1. About Life Processes & Nutrition

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1. What is Reproduction?

How do organisms reproduce

Sample question paper

  • What is difference between sexual reproduction and asexual reproduction
  • What is difference between binary fission and multiple fission
  • Explain the binary fission in case of amoeba
  • What do you mean by vegetative propagation and what are its advantages
  • Define grafting
  • What are artificial methods of reproduction what is the difference between cutting and layering
  • What do you mean by pollination what are the two different types of pollination explain them along with figure
  • What do you mean by fertilization
  • What are four different parts of the flower explain all of them along with their function
  • What is the other name of female part of a flower
  • What are angiosperm flowers

 

In order to get the answers of the sample paper  and recorded video lecture on different topics WhatsApp number 7007 8207 83

 

2. Respiration

notes added by teacher sudhanshu in section a

no need to add by Manas from section B

2. Coordination in Plants

Basics Revisited

Equation

An equation is a statement that two mathematical expressions having one or more variables are equal.

Linear Equation

Equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.

General form of a Linear Equation in Two Variables

The general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.

Representing linear equations for a word problem

To represent a word problem as a linear equation

  • Identify unknown quantities and denote them by variables.
  • Represent the relationships between quantities in a mathematical form, replacing the unknowns with variables.

Solution of a Linear Equation in 2 variables

The solution of a linear equation in two variables is a pair of values, one for x and the other for y, which makes the two sides of the equation equal.
Eg: If 2x+y=4, then (0,4) is one of its solutions as it satisfies the equation. A linear equation in two variables has infinitely many solutions.

Geometrical Representation of a Linear Equation

Geometrically, a linear equation in two variables can be represented as a straight line.
2x – y + 1 = 0

⇒ y = 2x + 1

CBSE Class 10 Maths Notes Chapter 3 graph-1

Graph of y = 2

x

+1

Plotting a Straight Line

The graph of a linear equation in two variables is a straight line. We plot the straight line as follows:

Pair of Linear Equations in Two Variables Class 10 Notes Chapter 3-1

Any additional points plotted in this manner will lie on the same line.

All about Lines

General form of a pair of linear equations in 2 variables

A pair of linear equations in two variables can be represented as follows
 

Pair of Linear Equations in Two Variables Class 10 Notes Chapter 3-2


The coefficients of x and y cannot be zero simultaneously for an equation.

Nature of 2 straight lines in a plane

For a pair of straight lines on a plane, there are three possibilities

i) They intersect at exactly one point

CBSE Class 10 Maths Notes Chapter 3 graph-2

pair of linear equations which intersect at a single point.

ii) They are parallel

CBSE Class 10 Maths Notes Chapter 3 graph-3

pair of linear equations which are parallel.

iii) They are coincident

CBSE Class 10 Maths Notes Chapter 3 graph-4

pair of linear equations which are coincident.

Graphical Solution

Representing pair of LE in 2 variables graphically

Graphically, a pair of linear equations in two variables can be represented by a pair of straight lines.

Graphical method of finding solution of a pair of Linear Equations

Graphical Method  of finding the solution to a pair of linear equations is as follows:

  • Plot both the equations (two straight lines)
  • Find the point of intersection of the lines.

The point of intersection is the solution.

Comparing the ratios of coefficients of a Linear Equation

Pair of Linear Equations in Two Variables Class 10 Notes Chapter 3-3

Algebraic Solution

Finding solution for consistent pair of Linear Equations

The solution of a pair of linear equations is of the form (x,y) which satisfies both the equations simultaneously. Solution for a consistent pair of linear equations can be found out using

i) Elimination method

ii) Substitution Method

iii) Cross-multiplication method

iv) Graphical method

Substitution Method of finding solution of a pair of Linear Equations

Substitution method:

y – 2x = 1

x + 2y = 12

(i) express one variable in terms of the other using one of the equations. In this case, y = 2x + 1.

(ii) substitute for this variable (y) in the second equation to get a linear equation in one variable, x. x + 2 × (2x + 1) = 12

⇒ 5 x + 2 = 12

(iii) Solve the linear equation in one variable to find the value of that variable.
5 x + 2 = 12
x = 2

(iv) Substitute this value in one of the equations to get the value of the other variable.

y = 2 × 2 + 1

⇒y = 5

So, (2,5) is the required solution of the pair of linear equations y – 2x = 1 and x + 2y = 12.

Elimination method of finding solution of a pair of Linear Equations

Elimination method
Consider x + 2y = 8 and 2x – 3y = 2

Step 1: Make the coefficients of any variable the same by multiplying the equations with constants. Multiplying the first equation by 2, we get,

2x + 4y = 16

Step 2: Add or subtract the equations to eliminate one variable, giving a single variable equation.
Subtract second equation from the previous equation
2x + 4y = 16
2x  – 3y =  2
–     +       –
———————–
0(x) + 7y =14
Step 3: Solve for one variable and substitute this in any equation to get the other variable.

y = 2,

x = 8 – 2 y

⇒ x = 8 – 4

⇒ x = 4

(4, 2) is the solution.

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