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 + (n-1)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)
- Slope-Intercept Form: y = mx + b
- Point-Slope 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:
- Double-Angle Formulas: sin 2θ = 2 sin θ cos θ, cos 2θ = cos² θ – sin² θ
- Half-Angle 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
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Quadratic Formula: The quadratic formula is used to solve quadratic equations and is given as:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
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Pythagorean Theorem: The Pythagorean theorem relates to the three sides of a right-angled 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
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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)
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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)
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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.
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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:
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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.
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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.
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Formula for Geometric Progression: The formula for the nth term of a geometric progression is:
an = a1 * r^(n-1)
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^(n-1)
- Formula for Linear Equations: y = mx + c
Geometry Formulas:
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Perimeter and Area Formulas: Students learn formulas for calculating the perimeter and area of various two-dimensional figures, such as triangles, rectangles, and circles.
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Volume Formulas: Students learn formulas for calculating the volume of various three-dimensional figures, such as cubes, spheres, cones, and cylinders.
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Pythagorean Theorem: As mentioned earlier, the Pythagorean theorem is a geometric formula relating to the sides of a right-angled 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:
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Sine, Cosine, and Tangent Formulas: Students learn about the trigonometric ratios sine, cosine, and tangent, and how to use them to solve problems involving right-angled triangles.
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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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