STEM Innovation Academy of Orange
NJIT’s MTH 111: AP- Calculus AB
Mr. Ahmed Salama
The overall goal of this course is to help students understand and apply the three big ideas of Calculus: limits, derivatives, and integrals and the Fundamental Theorem of Calculus. Imbedded throughout the big ideas are the mathematical practices for AP Calculus: reasoning with definitions and theorems, connecting concepts, implementing algebraic/computational processes, connecting multiple representations, building notational fluency, and communicating mathematics orally and in well-written sentences. All students are required to complete summer work reviewing Pre-calculus and Algebra 2 concepts prior to entry in the course. Students will be provided with and expected to regularly use a school-issued TI-Nspire CAS CX graphing calculator.
Unit 1: Functions, Limits, Continuity
Unit 2: Derivatives
Unit 3: Applications of Derivatives
Unit 4: Integration
Unit 5: Applications of Definite Integrals
Unit 6: Transcendental Functions Calculus
Unit 7: Differential Equations
Unit 1 -- Functions, Graphs, Limits and Continuity
- 1.0 Slopes & Velocities • 1.1 Limit of a Function • 1.2 Limit Properties • 1.3 Continuous Functions • 1.4 Formal Definition of Limit
Unit 2 -- The Derivative
- 2.0 Slope of a Tangent Line • 2.1 Definition of Derivative • 2.2 Differentiation Formulas • 2.3 More Differentiation Patterns • 2.4 Chain Rule (!!!) • 2.5 Using the Chain Rule • 2.6 Related Rates • 2.7 Newton's Method • 2.8 Linear Approximation • 2.9 Implicit Differentiation
Unit 3 -- Derivatives and Graphs
- 3.1 Introduction to Maximums & Minimums • 3.2 Mean Value Theorem • 3.3 f' and the Shape of f • 3.4 f'' and the Shape of f • 3.5 Applied Maximums & Minimums • 3.6 Asymptotes • 3.7 L'Hospital's Rule
Unit 4 -- The Integral
- 4.0 Introduction to Integrals • 4.1 Sigma Notation & Riemann Sums • 4.2 The Definite Integral • 4.3 Properties of the Definite Integral • 4.4 Areas, Integrals and Anti-derivatives • 4.5 The Fundamental Theorem of Calculus • 4.6 Finding Anti-derivatives • 4.7 First Applications of Definite Integrals • 4.8 Using Tables to Find Anti-derivatives • 4.9 Approximating Definite Integrals
Unit 5 -- Applications of Definite Integrals
- 5.0 Introduction to Applications • 5.1 Volumes • 5.2 Arc Lengths & Surface Areas • 5.3 More Work • 5.4 Moments & Centers of Mass • 5.5 Additional Applications
Unit 6 -- Transcendental Functions Calculus
6.1 Natural logarithmic function, differentiation. 6.2 Natural logarithmic function, differentiation. 6.3 Inverse function derivative and integration. 6.4 Exponential function.
Unit 7 -- Introduction to Differential Equations • 7.0 Introduction to Differential Equations • 7.1 Differential Equation y'=f(x) • 7.2 Separable Differential Equations • 7.3 Exponential Growth, Decay & Cooling
Mr. Ahmed Salama
- MS Mathematics/Science Education from the University of Suez Canal University
- BS in Physics from Kean University
- BS Mathematics from Kean University
- Educational Leadership from Montclair State University
See Mr. Salama featured on NJ Classroom Close Up https://classroomcloseup.org/segments/earth-space-science/
Online eBook Calculus 9th Edition by Ron-Larson. Bruce H, Edwards. It is available for all students on Google Classroom.
- mechanical pencil
- Graphing calculator (TI-84 or TI-Nspire)
3-ring binder with all items arranged chronologically
- graph paper
- Arrive to class prepared and on time each day
- Create a positive environment.
- Do ALL homework independently
- Ask for help if you do not understand
- Be a resource to your fellow students
- Follow all rules from the STEM Innovation Academy of Orange student handbook
- Cell phones must be stowed in your backpack and silenced.
- You must sign in and out of the class to use the restroom, only one student may leave at a time
- Respectful language and behavior are required at all times
- No food or drink is permitted besides water, which is not allowed near any electronics
Google Classroom Class Code gpuiow2
Links to handouts, PowerPoints, and other class materials will be posted here. Some assignments will be turned in by uploading into the Google Classroom.
Grades will be available to students and parents through the Genesis portal. Students are responsible for reviewing their grades at least once per week.
Extra resources Online (https://www.math.ucdavis.edu/~kouba/ProblemsList.html)
Students should expect homework most nights and weekends. Late assignments may be accepted for reduced credit. Late homework assignments will incur a 5 pt per school day deduction for five days and a 0 on the 6th school day; yielding a maximum score of 75% for late work. Students may request an extension but they have to exhaust the intervention opportunities first (advisory, office hours, lunch, before school, etc.). Exceptions may be given for extenuating circumstances, upon discussion with the teacher. See the STEM Academy Student Handbook for additional details on missing assignments policy.
Formative Assessments (20%)
Announced quizzes, Do-Now quizzes, and Exit Tickets are examples of formative assessments. Students that miss these assessments must make them up the following day.
Handouts and Google classroom questions are some examples of graded classwork. Students are expected to finish and submit classwork within the class period. If a student fails to complete the classwork by the end of the period, it may be submitted online by 5 PM.
Summative Evaluations/Tests (25%)
Tests are essential for demonstrating math skills and practices. Expect three to four tests every marking period. Students that miss a test due to an absence must have a note from a parent/guardian. Make-up tests must be scheduled within a week of the test date.
Authentic Assessments (25%)
Projects and presentations are to be expected. Authentic assessments are graded using separate rubrics that will be reviewed at the beginning of every assessment. These rubrics will be based on content knowledge, practice of 21st-century skills, embodiment of habits of mind and/or application of mathematical practices.
Homework: Just like sports, music, and numerous essential skills, practice is essential to mastery in mathematics. If there’s no struggle, there’s no progress. Much like sweating and working through frustrating performance plateaus in sports or physical training, you can work through the struggle in math by using the skills you already have, developing new skills I will teach you, and using the resources available to you (tutorials, website, textbook, study groups, tutors, online, etc.) Some of your practice will be in class, sometimes it might be done with your peers, often it will involve your calculator, but it will always involve your deliberate, concentrated efforts.
The back of your E-Book has the answers to most problems. After completing each problem, you should check your answer to that problem in the back of the book. If you got it correct, move on to the next problem. If you got it wrong, try to find your mistake. Use your notes as a reference; we likely did a similar problem in class. If you cannot figure out how to do the problem correctly, ask a classmate, a tutor, or Mrs. Aguirre for help. Notes: All notes should be kept organized in chronological order) inside a 3-ring binder. Do not throw away old notes. If you are absent, it is your responsibility to get the notes from a classmate
Classroom Rules/Expectations: • Students are expected to follow all regulations stated in the STEM Innovation Academy of Orange. The utmost respect for classmates, teachers, and self will be expected. Respect mistakes, and differences. No profanity, teasing, or put-downs. Raise your hand to be called on! • Be in your seat at the start of class. • Be prepared with materials and assignments. • Follow Directions. • Put all trash in trash can. • No use of iPad, cell phone use, or other electronic device unless the student has the instructor’s permission for an educational purpose in class.
We, the undersigned student and parent/guardian, have reviewed the expectations of the class/course outlined in the syllabus and accept the terms and expectations as laid out.
I, as the student, further understand that my parent may be contacted if I am found to be in default of my expectations, solely for the purpose of correcting the problem before my grades are put in jeopardy.
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