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The prime factorization of 13915 is

(a) 5 x 11 x x11 x 23             (b) 11 x 11 x 23
(c) 5 x 11 x 23                        (d) None of these
The prime factorization of 13915 is

(a) 5 x 11 x x11 x 23             (b) 11 x 11 x 23
(c) 5 x 11 x 23                        (d) None of these
1. Indian place value chart for a 9-digit number.
Crores Lakhs Thousands Ones Period
TC C TL L TTH Th H T O Place
2. International place value chart for a 9 digit number.
Millions Thousands Ones Period
HM TM M HTh TTh Th H T O Place
3. Comparing numbers
i. When numbers of digits are different, then the number having more number of digits is greater.
ii. When numbers of digits are the same, compare the leftmost digits in the two numbers. The
number with the greater leftmost digit is greater. In case, the leftmost digits are the same, then
compare the next left digits in both the numbers. The number with the greater digit is greater.
Continue this process until you come across unequal digits at the corresponding places, then
compare those two digits to find the greater number.
5. Place value of a digit in a number is the digit multiplied by its place.The number which is one more than the given number, is called its successor.
9. The number which is one less than the given number, is called its predecessor.
10. There are certain situations where we have to give an idea about a number without actual calculation.
This is called estimation.1. A point determines a location. It is denoted by a capital letter.
Point A, Point B
2. The shortest distance between two points is called a line segment.
3. A line is obtained when a line segment is extended on both sides indefinitely.
4. Two distinct lines meeting at a point are called intersecting lines.
5. Two lines in a plane are said to be parallel, if they Two lines in a plane are said to be parallel, if they do not meet, howsoever far they are extended.
6. Three or more lines in a plane are said to be concurrent, if, all of them pass through the same point.
7. A ray is a portion of a line starting at a point and going on in one direction endlessly.
8. A polygon is a simple closed curve made up of line segments.
i. The line segments forming a polygon are called its sides.
ii. Any two sides with a common end point are adjacent sides.
iii. The meeting point of a pair of sides is called a vertex.
iv. The end points of the same side are adjacent vertices.
v. The joint of any two non-adjacent vertices is called a diagonal.
A triangle is a 3 sided polygon.
10.A quadrilateral is a 4 sided polygon.
11.A circle is the path of a point moving at the same distance from a fixed point. The fixed point is called
the centre of the circle and the fixed distance is called the radius of the circle.1. A data is a collection of numbers gathered to give some information.
2. Data obtained in the original form is called raw data.
3. The representation of information through pictures is called a pictograph.
4. Data can also be represented through bar graphs. In a bar graph, bars of uniform width are drawn
horizontally or vertically with equal spacing between them.Perimeter is the distance around a closed figure when we go around the figure once.
So, perimeter = sum of the lengths of all the sides
2. Perimeter of a triangle is the sum of the lengths of all its three sides.
3. Perimeter of a square = (4

side) units
4. Perimeter of a rectangle = 2 (Length + Breadth) units
5. Perimeter of regular shapes = number of sides

length of one side
6. The measurement of the region enclosed by a plane figure is called the area of the figure.
7. Area is always expressed in square units.
8. Area of a rectangle = (length breadth) square unit9. Area of a square = (side side) square units1. The main feature of algebra is the use of letters, which allow us to write rules and formulae in a
general way.
2. In algebra, letters are used to represent unknown or unspecified numbers. These letters are called
variables. The word 'variable' means something that can vary/ change.
3. Variables can take different values, they have no fixed values. Yet, they are numbers. So, as in the
case of numbers, operations of addition, subtraction, multiplication and division can be done on them.
4. Any numeral, variable or a combination of a numeral and a variable connected by one or more
symbols such as '+', '-', is known as an algebraic expression.
5. An algebraic expression consists of two parts: Numerical factor and Literal factor.
For example, in the algebraic expression 4x, we have 4 as the numerical factor and x as the literal
factor.
6. Types of algebraic expressions:
Monomials: Expressions with single term are called monomials.
Example: -6x2
y, 5abc2
Binomials: Expressions with two terms are called binomials.
Example: -5a+2b, 6x2
y-2ab
Polynomials: Expressions with one or more Polynomials: Expressions with one or more terms are called polynomials.
Example: ab + bc + ca + a2
7. The terms having the same literal factors are called like terms; otherwise, they are called unlike terms.
8. An equation is an equality between two algebraic expressions. For example, 3x + 7 = 9
9. In a simple linear equation, there is one and only one variable and also its power is 1.The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation. We
say that, this definite value is the solution of the given equation.
TKS.