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Mathematics Magazine for Grades 1-12  

 

Grade 12

 

 

 

Theory:

Sets of Numbers

Any set inside a larger box is completely contained within that set.

Real Numbers (R)

Rational Numbers (Q)

Irrational Numbers

Integers(I)

Fractions and Decimals

 

Negative Integers

Whole Numbers

 

 

 

Imaginary Numbers

       

Real & Imaginary numbers form the set of Complex numbers (C).

Solutions from the Previous Issue: 

1.       

Solution: Substitute



=

=

=

; Substitute: t = cos (x); d t = - sin (x) dx

= Integrate the sum term by term and factor out constants

=

=

;
Substitute back for  t = cos x



=

=



2.       

Solution: Substitute t = F(x); dt = F(x)dx

   

=

; Substitute s = t + 1;  ds = dt

=

=

 Integrate the sum term by term and factor out constants. 

   =

; Substitute back s = t + 1
   =

; Substitute back t = F(x)

                = =

Proposed Exercises: 

  1. Solve the equation:

  2. Solve the equation: (x2 x)2 8(x2 x) + 12 = 0