## Please just briefly explain each topic

**Question**

pls just briefly explain each topic.

rational expressions

fractional equations

system of equation (word problems)

quadratic linear pair (solve algebraically)

graphing (transformations)

venn diagram

parellelogram/trapezoid

parabolas

area problem (shaded region-word problem)

circle graph

**Answer**

Let us begin.

1. rational expressions

A rational expression is an algebraic expression whose numerator & denominator both consists of rational numbers.

A rational number is a number in the form x/y where both x & y are integers. For example. E = ( X^2 -2X ) / ( y/2 – 1 ) where X and Y are both rational will imply E to be a rational expression.

2. fractional equations

I am not very sure about this one but it should be one of the two possibilities below :

(a) An equation where the variables or unknowns are in fractional numbers, i.e. fractions.

(b) There is concept called “fractional part”. For the number ‘x’, the symbol {x} is used t denote the ‘fractional part of x’. For example, take X = 3.545 Then by definition,

{X} = 0.545

Roughly, its the ‘part’ of the number whose value lie in the interval [0,1].

3. system of equation (word problems)

A system of equation relates to a group of equations. One will encounter the study of such equations in many variables in the field of Linear Algebra. Basically matrix theory is used by arranging the unknowns & coefficients to form an array. Then the solubility and also the properties of the group of equation is deduced mostly based on Linear Algebra techniques. One may even end up using vectors to represent these arrays in more advanced techniques.

4.quadratic linear pair (solve algebraically)

I believe what is meant here is that a solution for the general simultaneous equation where one is a quadratic while the other is a linear equation. We can proceed as follows:

I do not want to attempt a lengthy general solution but I believe you should be able to manipulate algebraically.

5. graphing (transformations)

Transformation & Graphing are actually different. Graphing refers to a kind of visual diagram in which one gets to see points being mapped in say a 3D space where the points that are graphed are predefined based on a set of rules.

To the human eye usually the ‘visualization’ is usually limited to 2D or 3D and sometimes a well defined 4D or above space.. Why I am mentioning this is because we don’t have a convention say ‘graph in 5D’ for example…

Transformations are basically mapping in space. There are three basic kind of transformations : translation, rotation & ‘stretching’. All other transformation of objects can be derived as a ( repeated ) combination of one or more of these basic transformations.

6. venn diagram

Venn diagrams are the basis of ‘visualizing set theory’. In a Venn diagram one has a sets and its number of elements that it contains respectively. Usually there is a ‘universal set’ which is the set that contains all the sets in concern for that particular case.

7. parellelogram/trapezoid

Parallelogram is a figure whose opposite sides are parallel.

Trapezoid? I think its a 3D trapezium.

8.parabolas

parabolas are points ( x,y ) which are defined by the following general equation :

y^2 = ax^2 + bx + c

9.area problem (shaded region-word problem)

Area…. The usual area problems are the ‘2D’ ones where one calculate area of various geometric shapes and solve problems that are associated with it. More advanced area problems are the ones involving Calculus. Integration techniques are often used to evaluate or sometimes approximate these areas, …

10.circle graph

Due you mean the graph of a circle? General equation? or ? Just a circle in all three cases! (graphically)

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