User:Sveldom

What is IGCSE?
IGCSE are a group of exams of the University of Cambridge, which certify the international secondary education of the students who present them.

IGCSE of math:
On of the exams of IGCSE is about math subject, where are asked topics such as:
 * Numeric
 * Algebraic
 * Probability
 * Stadistics/percentages


 * 1) ALGEBRA


 * 1) For the algebra we are going to see the inverse proportions,domain and range and the function notations.


 * INVERSE PROPORTIONS

 Key information: 


 * An inverse function is the one thata serves to another function
 * The inverse function use the connotation of f ⁻¹(x)
 * For the process of inverse function is used 4 steps:


 * 1) Change f(x) for y
 * 2) Interchange all the x in the excersice to y and viceversa
 * 3) Solve the y isolating
 * 4) Change the y to the inverse function  f ⁻¹(x)

EXAMPLE 1:

f(x):6x+4


 * 1) f(x):6x+4
 * y:6x+4 (You start puting the operaion in y)
 * x:6y+4(Then you put the operation in x)
 * 1) x-4:6y(You isolate and as you are moving to the other side the 4 it pass to do the opposite of adding)
 * 2) x-4/6:y(You isolate same the 6 and as it is multiplying, you pas to the left and it becomes to divide)
 * 3) x-4/6: f ⁻¹(x)

EXCERCISES TO PRACTICE:


 * f(x):3(x-6) to f ⁻¹(x)
 * f(x):x^2+7
 * f(x):2x+5


 * DOMAIN AND RANGE

 Key information: 


 * The domain of a function is the range of the inverse
 * The range of the function is the domain of the inverse
 * The domain (x) of f(x) is the range (x) of the f ⁻¹(x) and viceversa

EXAMPLE 1:

f(x):2x^2+4 Domain= all real numbers Range=?


 * y:2x^2+4 (You satr puting the operation to solve in y)
 * x:2y^2+4(You now put it in x)
 * x:$$\sqrt{2y+4}$$(Cancel de power puting a squer root)
 * $$\sqrt$$:y(Isolate and as you isolate the y and pss to the left, it is going to divine and not multiply
 * x-4 $$\geq$$0(2) (Take the range that is equal or bigger than)
 * x$$\geq$$4

EXCERCISES TO PRACTICE:


 * f(x):x^2-9 Domain=R Range:?
 * f:x $$\longmapsto$$2x+1 Domain=-1, 0, 1, 2 Range=?
 * g(x):x+2 Domain=x:x$$\geq$$ -2, x is an integer  Range=?


 * FUNCTION NOTATION

 Key information: 

EXAMPLE 1:

f(x):1/1+2x   f(2)   f(-1)   f(9)


 * f(2): 1/1+2(2) = 1/5
 * f(-1):1/1+2(-1) = -1
 * f(9):1/1+2(9) = 1/19

EXCERCISES TO PRACTICE:


 * h(x)=2 -1/x    h(2)    h(-2)    h(4)
 * h:x $$\longmapsto$$3x-2    h(2)    h(y)
 * g(x): $$\sqrt{x-1}$$  g(3)    g(-1)   g(99)