute
|Prepare for the
THESE are Dr. Edge's notes on Solving for the equation of the plane containing three given points.
HERE are Miss Welch's Chapter 12 Review notes.
||Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.||Test 12.1: Free
Response: you may use one 3 x 5 note card* and YOUR
calculator. Expect questions on
Project: Geometry of a Tetrahedron (p. 840).
the curve described by the vector function r(t)
= <sin t, t>.
Functions and Space Curves. The Angle Function activity.
JR: Use geometry to derive the formula to use to compute the length of a vector in "three-space" (e.g. r(t) = <a(t), b(t), c(t)>.
869-870 #1, 3, 7, 9.
||Compute the derivative of the vector function r(t) = <sin t, t>.||Derivatives
of Vector Functions. Velocity
Vectors activity. Note the theorem on
Pg. 872 regarding differentiation rules for vectors and
the table of derivatives on Pg. 874.
JR: In what way does a tangent vector to a curve at a point P and the unit tangent vector to a curve at point P differ?
876 #9, 19, 21, 23.
||Explain what it
means for a curve to be "smooth" and why this is important
in determining curvature.
||Arc Length and
Length of the Reaper activity.
JR: Examine how curvature is derived (see Pg. 879). What does this really mean in the context of standard functions in 2-d?
|Pg. 884 #1, 13,
particle moves along a curve defined by the equation y
= sin (πx). The x-coordinate, x(t),
satisfies the equation dx/dt = e2t.
When t = 0 the particle is located at the point
To Start activity.
JR: Consider a vector function v = <f(t), g(t), h(t)>. Is it true that |v'(t)| = |v(t)|'? Why or why not?
894 #1 (copy the table), 7, 9.
||The position vector of an object is r(t) = (t2, sin(t) ). Determine the velocity, speed, and acceleration of the object.||Motion In Space.
Tossing A Balloon activity.
A brief overview of Kepler's Laws.
JR: Explain the meaning of "curvature."
|Pg. 894 #7, 9, 15, 19.|
||What is the length of the curve r(t) = (12t, 5t). 10 ≤ t ≤ 10?||Checking Out the
JR: Graph in 3-d the function 8x + 2y + 3z = 0 for 4 ≤ x ≤ 4; 4 ≤ y ≤ 4; 10 ≤ z ≤ 10.
898 #4, 5, 8, 11, 17.
||Chapter 13 AP AB/BC Review Questions; AP13-1 (following page 900). Do them all and show all work!||In-class
review. Check answers.
JR: What does equation 12 (Pg. 893) have to do with Kepler's Laws? Explain the mathematical relationship!
|Prepare for the quiz.|
||Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.||Quiz
13.1. Free Response: you may use one 3 x 5 note
card* and YOUR calculator. Expect Questions on
everything you have that pertains to your previous work
with series (previous notes, homework, etc.).
Explore at least one of the following resources
Create and print your own graph paper at THIS Website.
Below are various documents on the
operation of the class
the additional items