IB+Higher+Level+-+Algebra

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The Algebra topic has remained largely unchanged in the new syllabus

1.1

Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.

Sigma notation.


 * Applications**

1.2

Exponents and logarithms.

Laws of exponents; laws of logarithms.

Change of base.

1.3

Counting priciples, including permutations and combinations.

The binomial theorem: expansion of //(a+b) n, n// e N.

1.4

Proof by mathematical induction.

Forming conjectures to be proved by mathematical induction.

1.5

Complex numbers: the number i (the square root of -1); the terms real oart, imaginary part, conjugate, modulus and argument.

Cartesian form //z = a + ib.//

Modulus-argument form //z = r(cos 0 + isin 0 ). =rcis 0 = re i 0 // **(1.6 in new syllabus)**

The complex plane **(1.6 in new syllabus)**

1.6

Sums, products and quotients of complex numbers

1.7

De Moivre's theorem.

Powers and roots of a complex number

1.8

Conjugate roots of polynomial equations with real coefficients.


 * 1.9 (new syllabus)**


 * Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinity of solutions or no solution.**

Pages relating to Algebra

 * **Page Name** || **Description** || **Chapter ref.** || **Added by** ||
 * An Introduction to Sequences and Series || Introduction of vocabulary; derivation of some of the important formulae; some simple problems. || 1.1 || J Gregg ||
 * Things to Remember about Logs || Five formulae that might come in handy || 1.2 || J Gregg ||
 * What is a Logarithm? || Quick explanation of what a logarithm is || 1.2 || J Gregg ||
 * Tarsia - Laws of Logs || Test your ability to match equivalent expressions containing logarithms || 1.2 || J Gregg ||