Class 7 -CBSE -Formulae She ets...1. The six elements of a triangle are its three angles and the...

Class 7-CBSE-Formulae Sheets

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INTEGERS

Important formulas and statements

1. Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.

2. Integers show some properties under by addition and subtraction.

(a) Integers are closed for addition and subtraction both, i.e., a b+ and a b− are again integers,

where a and b are any integers.

(b) Addition is commutative for integers, i.e., a b b a+ = + for all integers a and b.

(c) Addition is associative for integers, i.e., ( ) ( )ba b c a c+ + = + + for all integers a, b and c.

(d) Integer 0 is the identity under addition i.e., 0 0a a a+ = + = for every integer a.

3. Product of a positive and a negative integer is a negative integer, whereas the product of two negative

integers is a positive integer.

4. Product of even number of negative integers is positive, whereas the product of odd number of

negative integers is negative.

5. Integers show some properties under multiplication

(a) Integers are closed under multiplication i.e., a b is an integer for any two integers a and b.

(b) Multiplication is commutative for integers i.e., a b b a = for any integers a and b.

(c) The integer 1 is the identity under multiplication, i.e., 1 1a a a = = for any integer a.

(d) Multiplication is associative for integers, i.e., ( ) ( )a b c a b c = for any three integers a, b

and c.


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6. Under addition and multiplication, integers show a property called distributive property. i.e.,

( )a b c a b a c + = + for any three integers a, b and c.

7. The properties of commutativity, associativity under addition and multiplication, and the distributive

property help us to make our calculations easier.

8. Integers show some properties under division

(a) When a positive integer is divided by a negative integer, the quotient obtained is negative and

vice-versa.

(b) Division of a negative integer by another negative integer gives positive as quotient.

9. For any integer a, we have,

(a) 0a is not defined.

(b) 1a a =


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FRACTIONS AND DECIMALS


1. Two fractions are multiplied by multiplying their numerators and denominators separately and

writing the product as product of numerators

product of denominators

2. The product of two proper fractions is less than each of the fractions that are multiplied.

3. The product of a proper and an improper fraction is less than the improper fraction and greater than

the proper fraction.

4. The product of two improper fractions is greater than the two fractions.

5. A reciprocal of a fraction is obtained by inverting it upside down.

6. Division of two fractions

(a) While dividing a whole number by a fraction, we multiply the whole number with the

reciprocal of that fraction.

(b) While dividing a fraction by a whole number we multiply the fraction by the reciprocal of the

whole number.

(c) While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal

of the other.


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7. To multiply two decimal numbers:

(a) First multiply them as whole numbers.

(b) Count the number of digits to the right of the decimal point in both the decimal numbers.

(c) Add the number of digits counted.

(d) Put the decimal point in the product by counting the digits from its rightmost place.

(e) The count should be the sum obtained earlier.

8. To multiply a decimal number by 10, 100 or 1000, we move the decimal point in the number to the

right by as many places as there are zeros over 1.

9. To divide decimal numbers

(a) To divide a decimal number by a whole number, we first divide them as whole numbers. Then

place the decimal point in the quotient as in the decimal number.

(b) To divide a decimal number by 10, 100 or 1000, shift the digits in the decimal number to the

left by as many places as there are zeros over 1, to get the quotient.

(c) While dividing two decimal numbers, first shift the decimal point to the right by equal number

of places in both, to convert the divisor to a whole number. Then divide.


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DATA HANDLING


1. The collection, recording and presentation of data help us organize our experiences and draw

inferences from them.

2. The data that is collected needs to be organized in a proper table, so that it becomes easy to

understand and interpret.

3. Average is a number that represents or shows the central tendency of a group of observations

or data.

4. Arithmetic mean is one of the representative values of data.

5. Mode is another form of central tendency or representative value. The mode of a set of

observations is the observation that occurs most often.


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6. Median is also a form of representative value. It refers to the value which lies in the middle of

the data with half of the observations above it and the other half below it.

7. A bar graph is a representation of numbers using bars of uniform widths.

8. Double bar graphs help to compare two collections of data immediately.


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SIMPLE EQUATIONS


1. An equation is a condition on a variable such that two expressions in the variable should have equal

value.

