Topic 1
Quadratics focuses on solving quadratic equations using methods such as factoring, completing the square, and the quadratic formula. Students also learn to analyze roots using the discriminant and solve simultaneous equations involving quadratic and linear expressions. This topic builds essential algebraic skills for advanced mathematical applications.
Functions cover the fundamental concepts of mappings, domains, ranges, and inverses. Students learn to combine, transform, and sketch functions while analyzing their behavior. This topic is essential for understanding mathematical relationships and forms the basis for more advanced studies in algebra and calculus.
Coordinate geometry focuses on equations of straight lines, including concepts like gradients, midpoints, and distances between points. Students explore the geometry of circles, deriving equations and solving related problems. This topic builds a solid foundation for analyzing geometric relationships in a Cartesian plane, essential for advanced applications in mathematics.
Circular measure focuses on the radian as a unit of angle measurement and its applications in solving problems involving arcs and sectors of circles. Students learn to calculate arc lengths, areas of sectors, and segments using radian measure. This topic is fundamental for understanding trigonometry and its applications in geometry and calculus.
Trigonometry explores the properties and applications of trigonometric functions, including sine, cosine, and tangent. Students study identities, solve equations, and analyze graphs in both degrees and radians. This topic is essential for understanding angles, periodic behavior, and their applications in geometry and advanced mathematics.
Series introduces the concepts of arithmetic and geometric progressions, including their formulas and applications. Students learn to find sums, terms, and use sigma notation to express series compactly. This topic is fundamental for understanding sequences, patterns, and their applications in mathematical modeling and problem-solving.
Differentiation focuses on finding derivatives of functions using basic rules, including the power rule and sum rule. Students learn to apply differentiation to solve problems involving tangents, normals, rates of change, and stationary points. This topic is essential for understanding calculus and its applications in optimization and motion analysis.
Integration focuses on finding the area under curves and solving problems involving indefinite and definite integrals. Applications include kinematics and geometry.
Topic 2
Algebra covers advanced algebraic techniques, including solving equations and inequalities, and working with sequences and series.
Logarithmic and exponential functions explores the properties and applications of logarithmic and exponential functions, including their use in solving equations and modeling growth and decay.
Trigonometry focuses on advanced trigonometric identities, equations, and their applications in solving problems involving angles and periodic functions.
Differentiation develops techniques for finding derivatives and applying them to curve sketching, optimization, and motion problems.
Integration expands on basic integration methods to include more complex techniques and applications, such as finding volumes of revolution.
Numerical solution of equations introduces numerical methods like Newton-Raphson for solving equations that cannot be solved algebraically.
Topic 3
Further algebra covers polynomial equations, partial fractions, and advanced algebraic techniques.
Further calculus focuses on advanced differentiation and integration techniques, including applications to parametric equations and volumes of revolution.
Vectors explores 3D vectors, including their representation, manipulation, and applications to geometry and motion.
Differential equations introduces solving first-order and second-order differential equations, with applications to modeling real-world systems.
Complex numbers covers the arithmetic and geometric representation of complex numbers, including their use in solving polynomial equations.
Topic 4
Forces and equilibrium examines the principles of forces and their applications in maintaining or breaking equilibrium.
Kinematics of motion in a straight line focuses on the motion of objects along a straight path, involving equations of motion and graphs.
Momentum explores the conservation of momentum in collisions and explosions.
Newton’s laws of motion applies Newton’s three laws to solve problems involving forces and motion.
Energy, work, and power studies the relationships between energy transfer, work done, and power in mechanical systems.
Topic 5
Permutations and combinations focuses on counting techniques for arranging and selecting objects in various orders.
Probability covers the principles of probability, including conditional probability and independent events.
Discrete random variables introduces random variables, probability distributions, and expected values.
The binomial and geometric distributions explores the properties and applications of binomial and geometric probability distributions.
