CHAPTER 14 FACTORISATION
 

• Factorization of an expression means writing it as the product its factors.

 

• An irreducible factor is a factor which cannot be expressed further as a product of factors.

 

• Common factor method:
  • Write each term of the expression as a product of irreducible factors
  • Look for and separate the common factors
  • Combine the remaining factors in each term in accordance with the distributive law.

 

• Factorization can be done by using the algebraic identities.

 
                  CHAPTER 13 DIRECT AND INVERSE PROPORTIONS
 
DIRECT PROPORTION
x and y are said to be in direct proportion if  x/y = k or x = ky.
 
If x and y are in direct proportion, x1/y1=x2/y2
 
INVERSE PROPORTION
x and y are said to be in inverse proportion if xy=k.

​                    CHAPTER 11 MENSURATION
 
AREA OF TRAPEZIUM
Area of trapezium = half the sum of the lengths of parallel sides x perpendicular distance between them
 
SURFACE AREA
The surface of a solid is the sum of the areas of its faces.

CHAPTER 10 VISUALISING SOLID SHAPES
 
2-D SHAPES
When a solid object has only two measurements it is called a 2 dimensional shape.
 
3-D SHAPES
When a solid object has three measurements- length, breadth and depth, it is called a 3 dimensional shape.
3D shapes objects have a different views from different positions
 
MAP
A map depicts the location of a particular object in relation to other objects.
 
POLYHEDRON
A polyhedron is a solid made up of polygonal regions called faces. These faces meet at edges and edges meet at vertices. For any polyhedron,
                                                         F + V – E = 2
Where ‘F’ stands for the number of faces, V is the number of vertices and E stands for number of edges. This is Euler’s formula.

​CHAPTER 9 ALGEBRAIC EXPRESSIONS AND IDENTITIES
 

• Expressions are formed from variables and constants.

 

• An expression is made up of terms and terms are made up as product of factors.

 

• Types of expressions:
  • Monomials: Containing one term
  • Binomials: Containing two terms
  • Trinomials: Containing three terms
  • Polynomials: Any expression with one or more terms with non-zero coefficients

 

• While adding or subtracting polynomials, operate on the like terms and then move on to the unlike terms.

 

• An identity is an equality which is true for all values of the variables in the equality.

 

           CHAPTER 8 COMPARING QUANTITIES

• Discount:

Discount is a reduction given on marked price i.e. Discount= Marked Price-Sales Price

• Overhead expenses

The additional expenses made after buying an article are called overhead expenses. These additional expenses are added in the cost price of the article i.e.
                        CP= Buying price + Overhead expenses

• Sales tax

Sales tax is charged on the sale of an item by the government.
             Sales tax= tax% of Bill Amount

• Compound interest

Compound interest is calculated on previous year’s amount.

 
                                CHAPTER 6 SQUARE AND SQUARE ROOTS
 

• Square Number: If a natural number m can be expressed as n2, where n is also a natural number then m is a square number.

 

• Properties of square numbers:

 

• All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.
• Square numbers have only even number of zeros at the end.

 

• Square root: If a natural number m can be expressed as n2, where n is also a natural number then n is the square root of m.

 

• There are two integral square roots of a perfect square number.

 

• Positive square root of a number is denoted by the symbol √

 

• Methods of finding square root:

 

• Through repeated subtraction
• Through prime factorization
• Through division method

                 CHAPTER 5 DATA HANDLING
 
DATA
Information collected in the context of a situation to be studied is called data.
 
GRAPHICAL REPRESENTATION OF DATA
1. Pictograph: Pictorial representation of data using symbols.
2. Bar Graph: Representation of data using bars of uniform width, their heights being   proportional to the respective values.
3. Double Bar Graph: A bar graph that shows two sets of data simultaneously is called a double bar graph. This graph is used for comparison of data.
 
RAW DATA
Data that is in an unorganized form is called raw data. Raw data should be organized in order to gain any inference from it.
 
FREQUENCY
Frequency gives the number of times a particular entry occurs.
 
HISTOGRAM
Histogram is a type of bar diagram where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval.
There is no gap between the bars as there is no gap between the class intervals.
 
 
PIE CHART
A circle graph shows the relationship between a whole and its part.
 
PROBABILITY
A random experiment is the one whose outcomes cannot be predicted exactly in advance.
             Probability of an event=  (Number of outcomes that make the event)/(Total number of outcomes of the experiment)
An event is one or more outcomes of an experiment.