Calculus is a study of trigonometry, advanced Algebra, elementary analysis, and plane,
solid and analytic geometry designed to provide critical processing skills necessary for
success in Calculus. It will include topics outlined in the Textbook. The use of technology
will be incorporated in the course. Emphasis will be placed on justification of answers
through various forms of communication including writing.
Students intending to take the Calculus AP course should have completed courses in
which they have studied algebra, geometry, trigonometry, analytic geometry and
elementary functions. These functions include those that are linear, polynomial, rational,
exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined.
Students need to be familiar with the properties of functions, the algebra of functions,
and the graphs of functions. Students should also have some understanding of the
language of functions – domain, range, periodic, symmetric, zeroes, intercepts, etc., ‐
and know the values of the trig functions for 0, π/6, π/4, π/3, π/2, π, and their multiples.
This course requires the use of a graphing calculator. Students will be instructed in the
use of the calculator and are expected to use it in completing homework, class work,
and on the AP test. The course covers topics that will be tested on the AP Calculus AB
exam – functions, graphs and limits, continuity, derivatives at a point and as a function,
related rates of change, properties of integrals, Fundamental Theorem of Calculus,
techniques of anti‐differentiation, numerical approximations to definite integrals
including trapezoidal and Simpson’s rule, and the application of integration and
differentiation to real world problems. Further topics may include L’Hopital’s rule,
Taylor and MacLaurin series, polar integration.
NOTE: STUDENTS TAKING THIS COURSE MUST TAKE THE AP CALCULUS EXAM IN MAY
Course Standard
Students will:
1. Work functions in a variety of ways: graphical numerical, algebraic. Students
should understand the connections among these representations.
2. Understand the meaning of the derivative in terms of a rate of change and local
linear approximation and should be able to use derivatives to solve a variety of
problems.
3. Understand the meaning of the definite integral both as a limit of Riemann sums
and as a net accumulation of change and should be able to use integrals to solve
a variety of problems.
4. Understand the relationship between the derivative and the definite integral as
expressed in both parts of the Fundamental Theorem of Calculus.
5. Communicate mathematics and explain solutions to problems both verbally and
in written sentences.
6. Model a written description of a physical situation with a function, a differential
equation, or an integral.
7. Use technology to help solve problems, experiment, interpret results, and
support conclusions.
8. Determine the reasonableness of solutions, including sign, size, relative accuracy,
and units of measurement.
9. Develop an appreciation of calculus as both an inherent body of knowledge and
as a human accomplishment.
Textbook and Supplies
Calculus Early Trancendentals by Anton. Published by Wiley.
Course Outline
First Quarter
Week 1: Introduction to Trigonometry, definition of terms, angle in standard position.
Week 2: Converting Radian to degree and vice‐versa, solving radian measure using the
formula s = r and finding co‐terminal angles.
Week 3: Finding the supplement and complement of an angle, and solving the six
trigonometric functions.
Week 4 ‐ 5: Sines, cosines, and tangents of special angles, and solving trigonometric
functions using trigonometric identities.
Week 6 ‐ 7: Right triangle and Pythagorean Theorem, and application of SOH‐CAH‐TOA.
Week 8: Trigonometric functions of any angle, reference angles, and solving
trigonometric equations.
Week 9: Review and Midterm exams. Second Quarter
Week 10: Derivation of Law of Cosine and solving oblique triangles using the law of
cosine with Bearings.
Week 11: Derivation of the Law of Sine and the Law of Tangent, and problems involving
those laws with Bearings.
Week 12: Verifying/proving trigonometric identities.
Week 13 – 14: Sum and Difference Formulas for Sine, Cosine, and Tangent, and
evaluating trigonometric functions.
Week 15: Follow‐up for sum and difference formulas.
Week 16: Double‐angle and half‐angle formulas, and their applications.
Week 17: Vectors in plane and its introduction, and Component for of a vector.
Week 18: Review and Final Exams.
Evaluation
Grading Homework
- By Inspection During Class – Teacher will ask to see the work.
- When Handed In – some homework assignments are to be turned in for
grading.
- Late work is discounted 10% first class period, 25% the next class period,
and receives a zero if later than two class periods
Grading Tests
- Tests are 100 points each (sometimes extra credit is given on the test, so a
score over 100 is possible).
- Partial credit is given, wherever possible, for correct work. You must SHOW
YOUR WORK to receive partial credit.
- An incorrect answer with no work shown is fully discounted.
