7th Class

  Electricity and Light   Electricity All electrical devices such as torches, fans, washing machines, music systems, etc. work on electricity. These devices work when electric current flows through them. The flow of electricity is called current. Current flows through an electric device when voltage is supplied across the device. The amount of current that flows depends on the amount of voltage supplied.   The unit of measurement of voltage is volts (V). Voltage is supplied through electric cells and main electric supply.   Electric Circuit An electric circuit is a path through which electric current flows. An electric circuit includes a source of electricity, conductors and a device that uses electricity. The source of electricity can be a cell, the conductor can be a wire and a device that uses electricity can be an electric bulb.   more...

  Our Environment   Soil Soil the uppermost layer of the earth's crust. Soil is formed by the weathering of rocks. The weathering of rocks takes place as a result of natural factors such as temperature change, rain and wind. Soil supports growth of plants.   Layers of Soil Soil consists of layers. Layers of soil are called horizons. The various layers of soil are:   A-horizon: This is the uppermost layer of the soil. This layer is also called topsoil. It is dark in colour due to the presence of humus.   B-horizon: This layer is below the topsoil and is called subsoil. This soil is lighter in colour. The particles of this layer are coarser and porous. This layer does not contain much humans and thus not suitable for plants growth.   C-horizon: This layer is more...

  Number System and Its Operations   Integers Integers are the set of all positive and negative numbers including zero.   Addition of Integers

• The sum of two integers is an integer or integers are closed under addition.
• The sum of two integers is commutative.
• The addition of integers is associative.
• 0 is the additive identity for integers.

  Subtraction of Integers Integers are closed under subtraction but they are neither commutative nor associative. Thus, if a and b are two integers then \[a-b\] is also an integer.   Multiplication of Integers The product of two integers is an integer or integers are closed under multiplication. The product of two integers is commutative. Multiplication of integers is associative. 1 is the multiplicative identity for integers. For any integer \[a,\,a\times 0=0\times a=0\] While multiplying a positive integer and a negative-integer, we multiply them more...

  Exponents   Exponents The continued product of a number multiplied with itself a number of times can be written in exponent form as \[{{a}^{n}}\], where 'n' is a natural number and 'a' is any number. i.e. \[{{a}^{n}}=a\times a\times a\]..... up to n times. Here a is the base and n is exponent (or index or power).   For any rational number\[\left( \frac{p}{q} \right),{{\left( \frac{p}{q} \right)}^{n}}=\frac{p}{q}\times \frac{p}{q}\times \frac{p}{q}\times \].......... up to n times   Laws of Exponents The following are the laws of exponent: \[\Rightarrow \]\[{{X}^{m}}\times {{X}^{n}}={{X}^{m+n}}\]            \[\Rightarrow \]\[\frac{{{X}^{m}}}{{{X}^{n}}}={{X}^{m-n}}\] \[\Rightarrow \]\[{{X}^{m}}\times {{Y}^{m}}={{(X\times Y)}^{m}}\] \[\Rightarrow \]\[{{\left[ {{\left( \frac{X}{Y} \right)}^{n}} \right]}^{m}}={{\left( \frac{X}{Y} \right)}^{mn}}\] \[\Rightarrow \]\[{{\left( \frac{X}{Y} \right)}^{-n}}={{\left( \frac{Y}{X} \right)}^{n}}\]                 \[\Rightarrow \]\[{{X}^{0}}=1\] \[\Rightarrow \]\[{{X}^{1}}=X\] \[\Rightarrow \]\[{{X}^{-1}}=\frac{1}{X}\]   Uses of Exponents It is the way to represent the smaller as well as larger numbers which are not possible to write in the convenient way by existing number system. Suppose more...

  Algebraic Expression and Linear Equation   Algebraic Expression Algebraic expression is the combination of constants and variables along with the fundamental operations\[(+,-,\times ,\div )\]. The part of an algebraic expression which is separated by the sign of addition and subtraction are called terms.   Types of Algebraic Expression The following are the few types of algebraic expression:

• Monomials
• Binomials
• Trinomials

  Finding the Value of an Algebraic Expression To find the value of an algebraic expression, first simplify the given algebraic expression if possible and replace the variable with given numerical value.   Example: List the following algebraic expression into monomial, binomial or trinomial: \[3a+4b+5c,\,\,{{a}^{3}}+{{b}^{3}}-3ab,\,\,5a,\,\,6x+4y,\,\,35x+5y-35(x-y)\]                                     Solution: Monomial: \[3{{z}^{2}},5a,35x+5y-35(x-y),\] as these have only one term. Binomial: \[6x+4y\], because it has only two terms. Trinomial: \[3a+4b+5c\], \[{{a}^{3}}+{{b}^{3}}-3ab,\]because they have only 3 terms.   Algebraic Identities

• \[{{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\]
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  Ratio and Proportion Percentage and S.I. and C.I.   Ratio A ratio is a relation between two quantities of same kind. The ratio of a number x to another number y (Where\[y\ne 0\]) is written as \[x:y\].   Example: Daniel wants to divide 1530 L of water between David and Michael in the ratio\[8:9\]. Find the quantity received by David. (a) L 720                       (b) L 810 (c) L 900                       (d) L 820 (e) None of these Answer (a)   Explanation: Amount received by David  \[=\frac{1530}{17}\times 8=\,L\,720\]   Proportion A proportion is a name we give to a statement when two ratios are equal. It can be written in two ways:

• \[\frac{a}{b}=\frac{c}{d}\](two equal fractions)
• \[a:b::c:d\] (using a colon)

When two ratios are equal then, their cross products are equal. That is, for the proportion, \[a\,:\,b\,=\,c\,:\,d,\,a\times d=b\times c\] In more...

