Pure Mathematics · Secondary 3

15/15 weeks ready · Follows the order of Part One, Algebra and Analytic Solid Geometry, of the Egyptian Ministry of Education and Technical Education textbook Mathematics, Third Form Secondary (Grade 12), Science Section, as the plan for Term 1 (four units, eleven lessons, printed pages 4–100; the English and Arabic editions are the same book; Part Two, Differential and Integral Calculus, is not part of this plan). All explanations, exercises and quizzes are Darslab’s own.

Term 1Unit 1 The binomial theorem: Pascal’s triangle, the expansion, the general term, the middle term, terms containing x^k and free of x, ratios of consecutive terms and the greatest term; Unit 2 Complex numbers: the Argand plane, modulus and amplitude, trigonometric and exponential forms, De Moivre’s theorem, roots of complex numbers and the cube roots of unity; Unit 3 Geometry and measurement in two and three dimensions: the three-dimensional coordinate system, vectors in space, the scalar product, the vector product and the scalar triple product; Unit 4 Straight lines and planes in space: equations of a line, angles and positions of lines, equations of a plane, intersections, angles and distances

The binomial theorem: expansion, general term and sums of expansions The binomial theorem: Pascal’s triangle and combinations, the expansion of (x + a)^n, the general term, the term counted from the end, sums and differences of two expansions

Middle terms, sums of coefficients and the term containing a given power of x The middle term or terms of an expansion, mixed problems of Lesson 1, and finding the term that contains a given power of x

The term free of x, ratios of terms, and the greatest term The term free of x, ratios of consecutive terms and of their coefficients, three consecutive coefficients and the greatest term

Complex numbers as points: modulus, amplitude and trigonometric form Complex numbers on the Argand plane, conjugates, modulus and amplitude, the principal amplitude and the trigonometric form

Products, quotients and powers in trigonometric form, and the exponential form Products, quotients and powers in trigonometric form, and the exponential (Euler) form of a complex number

De Moivre’s theorem, n-th roots and square roots of complex numbers De Moivre’s theorem, n-th roots of a complex number, square roots of a complex number and quadratic equations with complex coefficients

The cube roots of unity: ω, its properties and its uses The cube roots of unity: the three roots, their properties, evaluating expressions and proving identities with ω

Space coordinates, distance, midpoint and the first vectors The three-dimensional coordinate system, the distance and the midpoint in space, and vectors in space: position vector, norm and addition

Scalar multiples, unit vectors, i j k, the vector AB and direction cosines Multiplying a vector by a number, equal vectors, unit vectors, the vectors i, j, k, the vector AB, direction angles and direction cosines

The scalar product, angles between vectors and components The scalar product: definition, properties, coordinates, the angle between two vectors, the component and the projection of one vector on another

The vector product, areas and the scalar triple product The vector product: definition, coordinates, parallel vectors, areas, the scalar triple product and volumes

Lines in space: direction vectors, three forms of equation and the angle between lines Lines in space: the direction vector, the vector, parametric and Cartesian equations, the angle between two lines, and parallel, perpendicular, intersecting and skew lines

Perpendiculars to a line, distances from a line and the equation of a plane A line meeting a given line at right angles, the distance from a point to a line, the equation of a plane in vector, standard and general form, a plane through three points or containing two lines

Lines and planes meeting, angles between planes, and distances Where a line meets a plane, the angle between planes, parallel and perpendicular planes, the line of intersection of two planes, distances from a point to a plane and between parallel planes, the intercept form

Term 1 review: binomial expansions, complex numbers, and vectors, lines and planes Term 1 review

The Egyptian Ministry of Education and Technical Education (MOETE) is not affiliated with, and does not endorse, Darslab. Lessons follow the order of the Ministry’s textbooks; all explanations, exercises and quizzes are Darslab’s own. Pictures of animals, plants and objects: Twemoji, CC BY 4.0.