Math Competitions

CEMC Grade 12 Calculus and Vectors

The CEMC Grade 12 Calculus and Vectors course is designed to challenge and inspire students in their math skills.

78%

of students score

90%

students get a top score of

CEMC Grade 12 Calculus and Vectors

80%

students showed exceptional
performance in their first semester of

CEMC Grade 12 Calculus and Vectors

Course Concept

The CEMC (Centre for Education in Mathematics and Computing) Grade 12 Calculus and Vectors course is an advanced educational program designed to provide high school students with a comprehensive understanding of calculus and its application to vectors and three-dimensional space. This course is tailored for students who are pursuing further studies in mathematics, engineering, science, and other related fields. It delves into the intricacies of calculus, vector operations, and applications of these concepts in real-world scenarios. Here's a detailed overview of the CEMC Grade 12 Calculus and Vectors course:

  • Purpose and Scope: The primary purpose of this course is to equip students with a deep understanding of calculus and vectors, enabling them to tackle complex mathematical problems and applications. The course aims to prepare students for university-level studies in mathematics, physics, engineering, and other STEM fields.
  • Target Audience: The Grade 12 Calculus and Vectors course is intended for high school students in their final year who have a strong interest in mathematics and are seeking to pursue careers or further education in mathematics-related disciplines.
  • Calculus Concepts: The course provides an in-depth exploration of calculus concepts, including limits, derivatives, integrals, and their applications.
  • Vector Operations: The course introduces vector operations, covering topics such as vector addition, scalar multiplication, dot product, cross product, and applications in geometry and physics.
  • Three-Dimensional Space: The course extends the concept of vectors to three-dimensional space, enabling students to visualize and work with objects in three dimensions.

CEMC Grade 12 Calculus and Vectors

Course Details:

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150000

+ GST

/

$

1850

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Syllabus

Best-in-class content by leading faculty and industry leaders in the form of videos, cases and projects, assignments and live sessions

COURSE SYLLABUS PDF
1. Functions, Graphs, and Limits
  • Introduction to Calculus: Limits and Rates of Change
  • Evaluating Limits Graphically
  • Properties of Limits
  • Continuity
  • Methods of Evaluating Limits of Polynomial and Rational Functions
  • Methods of Evaluating Limits: Functions Containing Radicals
  • Limits at Infinity
10. Introduction to Vectors
  • Vector Concepts
  • Vector Laws
  • Force as a Vector
  • Velocity as a Vector
11. Algebraic Vectors and Applications
  • Algebraic Vectors
  • Operations on Algebraic Vectors
  • The Dot Product of Two Vectors
  • The Cross Product of Two Vectors
  • Applications of the Dot and Cross Products
12. Equations and Intersections of Lines in R^2 and R^3
  • Parametric and Vector Equations of Lines in R^2
  • Scalar Equation of a Line in R^2
  • Equations of Lines in R^3
  • The Intersection of Two Lines in R2 and R3
  • Distance From a Point to a Line in R2 and R3
13. Equations and Intersections of Planes
  • Vector and Parametric Equations of a Plane
  • The Scalar Equation of a Plane
  • The Intersection of a Line and a Plane
  • The Intersection of Two Planes
  • The Intersection of Three Planes
  • The Intersection of Three Planes Continued
2. The Derivative
  • Definition of the Derivative and Differentiability
  • Differentiation Rules
  • Finding Equations of Tangent Lines
  • The Product Rule
  • The Chain Rule
  • The Quotient Rule
3. Applications of Derivatives
  • Higher Order Derivatives
  • Sketching the First and Second Derivative Functions
  • Applications of Rates of Change: Geometry, Life Sciences, and Social Sciences
  • Applications of the Derivative to Motion
4. Curve Sketching
  • Extreme Value Theorem
  • Mean Value Theorem
  • Curve Sketching and the First Derivative
  • Curve Sketching and the Second Derivative
  • Algorithm for Curve Sketching
5. Optimization and Related Rates
  • Optimization Problems
  • Optimization Problems in Economics
  • Implicit Differentiation
  • Introduction to Related Rates
  • Linearization and Newton’s Method
6. Derivatives of Exponential, Logarithmic, and Trigonometric Functions
  • Euler’s Number,  e , and the Natural Logarithm
  • Differentiating the Natural Logarithm Function:  f(x)=ln(x)
  • Differentiating Exponential Functions:  f(x)=a^x
  • Differentiating Logarithmic Functions:  f(x)=loga(x)
  • Derivatives of Sine and Cosine Functions
  • Derivatives of Tangent and Reciprocal Trigonometric Functions
7. Applications of Exponential, Logarithmic, and Trigonometric Functions
  • Rates of Change
  • Indeterminate Form and l’Hospital’s Rule
  • Curve Sketching
  • Optimization
  • Related Rates
8. Integral Calculus
  • Antiderivatives
  • Computing Areas
  • Sigma Notation and Riemann Sums
  • The Definite Integral
  • The Definite Integral as Net Area
  • Properties of Definite Integrals
  • The Fundamental Theorem of Calculus
  • Antiderivatives and Indefinite Integrals
  • Evaluating Definite Integrals Using Antiderivatives
  • Integration by Substitution
  • Integration by Parts
9. Applications of Integral Calculus
  • The Definite Integral as Net Change
  • Areas Between Curves
  • Volumes
  • Average Values and Lengths of Curves
  • Introduction to Differential Equations
  • Direction Fields and Solution Sketching
  • Solving Separable Differential Equations
  • Exponential Growth and Decay

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  • expert guidance at every step that involves interactive sessions, class notes, worksheets, class recordings, and access to past papers.
  • specialist subject tutors who have graduated from top universities with a passion for teaching and a dedicated program manager to track your progress.

