All Maths Formulas for Class 8
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important Maths formulas for class 8 to help you in your preparation for class 8
examination. These formulas are extremely important from the examinations’
point of view.
Maths is a subject where reasoning and logic are very
important. Students should have a clear understanding of the underlying
theories, concepts and formulas. They must understand that what are the
different formulas and what they mean actually. Only then, they will be able to
crack the mathematics questions asked in the examination. Here, we are
providing all the formulas chapter-wise for maths class 8.
Chapter-wise Maths Formulas for Class 8
Maths Formulas for Class 8 Rational Numbers
1. A number of the form p/q,
where p, q ∈ Z and q ≠ 0, is called a rational
number.
2. A rational number p/q is
said to be in standard form if q is positive and the integers p and q are co-prime
numbers.
3. The absolute value of a
rational number is the distance of the rational number from 0 on the number
line. For any rational number x, |x| = x if x ≥ 0 and |x| = –x if x < 0.
4. Rational numbers are not
closed under division. If zero is excluded then we can say rational numbers are
closed under division.
5. Addition and
multiplication of rational numbers are commutative.
6. Subtraction and division
of rational numbers are not commutative.
7. Addition and
multiplication are associative for rational numbers.
8. Subtraction and division
are not associative for rational numbers.
9. For any set of rational
numbers a, b and c, the distributive property of multiplication over addition
and subtraction states that a(b + c) = ab + ac, and a(b – c) = ab – ac.
Maths Formulas for Class 8 Powers and Exponents
1. The exponential form of a
given number is a way of expressing it using a base and a raised number called
exponent. For example, in 52, the base is 5 and the exponent is 2.
2. 128 = 2 × 2 × 2 × 2 × 2 ×
2 × 2 = 27 is product form of 128 with base 2.
3. We denote the reciprocal
of a number a by a–1, i.e. a–1 = 1/a . Hence, the
reciprocal of (p/q)m is (q/p)m.
4. The following are the laws
of exponents for a and b which are non-zero integers and m and n are whole
numbers.
·
am × an = am + n
·
am ÷ an = am – n , when m
> n
·
(am)n = amn
·
am × bm = (ab)m
·
am ÷ bm = (a/b)m
·
a0 = 1
5. (–1)even number
= 1 and (–1)odd number = –1
6. The standard form of a
number is a × 10b, where 1 ≤ a < 10 and b is an integer. For example,
61,20,000 can be written as 6.12 × 106.
Maths Formulas for Class 8 Squares and Square Roots
1. When a number is
multiplied by itself, the product so obtained is called the square of that
number.
2. A number whose square root
is a whole number is called a perfect square. For example 1, 4, 9, 16, 25, ...
are perfect squares.
3. Square numbers end in the
digits 0, 1, 4, 5, 6 or 9.
4. Square numbers do not end
in the digits 2, 3, 7 or 8.
5. If the sum of squares of
two numbers is equal to the square of a third number then three numbers form a
Pythagorean triplet.
6. The square root of a
number can be found by:
a. Repeated subtraction
method
b. Prime factorization method
c. Long division method
Maths Formulas for Class 8 Cubes and Cube Roots
1. The cube of a number is
obtained when a number is multiplied three times by itself.
2. The cube of an even number
is even and that of an odd number is odd.
3. The cube of a positive
number is positive, and the cube of a negative number is negative.
4. Cube root is the inverse
operation of cubing a number.
5. The cube root of a number
can be found by:
a. Prime Factorization
b. Estimation
Maths Formulas for Class 8 Playing with Numbers
1. Numbers can be written in
the generalized form. For a three-digit number, with c in the hundreds place, b
in the tens place and a in the units place, the generalized form would be 100c
+ 10b + a.
2. The difference between any
three-digit number and number obtained by reversing its digits is always
divisible by 99.
3. The sum of all the
three-digit numbers formed using the given three digits is always divisible by
37.
