List of Basic Math Formulas for O and A Level

FRACTIONS & DECIMALS – IMPORTANT FORMULAS

 FRACTIONS

Proper Fraction  numerator < denominator (e.g., )

Improper Fraction  numerator ≥ denominator (e.g., )

Mixed Fraction  whole number + fraction (e.g., )

 OPERATIONS ON FRACTIONS

 DECIMAL CONVERSION

Fraction to decimal  divide numerator by denominator (e.g., 0.25 )

Decimal to fraction  remove decimal and divide by power of 10 (e.g., 0.5== )

 PLACE VALUE OF DECIMALS

3 . 3 . 14 2                                                       Example; 3.142

Ones  tenths    hundredths            thousandths

TERMINATING & NON-TERMINATING DECIMALS

Terminating finite decimal (0.25, 0.75)

Non-terminating recurring repeating decimal (0.333 … , 0.666 … )

IMPORTANT RULES

To compare fractions  make denominators same

To add or subtract  LCM of denominators

SQUARES, CUBES & ROOTS – QUICK FORMULAS

SQUARES

   n²= nn

Squares from 1 to 10:

1²=1, 2²=4, 3²=9, 4²=16, 5²=25

6²=36, 7²= 49, 8²=64, 9²=81, 10²=100

CUBES

Cubes from 1 to 5:

n³ = nnn  1³=1, 2³=8, 3³=27, 4³=64, 5³=125

IMPORTANT IDENTITIES

(a +b)² = a² + 2ab + b²

(ab)² = a² 2ab + b²

 a² b² = (a+b)(a-b)

SQUARE ROOT

(a)² = aI=1, 4=2, 9= 3, 16 =4, 25 =5

CUBE ROOT

1=1, 8 = 2, 27=3, 64=4, 125=5

QUICK TIPS

Square of even number  even

Square of odd number  odd

SIMPLIFICATION (BODMAS) – FORMULA & RULES

Order of operations Brackets  Of Division Multiplication  Addition Subtraction

BODMAS RULE:

B Brackets

OOf

DDivision

MMultiplication

A Addition

S for Subtraction

IMPORTANT RULES:

Rules :

Division and multiplication are done from left to right

Addition and subtraction are done from left to right

“Of” means multiplication

FRACTION SIMPLIFICATION RULES :

Fraction Rules :

Common Mistakes:

•       Adding before division                              
• Ignoring brackets