Experienced Tutors

Our team of teachers boast top 1% scores for the subjects they teach. All of our teachers have demonstrated an exceptional ability to convey material in a fun, personalized, and results-driven way.

With AP Guru, each student gets...
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  • a subject specialist that will convey essential concepts in a clear and easily understandable manner
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Between each class, you'll get personalized assignments so you master what you learned

With AP Guru, you will get...
  • Topic-wise worksheets and graded assessments (with marking schemes) to ensure mastery of each topic tested on the school exams
  • Doubt sessions after every couple of classes to review incorrect questions
  • Additional worksheets on topic areas of concern

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Practice for the exam with our library of Topic-wise Tests and Past Papers.

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Mentoring & Support

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With AP Guru, you will get...
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  • dedicated support to resolve doubts, convenient class schedules and reminders for important sessions
  • Parents Teacher Meetings - We set up monthly parent teacher meetings for your to interact with the tutors

Grade Improvement: Exam Ready

The AP Guru course ensures that each student is exam ready regardless of the initial academic level at which they stand.

Exam Ready
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  • Last 2 months of Exam Improvement Pointers and Strategies for writing high-scoring answers.
One-to-One Classes

AP Guru offers highly customised and personalised SAT Prep delivered live online

Experienced Tutor

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Targeted Assessments

Between each class, you'll get personalized assignments so you master what you learned

Test Prep Manager

All of our students are paired with an experienced mentor to guide the student through his or her prep

Doubt Classes

We will conduct regular one-on-one feedback and doubt classes to go through your errors in mock tests and weekly assessments

Mock Tests

We offer more than 30 full length tests for our programs to our students with detailed explanations. 

Test Analytics

For each test you take, you will receive detailed reports of your performance as well as question explanations

Study Plan

The program manager will set test schedules, create reminders, set up doubt sessions, etc.

Strategy Guides

Our AP Guru SAT Strategy Guides cover every concept and strategy tested on the SAT

Weekly Progress Reports

Our curriculum is written by our tutors and founders based on their years of teaching experience.

Web Portal

The AP Guru online portal contain 100+ hours of SAT content - detailed lesson notes, and additional practice

Parent Teacher Meetings

Parents Teacher Meeting - We set up monthly parent teacher meetings for your to interact with the tutors

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Frequently Asked Questions

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  • Who are the AP Guru tutors?
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    We have hand-selected a small group of highly qualified tutors who have mastery over teaching and helping students in the programs they teach. Our tutors also need to have significant previous teaching experience and be very gifted, dynamic teachers.

  • Where are your Programs held?
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    We conduct our programs online.

    Is this a live class? Will it be a group or private class?
    All our classes are live instructor lead classes. All our academic tutoring are only one-on-one.

  • Is this a live class? Will it be a group or private class?
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    All our classes are live instructor lead classes. All our academic tutoring are only one-on-one.

  • When is the best time to get started?
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    The earlier the better! When students come to us right before it is time to apply to college, there is only so much we can do. We can certainly help these students with score improvements and craft as compelling an application as possible, but we are given experiences and data points that cannot be altered.

    When students come to us early in their educational careers, we pair them with a counselor to help them develop as applicants, students, and people early on. We help students strategize early, build their profiles, and stand out from their peers. We help students explore and develop their academic interests, engage in unique and meaningful extracurricular activities, strengthen their personal qualities and leadership skills, and ultimately, position them to get into the best schools possible.

    It takes A LOT of hard work, strategy, determination, and self-reflection to get into the school of your dreams. At AP Guru, we are here, every step of the way, to help you get there.

  • Do test prep courses work?
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    Yes! Standardized tests focus on a small, unique set of skills and topics. By knowing exactly what types of questions are on the test, a student gains a distinct advantage. Furthermore, a great tutoring company can build on this advantage by providing a highly individualized learning experience and a wealth of fantastic strategies for all types of students.  We have the evidence from thousands of students across 10+ years that great improvement is possible for nearly everyone.

  • Do you only help students who want to go to top schools?
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    No. We know that each student is different and has unique goals and aspirations. Our focus is to help each student excel in the tests and exams they are preparing towards.

  • What kind of results should I expect?
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    In terms of academic scores, for students not already at the top of the range, we typically want to see at least a 20 percentile rank improvement (the actual raw score this translates to varies across the scale). Going from the 50th to 70th percentile or from the 70th to 90th typically opens up a whole new range of schools for students.