4. A number is divisible by
·
2, if the unit’s digit of the number is 0, 2, 4, 6 or 8.
·
3, if the sum of the digits of the number is divisible by 3.
·
4, if the number formed by its digits in the tens place and
units place is divisible by 4.
·
5, if the unit’s digit is 0 or 5.
·
6, if the number is even and the sum of the digits of the
number is divisible by 3.
·
7, if the difference between twice the unit’s digit and the
number formed by the remaining digits is either 0 or a multiple of 7.
·
8, if the number formed by its digits in the hundreds place,
tens place and units place is divisible by 8.
·
9, if the sum of the digits is divisible by 9.
·
10, if the unit’s digit is 0.
·
11, if the difference of the sum of its digits in odd places
and the sum of its digits in even places (starting from the units place) is
either 0 or divisible by 11.
Maths Formulas for Class 8 Algebraic Expressions and Identities
1. A symbol that can take
different values is called a variable.
2. A symbol having a fixed
numerical value is called a constant.
3. When terms have the same
variables and if the powers of the variables are same, then they are called
like terms, else they are unlike terms.
4. The numerical factor in a
term is called its coefficient.
5. An algebraic expression
having exponents as non-negative integers is called a polynomial.
6. Polynomials having one,
two and three terms are called monomials, binomials and trinomials,
respectively.
7. The degree of a polynomial
is the degree of term having the highest exponent (or sum of exponents). For
example, the degree of 3x + 2x2y – 7 is 3 (therefore, the term 2x2y
has degree as 2 + 1 = 3).
8. If an equation is true for
all values of the variable, it is called an identity.
9. Some of the identities
are:
·
(a + b)2 = a2 + 2ab + b2
·
(a – b)2 = a2 – 2ab + b2
·
(a + b) (a – b) = a2 – b2
·
(x + a) (x + b) = x2 + (a + b)x + ab
·
(a + b)3 = a3 +
b3 + 3ab (a + b)
·
(a – b)3 = a3 –
b3 – 3ab (a – b)
Maths Formulas for Class 8 Factorization
1. Factorizing an algebraic
expression means expressing it as a product of various factors till they are
irreducible.
2. We use the following
methods for factorizing algebraic expressions:
· By taking out common factors:
For
example, 15a +
20b = 5(3a) + 5(4b) = 5(3a + 4b)
·
Grouping the terms:
For example, 49a +
42c – 7ay – 6cy = (49a – 7ay) + (42c – 6cy)
=
7a(7 – y) + 6c(7 – y)
= (7 – y) (7a + 6c)
·
Factorizing quadratic trinomials:
For example, x2 + 7x + 12 = x2 +
(4 + 3)x + 4 × 3
= x2 + 4x + 3x +
12
= x(x + 4) + 3(x + 4)
= (x + 4)(x +
3)
·
Factorization by using identities:
I.
Factorization using a2 + 2ab + b2 = (a
+ b)2
For example, x2
+ 18x + 81 = x2 + 2(x)(9) + 92 = (x + 9)2
II.
Factorization using a2 + 2ab + b2 = (a
+ b)2
For example,
4x2 – 20xy + 25y2 = (2x)2 – 2(2x)(5y) + (5y)2
= (2x – 5y)2
III.
Factorization using a2 – b2 = (a + b)
(a – b)
For example, 9x2 – 16y2 =
(3x)2 – (4y)2 = (3x + 4y) (3x – 4y)
Maths Formulas for Class 8 Linear Equations
1. An equation is a statement
of equality between two expressions involving variables and constants.
2. An equation has two sides
separated by the symbol (=). The two sides are LHS and RHS.
3. Linear expressions are
those in which the highest power of the variable is 1.
4. Linear equation in one
variable is of the form ax + b = c, where a, b and c are constants and a ≠ 0.
5. Methods of solving linear
equations in one variable:
·
Add the same term (constant and/or variable) to both sides of
an equation.