- The semester final is worth 20% of your final grade.
COMPONENTS OF GRADE
evaluation example
Quizzes
25%
Seatwork
20%
Homework
10%
Class Standing
15%
Examination
30%
Grading Scale:
Grading Scale
A+
97 - 100
4.0
A
94 - 96.99
4.0
A-
90 - 93.99
3.7
B+
87 - 89.99
3.3
B
84 - 86.99
3.0
B-
80 - 83.99
2.7
C+
77 - 79.99
2.3
C
74 - 76.99
2.0
C-
70 - 73.99
1.7
D+
67 - 69.99
1.3
D
64 - 66.99
1.0
D-
60 - 63.99
0.7
F
0 - 59.99
0
Course Requirement
Students should have successfully completed preCalculus or equivalent material,
or receive permission of the instructor.
Be prepared for class with pencil, notebook, and book.
Be on task at the appropriate times.
Work with others in an appropriate manner.
Your contribution to class discussions is expected and appreciated. ‐ AP free response problems
These problems are assigned randomly throughout the year, starting around November.
They are problems for which you have a week to arrive at a solution. These problems
are to help you with your problem solving skills and to prepare you for the AP test. They
are handed in and graded as homework, using the AP Test grading procedures. ‐ Notebook
You need a notebook that is dedicated to math.
DO NOT PURCHASE A ‘FIVE SUBJECT’ NOTEBOOK. You will be handing in the notebook
occasionally for the teacher to check homework, so it will not be available to you
Notebooks should be handed in during every test. The teacher is looking for:
1. Organization
2. Homework (not just the answers but the WORK)
The notebook is graded on a 5 point scale.
5 points: organized, all sections clearly delineated, all homework attempted.
0 points: no work or notebook missing on the day requested or obviously copied. ‐ Homework
Like any new language, you have to practice math or you will not learn it. You can
expect a homework assignment every day. Take notes, participate in class, the
homework will be a breeze.
Homework is your chance to test out, solidify, or ‘come to grip[s’ with what we’ve talked
about in class that day. It is graded when the teacher assess your notebook and in
homework quizzes.
1. Read directions carefully
2. Write each separate assignment on a new sheet in your notebook.
3. MAKE HOMEWORK CORRECTIONS. Write them next to the original work, in the
margin, wherever. Try to underline your mistakes, so when you review for a test,
you’ll know what kind of thinking to avoid.
4. You will generally have between 10 – 30 problems (or more) for homework. ‐ Homework quizzes
You will have many homework quizzes. This test is closed book. You will be expected to
use your notebook. Problems are identified by page number, section number, and
problem number. Copy the work from your notebook onto the quiz sheet. Occasionally
there will be free response questions on these quizzes as well. On these quizzes, just
writing down the answer (unless appropriate) is insufficient and will be counted as an
incorrect response. ‐ Tests
1. Occur every two to three weeks.
2. Test will cover ANY MATERIAL WE HAVE DISCUSSE#D IN CLASS. Don’t just
assume the test will only cover the ‘new’ material. Anything we’ve had thus far
is fair game to be included. Unless otherwise indicated, tests are closed book.
3. On your test, always circle the final answer.
4. Always round to two decimal places.(9.213; NOT 9.2)
- The AP Test expects all answers to be three decimal places – you will lose
points for not doing this.
5. Always indicate units where appropriate (m/sec or kg m/sec2)
- The AP Test expects units to be shown – you will lose points for not
indicating units on tests and worksheets.
6. Always show your work – if the answer is wrong you may still receive partial
credit for the correct procedure.
7. No work shown usually results in a poorer grade.
8. YOU MAY NOT USE ELECTRONIC TRANSLATORS FOR A TEST. IF YOU HAVE
TROUBLE WITH VOCABULARY ASK THE TEACHER FOR HELP.
9. Portions of the AP Test require the use of a graphing calculator. LEARN TO USE IT
EFFICIENTLY TO HELP YOU SOLVE PROBLEMS.
10.CHEATING ON A TEST (OR HOMEWORK) RESULTS IN A GRADE OF ZERO FOR THAT
ASSIGNMENT FOR BOTH PARTIES. ‐ Calculators
1. You are expected to have a calculator. A TI‐83+ (or better) graphing calculator is
used throughout the course. You should at the least have a scientific calculator
to use on homework.
2. School calculators do not leave the classroom. UNLESS THEY ARE ASSIGNED OR
RENTED TO YOU
3. If assigned, they are to be returned the NEXT DAY.
4. If the calculator is lost or broken while in your possession, you are responsible
for replacing the calculator (cost $100).
