Master Math with Our Ultimate Guide Formulas Solve Problems Quickly
Master Math with Our Ultimate Guide Formulas Solve Problems Quickly
Arithmetic Formulas:
 Compound Interest: A = P(1 + r/n)^(nt)
 Simple Interest: I = PRT/100
 Direct Variation: y = kx
 Inverse Variation: xy = k
 Exponentiation: aⁿ = a x a x … x a (n times)
 Square Root: √a = b
 Cube Root: ∛a = b
 Percentage: (a / b) x 100 = c
 Mean (Average): mean = (sum of values) / (number of values)
 Addition: a + b = c
 Subtraction: a – b = c
 Multiplication: a x b = c
 Division: a / b = c
Algebra Formulas:
 Sum of the First n Terms of an Arithmetic Sequence: Sₙ = n/2(2a + (n1)d)
 Sum of the First n Terms of a Geometric Sequence: Sₙ = a(1 – rⁿ) / (1 – r)
 Discriminant: b² – 4ac
 Completing the Square: (x + p/2)² – (q – p²/4) = 0
 Quadratic Equation: ax² + bx + c = 0
 Linear Equation: y = mx + b
 Factoring: a² – b² = (a + b)(a – b)
 FOIL (Multiplying Binomials): (a + b)(c + d) = ac + ad + bc + bd
 Quadratic Formula: x = (b ± √(b² – 4ac)) / 2a
 Pythagorean Theorem: a² + b² = c²
 Distance Formula: d = √((x₂ – x₁)² + (y₂ – y₁)²)
 Slope Formula: m = (y₂ – y₁) / (x₂ – x₁)
Geometry Formulas:
 Midpoint Formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)
 Distance between Two Points: √((x₂ – x₁)² + (y₂ – y₁)²)
 SlopeIntercept Form: y = mx + b
 PointSlope Form: y – y₁ = m(x – x₁)
 Volume of a Sphere: V = 4/3πr³
 Surface Area of a Sphere: A = 4πr²
 Volume of a Cylinder: V = πr²h
 Surface Area of a Cylinder: A = 2πr² + 2πrh
 Volume of a Rectangular Prism: V = lwh
 Surface Area of a Rectangular Prism: A = 2lw + 2lh + 2wh
 Area of a Circle: A = πr²
 Perimeter of a Circle: P = 2πr
 Area of a Triangle: A = 1/2bh
 Perimeter of a Triangle: P = a + b + c
 Area of a Rectangle: A = lw
 Perimeter of a Rectangle: P = 2l + 2w
Trigonometry Formulas:
 DoubleAngle Formulas: sin 2θ = 2 sin θ cos θ, cos 2θ = cos² θ – sin² θ
 HalfAngle Formulas: sin (θ/2) = ± √((1 – cos θ) / 2), cos (θ/2) = ± √((1 + cos θ) / 2)
 Area of a Triangle using Trigonometry: A = 1/2 ab sin C
 Law of Tangents: (a – b) / (a + b) = (tan(1/2(A – B)) / tan(1/2(A + B)))
 Law of Sines: a / sin A = b / sin B = c / sin C
 Law of Cosines: c² = a² + b² – 2ab cos C
 Inverse Trigonometric Functions: sin⁻¹x, cos⁻¹x, tan⁻¹x
 Sine Formula: sinθ = opposite / hypotenuse
 Cosine Formula: cosθ = adjacent / hypotenuse
 Tangent Formula: tanθ = opposite / adjacent
 Pythagorean Identity: sin²θ + cos²θ = 1
Master Math with Our Ultimate Guide Formulas Solve Problems Quickly
Arithmetic Formulas

Quadratic Formula: The quadratic formula is used to solve quadratic equations and is given as:
x = (b ± sqrt(b^2 – 4ac)) / 2a

Pythagorean Theorem: The Pythagorean theorem relates to the three sides of a rightangled triangle and states that the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
a^2 + b^2 = c^2

Distance Formula: The distance formula is used to find the distance between two points in a coordinate plane and is given as:
d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

Midpoint Formula: The midpoint formula is used to find the midpoint between two points in a coordinate plane and is given as:
((x1 + x2)/2, (y1 + y2)/2)

Surface Area and Volume Formulas for Solids: Students in standard 9 learn formulas for calculating the surface area and volume of various solids, such as cubes, spheres, cones, and cylinders.

