Questions - 1 Notation Of the various notations in use the...

1.
Notation
Of the various notations in use, the IBO has chosen to adopt a system of notation based on the
recommendations of the International Organization for Standardization (ISO). This notation is
used in the examination papers for this course without explanation. If forms of notation other
than those listed in this guide are used on a particular examination paper, they are defined
within the question in which they appear.
Because students are required to recognize, though not necessarily use, IBO notation in
examinations, it is recommended that teachers introduce students to this notation at the earliest
opportunity. Students are not allowed access to information about this notation in the
examinations.
In a small number of cases, students may need to use alternative forms of notation in their
written answers. This is because not all forms of IBO notation can be directly transferred into
handwritten form. For vectors in particular the IBO notation uses a bold, italic typeface that
cannot adequately be transferred into handwritten form. In this case, teachers should advise
students to use alternative forms of notation in their written work (for example, , or ). x
r
x x
Students must always use correct mathematical notation, not calculator notation.
the set of positive integers and zero,
{0,1, 2, 3, ...}
the set of integers,
{0, 1, 2, 3, ...} ± ± ±
++
the set of positive integers, {1, 2, 3, ...}
the set of rational numbers
+
the set of positive rational numbers, { x  x ∈ , x > 0}
the set of real numbers
+
the set of positive real numbers, { x  x ∈ , x > 0}
the set with elements
1 2
{ , , ...} x x
1 2
, , ... x x
the number of elements in the finite set A ( ) n A
the set of all x such that { | } x
is an element of ∈
is not an element of ∉
the empty (null) set
∅
the universal set
U
union ∪
intersection
∩
is a proper subset of ⊂
is a subset of
⊆
1

the complement of the set A A
′
a divides b
| a b
, a to the power of , root of a (if then ) 1/ n a n a
1
n
th n
0 a ≥
0 n a ≥
, a to the power , square root of a (if then )
1/ 2
a
a
1
2
0 a ≥
0 a ≥
the modulus or absolute value of x , that is x



∈ < -
∈ ≥
R , 0 for
R , 0 for
x x x
x x x
is approximately equal to
≈
is greater than
is greater than or equal to
≥
is less than
<
is less than or equal to ≤
is not greater than
/
is not less than <
/
the term of a sequence or series
n
u th n
the common difference of an arithmetic sequence
d
the common ratio of a geometric sequence r
the sum of the first n terms of a sequence,
n
S
1 2
...
n
u u u + + +
the sum to infinity of a sequence,
S
∞ 1 2
... u u + +
1
n
i
i
u
=
∑
1 2
...
n
u u u + + +
1
n
i
i
u
=
∏
1 2
...
n
u u u × × ×
the binomial coefficient, , in the expansion of
n
r
 
 
 
th r 0,1, 2,... r = ( ) n a b +
2

is a function under which each element of set A has an image in set B : f A B → f
is a function under which is mapped to : f x y a f x y
the image of under the function ( ) f x x f
the inverse function of the function 1 f - f
the composite function of and f g o f g
the limit of as tends to lim ( )
x a
f x
→
( ) f x x a
the derivative of with respect to
d
d
y
x
y
x
the derivative of