Mathematics Reference Manual Quadratic Equations Forming Quadratic Polynomials A quadratic polynomial is of the form (ax^2 + bx + c). Example: Form a quadratic polynomial given the roots (alpha = 3) and (beta = -2). Sum of roots: (alpha + beta = 1) Product of roots: (alpha beta = -6) Quadratic polynomial: (x^2 – (alpha …
Newton’s Laws and Motion Q&A About Newton’s Laws, Gravity, and Motion Q1: What is inertia? Inertia is the property of an object to resist changes in its state of motion. This means that an object at rest will stay at rest, and an object in motion will continue moving at a constant velocity unless acted …
Worksheet Solutions Assertion (A) – Reason (R) based questions Select the correct answer to these questions from the codes given below: Both (A) and (R) are true but (R) is the correct explanation of the (A). Both (A) and (R) are true but (R) is not the correct explanation of the (A). (A) is true …
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Grade XII Applied Mathematics Practice Questions 1. Which equation represents the eigenvalues of the matrix ( begin{bmatrix} 2 & 1 \ 1 & 2 end{bmatrix} )? (lambda^2 – 4lambda + 3 = 0) (lambda^2 – 4lambda + 4 = 0) (lambda^2 – 3lambda + 2 = 0) (lambda – 3 = 0) 2. The area …
Grade XII Applied Mathematics Worksheet 1. The determinant of a 3×3 matrix (A) is 5. What is the determinant of (3A)? 15 45 135 None of the above 2. Find the inverse of the matrix ( begin{bmatrix} 2 & 3 \ 1 & 4 end{bmatrix} ). ( begin{bmatrix} 4 & -3 \ -1 & 2 …
Basic Trigonometric Integration Questions Integrate: ( int sin(x) , dx ) Integrate: ( int cos(x) , dx ) Integrate: ( int tan(x) , dx ) Integrate: ( int cot(x) , dx ) Integrate: ( int sec(x) , dx ) Integrate: ( int csc(x) , dx ) Integrate: ( int sin^2(x) , dx ) Integrate: ( …
Basic Integration Formulas ( int 0 , dx = C ) ( int 1 , dx = x + C ) ( int x^n , dx = frac{x^{n+1}}{n+1} + C ), where ( n neq -1 ) ( int frac{1}{x} , dx = ln|x| + C ) Trigonometric Functions ( int sin x , dx …
1 Definition and Meaning: Modulo arithmetic deals with the remainder when one number is divided by another. Question: What is the remainder when 15 is divided by 4 ? Answer: 3. 2 Introduction to Modulo Operator: The modulo operator ‘ ‘ gives the remainder of the division of two numbers. Question: What is ‘ ? …
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