MATHEMATICS
, Key – core concepts
REAL NUMBERS NATURAL NUMBERS
NUMBERS “FAMILY”/SYSTEM
The number line consists of all the Rational
(Q) and Irrational (Q') numbers which
Even numbers : 2;4;6;8….
together form the set of Real (ℝ) numbers.
Odd numbers : 1;3;5;7…
UNREAL NUMBERS
Prime numbers : 2;3;5;7;11;13… (1 is not a prime
√−25 is an example of a non-real number. number)
There is no number that, when squared, will
Composite numbers : 4;6;8;9;10;12 (numbers with
equal -25.
more than 2 factors)
√−25 does not exist on the number line. Square numbers : 1;4;9;16;25…
The real and non-real numbers together
form the complex numbers. Cubic numbers : 1;8;27;64;125…
COUNTING NUMBERS
INTEGERS
RASIONAL NUMBER
any number that can be written as a fraction, i.e. a
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐴
or [where A & B ∈ Z ; B ≠ 0]
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐵
W All integers.
W All fractions.
W All terminating decimal fractions.
W All repeating decimal fractions.
IRRASIONAL NUMBERS
W All non-terminating, non-repeating decimal
Can only be written in a number form with infinite, numbers
non-repeating digits after the decimal point, the W Pi (π)
numbers can NOT be written as a FRACTION W √Positive non − square
3
W √Positive non − cubic
, Key – core concepts
BODMAS CALCULATIONS WITH BRACKETS ()
NB ! At minus - and brackets ()
Inside the bracket (-3)² = (-3)(-3) =+9
No bracket -3² =-(3)(3) = -9
Outside the bracket -(3)² =-(3)(3) = -9
CALCULATIONS WITH ROOTS √
+ or – under √ [first SIMPLIFY under the √]
W √16 + 9=√25
W √16 + 9≠√16 + √9
x or ÷ under die √ [divide √ and work out each
part's √ separately]
W √16 × 9=√144
SIGN RULES [X ÷] W √16 × 9=√16 × √9
, Key – core concepts
REAL NUMBERS NATURAL NUMBERS
NUMBERS “FAMILY”/SYSTEM
The number line consists of all the Rational
(Q) and Irrational (Q') numbers which
Even numbers : 2;4;6;8….
together form the set of Real (ℝ) numbers.
Odd numbers : 1;3;5;7…
UNREAL NUMBERS
Prime numbers : 2;3;5;7;11;13… (1 is not a prime
√−25 is an example of a non-real number. number)
There is no number that, when squared, will
Composite numbers : 4;6;8;9;10;12 (numbers with
equal -25.
more than 2 factors)
√−25 does not exist on the number line. Square numbers : 1;4;9;16;25…
The real and non-real numbers together
form the complex numbers. Cubic numbers : 1;8;27;64;125…
COUNTING NUMBERS
INTEGERS
RASIONAL NUMBER
any number that can be written as a fraction, i.e. a
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐴
or [where A & B ∈ Z ; B ≠ 0]
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐵
W All integers.
W All fractions.
W All terminating decimal fractions.
W All repeating decimal fractions.
IRRASIONAL NUMBERS
W All non-terminating, non-repeating decimal
Can only be written in a number form with infinite, numbers
non-repeating digits after the decimal point, the W Pi (π)
numbers can NOT be written as a FRACTION W √Positive non − square
3
W √Positive non − cubic
, Key – core concepts
BODMAS CALCULATIONS WITH BRACKETS ()
NB ! At minus - and brackets ()
Inside the bracket (-3)² = (-3)(-3) =+9
No bracket -3² =-(3)(3) = -9
Outside the bracket -(3)² =-(3)(3) = -9
CALCULATIONS WITH ROOTS √
+ or – under √ [first SIMPLIFY under the √]
W √16 + 9=√25
W √16 + 9≠√16 + √9
x or ÷ under die √ [divide √ and work out each
part's √ separately]
W √16 × 9=√144
SIGN RULES [X ÷] W √16 × 9=√16 × √9
