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Term 1
Unit 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
1
نظرية ذات الحدين: المفكوك والحد العام ومجموع مفكوكين
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
2
الحد الأوسط ومجموع المعاملات والحد المشتمل على قوة معينة من 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
3
الحد الخالي من x والنسب بين الحدود والحد الأكبر
The term free of x, ratios of consecutive terms and of their coefficients, three consecutive coefficients and the greatest term
4
الأعداد المركبة نقاطًا: المقياس والسعة والصورة المثلثية
Complex numbers on the Argand plane, conjugates, modulus and amplitude, the principal amplitude and the trigonometric form
5
الضرب والقسمة والقوى بالصورة المثلثية والصورة الأسية
Products, quotients and powers in trigonometric form, and the exponential (Euler) form of a complex number
6
نظرية ديموافر والجذور النونية والجذور التربيعية للأعداد المركبة
De Moivre’s theorem, n-th roots of a complex number, square roots of a complex number and quadratic equations with complex coefficients
7
الجذور التكعيبية للواحد الصحيح: ω وخواصها واستعمالاتها
The cube roots of unity: the three roots, their properties, evaluating expressions and proving identities with ω
8
الإحداثيات في الفراغ والمسافة والمنتصف وأولى خطوات المتجهات
The three-dimensional coordinate system, the distance and the midpoint in space, and vectors in space: position vector, norm and addition
9
مضاعفات المتجه ومتجهات الوحدة وi, j, k والمتجه AB وجيوب تمام الاتجاه
Multiplying a vector by a number, equal vectors, unit vectors, the vectors i, j, k, the vector AB, direction angles and direction cosines
10
الضرب القياسي والزاوية بين متجهين ومركبة المتجه
The scalar product: definition, properties, coordinates, the angle between two vectors, the component and the projection of one vector on another
11
الضرب الاتجاهي والمساحات والضرب الثلاثي القياسي
The vector product: definition, coordinates, parallel vectors, areas, the scalar triple product and volumes
12
المستقيم في الفراغ: متجه الاتجاه وصور المعادلة الثلاث والزاوية بين مستقيمين
Lines in space: the direction vector, the vector, parametric and Cartesian equations, the angle between two lines, and parallel, perpendicular, intersecting and skew lines
13
العمود على مستقيم والبعد عن مستقيم ومعادلة المستوى
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
14
تقاطع المستقيم والمستوى والزاوية بين مستويين والأبعاد
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
15
مراجعة الفصل الدراسي الأول: ذات الحدين والأعداد المركبة والمتجهات والمستقيمات والمستويات
Term 1 review
☰ Year plan · Pure Mathematics (Arabic)
Egypt
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Secondary 3
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Pure Mathematics (Arabic)
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Week 6
نظرية ديموافر والجذور النونية والجذور التربيعية للأعداد المركبة
Week 6 · De Moivre’s theorem, n-th roots of a complex number, square roots of a complex number and quadratic equations with complex coefficients · 3 lessons
Lesson 1
Lesson 2
Lesson 3
Quiz
8
Homework
5
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Week 6 ·
الجذران التربيعيان لعدد مركب بالصورة x + yi، والمعادلات التربيعية ذات المعاملات المركبة
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Week 6 · Homework
