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.

In this wiki, you can see examples and exercises regarding some of the topics most viewed by tenth grade students, who are the ones who take the official international exams of the University of Cambridge, better known as IGCSE. The purpose of this page is to be able to explain various topics in the categories of numeric, algebra and geometry, through a step-by-step explanation, solved examples and the explanation of these; In addition to including practice exercises, with which whoever is viewing the wiki can practice and demonstrate their understanding of the topic. All this in order that the topics can be understood more easily and whoever sees the wiki prepares more and more to present their exams.

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


 * 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:

3. GEOMETRY
 * 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)

3. For the geometry part, we are going to see the addition of vector, the sine rule and area of a triangle


 * ADITION OF VECTORS

 Key information: 

HOW TO SOLVE IT?
 * A vector has a magnitude, that is the size, and a direction
 * The magnitud of the vector is the length
 * The magnitude is :Uop.png
 * The result of the additon of vectors is the representation of the total effect
 * To add a number of vectors, they are placed end to end so that the next vector starts, where the last one finished.


 * 1) You look the vector that mey look like these:

2. Then you put side to side, as in a normal addition, the vectors that are goint to be added

3. You add the vector as in a normal addition


 * Recommendations:
 * Look the vector as two numbers that are divide by a line. The numbers that are above the line, add them all together, as in the one below:
 * ej:

4. After you have the result you are going to discover de magnitud of the vector. For these you are going to use thse formula: For using these formula, the number up is going to be the x, and the one below is the y


 * ej:

5. Then, you must have the square root simplified, so ypu pass to a decimal number

EXAMPLE 1:


 * 1) You have two vectors

2. You added the vectos and the answer must be: 3. Then you need to find the magnitude with the formula mentioned EXCERCISE TO PRACTICE:


 * THE SINE RULE

Key information:


 * Ej:





EXAMPLE 1: Here we already have the three angles of the triangle, but we are missing the a value


 * Recommendation:

Do a table to organize the values that you already have and the ones that you need to find, like these one:

So, after we complete the table with the data, we are going to start looking wich operation is the one that we need. In these case, the operation is: These operation is used because, we have both answers of B, both we only have one for A. So what we do is to isolate ans star solving the operation.

EXCERCISE TO PRACTICE: