Sudan Secondary 3 Mathematics

This course comprehensively covers the Secondary 3 Mathematics syllabus as developed by the Ministry of General Education and Instruction, South Sudan. It aims to provide a fun and practical approach to mathematics while imparting lifelong skills. The course consists of four units:

Unit 1: Logarithms

• What is a logarithm? Logarithms express one number in terms of a "base" number raised to some power. The logarithm of a number is the power to which the base must be raised to give that number. For example, log₂8 = 3 because 2³ = 8.
• Laws of logarithms: These laws govern how to manipulate logarithmic expressions:
• logA + logB = logAB
• logA - logB = log(A/B)
• logAⁿ = nlogA
• Solving logarithmic equations: This involves solving equations that contain logarithms, often by converting between logarithmic and exponential forms.
• Applications of logarithms: Logarithms are used in various fields, including:
• pH scale: pH = -log([H+])
• Counting multiplications: Logarithms can simplify calculations involving repeated multiplication.
• Order of magnitude: Used to express large differences in scale, such as in computer science (bits) or measuring earthquakes (Richter scale).
• Interest rates and growth rates: Logarithms help determine growth rates from data.
• Measurement scales (Richter, Decibel): Used to represent values that vary over a wide range on a smaller, more manageable scale.

Unit 2: Measurement and Geometry

• Accuracy and Approximation: This involves rounding whole numbers and decimals to a given number of decimal places or significant figures. The concept of upper and lower bounds is also covered.
• Loci: A locus is the path of a point that moves according to a rule. Different types of loci are investigated, such as the locus of points equidistant from a given point (a circle) or a given line.
• Equation of a circle: The equation of a circle with center (a, b) and radius r is given by (x - a)² + (y - b)² = r².

Unit 3: Algebra

• Quadratic equations: Solving quadratic equations using factorization, completing the square, and the quadratic formula.
• Perfect squares: Understanding and manipulating perfect square trinomials.
• Binomial expansion: Expanding expressions of the form (a + b)ⁿ using Pascal's triangle or the binomial theorem.
• Compound proportions, mixtures, and rates of work: Solving problems involving these concepts.
• Vectors: Vector algebra, including magnitude, direction, and midpoint of a vector.
• Sequences and series: Arithmetic and geometric progressions, including finding the nth term and the sum of the first n terms.
• Matrices and transformations: Representing transformations (reflection, rotation, enlargement, shear, stretch) using matrices and applying them to points on the Cartesian plane. Finding the inverse and determinant of a matrix. Distinguishing between isometric and non-isometric transformations.

Unit 4: Calculus

• Differentiation: Finding the derivative of a function, which represents the gradient of the tangent to the curve at a given point. Rules of differentiation, including the power rule, product rule, and quotient rule.
• Equations of tangents and normals: Finding the equations of the tangent and normal lines to a curve at a given point.
• Stationary points: Identifying and classifying stationary points (maximum, minimum, point of inflection) using the first and second derivatives.
• Kinematics: Applying differentiation to find velocity and acceleration from displacement and velocity functions, respectively.
• Integration: The reverse process of differentiation. Finding indefinite integrals and applying integration to find the area under a curve (definite integrals).