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Chapter 0 Prior Knowledge
This first chapter is not part of the IB syllabus, but contains presumed knowledge. As the SL Paper 1 is a non-calculator exam some basic Math skills are required.
This revision guide has been purchased, because you have chosen the IB Diploma Programme. To have reached this level, you must have completed a pre-DP course, whether it was the MYP, the IGCSE or any other curriculum and those Math skills should have been picked up along the way.
But maybe, after the long summer break, you may have lost a few of those skills, therefore first a small revision.
Real numbers
For Mathematics SL only knowledge of the real numbers set R is required, the complex numbers are saved for Mathematics HL.
An overview of the subsets of R:
N Natural numbers {1, 2, 3 …..} or {0, 1 , 2, 3, ……….}
Z Integers {……-3, -2, -1, 0, 1 , 2, 3, ……….}
Z^+ Positive integers {1, 2, 3 …..}
Q Rational numbers Any number that can be written as the ratio a/b of two integers
Irrational numbers Any real number that can’t be written as a rational number, e.g. √2 or π
R Real numbers All rational and irrational numbers
Or as a Venn diagram
Figure 0.1
As can be seen, N is a subset of Z, as every element of N can also be found in Z. In mathematical notation:
N⊂ Z
Furthermore, Z is a subset of Q, as every of the first set can be found in the latter, because every integer can be written as a fraction: 5= 5/1.
And the rational numbers Q are a subset of the real numbers R.
ELEMENTS
The symbol ∈ denotes that a number, or a number assigned to a variable is an element of a set.
34 ∈Z means that 34 is an element of the set of integers.
B = {x ∈Z |-5 ≤x≤5} means indicates that B is the set of all x such that x is an integer greater than or equal to -5 and less than or equal to +5.
INTERSECTION AND UNION
The intersection of A and B, A∩B, is the set of elements that are in both A and B
The union of A and B, A∪B, is the set of elements that are in set A or in set B (or both)
Figure 0.2 Intersection, A∩B Figure 0.3 Union, A∪B
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Thuiswinkel Waarborg