SUMMARY of Formulas and Rules for Mathematics for Pre-MSc

Formulas and rules mathematics exam

!" ! $ !" "(&
Solving (in)equalities, like… (" $ &)!
− )" ! ( )
≥4
To solve follow this list basic algebraic operations:
• Formulation the condition, if any à finding all real values of x for which the
denominator equals zero.
• Simplifying fractions (with letter in it)
• Finding the LCD
• Adding and subtracting fractions (with letters in it)
• Simplifying expressions (with parentheses in it)
• Factoring expressions (or applying the abc-formula)
• Using a sign diagram to solve an inequality

General Information
[ 𝑐𝑙𝑜𝑠𝑒𝑑 ] = [ 0, 2 ] ⇒ 𝑚𝑒𝑎𝑛𝑖𝑛𝑔 𝑡ℎ𝑒 0 𝑎𝑛𝑑 2 𝑎𝑟𝑒 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑
( 𝑜𝑝𝑒𝑛 ) = ( 0,2 ) ⇒ 𝑚𝑒𝑎𝑛𝑖𝑛𝑔 𝑡ℎ𝑒 0 𝑎𝑛𝑑 2 𝑎𝑟𝑒 𝑒𝑥𝑐𝑙𝑢𝑑𝑒𝑑

General Algebraic Rules
*
If b ≠ 0 then, + = 0 ⟺ a = 0

pa ∙ pb = pa+b
(pa)b = pab
(a + b)(a – b) = a2 – b2
(a + b)(a + b) = a2 + 2ab + b2
(a – b)(a – b) = a2 - 2ab + b2

Negative Exponents
& &
*
= a-1 *"
= a-n (a ≠ 0)
& &
=a * #"
= an (a ≠ 0)
* #$


Fractional Exponents
&
√𝑎 = 𝑎)
&
"
√𝑎 = 𝑎 ,
%
"
√𝑎 - = 𝑎 "

! &
Solve 5" $!" = ).
Solution:
!
1. Make the base numbers equal: 5" $!" = 5-2
2. When the base numbers are equal, the exponents must be equal: x2 + 3x = -2