·
Subtract the same term (constant and/or variable) from both
sides.
·
Multiply both sides by the same term (constant and/or
variable).
·
Divide both sides by the same term (constant and/or
variable).
Maths Formulas for Class 8 Applications of Percentages
1. Per cent means per hundred
or for every hundred.
2. The numerator of a
fraction with denominator 100 represents percentage.
3. To convert a fraction into
a per cent, multiply the fraction by 100.
4. To convert a ratio into a
per cent, write it as fraction and multiply it by 100.
5. To convert a decimal into
a per cent, shift the decimal point two places to the right.
6. To convert a per cent into
a fraction, divide it by 100 after removing the symbol of %.
7. Increase = Increased value
– Original value.
8. Percentage increase =
(Increase/Original value) × 100% and increased value = (100% + increase %) ×
original value.
9. Decrease = Original value
– Decreased value.
10. Percentage decrease =
(Decrease/Original value) × 100% and decreased value = (100% – decrease %) ×
original value.
11. Discount = Marked price –
Selling price.
12. Percentage discount =
(Discount/Marked price) × 100%.
13. Selling price = Marked
price × (100% – Percentage discount).
14. GST stands for Goods and
Services Tax.
15. GST = Price before GST ×
GST rate.
16. Price after GST = Price
before GST × (100% + GST rate).
Maths Formulas for Class 8 Simple and Compound Interest
1. The money taken as loan or
invested is called the principal.
2. The additional amount that
a borrower has to repay is called the interest.
3. Simple Interest = P × R ×
T/100
4. The interest calculated on
both the principal and the accrued interest is called the compound interest.
5.
Compound
Interest = [P(1 + R%)n] – P = P[(1 + R%)n –
1]
(Where P = Principal, R = annual interest rate in percentage terms, and n = number
of compounding periods.)
6. Compound Interest (C.I.) =
A – P.
7. If rates are different for
the consecutive years, then amount is P(1 + R1) (1 + R2) (1 + R3)…
where R1
is rate percent for 1st year, R2 is rate percent for 2nd year, R3
is rate percent for 3rd year and so on.
8. In case of depreciation,
the rate R is replaced by (–R) in the formula.
So, A = P(1 + R%)n becomes A = P(1 – R%)n
Maths Formulas for Class 8 Direct and Inverse Proportions
1. Two quantities are in
direct proportion, if the increase in one quantity causes an increase in the
other and vice-versa.
2. If two quantities x and y
are in direct proportion, then the ratio of their corresponding values remains
constant. For example, x1/y1 = x2/y2
3. Two quantities are in
inverse proportion, if the increase in one quantity causes decrease in the
other and vice-versa.
4. If two quantities x and y
are in inverse proportion, then the product of their corresponding values
remains constant. For example, x1y1 = x2y2
5. Speed = Distance/Time;
Time = Distance/Speed; Distance = Speed × Time.
6. If A can do a piece of
work in n days, then A’s one day’s work = 1/n of the work.
7. Number of days to complete
the work = 1/One day's work.
8. Time required to do a certain
work = Work to be done/One day's work.
Maths Formulas for Class 8 Understanding Quadrilaterals
1. A polygon is a closed
figure made up of three or more line segments.
2. The polygon in which all
the sides and all the angles are equal is called a regular polygon.
3. The sum of the interior
angles of a convex polygon of n sides = (n – 2) × 180°
4. The sum of the exterior
angles of a convex polygon is 360°.
5. A rectilinear closed
figure with four sides is called a quadrilateral.
6. A parallelogram is a
quadrilateral with each pair of opposite sides being parallel, such that
·
opposite sides are equal,
·
opposite angles are equal, and
·
diagonals bisect each other.
7. A rhombus is a
parallelogram with all sides of equal length and
·
holding all properties of a parallelogram,
·
diagonals are perpendicular to each other.
8. A rectangle is a
parallelogram with all right angles and
·
holding all properties of a parallelogram,
·
diagonals are equal.
