Yakili | Uppersixth Commercial TST Pure Mathematics

Course / Course Details

Uppersixth Commercial TST Pure Mathematics

By - Michael Rolex
0 students
166 Hours 40 Min
(0)

Course Requirements

The Upper Sixth Commercial Technical Secondary and Technical (TST) Pure Mathematics course, often aligned with the Cameroon GCE Advanced Level Pure Mathematics syllabus, requires a deep and rigorous study of advanced mathematical concepts. While students in the Commercial stream often take Pure Mathematics with Statistics, the core Pure Mathematics topics remain consistent. The curriculum builds on Lower Sixth concepts, with a heavy emphasis on Calculus (Differentiation and Integration) and complex algebraic structures like Complex Numbers and Differential Equations.

The syllabus must cover advanced topics essential for university-level studies in science, commerce, and engineering.

Core Modules for Upper Sixth Pure Mathematics

Module	Key Topics (Examples)	Mathematical Focus
1. Complex Numbers	Definition and representation (Cartesian $x+iy$ and Polar $r(\cos\theta + i\sin\theta)$ forms). Argand Diagram. Operations: addition, subtraction, multiplication, division. De Moivre's Theorem for powers and roots.	Representing and manipulating numbers in the complex plane.
2. Polynomials and Rational Functions	Remainder and Factor Theorems. Solving polynomial equations up to degree four. Partial Fractions (all cases). Finding the Range of a function (e.g., $y=\frac{ax^2+bx+c}{px^2+qx+r}$ ).	Advanced algebraic techniques for expression manipulation and equation solving.
3. Functions and Graphing	Types of Functions (Injective, Surjective, Bijective). Composite and Inverse functions. Modulus function ($	f(x)
4. Differentiation (Calculus I)	Derivatives of standard functions (trigonometric, exponential, logarithmic). Product, Quotient, and Chain Rules. Implicit Differentiation. Parametric Differentiation. Applications: stationary points, maximum/minimum problems, rates of change.	Mastering the rules of differentiation and applying them to optimization problems.
5. Integration (Calculus II)	Integration of standard functions. Techniques of Integration (by substitution, by parts, partial fractions). Definite and Indefinite Integrals. Applications: Area under a curve, Volume of revolution.	Developing skills in reverse differentiation and applying them to geometric problems.
6. Differential Equations	Formation of simple differential equations. Solving First-Order Differential Equations (Separation of Variables, Homogeneous, Integrating Factor). Applications (e.g., growth and decay problems).	Modeling real-world problems involving rates of change.
7. Vectors	Vector Algebra (addition, scalar multiplication). Scalar (Dot) Product and angle between vectors. Vector Equation of a Line. Intersection of Lines and shortest distance problems.	Working with quantities that have both magnitude and direction in 2D and 3D space.

The course needs tools for complex mathematical visualization and problem-solving practice.

Interactive Graphing Tool: An integrated tool for visualizing complex numbers on the Argand diagram and observing the transformations of functions or the area under a curve (Integration).
Step-by-Step Problem Solvers: Provide detailed, step-by-step solutions for complex problems (e.g., "Integration by Parts" or "Solving a Differential Equation") to help students track their work and identify errors.
Formula Reference: A quick-access, searchable library of all required formulae, identities, and theorems (e.g., De Moivre's Theorem, integration rules).
Practice Banks: Extensive question banks for each module, categorized by difficulty, with emphasis on GCE past paper style questions for rigorous exam preparation.

Course Description

This Yakili online course, aligned with the rigorous requirements of the Cameroon GCE Advanced Level Pure Mathematics syllabus for the Commercial TST stream, provides a deep and comprehensive study of advanced mathematical structures and calculus. The curriculum builds a strong foundation necessary for further studies in commerce, finance, and engineering. Key areas of focus include Advanced Algebra (Polynomials, Partial Fractions, Modulus Functions), the representation and manipulation of Complex Numbers using the Argand Diagram and De Moivre's Theorem, and the mastery of Calculus. The course extensively covers all rules and applications of Differentiation (including implicit and parametric forms for optimization problems) and Integration (including techniques like substitution and by parts for finding areas and volumes). Finally, students gain proficiency in Differential Equations (first-order solutions) and Vectors in three dimensions (lines, intersection, and distance). Delivered through detailed theoretical explanations, interactive visualizations, and extensive practice problems modeled after GCE past papers, this course ensures students develop the analytical rigor and problem-solving skills necessary for exam success and higher education.

Course Outcomes

Upon completion, the student will be able to:

Algebraic Mastery: $\checkmark$ Solve complex equations using polynomial, rational, and modulus techniques, and correctly apply the Binomial Theorem for fractional/negative powers.
Complex Number Application: $\checkmark$ Manipulate complex numbers in Cartesian and Polar forms and utilize De Moivre's Theorem to solve problems involving powers and roots.
Advanced Calculus: $\checkmark$ Apply all rules of Differentiation (Product, Quotient, Chain, Implicit, Parametric) and master Integration Techniques (Substitution, By Parts, Partial Fractions) to solve geometric and optimization problems.
Modeling and Solutions: $\checkmark$ Formulate and solve simple First-Order Differential Equations and use Vectors to solve problems related to lines in three dimensions.