2. The value of the variable for which the equation is satisfied is called the solution of the equation.

3. An equation remains the same if the LHS and the RHS are interchanged.

4. In case of the balanced equation, if we

a) add the same number to both the sides, or

b) subtract the same number from both the sides, or

c) multiply both sides by the same number, or

d) divide both sides by the same number,

the balance remains undisturbed, i.e., the value of the LHS remains equal to the value of the RHS.


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5. The above property gives a systematic method of solving an equation.

We carry out a series of identical mathematical operations on the two sides of the equation in such a

way that on one of the sides we get just the variable.

The last step is the solution of the equation.

6. Transposing means moving to the other side. Transposition of a number has the same effect as adding

same number to (or subtracting the same number from) both sides of the equation.

When we transpose a number from one side of the equation to the other side, we change its sign.

We can carry out the transposition of an expression in the same way as the transposition of a number.


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LINES AND ANGLES


1. A line-segment has two end points.

2. A ray has only one end point (its initial point).

3. A line has no end points on either side.

4. An angle is formed when two lines (or rays or line-segments) meet.

5. Two complementary angles measures add up to 90°.

6. Two supplementary angles measures add up to 180°.

7. Two adjacent angles have a common vertex and a common arm but no common interior.

8. Linear pair are adjacent and supplementary.

9. When two lines l and m meet, we say they intersect; the meeting point is called the point of

intersection.

10. When lines drawn on a sheet of paper do not meet, however far produced, we call them to be parallel

lines.

11. When two lines intersect (looking like the letter X) we have two pairs of opposite angles. They are

called vertically opposite angles. They are equal in measure.

In the given above figure; AOC BOD = and AOD BOC =


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12. A transversal is a line that intersects two or more lines at distinct points.

13. A transversal gives rise to several types of angles. In the figure, we have

(a) Interior angles 3, 4, 5, 6

(b) Exterior angles 1, 2, 7, 8

(c) Alternate interior angles 3& 5, 4 & 6

(d) Alternate exterior angles 1& 7, 2 & 8

(e) Interior angles, on the same side of transversal 3& 6, 4 & 5

(f) Corresponding angles 1 & 5, 2 & 6,

3& 7, 4 & 8


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14. When a transversal cuts two parallel lines, we have the following interesting relationships:

(a) Each pair of corresponding angles are equal

i.e., 1 5, 3 7, 2 6, 4 8 = = = =

(b) Each pair of alternate interior angles are equal.

i.e., 3 5, 4 6 = =

(c) Each pair of interior angles on the same side of transversal are supplementary.

i.e., 3 6 180 , 4 5 180 + = + =


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TRIANGLE AND ITS PROPERTIES


1. The six elements of a triangle are its three angles and the three sides.

2. The line segment joining a vertex of a triangle to the midpoint of its opposite side is called a

median of the triangle. A triangle has 3 medians.

3. The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude

of the triangle. A triangle has 3 altitudes.

4. An exterior angle of a triangle is formed, when a side of a triangle is produced. At each vertex,

you have two ways of forming an exterior angle.

5. A triangle is said to be equilateral, if each one of its sides has the same length. In an equilateral

triangle, each angle has measure 60°.

6. A triangle is said to be isosceles, if at least any two of its sides are of same length. The non-equal

side of an isosceles triangle is called its base; the base angles of an isosceles triangle have equal

measure.

7. In a right-angled triangle, the side opposite to the right angle is called the hypotenuse and the other

two sides are called its legs.


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8. Property of the lengths of sides of a triangle:

a) The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

b) The difference between the lengths of any two sides is smaller than the length of the third side.

This property is useful to know if it is possible to draw a triangle when the lengths of the three sides

are known.

9. Pythagoras property:

a) In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on its

legs.

b) If a triangle is not right-angled, this property does not hold good.

This property is useful to decide whether a given triangle is right-angled or not.

10. A property of exterior angles:

The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior

opposite angles.

11. The angle sum property of a triangle:

The total measure of the three angles of a triangle is 180°.


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CONGRUENCE OF TRIANGLES


1. Congruent objects are exact copies of one another.

2. The method of superposition examines the congruence of plane figures.

3. Two plane figures, say, X and Y are congruent if the trace-copy of X fits exactly on that of

Y. We write this as X Y .

4. Two line-segments are congruent if they have equal lengths.

Say, AB and CD have equal length. We write this as AB CD . However, it is common to

write it as AB CD= .