5. If you need a calculator for the year, see the office staff to arrange a possible
rental.
Weekly Informational Knowledge Overview - (Students will know...)
…This week is all review of previous
materials in Pre‐Calculus.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…graph exponential functions, trigonometric
functions, etc.
Monday
Tuesday
Wednesday
Thursday
Friday
***FIRST DAY OF CLASS***
Mon. Main Activity/Lesson:
Today is the introduction to the course. Distribute syllabus,
calculators, text books. Discuss at length the syllabus of the class and
the class expectations.
Evaluation:
Vocabulary:
Homework:
Tues. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Wed.Main Activity/Lesson:
Review pre‐calculus materials and information. Exponential
functions, trigonometric functions, etc.
Evaluation:
Vocabulary:
Homework:
Thurs.Main Activity/Lesson:
Review key concepts of Pre‐Calculus again.
Evaluation:
Vocabulary:
Homework:
Fri.Main Activity/Lesson:
QUIZ ON PRE‐CALCULUS REVIEW
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
…some strategies for finding limits of
functions;
…how to apply limits in word problems;
…the limits of trigonometric functions.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find limits of polynomial, rational and
trigonometric functions.
…recall some trigonometric identities.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson:
Limits of Polynomial and Rational Functions
Evaluation:
Seatwork ‐ #s 5 – 22, p. 65
Vocabulary:
limit, rational function
Homework:
#s 23 – 26, p.65
Tues. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Weds. Main Activity/Lesson:
The limit of Composite Function and Limits of Trigonometric
Functions
Evaluation:
First 3 and seatwork
Vocabulary:
Homework:
#s 27 – 34, p 65
Thurs. Main Activity/Lesson:
Theorem 1.7 – Functions that Agree at all but one point:
Evaluation:
Seatwork
Vocabulary:
Homework:
Fri. Main Activity/Lesson:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
...the trigonometric identities;
…the identities of each trigonometric
function;
…the limits of trigonometric functions.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…recall the basic trigonometric identities;
…use the different identities to find the
limits of trigonometric functions;
…prove/verify some trigonometric identities.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson:
REVIEW – Trigonometric Identities
Theorem 1.9 – Two Special Trigonometric Limits:
Evaluation:
Teacher’s own formulated equation (not from the book)
Vocabulary:
identity
Homework:
Read Theorem 1.9, p. 63.
Tues. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Wed. Main Activity/Lesson:
Theorem 1.9 – Two Special Trigonometric Limits:
Evaluation:
seatwork ‐
Vocabulary:
Homework:
Thurs. Main Activity/Lesson:
Follow‐up discussion about trigonometric identities
Evaluation:
more exercises from the teacher
Vocabulary:
speed, arc, linear speed
Homework:
study for the quiz
Fri. Main Activity/Lesson:
QUIZ # 3
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
…the discontinuity of a given function;
…identify the domain and range of a given
function;
…the difference between the removable and
non‐removable discontinuity.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…determine the domain and range of a
function;
…discuss the discontinuity of given
functions;
…read the graph of continuous and
discontinuous functions.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson:
QUIZ # 2
Evaluation:
(The quiz last Friday was postponed)
Vocabulary:
Homework:
Tues. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Weds. Main Activity/Lesson:
Continuity at a point and on an Open Interval
(Discussion throughout the period)
Evaluation:
Vocabulary:
Homework:
#s 1‐6, p. 76
Thurs. Main Activity/Lesson:
Continuity at a point and on an Open Interval (Day 2)
Evaluation:
Seatwork ‐ #s 25‐28, p. 76
Vocabulary:
Homework:
Fri. Main Activity/Lesson:
QUIZ # 3
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
Know the different families of functions and
the concept of inverse proportions
About Power functions with non‐integer
proportions
Polynomials and algebraic functions
Weekly Procedural Knowledge Overview - (Students will be able to...)
… make sketches of graphs to show their
period and amplitude
… demonstrate if data is inversely or directly
proportional to variables.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson: Angle Relationship ‐
We will study the families of curves and the different parameters that
are available. We will also look at the power functions and the family
y=x^n
Evaluation:
Vocabulary:
parameters, proportionality
Homework:
Exercise Set 0.3, #s 1‐12
Tues.Main Activity/Lesson:
We will look at polynomials and functions with non‐integer
exponents.
