الرياضيات — الصف الثالث الثانوي

Estimated duration: full year ≈ 30 weeks (13 units → 35 academy lessons, one per official lesson)

What you will learn

• Expand (a + b)ⁿ for positive integer n, find a general, specified, middle or constant term, use the ratio of consecutive terms and find the greatest term and coefficient
• Represent complex numbers on the Argand plane, find modulus and argument, convert between algebraic, trigonometric and exponential (Euler) forms, apply De Moivre's theorem to powers and nth roots, and use the properties of the cube roots of unity
• Use 3-D coordinates, vectors in space, unit vectors, direction cosines, dot, cross and scalar triple products; write vector, parametric and Cartesian equations of a line and general/standard equations of a plane; find angles, intersections and distances in space
• Differentiate explicit, implicit and parametric functions, find higher derivatives, differentiate exponential and logarithmic functions, and solve related-rates problems
• Use the first and second derivatives to study increase/decrease, local and absolute extrema, concavity and inflection, sketch curves and solve optimisation problems
• Integrate exponential, logarithmic and f′/f forms, integrate by substitution and by parts, evaluate definite integrals with their properties (incl. odd/even functions), and find plane areas and volumes of revolution about the x-axis
• Find the moment of a force about a point (vector form in 2-D), the resultant of parallel coplanar forces, the conditions for equilibrium of coplanar forces (rods, ladders), and work with couples, their moments and resultant couples
• Differentiate and integrate vector functions of time for motion in a line, apply Newton's laws (variable mass or acceleration, lifts, connected bodies, pulleys), relate impulse to change of momentum, and apply work, kinetic and potential energy, the work–energy principle and power

Who it is for: S3 general-system mathematics-section students preparing the year-end Thanaweya Amma examination

Prerequisites: S2 scientific mathematics (functions, logarithms, limits, statics of concurrent forces)