5. Two angles are congruent if their measures are equal.

Say, ABC and PQR , We write this as ABC PQR or as m ABC m PQR = . However,

in practice, it is common to write it as ABC PQR = .

6. SSS Congruence of two triangles:

Under a given correspondence, two triangles are congruent if the three sides of the one are

equal to the three corresponding sides of the other.

If in ABC and PQR , ,AB PQ BC QR= = and CA RP=

Then we write ABC PQR .


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7. SAS Congruence of two triangles:

Under a given correspondence, two triangles are congruent if two sides and the angle

included between them in one of the triangles are equal to the corresponding sides and the

angle included between them of the other triangle.

If in ABC and PQR , ,AB PQ BC QR= = and B Q =


8. ASA Congruence of two triangles:

Under a given correspondence, two triangles are congruent if two angles and the side

included between them in one of the triangles are equal to the corresponding angles and

the side included between them of the other triangle.

If in ABC and PQR , ,AB PQ A P= = and B Q =


9. RHS Congruence of two right-angled triangles:

Under a given correspondence, two right-angled triangles are congruent if the hypotenuse

and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of

the other triangle.

If in ABC and PQR , 90B Q = = , hypotenuse AC PR= and BC QR= or AB PQ=



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10. If two triangles are congruent then their corresponding parts are equal. We use ‘CPCT’ as

abbreviation.

If ABC PQR , then

i. ,AB PQ BC QR= = and CA RP=

ii. ,A P B Q = = and C R =

11. There is no such thing as AAA Congruence of two triangles. Two triangles with equal

corresponding angles need not be congruent. In such a correspondence, one of them can be

an enlarged copy of the other. (They would be congruent only if they are exact copies of

one another).


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COMPARING QUANTITIES


1. While comparing lengths of two objects with lengths 200 cm and 150 cm, we write it as

the ratio 200 :150 or 4:3 .

2. Two ratios can be compared by converting them to like fractions. If the two fractions are

equal, we say the two given ratios are equivalent.

3. If two ratios are equivalent, then the four quantities are said to be in proportion.

For example, the ratios 4:3 and 8: 6 are equivalent therefore 4, 3, 8 and 6 are in proportion.

4. A way of comparing quantities is percentage. Percentages are numerators of fractions with

denominator 100. Per cent means per hundred.

For example, 56% marks means 56 marks out of 100.


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5. Fractions can be converted to percentages and vice-versa.

For example,

3 3100% 75%

4 4= = whereas,

50 150%

100 2= = .

6. Decimals too can be converted to percentages and vice-versa.

For example,

0.45 0.45 100% 45%= = .


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RATIONAL NUMBERS


1. A number is called a rational number, if it can be written in the form p

q, where p and q are

integers and 0q . e.g. 2 3 5

1, , , ,0, 2,3 4 2

− −− .

2. All integers and fractions are rational numbers.

3. If the numerator and denominator of a rational number are multiplied or divided by a non-

zero integer, we get a rational number which is said to be equivalent to the given rational

number.

4. Rational numbers are classified as Positive and Negative rational numbers. When the

numerator and denominator, both, are positive integers, it is a positive rational number.

When either the numerator or the denominator is a negative integer, it is a negative rational

number.

5. The number 0 is neither a positive nor a negative rational number.

6. A rational number is said to be in the standard form if its denominator is a positive integer

and the numerator and denominator have no common factor other than 1.


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7. There are unlimited number of rational numbers between two rational numbers.

8. Two rational numbers with the same denominator can be added by adding their numerators,

keeping the denominator same.

9. Two rational numbers with different denominators are added by first taking the LCM of

the two denominators and then converting both the rational numbers to their equivalent

forms having the LCM as the denominator.

10. While subtracting two rational numbers, we add the additive inverse of the rational number

to be subtracted to the other rational number.

11. To multiply two rational numbers, we multiply their numerators and denominators

separately, and write the product as

product of numerators

product of denominators

12. To divide one rational number by the other non-zero rational number, we multiply the

rational number by the reciprocal of the other


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PERIMETER AND AREA


1. Perimeter is the distance around a closed figure whereas area is the part of plane occupied

by the closed figure.

