“Grade 10
IEB Maths
Notes
P1”
“Algebraic Expressions”
“Exponents”
“Number Patterns”
“Equations & Inequalities”
“Functions”
“Finance”
“Probability”
, “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)
IEB Maths
Notes
P1”
“Algebraic Expressions”
“Exponents”
“Number Patterns”
“Equations & Inequalities”
“Functions”
“Finance”
“Probability”
, “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)
