Grade 10 ieb Maths summarised notes to help remember important things and provide pointers for certain topics in the Math Syllabus. You can also add on your own notes should you choose to print out the document as there are certain rules or examples that one needs to keep in mind when studying for ...
, “ALGEBRAIC
EXPRESSIONS”
“The Number System”
Real Numbers
Rational Numbers (Q)
- Natural Numbers (N) - Common Fractions - Recurring Decimals
N = {1, 2, 3, 4…} ½;¾;2½ 0,132132…
0,55555….
- Whole Numbers (No) - Terminating Decimals
No = {0, 1, 2, 3…} 0,2; 0,125; 1,645 - Integers (Z)
Z = {-2, -1, 0, 1, 2, 3…}
Irrational Numbers (Q’)
- Numbers that can be expressed in the - Non-terminating decimals
form a/b
- Non-recurring decimals
- π, √5, -√11
Non-real Numbers
- Square roots of negative numbers
- Division by zero (undefined)
Set Builder Notation
{ x; x ≥ 4; x ∈ N}
• Equal to
o Not equal to
, Interval Notation
( -1 ; 3]
( - Including
[ - Excluding
Expressing recurring decimals as a fraction (a/b)
0,3˙
x = 0,33333….
10x = 3,33333….
10x – x = 3,333…. – 0,333….
9x = 3
x = 1/3
Between which two consecutive integers do the
following irrational numbers lie
√12
√9 < √12 < √16
3 < √12 < 4
∴ √12 lies between 3 and 4
Representing Real Numbers on a number line
{ x; x ≥ 4; x ∈ N}
- Set Builder Notation {}
{ x; x ≥ 4; x ∈ Z} (Start counting from 1
because it’s a Natural
• F• F• F number)
4 5 6
, { x; -5 ≤ x < 4; x ∈ R} • Equal to
o Not equal to
• F o F
-5 4
(can include decimals because it’s a real number ∴ straight
line between numbers )
{ x; -2 ≤ x ≤ 2; x ∈ Z}
• • • • •
-2 -1 0 1 2
(integers ∴ use single dots on each number as decimals
aren’t included)
- Interval Notation ( ] ( 3; ∞)
smallest ; biggest (infinity always has a round bracket)
o
( -1; 3]
o •
3
-1 3
REAL NUMBERS (R) – All numbers that exist
RATIONAL NUMBERS (Q) – Numbers that can be written in the form a/b
IRRATIONAL NUMBERS (Q’) – Numbers that cant be expressed in the form a/b
NON-REAL NUMBERS – Square roots of negative numbers // Division by zero (undefined)
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