2. Perimeter and area of a square and rectangle are:

(a) Perimeter of a square 4 side=

(b) Perimeter of a rectangle ( )2 length breadth= +

(c) Area of a square side side=

(d) Area of a rectangle length breadth=

3. Area of a parallelogram base height= .

4. Area of a triangle 1

2base height= .


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5. The distance around a circular region is known as its circumference.

Circumference of a circle d= or 2 r , where d is the diameter, r is the radius of a circle

and 22

7 = or 3.14 approximately.

6. Area of a circle 2r= , where r is the radius of the circle.


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ALGEBRAIC EXPRESSIONS


1. Algebraic expressions are formed from variables and constants. We use the operations of

addition, subtraction, multiplication and division on the variables and constants to form

expressions.

For example, the expression 3 2xy + is formed from the variables x and y and constants 2

and 3. The constant 3 and the variables x and y are multiplied to give the product 3xy and

the constant 2 is added to this product to give the expression.

2. Expressions are made up of terms. Terms are added to make an expression. For example,

the addition of the terms 3xy and 2 gives the expression 3 2xy + .

3. A term is a product of factors. The term 3xy in the expression 3 2xy + is a product of factors

x, y and 2. Factors containing variables are said to be algebraic factors.

4. The coefficient is the numerical factor in the term. Sometimes any one factor in a term is

called the coefficient of the remaining part of the term.

5. Any expression with one or more terms is called a polynomial. Specifically,

i. a one term expression is called a monomial.

ii. a two-term expression is called a binomial.

iii. a three-term expression is called a trinomial.


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6. Terms which have the same algebraic factors are like terms. Terms which have different

algebraic factors are unlike terms.

For example, terms 3xy and 3xy− are like terms; but terms 3xy and 3x− are not like terms.

7. The sum (or difference) of two like terms is a like term with coefficient equal to the sum

(or difference) of the coefficients of the two like terms. Thus, ( )6 – 2 6 – 2xy xy xy= , i.e., 4xy

.

8. When we add two algebraic expressions, the like terms are added as given above; the unlike

terms are left as they are.

For example, the sum of 23 2x x+ and 3 4x+ is 23 5 4x x+ + ; the like terms 2x and 3x add to

5x; the unlike terms 23x and 3 are left as they are.

9. In situations such as solving an equation and using a formula, we find the value of an

expression. The value of the expression depends on the value of the variable from which

the expression is formed.

For example, the value of 4 3x+ for 2x = is 11, since ( )4 2 3 8 3 11 + = + = .


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EXPONENTS AND POWERS


1. Very large numbers are difficult to read, understand, compare and operate upon. To make

all these easier, we use exponents, converting many of the large numbers in a shorter form.

2. The following are exponential forms of some numbers:

5100000 10= (read as 10 raised to 5)

615625 5= (read as 5 raised to 6)

8256 2= (read as 2 raised to 8)

Here, 10, 5 and 2 are the bases, whereas 5, 6 and 8 are their respective exponents. We also

say, 100000 is the 5th power of 10, 15625 is the 6th power of 5, etc.


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3. Numbers in exponential form obey certain laws, which are:

For any non-zero integers a and b and whole numbers m and n,

i. m n m na a a + =

ii. m n m na a a − =

iii. ( )n

m mna a=

iv. ( )mm ma b ab =

v.

m

m m aa b

b

=

vi. 0 1a =

vii. ( )even number

1 1− =

viii. ( )odd number

1 1− = −


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SYMMETRY


1. A figure has line symmetry, if there is a line about which the figure may be folded so that the two

parts of the figure will coincide.

2. Regular polygons have equal sides and equal angles. They have multiple (i.e., more than one)

lines of symmetry.

3. Each regular polygon has as many lines of symmetry as it has sides.

Regular Hexagon 6→

Regular Pentagon 5→

Square 4→

Equilateral Triangle 3→

4. Mirror reflection leads to symmetry, under which the left-right orientation must be taken care of.

5. Rotation turns an object about a fixed point. This fixed point is the center of rotation. The angle

by which the object rotates is the angle of rotation. A half-turn means rotation by 180o; a quarter-

turn means rotation by 90o. Rotation may be clockwise or anticlockwise.


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6. If, after a rotation, an object looks the same, we say that it has a rotational symmetry.

7. In a complete turn (of 360o), the number of times an object looks the same is called the order of

rotational symmetry.

For example, the order of symmetry of a square is 4 while, for an equilateral triangle, it is 3.

