Linear Equations
One Variableax+b=0a≠0 and a&b are real numbersTwo variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbersThree Variableax+by+cz+d=0a≠0 , b≠0, c≠0 and a,b,c,d are real numbers
Pair of Linear Equations in two variables:
a1x+b1y+c1=0
a2x+b2y+c2=0
Where
a1, b1, c1, a2, b2, and c2 are all real numbers and
a12+b12 ≠ 0 & a22 + b22 ≠ 0
It should be noted that linear equations in two variables can also be represented in graphical form.
Algebra or Algebraic Equations
The standard form of a Quadratic Equation is:
ax2+bx+c=0 where a ≠ 0
And x = [-b ± √(b2 – 4ac)]/2a
Algebraic formulas:
(a+b)2 = a2 + b2 + 2ab
(a-b)2 = a2 + b2 – 2ab
(a+b) (a-b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(x – a)(x + b) = x2 + (b – a)x – ab
(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)
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
x2 + y2 =½ [(x + y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
x3 + y3= (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
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Basic formulas for powers
pm x pn = pm+n
{pm}⁄{pn} = pm-n
(pm)n = pmn
p-m = 1/pm
p1 = p
P0 = 1
Arithmetic Progression(AP) Formulas
If a1, a2, a3, a4, a5, a6,… are the terms of AP and d is the common difference between each term, then we can write the sequence as; a, a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, nth term for arithmetic progression is given as;
nth term = a + (n-1) d
Sum of the first n terms in Arithmetic Progression;
Sn = n/2 [2a + (n-1) d]
Trigonometry Formulas For Class 10
Trigonometry maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle triangle. Also, in trigonometry, the functions sec, cosec and cot formulas can be derived with the help of sin, cos and tan formulas.
Let a right-angled triangle ABC is right-angled at point B and have ∠θ.
Sin θ= SideoppositetoangleθHypotenuse=PerpendicularHypotenuse = P/H
Cos θ = AdjacentsidetoangleθHypotenuse = BaseHypotenuse = B/H
Tan θ = SideoppositetoangleθAdjacentsidetoangleθ = P/B
Sec θ = 1cosθ
Cot θ = 1tanθ
Cosec θ = 1sinθ
Tan θ = SinθCosθ
Trigonometry Table:
Angle0°30°45°60°90°Sinθ01/21/√2√3/21Cosθ1√3/21/√2½0Tanθ01/√31√3UndefinedCotθUndefined√311/√30Secθ12/√3√22UndefinedCosecθUndefined2√22/√31
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Other Trigonometric formulas:
sin(90° – θ) = cos θ
cos(90° – θ) = sin θ
tan(90° – θ) = cot θ
cot(90° – θ) = tan θ
sec(90° – θ) = cosecθ
cosec(90° – θ) = secθ
sin2θ + cos2 θ = 1
sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Get complete Trigonometry Formulas list here
Circles Formulas For Class 10
Circumference of the circle = 2 π r
Area of the circle = π r2
Area of the sector of angle θ = (θ/360) × π r2
Length of an arc of a sector of angle θ = (θ/360) × 2 π r
(r = radius of the circle)
Surface Area and Volumes Formulas For Class 10
The common formulas from the surface area and volumes chapter in 10th class include the following:
Sphere Formulas
Diameter of sphere2rSurface area of sphere4 π r2Volume of Sphere4/3 π r3
Cylinder Formulas
Curved surface area of Cylinder2 πrhArea of two circular bases2 πr2Total surface area of CylinderCircumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2Volume of Cylinderπ r2 h
Cone Formulas
Slant height of conel = √(r2 + h2)Curved surface area of coneπrlTotal surface area of coneπr (l + r)Volume of cone⅓ π r2 h
Cuboid Formulas
Perimeter of cuboid4(l + b +h)Length of the longest diagonal of a cuboid√(l2 + b2 + h2)Total surface area of cuboid2(l×b + b×h + l×h)Volume of Cuboidl × b × h
Here, l = length, b = breadth and h = height In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes.
Statistics Formulas for Class 10
In class 10, the chapter statistics mostly deals with finding the mean, median and mode of grouped data.
(I) The mean of the grouped data can be found by 3 methods.
Direct Method: x̅ = ∑ni=1fixi∑ni=1fi, where ∑fi xi is the sum of observations from value i = 1 to n And ∑fi is the number of observations from value i = 1 to n
Assumed mean method : x̅ = a+∑ni=1fidi∑ni=1fi
Step deviation method : x̅ = a+∑ni=1fiui∑ni=1fi×h
(II) The mode of grouped data:
Mode = l+f1–f02f1–f0–f2×h
(III) The median for a grouped data:
Median = l+n2–cff×h
Subhalaxmi P 4 years, 10 months ago
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