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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Syllabus

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COURSE SYLLABUS PDF

Months

108

Assignments

Live Sessions

1. Functions, Graphs, and Limits

Hours

Assignment

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

Hours

Assignment

Vector Concepts
Vector Laws
Force as a Vector
Velocity as a Vector

11. Algebraic Vectors and Applications

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

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

Hours

Assignment

Rates of Change
Indeterminate Form and l’Hospital’s Rule
Curve Sketching
Optimization
Related Rates

8. Integral Calculus

Hours

Assignment

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

Hours

Assignment

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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