Evaluation:
Vocabulary:
Homework:
Exercise Set 0.3, #s 13‐28
Wed.Thurs. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Thurs. Main Activity/Lesson:
We will look at algebraic functions, as well as the families y=A sinBx
and y=A cos Bx
Evaluation:
Vocabulary:
Homework:
0.3 Exercise set 29‐38
Fri. Main Activity/Lesson:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
…the derivatives of composition;
…the alternative versions of chain rule;
…how to apply the chain rule in finding the
derivative of a function.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…apply the chain rule in finding the
derivative of a function;
…solve real‐world problems involving chain
rule.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Applying the derivative of trigonometric functions in solving word
problems
Evaluation:
(no time for seatwork, the lesson is too long)
Vocabulary:
171‐173
Homework:
Learning Objective:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Solving real‐world problems involving derivatives of trigonometric
functions – Rates of change in distance
Evaluation:
Vocabulary:
Homework:
Learning Objective:
THE CHAIN RULE –Derivatives of Composition
Evaluation:
answer #s 7‐15, p. 179
Vocabulary:
Homework:
Learning Objective:
SCHOOL TRIP
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the derivative of trigonometric functions in
complex form;
…how to represent an expression as one
variable;
…how to apply chain rule in finding the
derivatives of some functions.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…derive some trigonometric functions;
…apply the chain rule in finding the
derivatives of some functions.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
CHAIN RULE – Derivative of Compositions
Let u = any expression in a complex form
Evaluation:
Seatwork
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Derivative of Compositions – Trigonometric functions
e.g. If f(x) = sin 2x, then f’(x) = (cos 2x)(2) or 2cos 2x
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Derivative of Compositions – Trigonometric functions
e.g. If f(x) = sin 2x, then f’(x) = (cos 2x)(2) or 2cos 2x
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to find the derivatives of functions
using implicit process;
…the difference between implicit and
explicit;
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the derivatives of some functions
defined implicitly by equation.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
Implicit and Explicit Differentiation
(This lesson has to be discussed to the students for 3 days)
Evaluation:
Vocabulary:
Implicit and Explicit
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Implicit and Explicit Differentiation
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Implicit and Explicit Differentiation
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
Please see Lesson Plan dated October 21‐25
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
PLEASE SEE LESSONN PLAN DATED October 21‐25
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the lessons covered in the midterm exams.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
***REVIEW FOR THE MIDTERM***
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
MIDTERM EXAMINATION
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
PREPARATION FOR NUMBO
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
NUMBO GAME
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to find the derivative of exponential
function;
…the derivation of the derivative of
exponential function;
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the derivative of each exponential
function;
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Derivative of EXPONENTIAL FUNCTION (Formula 1 and 2)
DISCUSSION FOR THE ENTIRE PERIOD
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Study the Derivative of Exponential Function
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Derivative of Exponential Functions (Formula 3 and 4)
DISCUSSION AND DERIVATION OF FORMULA 3 and 4
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Review plus exercises about formula 1, 2, 3 and 4
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 1
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to find the derivative of exponential
function;
…the derivation of the derivative of
exponential function;
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the derivative of each exponential
function;
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
Derivative of Exponential Function with CHAIN RULE
Evaluation:
Exercises
Vocabulary:
Exponential Function
Homework:
Answer the problems left in the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Derivative of Exponential function in IMPLICIT FORM
Evaluation:
Vocabulary:
implicit form
Homework:
Learning Objective:
Language Objective:
Main Activity:
(…continuation of the previous lesson)
Evaluation:
drills
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 1
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to apply differentiation to solve word
problems; …the use of the value of
Weekly Procedural Knowledge Overview - (Students will be able to...)
