Class notes precalc
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(1) The document contains class notes on pre-calculus topics including simplifying expressions, solving equations, and determining properties of functions. (2) Examples are provided of adding, multiplying, and simplifying terms with variables and exponents. (3) Steps are shown for finding the minimum value, vertex, domain and range of the quadratic function f(x) = x^2 - 5x + 4.
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Class XII CBSE Mathematics Sample question paper with solutionPratima Nayak ,Kendriya Vidyalaya Sangathan
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The document is a sample question paper for Class XII Mathematics. It consists of 3 sections - Section A has 10 one-mark questions, Section B has 12 four-mark questions, and Section C has 7 six-mark questions. All questions are compulsory. The paper tests concepts related to matrices, trigonometry, calculus, differential equations, and vectors. Internal choices are provided in some questions. Calculators are not permitted.Class XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solutionPratima Nayak ,Kendriya Vidyalaya Sangathan
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Class notes precalc
- 1. Class Notes: 29-8-2012 Pre-Calculus Group A Contributed by Jose Antonio Weymann Simplify: (6+5i) + (-3+2i) Add like terms. (3+7i) (-3+3i)(-2+2i) Foil multiply. 6-6i-6i+6i^2 Add like terms. -12i (3+i) (5+2i) 15+6i+5i+2i^2 13+11i 13 11i (5-2i) (5+2i) 25+10i-10i-4i^2 29 29 29 Determine if Function has a maximum or minimum, find the value, then determine the domain and range. f(x) = a^2+b+c f(x) = x^2-5x+4 Because the a (x) is positive this function has a minimum value. For a parabola with and equation y= ax^2+bx+c The y-coordinate of the vertex, h is given by h= -b/2a Minimum: -2.25 Domain: (3,-3) Range: [oo, -3) Solve each equation. By factoring or Quadratic Equation x^2-x-20 = 0 We can solve this function by factoring. (x-5) (x+4) The product of c is the sum of b. x = 5 x = -4 Zero Product Property Simplify each expression.
- 2. ^6 x^12y^15 ^6 x^6*x^6*y^6*y^6*y^3 x^2 * y^2 * ^6 Simplified _ _ 5^2* r^2 * r^2 * r * t^2 * t^2 5* r^2 * t^2 * u