Algebra

Algebraic Expressions and Equations

• Investigate and identify the properties of polynomials, specifically observing the structure of their graphs.
• Distinguish and work with rational expressions, concurrently incorporating operations such as addition, multiplication, subtraction, and division.
• Solve equations and differential equations, understanding the principles for first and second-order differential equations.
• Understand and apply the concept of a proof in algebra, particularly proof by contradiction and proof by exhaustion.

Functions

• Define and interpret functions, particularly the notions of one-to-one, onto, inverse, and composite functions.
• Work with special types of functions including polynomial, trigonometric, exponential, and logarithmic functions and their properties.
• Understand how to transformations of functions graphically.
• Analyse functions using the first and second derivative.

Sequences and Series

• Determine sequences using induction, and apply the method to solve problems.
• Recognize arithmetic and geometric sequences and series, and use formulas to find specific terms and sums.
• Understand and apply the binomial theorem for positive integral exponents and rational ones.

Complex Numbers

• Recognize and understand the importance of the imaginary unit i in complex numbers.
• Perform operations on complex numbers including addition, subtraction, multiplication, division, and finding powers and roots.
• Use of Argand diagram and polar form of complex numbers, including DeMoivre’s theorem and its applications.

Vectors

• Understand and interpret vectors geometrically.
• Handle vector properties and operations, including vector addition, scalar multiplication and dot product.
• Learn and apply the vector equation of a line and a plane.
• Apply vector concepts to solve problems involving distance and intersection.