  Data Handling   Modern society is information oriented. Every person wants numeric information of different fields of the society like the marks obtained in a particular subject by the students, five year plans etc. Statistics is a branch of mathematics which deals with the process, analyzing and interpreting the data.   Terms Related to Data

• Data: It is defined as the particular information in numeric form.
• Primary data: Primary data means the data that have been collected by collector for some purpose.
• Secondary data: Secondary data is data that have been collected by others and used by other observer.
• Raw data: It is the original form of the data.
• Frequency: The number of times a particular observation occurs in a data is called frequency.
• Range: The difference between maximum and minimum value of the observation is called range.
• Class Interval: The interval more...

  Geometry   In our daily life we observe different geometrical shapes. These geometrical shapes are not only the matter of study of mathematics but are directly related with our daily life. The basic geometrical figures are made up of lines and angles.   Line Segment It is the straight path between two points. In other words we can say that it has two end points and is of finite length.   Ray When a line segment extends infinitely in one direction, it is called a ray. Simply we can say that a ray has one end point and infinite length.   Line When both end of a line segment extended infinitely, it is known as a line. Simply we can say that a line has no end point and infinite length.   Parallel Lines Two lines are said to be parallel if the distance between more...

  Mensuration   Standard Units of Area The inter relationship among various units of measurement of area are listed below.   \[1\,{{m}^{2}}\]                      =         \[(100\times 100)\,c{{m}^{2}}={{10}^{4}}\,c{{m}^{2}}\] \[1\,{{m}^{2}}\]                      =         \[(10\times 10)\,d{{m}^{2}}=100\,d{{m}^{2}}\] \[1\,d{{m}^{2}}\]        =         \[(10\times 10)\,c{{m}^{2}}=100\,c{{m}^{2}}\] \[1\,da{{m}^{2}}\]       =         \[(10\times 10)\,{{m}^{2}}=100\,{{m}^{2}}\] \[1\,h{{m}^{2}}\]                    =         \[(100\times 100)\,{{m}^{2}}={{10}^{4}}{{m}^{2}}\] \[1\,k{{m}^{2}}\]                     =         \[(1000\times 1000)\,{{m}^{2}}={{10}^{6}}\,{{m}^{2}}\] \[1\,hectare\]      =         \[10000\,{{m}^{2}}\] \[1\,k{{m}^{2}}\]                     =         \[100\,hectare\]   Formula Related to Perimetre and Area

• Area of a triangle \[=\frac{1}{2}\times b\times h\]
• Area of an equilateral triangle \[=\frac{\sqrt{3}}{4}\times {{a}^{2}}\]
• Perimetre of a rectangle \[=2(Length+breadth)\]
• Area of a rectangle \[=Length\times breadth\]
• Diagonal of a rectangle \[=\sqrt{{{(length)}^{2}}+{{(breadth)}^{2}}}\]
• Perimetre of a square \[=4\times side\]
• Area of a square \[=sid{{e}^{2}}=\frac{1}{2}\times {{(diagonal)}^{2}}\]
• Side of a square \[=\sqrt{area}\]
• Diagonal of a square \[=side\times \sqrt{2}\]
• Perimetre of a parallelogram \[=2\times sum\,of\,length\,of\,adjacent\,sides.\]
• Area of a parallelogram \[=base\times corresponding\,height.\]
• Perimetre of a rhombus \[=4\times side\]
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  Algebraic Expressions   In an algebraic expression constant and variables are linked with arithmetic operations. The value of unknown variable is obtained by simplification of the given expression.   Terms of an algebraic Expression   Variables Alphabetical symbols used in algebraic expressions are called variables a, b, c, d, m, n, x, y, z ........... etc. are some common letters which are used for variables.   Constant Terms The symbol which itself indicate a permanent value is called constant. All numbers are constant. \[6,10,\frac{10}{11},15,-6,\sqrt{3}....\]etc. are constants because, their values are fixed.   Variable Terms A term which contains various numerical values is called variable term. For example. Product of \[\text{X=4 }\!\!\times\!\!\text{ }\,\text{X=4X}\]Product of \[\text{2,X,}{{\text{Y}}^{2\,}}\] and \[\text{Z=}\,\text{2 }\!\!\times\!\!\text{ X }\!\!\times\!\!\text{ }{{\text{Y}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ Z=2X}{{\text{Y}}^{\text{2}}}\text{Z}\] Thus, 4X and \[\text{2X}{{\text{Y}}^{\text{2}}}\text{Z}\] are variable terms   Types of Terms There are two types of terms, like and unlike. Terms are classified more...