9. A square is a rectangle
with all sides of equal length and holding all properties of a parallelogram, a
rhombus and a rectangle.
10. A trapezium is a
quadrilateral with one pair of opposite sides parallel.
11. A kite is a quadrilateral
with exactly two pairs of equal adjacent sides and
·
the diagonals are perpendicular to each other.
·
one of the diagonals bisects the other.
12. The relation between the
number of sides (n) of a polygon and the number of diagonals (D) is D = ½ × n(n – 3).
Maths Formulas for Class 8 Representing Solids on a Paper
1. A polyhedron is a 3D shape
that is formed by polygons.
2. If the faces of a
polyhedron are regular polygons and the same number of faces meet at each
vertex, then the polyhedron is called regular polyhedron.
3. The intersection of two
adjacent faces of a solid is called an edge.
4. A plane surface enclosed
by edges is called a face.
5. A point where three edges
meet is called a vertex.
6. A net of a solid is a
plane figure (2D shape) that can be folded up to form the solid (3D shape).
7. A prism is a polyhedron
for which the top and bottom faces are congruent polygons and all other faces
are parallelograms.
8. A pyramid is a polyhedron
whose base is a polygon and whose lateral faces are triangles having a common
vertex.
9. For a polyhedron, if F is
the number of faces, V is the number of vertices and E is the number of edges,
then F + V – E = 2. It is called Euler’s formula.
10. A map scale is usually
represented as a ratio (for example, 1 : r) or as a fraction (for example, 1/r
).
Maths Formulas for Class 8 Construction of Quadrilaterals
1. We need at least five
elements of a quadrilateral to determine it uniquely.
2. A unique quadrilateral can
be drawn:
·
if its four sides and one diagonal are given.
·
if its three sides and two diagonals are given.
·
if its three sides and two included angles are given.
·
if its four sides and one angle are given.
·
if its three sides,
one diagonal and one angle are given.
3. A square can be
constructed if its side is known.
4. A parallelogram can be
constructed if its two adjacent sides and one angle are known.
5. A rectangle can be
constructed if its two adjacent sides are known.
6. A rhombus can be
constructed if the lengths of its both diagonals are known.
Maths Formulas for Class 8 Area of Polygons
1. Perimeter of a rectangle =
2 × (length + breadth).
2. Perimeter of a square = 4
× length of a side.
3. Perimeter of a triangle =
sum of all its sides.
4. Perimeter of a parallelogram
= 2 × (length + breadth).
5. Perimeter of a rhombus = 4
× length of a side.
6. Circumference of a circle =
2Ï€r, where r is the radius of the circle.
7. The ratio of the
circumference of a circle to its diameter is denoted using the notation ‘Ï€’.
8. The approximate value of π
is 22/7 or 3.14.
9. Perimeter of a regular
polygon = (Number of sides of polygon) × (length of a side).
10. Area of a rectangle =
length × breadth.
11. Area of a square = side ×
side.
12. Area of a triangle = 1/2 ×
base × height.
13. The area of a circle of
radius r is πr2.
14. Area of a parallelogram = base
× perpendicular height.
15. Area of a rhombus = 1/2 ×
product of its diagonals.
16. Area of a trapezium = 1/2
× sum of parallel sides × height.
17. Area of a quadrilateral =
1/2 × (one diagonal) × (sum of the perpendiculars to the diagonal from the
opposite vertices).
18. Area of a polygon = Sum of
the areas of various triangles and trapeziums into which the polygon is
splitted.
19. The units of area are
square units, such as 1 cm2 = 100 mm2 ; 1 m2 =
10,000 cm2 ; 1 km2 = 10,00,000 m2 ; 1 hectare
= 10,000 m2 ; 1 acre = 4046.86 sq. m.
Maths Formulas for Class 8 Surface Area and Volume
1. Amount of space occupied
by a 3D object is called its volume.