8. Some shapes have only one line of symmetry, like the letter E; some have only rotational

symmetry, like the letter S; and some have both symmetries like the letter H.

9. The study of symmetry is important because of its frequent use in day-to-day life and more

because of the beautiful designs it can provide us


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VISUALISING SOLID SHAPES


1. The circle, the square, the rectangle, the quadrilateral and the triangle are examples of plane

figures; the cube, the cuboid, the sphere, the cylinder, the cone and the pyramid are examples of

solid shapes.

2. Plane figures are of two-dimensions (2-D) and the solid shapes are of three-dimensions (3-D).

3. The corners of a solid shape are called its vertices; the line segments of its skeleton are its edges;

and its flat surfaces are its faces.

4. A net is a skeleton-outline of a solid that can be folded to make it. The same solid can have several

types of nets.

5. Solid shapes can be drawn on a flat surface (like paper) realistically. We call this 2-D

representation of a 3-D solid.

6. Two types of sketches of a solid are possible:

i. An oblique sketch does not have proportional lengths. Still it conveys all important aspects

of the appearance of the solid.

ii. An isometric sketch is drawn on an isometric dot paper, a sample of which is given at the

end of this book. In an isometric sketch of the solid the measurements kept proportional.


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7. Visualizing solid shapes is a very useful skill. We should be able to see ‘hidden’ parts of the solid

shape.

8. Different sections of a solid can be viewed in many ways:

i. One way is to view by cutting or slicing the shape, which would result in the cross-section

of the solid.

ii. Another way is by observing a 2-D shadow of a 3-D shape.

iii. A third way is to look at the shape from different angles; the front-view, the side-view and

the top-view can provide a lot of information about the shape observed.


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RATIONAL NUMBERS


1. The operations addition and multiplication are

(i) commutative for rational numbers.

(ii) associative for rational numbers.

2. The rational number 0 is the additive identity for rational numbers.

3. The rational number 1 is the multiplicative identity for rational numbers.

4. The additive inverse of the rational number a

b is

a

b− and vice-versa.

5. The reciprocal or multiplicative inverse of the rational number a

b is

c

d

if 1a c

b d =


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6. Distributivity of rational numbers: For all rational numbers a, b and c,

( )a b c ab ac=+ + and ( ) –a b c ab ac=−

7. Between any two given rational numbers there are countless rational numbers.


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UNDERSTANDING QUADRILATERALS


1. Parallelogram:

A quadrilateral with each pair of opposite sides parallel.

(i) Opposite sides are equal.

(ii) Opposite angles are equal.

(iii) Diagonals bisect one another.

2. Rhombus:

A parallelogram with sides of equal length.

(i) All the properties of a parallelogram.

(ii) Diagonals are perpendicular to each other.

3. Rectangle:

A parallelogram with a right angle.

(i) All the properties of a parallelogram.

(ii) Each of the angles is a right angle.

(iii) Diagonals are equal.


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4. Square:

A rectangle with sides of equal length.

(i) All the properties of a parallelogram, rhombus and a rectangle.

5. Kite:

A quadrilateral with exactly two pairs of equal consecutive sides.

(i) The diagonals are perpendicular to one another

(ii) One of the diagonals bisects the other.


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DATA HANDLING


1. Frequency gives the number of times that a particular entry occurs.

2. Data mostly available to us in an unorganised form is called raw data.

3. 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. Also, there is no gap

between the bars as there is no gap between the class intervals.

4. Data can also be presented using circle graph or pie chart. A circle graph shows the

relationship between a whole and its part.


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5. A random experiment is one whose outcome cannot be predicted exactly in advance.

6. When the outcomes are equally likely

Number of outcomes that make an event Probability of an event

Total number of outcomes of the experiment =

7. One or more outcomes of an experiment make an event.


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SQUARES AND SQUARE ROOTS


1. If a natural number m can be expressed as n2, where n is also a natural number,

then m is a square number.

2. All square numbers end with 0, 1, 4, 5, 6 or 9 at unit place.

3. Square numbers can only have even number of zeros at the end.

4. Square root is the inverse operation of square.

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

6. Square root of a number can be found by three methods:

i) Prime factorisation

ii) Successive subtractions with odd numbers

iii) Division methods

7. Positive square root of a number is denoted by the symbol .

For example, 22 4= gives 4 2= .


