Mathematics is a crucial subject in the NDA (National Defence Academy) exam and requires a strong understanding of concepts and formulas. To excel in the mathematics section of the NDA exam, it is essential to have a solid grasp of the important formulas. In this article, we will provide a comprehensive list of important formulas for NDA Mathematics that will help you in your preparation for the NDA Exam 2023.
1. Algebra Formulas:
– Quadratic Formula: The solutions for the quadratic equation ax^2 + bx + c = 0 can be found using the formula x = (-b ± √(b^2 – 4ac)) / 2a.
– Binomial Theorem: (a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + … + nCn * a^0 * b^n, where nCk represents the binomial coefficient.
– Arithmetic Progression (AP) Formulas: The nth term of an AP is given by tn = a + (n – 1)d, where a is the first term and d is the common difference.
2. Trigonometry Formulas:
– Pythagorean Identities: sin^2θ + cos^2θ = 1 and tan^2θ + 1 = sec^2θ.
– Sine and Cosine Rules: In a triangle ABC, the sine rule states that a/sinA = b/sinB = c/sinC, and the cosine rule states that c^2 = a^2 + b^2 – 2abcosC.
– Trigonometric Identities: Some important identities include sin(A ± B) = sinAcosB ± cosAsinB, cos(A ± B) = cosAcosB ∓ sinAsinB, and tan(A ± B) = (tanA ± tanB) / (1 ∓ tanAtanB).
3. Geometry Formulas:
– Area of Triangle: The area of a triangle can be calculated using the formula 1/2 * base * height or Heron’s formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter and a, b, c are the lengths of the sides.
– Perimeter and Area of a Circle: The perimeter of a circle is given by 2πr, and the area is given by πr^2, where r is the radius.
– Volume and Surface Area of 3D Shapes: Formulas for volume and surface area of shapes like cubes, cylinders, spheres, and cones should be memorized.
4. Calculus Formulas:
– Derivative Rules: Important derivative rules include the power rule (d/dx[x^n] = nx^(n-1)), product rule (d/dx[uv] = u’v + uv’), and chain rule (d/dx[f(g(x))] = f'(g(x))g'(x)).
– Integration Formulas: Some common integration formulas include ∫kdx = kx + C (where k is a constant), ∫x^n dx = (x^(n+1))/(n+1) + C (for n ≠ -1), and ∫e^xdx = e^x + C.
In the NDA Mathematics section, understanding and applying formulas correctly is crucial for solving problems efficiently. By familiarizing yourself with these important formulas and practicing their application, you will enhance your mathematical skills and boost your chances