2. For a cuboid whose length
is l units, breadth is b units and height is h units,
·
Volume of a cuboid = (l × b × h) cubic units
·
Total surface area of a cuboid = 2 (l × b + b × h + h × l)
sq. units
·
Lateral surface area of a cuboid or area of four walls = 2 (l
+ b ) × h sq. units
·
The length of the diagonal of a cuboid = sqrt(l2 +
b2 + h2) units
3. For a cube of side a
units,
·
Volume of a cube = a3 cubic units
·
Total surface area of a cube = 6a2 sq. units
·
Lateral surface area of a cube = 4a2 sq. units
·
Length of the diagonal of a cube = sqrt(3) × a units
4. For a right circular
cylinder of radius r units and height h units,
·
Volume of a cylinder = πr2h cubic units
·
Curved surface area of a cylinder = 2Ï€rh sq. units
·
Total surface area of a cylinder = 2Ï€r(r + h) sq. units
5. For a hollow right
circular cylinder of outer radius R units and inner radius r units,
·
Curved surface area = 2Ï€h(R + r) sq. units
·
Total surface area = 2Ï€(R + r) (h + R – r) sq. units
·
Volume = Ï€h(R2 – r2 ) cubic units
6. For a right circular cone
of radius r units, height h units and slant height l units,
·
Volume of a cone = 1/3 πr2h cubic units
·
Curved surface area of a cone = πrl sq. units
·
Total surface area of a cone = πr(l + r) sq. units
7. 1 cm3 = 1 mL,
1000 cm3 = 1 L, 1000000 cm3 = 1 m3 = 1 kL.
Maths Formulas for Class 8 Data Handling and Graphs
1. Data is a collection of
numbers, figures, names or any items collected to give some information.
2. The data which has not
been organized is called raw data.
3. The difference between the
highest and the lowest observations is called the range of the data. Range =
Value of the highest observation – Value of the lowest observation.
4. When numerical data is
represented as columns then it is called a bar graph. It is also known as
column graph.
5. The double bar graph helps
us to compare or present more than one kind of information.
6. The difference between the
upper limit and lower limit of a class is called the class width or size of the
interval.
7. In a histogram, the
heights of various bars are proportional to their frequencies and the bars are
drawn without any gaps between them.
8. A pie chart is used to
show the relationship between a whole and its parts.
9. When the numerical data is
represented by a sector of a circle, it is called pie chart or pie graph. The
angle of the sector depends upon the value of that item in the data. Angle of
sector = (Value of item/Sum of all items) × 360°.
10. The line graph displays
those data that changes over a period of time. A line graph consists of bits of
line segments joined consecutively.
11. A linear relationship is a
relationship between two variables in which the amount of both the variables
increases or decreases by same quantity. Linear graph is a graph that explains
a linear relationship.
12. Two mutually perpendicular
axes intersect at a point called the origin. Coordinates of the origin are (0,
0).
13. The coordinate axes divide
the plane of a graph paper into four regions called quadrants.
Maths Formulas for Class 8 Probability
1. Probability is a branch of
mathematics that deals with the chance of occurrence of an event.
2. There are three different
situations that we come across in our daily life. They may be
·
sure to happen
·
impossible to happen
·
having some chances of happening.
3. A random experiment is a
process whose outcome (result) cannot be predicted in advance.
4. Outcomes of an experiment
are equally likely if each has the same chance of occurring.
5. The collection of outcomes
is called an event.
6. The sample space of an
event is the list of all possible outcomes of an event.
7. The probability of an event E is denoted by P(E).
8. Symbolically, for finite
number of possible outcomes, Probability of an event E, P(E) = n(E)/n(S), where,
n(E) is the number of favorable outcomes and n(S) is the number of possible
outcomes.
9. Probability of an event
lies between 0 and 1, inclusive of both.
10. The probability of a sure
event is always 1 and the probability of an impossible event is always 0.