Simultaneous Equations: In standard 9, students learn how to solve systems of simultaneous equations using methods such as substitution, elimination, and graphing.
 Arithmetic Formulas:
 Addition formula: a + b = c
 Subtraction formula: a – b = c
 Multiplication formula: a × b = c
 Division formula: a ÷ b = c
 Percentage formula: (a/b) × 100 = c%
 Profit and Loss formula: Profit% = (Profit/Cost price) × 100, Loss% = (Loss/Cost price) × 100
 Simple Interest formula: SI = (P × R × T) / 100
 Compound Interest formula: A = P(1 + (R/100))^t
Algebra Formulas:

Factorization Formula: Students learn how to factorize algebraic expressions of the form ax^2 + bx + c using methods such as grouping, splitting the middle term, and the quadratic formula.

Formula for Arithmetic Progression: The formula for the nth term of an arithmetic progression is:
an = a1 + (n – 1)d
where a1 is the first term, d is the common difference, and n is the nth term.

Formula for Geometric Progression: The formula for the nth term of a geometric progression is:
an = a1 * r^(n1)
where a1 is the first term, r is the common ratio, and n is the nth term.
 Algebra Formulas:
 Factorization formula: ax^2 + bx + c = 0
 Quadratic formula: x = (b ± sqrt(b^2 – 4ac)) / 2a
 Formula for Arithmetic Progression: an = a1 + (n – 1)d
 Formula for Geometric Progression: an = a1 * r^(n1)
 Formula for Linear Equations: y = mx + c
Geometry Formulas:

Perimeter and Area Formulas: Students learn formulas for calculating the perimeter and area of various twodimensional figures, such as triangles, rectangles, and circles.

Volume Formulas: Students learn formulas for calculating the volume of various threedimensional figures, such as cubes, spheres, cones, and cylinders.

Pythagorean Theorem: As mentioned earlier, the Pythagorean theorem is a geometric formula relating to the sides of a rightangled triangle
 Geometry Formulas:
 Perimeter and Area formulas:
 Triangle: Perimeter = a + b + c, Area = 1/2 × b × h
 Rectangle: Perimeter = 2l + 2w, Area = l × w
 Circle: Circumference = 2πr, Area = πr^2
 Volume formulas:
 Cube: Volume = s^3
 Sphere: Volume = (4/3)πr^3
 Cone: Volume = (1/3)πr^2h
 Cylinder: Volume = πr^2h
Trigonometry Formulas:

Sine, Cosine, and Tangent Formulas: Students learn about the trigonometric ratios sine, cosine, and tangent, and how to use them to solve problems involving rightangled triangles.

Trigonometric Identities: Students learn various trigonometric identities, such as the Pythagorean identity and the double angle identity, and how to use them to simplify trigonometric expressions.
 Trigonometry Formulas:
 Sine, Cosine, and Tangent formulas: sinθ = Opposite/Hypotenuse, cosθ = Adjacent/Hypotenuse, tanθ = Opposite/Adjacent
 Trigonometric Identities: sin^2θ + cos^2θ = 1, tanθ = sinθ/cosθ, 1 + tan^2θ = sec^2θ, 1 + cot^2θ = cosec^2θ
Master Math with Our Ultimate Guide Formulas Solve Problems Quickly
 Algebraic Formulas:
 (a + b)^2 = a^2 + 2ab + b^2
 (a – b)^2 = a^2 – 2ab + b^2
 a^2 – b^2 = (a + b)(a – b)
 (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ac)
 (a – b – c)^2 = a^2 + b^2 + c^2 – 2(ab + bc + ac)
 Geometric Formulas:
 Perimeter of a square = 4 x side
 Perimeter of a rectangle = 2 x (length + breadth)
 Area of a triangle = 1/2 x base x height
 Area of a parallelogram = base x height
 Circumference of a circle = 2πr
 Area of a circle = πr^2
 Trigonometric Formulas:
 sin θ = Opposite side / Hypotenuse
 cos θ = Adjacent side / Hypotenuse
 tan θ = Opposite side / Adjacent side
 Pythagorean Theorem: a^2 + b^2 = c^2
 Mensuration Formulas:
 Volume of a cube = side^3
 Volume of a cuboid = length x breadth x height
 Surface area of a cube = 6 x side^2
 Surface area of a cuboid = 2(lb + bh + hl)
Master Math with Our Ultimate Guide Formulas Solve Problems Quickly
Master Math with Our Ultimate Guide Formulas Solve Problems Quickly
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