…realize the importance of differential
calculus in solving real‐world problems;
…find enjoyment in solving calculus
problems;
…follow the step‐by‐step process of solving
functions that are differentiable by dt.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
Differentiating Equations to Relate Rates – (word problems)
DISCUSSION
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Please see Lesson Plan dated MONDAY APPLICATION
(continuation)
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
RELATED RATES (Day 3)
Evaluation:
Vocabulary:
Homework:
Review for the quiz
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how the volume of solids is applied in
Calculus;
…how fast the change is when one variable
changes.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…recall how to solve volume of solids;
…apply the chain rule in solving related rates
in the volume of solids.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Have an advance reading of Related Rates – VOLUME OF SOLIDS
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Related Rates – VOLUME OF SOLIDS
Word Problems
Introductions
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Related Rates ‐ Volume of Solids DAY 2 (Solving word problems)
Evaluation:
seatwork
Vocabulary:
Homework:
question 46 and 47
Learning Objective:
Language Objective:
Main Activity:
Group activity
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…that L’Hồpital’s Rule is used to find the
limits using derivative of any function;
…how to determine whether the given
function is indeterminate form.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the limits of functions using L’Hồpital’s
Rule;
…derive the L’Hồpital’s Rule.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 3
Evaluation:
Vocabulary:
Homework:
Havean advance reading about the L’Hồpital’s Rule
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
The L’Hồpital’s Rule for Indeterminate Form 0/0
(One week Discussion)
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
The L’Hồpital’s Rule for Indeterminate Form �0/0
(One week Discussion)
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
The L’Hồpital’s Rule for Indeterminate Form �0/0
(One week Discussion)
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to find the derivative of a function in
the form
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the derivative of a function of form …find enjoyment in playing NUMBO –
Christmas Edition
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 4 – L’Hopital’s Rule Indeterminate form 0/0
Evaluation:
Vocabulary:
Homework:
Make an advanced reading about L’Hopital’s Rule of the form
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
L’Hopital’s Rule (Second week) Indeterminate Form
Evaluation:
Seatwork, Drills
Vocabulary:
Homework:
Complete your numbo card
Learning Objective:
Language Objective:
Main Activity:
NUMBO – Christmas Edition
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
MERRY CHRISTMAS and A HAPPY NEW YEAR!!!
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to sketch the graph of a continuous
function f with different properties;
…the critical points of some functions.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the relative maxima and minima of a
function;
...determine the critical points of a function.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
Short review of L’Hopital’s Rule
L’Hopital’s Rule –Indeterminate form
Evaluation:
Seatwork, exercises
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Relative Maxima and Minima ‐ GRAPHING POLYNOMIALS
Evaluation:
exercises and drills
Vocabulary:
Maxima and Minima
Homework:
Learning Objective:
Language Objective:
Main Activity:
Relative Maxima and Minima
Evaluation:
group work
Vocabulary:
Homework:
Review for the quiz
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 5
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the indeterminate form 0 x ∞;
…how to find the derivative of such
expression.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the derivative of expressions in the
form 0 x ∞.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
INDETERMINATE FORM OF TYPE
Evaluation:
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INDETERMINATE FORM OF TYPE 0 ∙ ∞
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
continuation of the lesson dated January 15, 2014
Evaluation:
seatwork
Vocabulary:
Homework:
review for the quiz
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 6
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…Final examinations week
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
REVIEW FOR THE FINAL EXAMINATIONS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
REVIEW FOR THE FINAL EXAMINATIONS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
FINAL EXAMINATION – DAY 1
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
FINAL EXAMINATION – DAY 2
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
FINAL EXAMINATION – DAY 3
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the students shall be able to define
integral calculus;
…recall the process of finding the derivative
of a function;
…find the area of a region under a curve of a
graph using Rectangle Method and Newton’s
Method.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…the students shall be able to define
integral calculus;
…recall the process of finding the derivative
of a function;
…find the area of a region under a curve of a
graph using Rectangle Method and Newton’s
Method.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
INTRODUCTION TO INTEGRAL CALCULUS
***Discussion and Definition of Integral Calculus***
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
AREA PROBLEM – by Rectangle Method
Evaluation:
Drill , seatwork
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
…continuation of AREA PROBLEM
Rectangle method (Trigonometric Functions)
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
AREA PROBLEM – Newton’s Method
It states that the derivative of the area is Equal to the value of f(x).
In symbols,A’(x) = f(x)
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the students shall be able to define
integral calculus;
…recall the process of finding the derivative
of a function;
…find the area of a region under a curve of a
graph using Rectangle Method and Newton’s
Method.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
(…continuation of) Newton’s Method for Area Problem –
More examples
Review for the first quiz
Evaluation:
Vocabulary:
Homework:
review for the quiz
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 1
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Discussion of the answers from the Quiz
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the parts of integration;
…students shall be able to write the
derivative and anti‐derivative formula of a
function;
…students shall be able to find the integral
of a given polynomial.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to find the integral of polynomial
functions;
…name the properties of integration;
…identify the parts of integration.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
INTEGRATION – Definition of Anti‐derivatives and antidifferentiation
Rewriting derivatives to integration (DISCUSSION FOR THE ENTIRE PERIOD)
Evaluation:
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INTEGRATING POLYNOMIALS
Evaluation:
drill
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
INTEGRATING POLYNOMIALS
(DAY 2)
Evaluation:
Vocabulary:
Homework:
Exercises from the book
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INTEGRATING POLYNOMIAL ‐ Application of the lesson
Evaluation:
seatwork, drill, first 3
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Application of INTEGRATING POLYNOMIALS –
PARTICULAR SOLUTIONS
Evaluation:
Seatwork �
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…apply the integration of polynomials in
solving word problems;
…recall the equation and formula of
different lesson in trigonometry.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to recall some formulas needed to solve
word problems;
…to find the particular solutions for each
given problem;
…to solve real‐world problems.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
NO CLASSES
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
HOLIDAY – EDSA People Power
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
WORD PROBLEMS – Particular Solutions (Integral of Polynomials)
Evaluation:
seatwork, drills
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
The same lesson as Wed.
