South Sudan Senior 4 Secondary School Curriculum - Additional Mathematics

The Additional Mathematics curriculum for Senior Secondary 4 in South Sudan covers six core units: Limits, Trigonometry, Calculus, Partial Fractions, Vectors, and Complex Numbers. The curriculum emphasizes a practical approach to mathematics, aiming to equip students with lifelong skills applicable to real-world situations. The curriculum encourages active learning through activities, discussions, and group work, supplemented by the use of the internet and additional reference materials.

1. Limits (Rational Functions)

This unit introduces the concept of limits, focusing on polynomial and rational functions. Students explore methods for evaluating limits, including numerical estimation, graphical analysis, and direct substitution. The curriculum addresses situations where direct substitution yields undefined results, such as indeterminate forms. Key concepts include limits of non-continuous functions, unbounded limits, oscillating behavior, trigonometric limits, one-sided limits, and continuity on intervals. Applications of limits in calculus, such as determining the gradient of curves and the area under a curve, are also explored.

2. Trigonometry

This unit builds upon prior knowledge of trigonometry, focusing on simplifying trigonometric ratios (identities) and solving trigonometric equations. Students investigate factor formulae (sum and difference of two angles), trigonometric functions of the form acos(x) + bsin(x), and equations of the form acos(x) + bsin(x) = c. The curriculum emphasizes the application of trigonometric equations to real-life problems.

3. Calculus

This unit expands on previous calculus concepts, introducing the product and quotient rules for differentiation, implicit differentiation, and derivatives of trigonometric, exponential, and logarithmic functions. Integration is applied to finding the area under a curve, and techniques for integrating powers of linear functions and trigonometric functions are explored. Applications of integration to kinematics are also covered.

4. Partial Fractions

This unit introduces partial fractions, focusing on denominators with linear factors, irreducible quadratic factors, and repeated factors. Students learn to express partial fractions as single fractions and apply partial fractions to solve problems in mathematics and other subjects, particularly in integration.

5. Vectors

This unit covers expressing vectors in terms of i, j, and k components, adding and subtracting vectors, and geometrically representing position vectors. Students learn to apply vectors to find the equation of a line, calculate the length of a line using the Pythagorean theorem, and determine the scalar product of two vectors. The distributive law of vectors and its applications are also explored.

6. Complex Numbers

This unit explores graphical representation of complex numbers using Argand diagrams and polar form. Students learn about properties of the polar form, powers of complex numbers, De Moivre's theorem, roots of complex numbers, and solutions of quadratic equations involving complex numbers. The curriculum highlights the applications of complex numbers in fields like quantum mechanics and wave theory.