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Titel
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Algebra, part 1
Topics covered:
Ch. 1, Book 1: Lines (lines, perpendicular bisectors, systems of equations)
Ch. 11, Book 2: Systems of equations (row operations, 2x2 systems, 3x3 systems)
Ch. 3, Book 1: Surds and exponents (surds, exponents, exponent laws, scientific notation)
Ch. 4, Book 1: Equations (power equations, null factor law, quadratic equations, completing the square, discriminant, sum and product of roots, solving equations using technology)
Ch. 5, Book 1: Sequences and series (sequences, arithmetic and geometric sequences, growth and decay, finantial math, series, arithmetice series, geometric series, infinite geometric serites).
Learning objectives:
Giving information about a line, writing its equations in different forms (gradient-intercept, point-gradient, general form) and graph it.
Finding the perpendicular bisector of a segment and understanding its properties
Solving 2x2 systems of linear equations by substitution and elimination
Applying row operations to solve systems of 2x2 and 3x3 linear equations
Recognising from the row reduced form whether the system has a unique solution, infinitely many solutions or no solution
Solving systems of equations with one or two parameters, and interpreting the result in terms of the parameter
Rationalizing the denominator, simplify expressions with surds
Applying exponent laws to simplify expressions (also rational exponents)
Converting to and from scientific notation
Solving power equations, applying the null factor law, different methods to solve quadratic equations (factorisation and NFL, quadratic formula, completing the square).
Looking at the discriminant to decide whether a quadratic equation has 2 real solutions (rational or not), a repeated solution (rational or not) or no solutions.
Deducing the relationship between the roots and coefficients of a quadratic equation. Applying this relationship to find new equations and to solve for parameters on the coefficients.
Using technology to solve equations: graphing and polynomial tools.
Deducing the pattern of a sequence. Deciding whether a sequence is arithmetic, geometric or neither. Recognizing and find terms of sequence given by a recursive formula (Fibonacci is an example).
Applying sequences to grow and decay problems.
Financial mathematics: compound interest, inflation, real value and depreciation: finding them or knowing them finding the initial value, or the time (use of calculator).
Finding the sum of the first n terms of an arithmetic or geometric sequence, or of any sequence using a calculator. Using sigma notation.
Understanding the concept of an infinite series as a limiting process. Deciding whether an geometric series converges or not, and finding its sum when it does.
Concepts:
Approximation of an infinite sum
Change on the terms of a sequence
Equivalent forms of the equation of a line
Equivalent forms of a system of equations
Generalizing the method of elimination from 2x2 to 3x3 systems
Modelling with sequences (growth and decay, financial mathematics)
Pattern of a sequence or a series
Quantities expressed in scientific notation
Relationship between the roots and the coefficients of a quadratic equation
Representation of a sequence explicitely or recursively
Space as en extension of a plane, systems of 3x3 are intersections of planes but this will be clear when we work with vectors.
Systems of linear equations (with or without parameters)
TOK links:
we extend systems of equations from 2x2 to 3x3, and this has a geometrical interpretation (intersection of planes). What about 4x4? what does R^4, or R^n, represent? Can we understand those spaces, since we can mathematically work with them? Do those spaces exist, since we can mathematically work with them?
ATL links:
new class, so time to develop some social skills. Self-management to catch up with the starting point of the course, since the students come from different backgrouds, are used to different teaching rutines and different notations.
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