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Maths Formulas E-book

This Math Formulas eBook is a compact and easy-to-understand guide covering essential formulas from algebra, geometry, trigonometry, calculus, and more. Perfect for students and exam aspirants, it helps with quick revision and boosts problem-solving speed. Ideal for daily study and last-minute prep.<br>

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Maths Formulas E-book

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  1. MATHS FORMULAS

  2. Basic Arithmetic Basic Arithmetic Addition and Subtraction: a + b = c, a − b = c Multiplication and Division: a × b = c, a ÷ b = c Geometry Geometry Area of a Rectangle: A = length × width Area of a Triangle: A = 1/2 × base × height

  3. Geometry Geometry Perimeter of a Rectangle: P = 2 (l + w) Circumference of a Circle: C = 2πr Surface Area of a Cylinder: A = 2πr (r + h) Sum of Interior Angles of a Polygon (n − 2) × 180∘

  4. Sequences and Series Sequences and Series Arithmetic Sequence (nth term) an = a1 + (n − 1) d Sum of an Arithmetic Series Sn = n/2 (2a + (n − 1) d) Coordinate Geometry Coordinate Geometry Distance Formula (2D): √[(x₂ - x₁)² + (y₂ - y₁)²] Midpoint Formula (2D): [(x₁ + x₂)/2, (y₁ + y₂)/2]

  5. Algebraic Identities: Algebraic Identities: (a + b)² = a² + 2ab + b² (a - b)² = a² - 2ab + b² a² - b² = (a + b)(a - b) (a + b)³ = a³ + 3a²b + 3ab² + b³ (a - b)³ = a³ - 3a²b + 3ab² - b³ a³ + b³ = (a + b)(a² - ab + b²) Pythagorean Identities Pythagorean Identities sin²(θ) + cos²(θ) = 1 1 + tan²(θ) = sec²(θ) 1 + cot²(θ) = csc²(θ)

  6. Angle Sum/Difference Angle Sum/Difference sin(A + B) = sinAcosB + cosAsinB sin(A - B) = sinAcosB - cosAsinB cos(A + B) = cosAcosB - sinAsinB cos(A - B) = cosAcosB + sinAsinB tan(A + B) = (tanA + tanB) / (1 - tanAtanB) tan(A - B) = (tanA - tanB) / (1 + tanAtanB) Reciprocal Ratios Reciprocal Ratios csc(θ) = 1 / sin(θ) sec(θ) = 1 / cos(θ) cot(θ) = 1 / tan(θ)

  7. Calculus Calculus Derivative of xⁿ: nxⁿ⁻¹ Derivative of sin(x): cos(x) Derivative of cos(x): -sin(x) Derivative of eˣ: eˣ Product Rule: (uv)' = u'v + uv' Quotient Rule: (u/v)' = (u'v - uv') / v² Chain Rule: dy/dx = dy/du * du/dx Integral of xⁿ: (xⁿ⁺¹) / (n + 1) + C Integral of sin(x): -cos(x) + C Integral of cos(x): sin(x) + C Integral of eˣ: eˣ + C

  8. BASIC SCIENCE BASIC SCIENCE What is the chemical symbol for water? Answer: H₂O What is the process by which plants make their own food? Answer: Photosynthesis What is the largest planet in our solar system? Answer: Jupiter What gas do humans breathe in? Answer: Oxygen

  9. HUMAN BODY HUMAN BODY What is the largest organ in the human body? Answer: The skin. What is the powerhouse of the cell? Answer: Mitochondria. CHEMISTRY CHEMISTRY What is table salt's chemical name? Answer: Sodium chloride

  10. What is the process of a liquid turning into a gas called? Answer: evaporation, or boiling BIOLOGY BIOLOGY What is the scientific name for the "windpipe"? Answer: Trachea What are the building blocks of proteins? Answer: Amino acids What is the study of living organisms called? Answer: Biology.

  11. BIOLOGY BIOLOGY What is the genetic material in cells called? Answer: DNA What is the function of white blood cells? Answer: To fight infections What is the name of the green pigment in plants? Answer: Chlorophyll What is the study of animals called? Answer: Zoology

  12. BIOLOGY BIOLOGY What is the study of plants called? Answer: Botany What is the term for an organism that only eats plants? Answer: Herbivore PHYSICS What is the unit of force? PHYSICS Answer: Newton (N) What is the unit of energy? Answer: Joule (J).

  13. PHYSICS PHYSICS What is the unit of power? Answer: Watt (W) What is the measure of how hot or cold something is? Answer: Temperature. What is the transfer of heat through direct contact called? Answer: Conduction What is the bouncing of light off a surface called? Answer: Reflection

  14. CHEMISTRY CHEMISTRY What is H₂SO₄? Answer: Sulfuric acid. What is NaCl? Answer: Sodium chloride (table salt) What is pH? Answer: A measure of acidity/alkalinity. What is an ion? Answer: A charged atom. What is an acid? Answer: Proton donor

  15. CHEMISTRY CHEMISTRY What is a base? Answer: Proton acceptor. What is oxidation? Answer: Loss of electrons What is reduction? Answer: Gain of electrons What is an atom? Answer: Basic unit of matter. What is a bond? Answer: Force holding atoms together.

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