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.

#### Course Details:

Dedicated Test Prep Manager to Oversee Your Program

Test Reports

Personalized Assignments

150000

+ GST

/

\$

1850

## Syllabus

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

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

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

• Track your progress including topic, class and homework discussion
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##### One-to-One Classes

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

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

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##### Strategy Guides

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##### 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

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

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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.