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CUBES AND CUBE ROOTS


1. Numbers obtained when a number is multiplied by itself three times are known as cube

numbers. For example, 1, 8, 27, ... etc.

2. If in the prime factorisation of any number each factor appears three times, then the number

is a perfect cube.

3. The symbol 3

denotes cube root.


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COMPARING QUANTITIES


1. Discount is a reduction given on marked price.

Discount Marked Price –Sale Price.=

2. Discount can be calculated when discount percentage is given.

Discount Discount % of Marked Price=

3. Additional expenses made after buying an article are included in the cost price and are

known as overhead expenses.

Cost Price Buying Price Overhead expenses= +

4. Sales tax is charged on the sale of an item by the government and is added to the Bill

Amount.

Sales Tax Tax % of Bill Amount=


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5. Compound interest is the interest calculated on the previous year’s amount

Compound Interest Amount Principal

CI A P

= −

= −

6. Amount when interest is compounded annually

1100

nR

A P

= +

where A is amount, P is principal, R is rate of interest and n is time period.

7. Amount when interest is compounded half yearly

2

1200

nR

A P

= +

where A is amount, P is principal, R is rate of interest and n is time period.


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ALGEBRAIC EXPRESSIONS AND IDENTITIES


1. ( )2 2 22a b a ab b+ = + +

2. ( )2 2 22a b a ab b− = − +

3. ( )( ) 2 2a b a b a b+ − = −

4. ( )( ) ( )2x a x b x a b x ab+ + = + + +


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VISUALISING SOLID SHAPES


For any polyhedron,

2F V E+ − =

where ‘F’ stands for number of faces, V stands for number of vertices and E stands for number

of edges. This relationship is called Euler’s formula.


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MENSURATION


1. Area of a trapezium ( )1

2sum of the lengths of parallel sides height=

2. Area of a trapezium ( )1

2product of the diagonals=

3. Surface area of a cuboid 2( )lb bh hl= + +

4. Surface area of a cube 26l=

5. Surface area of a cylinder 2 ( )r r h= +

6. Volume of a cuboid l b h=

7. Volume of a cube 3= l

8. Volume of a cylinder 2r h=

9. 3(i) 1cm 1mL=

3

3 3

(ii) 1L 1000cm

(iii) 1m 1000000cm 1000L

=

= =


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EXPONENTS AND POWERS


1. m n m na a a + =

2. m n m na a a − =

3. ( )n

m mna a=

4. ( )m m ma b ab =

5. 0 1a =

6.

mm

m

a a

b b

=

7. Very small numbers can be expressed in standard form using negative exponents.


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DIRECT AND INVERSE PROPORTIONS


1. Direct proportions:

Two quantities x and y are said to be in direct proportion if they increase or decrease

together in such a manner that the ratio of their corresponding values remains constant.

i.e.,

xk

y= ,

where k is a positive integer,

then x and y are said to vary directly

If y1, y2 are the values of y corresponding to the values x1, x2 of x respectively then

1 2

1 2

x x

y y=


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2. Inverse proportions:

Two quantities x and y are said to be in inverse proportion if an increase in x causes a

proportional decrease in y and vice-versa, in such a manner that the product of their

corresponding values remains constant.

i.e., xy k= ,

where k is a positive integer,

then x and y are said to vary inversely.

If y1, y2 are the values of y corresponding to the values x1, x2 of x respectively then

1 21 1 2 2

2 1

x y

x y x y orx y

= =


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FACTORISATION


1. ( )22 22a ab b a b+ + +=

2. ( )22 22a ab b a b− + −=

3. ( )( )2 2a b a b a b− = − +

4. ( ) ( )( )2x a b x ab x a x b+ + + = + +


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PLAYING WITH NUMBERS


1. A two-digit number ab will be written as, 10ab a b= + .

2. If the one’s digit of a number is 0, then the number is a multiple of 10

3. If the one’s digit of a number is 0 or 5, then it is divisible by 5.

4. If the one’s digit of a number is 0, 2, 4, 6 or 8 then the number is divisible by 2.

5. A number N is divisible by 3 if the sum of its digits is divisible by 3.

6. A number N is divisible by 9 if the sum of its digits is divisible by 9.

Class 7 -CBSE -Formulae She ets...1. The six elements of a triangle are its three angles and the...

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