In class X there are many vital chapters in Mathematics. As per NCERT book chapter names are
- REAL NUMBERS
- PAIR OF LINEAR EQUATION IN TWO VARIABLES
- QUADRATIC EQUATIONS
- ARITHMETIC PROGRESSION
- COORDINATE GEOMETRY
- INTRODUCTION TO TRIGONOMETRY
- SURFACE AREA AND VOLUMES
class 10 math formula
In this article we are going to provide and read some necessary formulae of significant chapters which are given above.
Euclid Division Theorem
Relation between Divisor(g), dividend(P) , quotient(q) and remainder(R) is given by:
Where R is smaller than G(x) and G(x) is not equal to ZERO.
HCF & LCM
Relationship between HCF and LCM of two numbers(A & B) is given by
Suppose you are given an equation
ax²+bx+c=0 where a, b and c are not equal to zero at once*.
In this case if x-a=0 is the factor of the given equation then ‘a’ is the solution/zero of this equation also.
Also, ax²+bx+c=0 where a, b and c are not equal to zero at once*.
In this case, Sum of zeroes is given by – b/a
Product of zeroes is given by= c/a
Similarly if we have cubic equation then
ax³+bx²+cx+d=0 in which a, b, c and d are not equal to zero at once.
Sum of zeroes is given by=(-b/a)
Sum and product of zeroes =(c/a)
Product of roots =(-d/a)
Equation having its variable with degree 2 with some constant is called a quadratic equation.
Ax²+Bx+C=0 (coefficient of X² should never be Zero)
Zeros of this equation is given by
This formula is known as the Quadratic Formula of Dharacharya Sutra.
Where D is Discriminant given by D=B²-4AC
If D is negative then roots will be imaginary
If D is positive then roots will be real and distinct
If D is zero then an equal and real root will be obtained from the quadratic formula.
Linear Equation in two variables
Suppose there are two linear equations,
In this condition, the given equation will probably intersect at infinity thus there will be no zeroes of that equation.
This condition is known as an overlapping condition where an infinite number of zeroes of the equation will be available.
In this case, only one solution of the equation will be available, meaning the lines of equations will cut at one point only.
Suppose you are given an AP a, a+d, a+2d, a+3d,……a+(n)d
Then last term or nth term is given by
Where an & Tn are last or nth term, a is first term of AP, n is the number of terms in AP and d is the common difference of any two consecutive terms.
Sum of n terms of AP =n/2[2a+(n-1)d]=n/2(a+l)
Here also all terms a, n, d means the same as above but L means the last term of the AP.
Here Distance between two is given by D²=(x2-x1)²+(y2-y1)²
Area of triangle formed by three points is 🔽=½[x1(y2-y3)+x2(y3-y1)+x3(y3-y1)]
Where x and y with different variants are Coordinate points.
Section formula for the division in line is given by
Where m and n are ratios of division and x and y variants are points of/on line.
Circles and Surface Area
- Circumference of the circle = 2πr
- Area of the circle = πr²
- Area of the sector of angle θ = (θ/360)×πr²
- Length of an arc of a sector of angle θ = (θ/360) × 2πr
(r = radius of the circle)
- Diameter of sphere=2r
- Surface area of sphere=4πr²
- Volume of Sphere=4/3πr³
- Curved surface area of Cylinder 2 πrh
- Area of two circular bases 2πr²
- Total surface area of Cylinder Circumference of Cylinder + Curved surface area of Cylinder = 2πrh + 2πr²
- Volume of Cylinder πr2h
- Slant height of cone l = √(r2 + h2)
- Curved surface area of cone πrl
- Total surface area of cone=πr (l + r)
- Volume of cone=⅓ πr²h
- Perimeter of cuboid=4(l+b+h)
- Length of the longest diagonal of a cuboid=√(l²+b²+h²)
- Total surface area of cuboid= 2(l×b+b×h+l×h)
- Volume of Cuboid l×b×h
Here, l = length, b = breadth and h = height. In the case of Cube, put l = b = h = a, as the cube has all its sides of equal length, so you can treat the cube as a cuboid to find out the volume, surface area etc.
Other useful links:
- Class 10 science NCERT book PDF
- Life Processes class 10
- Nelson mandela class 10 PDF
- 10th class all subject books pdf
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