Class 10th NCERT math all formulas and thereom

Study with us! Topic is theorems and formulas of all math chapters.

Chapter 1 - Real Numbers.

Formulas:-

1) a = bq + r, where 0≤r<q

2) LCM X HCF = Product of two number.

3) Terminating decimal expansion P/q where q=(2n5m)

4) Non Terminating decimal expansion P/q where q≠(2n5m)

Chapter 2 - Polynomials.

Formulas:-

1) Sum of zeroes( α + β) = -b/a

2) Product of zeroes (αβ) = c/a

3) Quadratic polynomial = k[ x2-x(sum of zeroes)+Product of zeroes]

4) Dividend p(x) = Divisor g(x) × Quotient q(x) + Remainder (x)

Chapter 3 - Pair of Linear Equation in Two Variables.

Formulas:-

1) a1/a2 ≠ b1/b2, Intersecting and consistent and unique solution.

2) a1/a2 = b1/b2 = c1/c2, Coincident and consistent and many solution.

3) a1/a2 = b1/b2 ≠ c1/c2, Parallel lines and inconsistent and no solution.

4) Cross Multiplication Method:-

    x/(b1c2 - b2c1) = y/(c1a2 - c2a1) = 1/(a1b2 - a2b1)

Chapter 4 - Quadratic Equations.

Formulas:-

1) Discriminat (D) = b2 - 4ac, where D>0 have two different roots, D=0 have two equal roots and D<0 then no real roots exec.

2) Roots:-

Chapter 5 - Asthmatic Progression.

Formulas:-

1) Common difference (d) = a2 - a1

2) nth term of an AP, an = a+(n - 1)d

3) Sum of first n therms (S) = n/2×[2a+(n-1)d]; n/2×(a+an)

4) Selection of terms in an AP

No. of terms      Terms

3                           a-d,a,a+d

4                           a-3d,a-d,a+d,a+3d

5                           a-2d,a-d,a,a+d,a+2d

6                           a-5d,a-3d,a-d,a+d,a+3d,a+5d

Chapter 6 - Triangles.

Theorem:-

1) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

2) If a line divides any two sides of a triangle in the same ratio then the line is parallel to the third side.

3) If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

4) If in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

5) If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

6) The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

7) If a perpendicular is drown from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

8) In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

9) In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Chapter 7 - Coordinate Geometry.

Formulas:-

1) Distance formula = √[(x2- x1)2 + (y2-y1)2]

2) Section formula,

    x = (m1x2 + m2x1)/(m1 + m2),

    y = (m1y2 + m2y1)/(m1 + m2)

3) Area of triangle = 1/2×[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

Chapter 8 - Introduction to Trigonometry.

Formulas:-

1) sinθ = opposite side/hypotenuse

2) cosθ = adjacent side/hypotenuse

3) tanθ = opposite side/adjacent side

4) cosecθ = 1/sinθ = hypotenuse/opposite side

5) secθ = 1/cosθ = hypotenuse/adjacent side

6) cotθ = 1/tanθ = adjacent side/opposite side

7) tanθ = sinθ/cosθ = secθ/cosecθ

8) cotθ = cosθ/sinθ = cosecθ/secθ

9) cosecθ = secθ/tanθ

10) secθ = cosecθ/cotθ

11) θ            0          30          45           60           90

     sinθ          0           1/2          1/√2         √3/2            1

     cosθ          1         √3/2         1/√2           1/2             0

     tanθ          0          1/√3           1              √3           not defined

12) sin(90 - θ) = cosθ,              cos(90 - θ) = sinθ

13) tan(90 - θ) = cotθ,               cot(90 - θ) = tanθ

14) sec(90 - θ) = cosecθ,         cosec(90 - θ) = secθ

15) cos2θ + sin2θ = 1

16) sec2θ - tan2θ = 1

17) cosec2θ - cot2θ = 1

Chapter 10 - Circles.

Theorem:-

1) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2) The lengths of tangents drown from an external point to a circle are equal.

Chapter 12 - Area Related to Circles.

Formulas:-

1) Circumference  of  circle = 2πr

2) Area of circle = πr2

3) Area of the sector of angleθ = θ/360×πr2

4) Length of an arc of a sector of angle θ = θ/360×2πr

Chapter 13 - Surface Area and Volumes.

Formulas:-

1) Cubaid

    Curved Surface Area = 2(l+b)h

    Total Surface Area = 2(lb+bh+hl)

    Volume = l×b×h

2) Cube

    Curved Surface Area = 4a2

  Total surface Area = 6a2
    Volume = a3

3) Cylinder
    Curved Surface Area = 2πrh
    Total surface Area = 2πr(h + r)
    Volume = πr2h

4) Cone
    Curved Surface Area = πrl
    Total surface Area = πr(l+r)
    Volume =1/3×πr2h

5) Sphere
    Total surface Area = 4πr2
    Volume = 4/3πr3

6) Hemisphere
    Curved Surface Area = 2πr2
    Total surface Area = 3πr2
    Volume =2/3πr3

7) Frustum of Cone
    Curved Surface Area = πl(r1 + r2)2 where, l = √[h2+(r1-r2)2]
    Total surface Area = π[l(r1 + r2) + (r12+r22)]
    Volume = 1/3×πh(r12+r22+r1r2)

Chapter 14 - Statistics.

Formulas:-

1) Direct Method, mean (x̅) = ∑f_iX_i / ∑f_i

2) Assumed Mean Method, mean (d) = ∑f_id_i / ∑f_iu were, d_i = X_i - a

3) Step-deviation method, mean (u) = ∑f_iu_i / ∑f_{i were,} u_i = d_i / h

4) Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]×h

5) Median = l + [(n/2 - cf)/f]×h

6) 3Median = Mode + 2Mean

Chapter 15 - Probability.

Formulas:-

1) Probability P(E) = No. of events/Total No. of outcomes

2) P(x) + P(x̅) = 1