Cycle B4 Calendar

Date

Topics

Assignment

Thu, Apr 29

B4 - 24 days - ends June 2

Review
• None
Fri, Apr 30
Review
• None

Mon, May 3

Review

Review Assignment:

• Scan each section in Ch 12. In particular, refresh your memory on the material in the colored boxes, and read through the example problems. Then work the exercises below:
• 12-1 (p. 423) Written Exercises #1, 3
• 12-2 (p. 429) WE #9, 11
• 12-3 (p.435) WE #1, 3, 5
• 12-4 (p. 444) WE #1, 3, 5
• 12-5 (p. 450) WE #7, 9
• 12-6 (p. 455) WE #1, 9

Tue, May 4

12-7 Determinants

• What is a determinant?
• rows and columns
• size of a determinant
• Evaluating a 2x2 determinant
• • Evaluating larger determinants
• minors
• the minor of an element is the determinant formed after you cross off the row and column containing that element
• • sign of a minor
• alternates, starting with "+"
• • evaluating a determinant using minors
• • You can add or subtract any multiple of any row/column to any other row/column in a determinant without changing the determinant's value
• 12-7 and study the examples
• Work:
• 12-7 Written Exercises #1-13

Wed, May 5

12-8 Applications of Determinants

• Cramer's Rule
• Solving 2 equations with 2 unknowns. If
ax + by = c
dx + ey = f, then • Solving 3 equations with 3 unknowns
• Geometry
• Area of parallelogram determined by A = (xa, ya) and B = (xb, yb) is:
Area = absolute value of • Area of parallelepiped determined by A = (xa, ya, za), B = (xb, yb, zb) and C = (xc, yc, zc)is:
Area = absolute value of • 12-8 and study the examples
• Work:
• 12-8 Written Exercises #1-17odd, 21
Thu, May 6

12-9 Determinants and Vectors in Three Dimensions

• Unit Vectors
• a unit vector is a vector whose length is 1
• Special unit vectors
• i is a unit vector in the +x direction
• j is a unit vector in the +y direction
• k is a unit vector in the +z direction
• Unit vector notation
• (3, 4, 5) = 3i + 4j + 5k
• Cross Product
• The cross product of two vectors A x B is a vector which is perpendicular to both A and B.
• If A = (xa, ya, za) and B = (xb, yb, zb) then • Geometric cross product
• If is the angle between vectors A and B, then
|A x B| = |A||B|sin • The direction of A x B is given by the right hand rule:
"Point the fingers of your right hand in the direction of A, then curl them toward the direction of B. Your thumb points in the direction of A x B."
• Properties of the Cross Product
• A x B is perpendicular to both A and B .
• A x B = -(B x A) . This means that the vectors A x B and B x A are opposite in direction - The cross product is NOT a commutative operation!
• A x (B + C) = (A x B) + (A x C). The cross product is distributive across (vector) addition.
• |A x B| is the area of the parallelogram formed by vectors A and B.
• A x B = 0 means that A and B are parallel (and vice versa).
• Cross product and dot product on the TI-89
• 12-9 and study the examples
• Work:
• 12-9 Written Exercises (p. 467) #1-9, 11-15odd
Fri, May 7
12-9 Determinants and Vectors in Three Dimensions
• Finish the 12-9 assignment

Mon, May 10

Cellular Automata - 1 Assignment
Tue, May 11
Cellular Automata - 2
Wed May 12
Cellular Automata - 3

Thu, May 13

Cellular Automata - 4

Fri, May 14

(Mr. S absent)

Review
• Chapter Summary on P. 468-469
• Chapter Test (p. 469) #1-13
• [Hint for #10: The center of the sphere is the point (0, -1, 3), so a vector normal (perpendicular) to the plane goes through the points (0, -1, 3) and (2, -3, -2).]

Mon, May 17

Reward Day
• None

Tue, May 18

Review
• None

Wed, May 19

Test - Ch 12 & Cellular Automata

• None
Thu, May 20

13-1 Arithmetic and Geometric Sequences

• Sequence
• function whose domain is usually the positive integers (natural numbers)
• first term, t1, second term t2, nth term tn
• can be specified by a formula:
tn = n2 - 1
• Arithmetic Sequences
• common difference, d = difference between any two adjacent terms
• the nth term:
• tn = t1 + d(n - 1)
• Example:
• 1, 4, 7, 10, 13, ... is an arithmetic sequence with common difference, d = 3.
• t1 = 1, t2 = 4, etc.
• the seventh term, t7 = 1 + 3(7-1) = 1 + 18 = 19
• Geometric Sequences
• common ratio, r = quotient of any two adjacent terms
• the nth term:
• tn = t1rn-1
• Example:
• 1, 4, 16, 64, 256... is a geometric sequence with common ratio, r = 4.
• the seventh term, t7 = (1)(47-1) = 46 = 4096

• 13-1 and study the examples
• Work:
• 13-1 Written Exercises (p. 476) #1-41odd
Fri, May 21

13-2 Recursive Definitions

• The formulas we used in 13-1 are called explicit definitions
• An explicit definition lets you calculate the value of any term
• A recursive definition has two parts:
• initial condition tells where the sequence starts
• recursion formula tells how to get the next term from the current term
• Finding:
• an explicit definition from a recursive definition
• Example: What is an explicit definition for the sequence t1 = 1, tn = tn-1 + 4?
• Generate some terms: 1, 5, 9, 13, 17, ...
• Recognize: This is an arithmetic sequence with t1 = 1 and d = 4.
• Since tn = t1 + d(n - 1) for an arithmetic sequence, tn = 1 + 4(n - 1), which simplifies to tn = 4n - 3.
• a recursive definition from an explicit definition
• a recursive definition from a description
• Some recursive functions
• 13-2 and study the examples
• Work:
• 13-2 Written Exercises (p. 481) #1-5odd, 11-19odd, 21-25

Mon, May 24

13-3 Sums of Arithmetic and Geometric Series

• Arithmetic Series
• • The sum equals n times the "average term"
• Geometric Series
• • Sn = nt1 (if r = 1)
• Calculating sums of series using a spreadsheet
• 13-3 and study the examples
• Work:
• 13-3 Written Exercises (p. 489) #1-9odd, 17-23odd, 29, 31
Tue, May 25

13-4 Limits of Infinite Sequences

• In mathematics, "limit" does not mean "limitation" or "handicap" - it means "a number that the terms of the sequence get closer and closer to, or homes in on" - it is a "target."
• means "As the number of terms gets larger and larger, the value of the terms of sequence S get closer and closer to (or homes in on) L"
• • limits that "do not exist"
• infinite limits
• 13-4 and study the examples
• Work:
• 13-4 Written Exercises (p. 496) #1-6, 9 (ans: 0), 10, 13, 15, 19, 20, 26
Wed, May 26
Quiz - Chapter 13
• Seniors - turn in books

Thu, May 27

(Last day for seniors with privileges)

• Seniors
• turn in books
• last day to turn in assignments

Fri, May 28

No Seniors (who still have senior privileges)

Mon, May 31

Memorial Day - No School

• None
Tue, June 1

Wed, June 2

End of B4 - 23 days

Have a GREAT summer break!

Last update by JL Stanbrough