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
The same lesson as Wed.
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the consumption of energy in the year
1999;
…the GENERAL POWER RULE;
…how to apply the general power rule.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to find the integral of a function using the
general power rule;
…to apply the general power rule in solving
word problems.
have an advance reading about the power rule of integral
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
THE GENERAL POWER RULE
If u is differentiable function of x, then
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
GENERAL POWER RULE
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
APPLICATION OF GENERAL POWER RULE
Evaluation: EXERCISES/Seatwork
Evaluation:
Vocabulary:
Homework:
review for the quiz on Monday
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the parts of integration;
…students shall be able to write the
derivative and anti‐derivative formula of a
function;
…students shall be able to find the integral
of a given polynomial.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to find the integral of polynomial
functions;
…name the properties of integration;
…identify the parts of integration.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
INTEGRATION – Definition of anti‐derivatives and
anti‐differentiation
Rewriting derivatives to integration (DISCUSSION FOR THE ENTIRE PERIOD)
Evaluation:
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INTEGRATING POLYNOMIALS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INTEGRATING POLYNOMIALS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the integral of exponential and logarithmic
functions;
…how to find the integral of an exponent
that is differentiable function of x.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to find the integral of exponential and
logarithmic functions.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
INTEGRAL OF EXPONENTIAL FUNCTION
Derivation of Formula
Evaluation:
seatwork
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INTEGRAL OF EXPONENTIAL FUNCTION
Derivation of Formula
Evaluation:
seatwork, drills
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
INTEGRAL OF EXPONENTIAL FUNCTION Using the Log Rule
Evaluation:
seatwork, drills
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
INTEGRAL OF EXPONENTIAL FUNCTION Using the Log Rule
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
...the integral of natural logarithmic
functions;
…how to apply the integrals of natural
logarithmic functions to solve real‐world
problems;
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
INTEGRALS OF NATURAL LOGARITHMIC FUNCTIONS
Application and WORD PROBLEMS
Evaluation:
seatwork, drills
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
QUIZ # 5
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
DISCUSSION OF ANSWERS IN THE QUIZ
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
SPAS OLYMPICS
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…MIDTERM EXAMS
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
ACTIVITY – NUMBO GAME
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
REVIEW FOR THE MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
REVIEW FOR THE MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
REVIEW FOR THE MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
REVIEW FOR THE MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…evaluate integrals;
…evaluate definite integrals using the
Fundamental theorem of Calculus;
…Use definite integrals to solve marginal
analysis problems;
…Find the average values of function over
closed interval.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
DEFINITE INTEGRAL – Definition and derivation of formula
Language Objective:
Main Activity:
Evaluation:
seatwork and drill
Vocabulary:
upper and lower limits
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
…continuation of the lesson from Monday
Evaluation:
seatwork and drills
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
The Fundamental Theorem of Calculus
Definition and formula
Evaluation:
seatwork and drills
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
The Fundamental Theorem of Calculus
Evaluation:
Vocabulary:
Homework:
exercises from the book
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…find the definite integral using the
Fundamental Theorem of Calculus.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Language Objective:
Main Activity:
Fundamental Theorem of Calculus
Evaluation:
seatwork
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
PROPERTIES OF DEFINITE INTEGRALS
Evaluation:
seatwork
Vocabulary:
Homework:
exercises from the book
Learning Objective:
Language Objective:
Main Activity:
HOLIDAY – Labor Day
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Language Objective:
Main Activity:
(…continuation of the previous lesson)
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to find the definite integrals of natural
logarithm and radicals.
Weekly Procedural Knowledge Overview - (Students will be able to...)