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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
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
The vector product, areas and the scalar triple product
The vector product: definition, coordinates, parallel vectors, areas, the scalar triple product and volumes
12
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
13
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
14
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
15
Term 1 review: binomial expansions, complex numbers, and vectors, lines and planes
Term 1 review
☰ Year plan · Pure Mathematics
Egypt
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Secondary 3
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Pure Mathematics
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Week 7
The cube roots of unity: ω, its properties and its uses
Week 7 · The cube roots of unity: the three roots, their properties, evaluating expressions and proving identities with ω · 3 lessons
Lesson 1
Lesson 2
Lesson 3
Quiz
8
Homework
5
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Evaluating and proving with ω, and forming equations whose roots are expressions in ω
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