South Sudan Secondary School Syllabus - Mathematics (Secondary 4)

This course comprehensively covers the Secondary 4 syllabus as developed by the Ministry of General Education and Instruction, South Sudan. The course aims to provide a fun and practical approach to mathematics while imparting lifelong skills. The Student's Book and Teacher's Guide cover the national syllabus, providing a strong foundation in mathematical basics, clear explanations, practice exercises, group work activities, and stimulating illustrations.

Unit 1: Complex Numbers

• Complex Numbers: Introduction to complex numbers, defining the standard format (a + bi) and explaining real and imaginary numbers within the complex number system. Includes examples of simplifying square roots of negative numbers.
• Argand Diagram: Representing complex numbers graphically on a coordinate plane, with the horizontal axis as the real axis and the vertical axis as the imaginary axis. Plotting complex numbers and understanding the positions of real, imaginary, and complex conjugate pairs.
• Conjugates of Complex Numbers: Defining complex conjugates and explaining how to find them by changing the sign of the imaginary part.
• Operations on Complex Numbers: Performing arithmetic operations (addition, subtraction, multiplication, and division) with complex numbers, including the use of conjugates in division.
• Polar Form of Complex Numbers: Representing complex numbers in polar form (r, θ) and converting between Cartesian and polar forms. Includes examples of plotting complex numbers in polar form and finding their Cartesian equivalents.
• Uses of Complex Numbers: Applications of complex numbers in solving quadratic equations and in fields like electronics and electromagnetism.

Unit 2: Measurement and Trigonometry

• Area: Defining area and explaining how to calculate the area of basic and irregular shapes. Includes activities for approximating the area of irregular shapes using grid paper and methods for improving approximation accuracy.
• Area Estimation:
• Mid-Ordinate Rule: Approximating the area of irregular shapes by dividing them into rectangular strips of equal width and summing their areas.
• Trapezium Rule: Approximating area using trapeziums instead of rectangles for increased accuracy.
• Equation of a Circle:
• Equation of a circle centered at the origin.
• General equation of a circle.
• Finding the center and radius of a circle.
• Equation of a circle passing through two points and touching the x-axis.
• Graphs of Trigonometric Functions: Plotting graphs of simple trigonometric functions (sine, cosine, tangent) and using them to solve trigonometric equations.

Unit 3: Inequalities and Vectors

• Linear Inequalities: Introduction to inequality signs, forming inequalities from word problems, and solving linear programming problems graphically. Includes examples of representing real-life situations with inequalities and finding the solution region.
• Optimization: Using linear programming to find maximum and minimum values of objective functions within defined regions. Includes examples of maximizing profit or minimizing cost under given constraints.
• Permutation and Combination Formula: Defining permutation and combination, and applying the formulas to solve problems involving arrangements and selections.
• Vectors:
• Definition of a vector.
• Vector representation as column vectors.
• Position vectors.
• Mid-point of a line segment.
• Magnitude of a vector.
• Multiplication by a scalar.
• Parallel vectors.
• Coordinates in Three Dimensions: Representing points and vectors in three dimensions, calculating magnitude and midpoint.

Unit 4: Calculus

• Derivative: Defining the derivative as the instantaneous rate of change and its geometric interpretation as the slope of the tangent line.
• Derivative of a Polynomial: Calculating derivatives of polynomials using the power rule and the sum/constant multiple rules.
• Equation of Tangent and Normal: Finding the equations of tangent and normal lines to a curve at a given point.
• Stationary Points: Identifying and classifying stationary points (maximum, minimum, and inflection points) using the first and second derivatives.
• Application to Kinematics: Applying calculus to calculate velocity and acceleration from displacement and velocity functions, respectively.
• Integration and Area under a Curve: Defining integration as the reverse of differentiation and using it to find the area under a curve.