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Calculus

REVIEW ON ALGEBR before Calc

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Algebra 2 review before Calculus

Honors Pre- Calculus Packet #1: Sections 1 ? 13, TEACHER?S EDITION Section 1. Find the product of the polynomials. 1. 2. 3. 4. 1) 16x2-8x+1 2) 4x2-20x+25 3) 2x3+18x2+54x+54 4) 2x3+21x2-31x+60 5. 6. 7. 8. 5) 4x2-9 6) 49x2-16 7) 2x2+12x+18 8) 9. (x ? 2)(x2 + 2x + 4) 10. 11. 12. 9) x3-8 10) 8x3+36x2+54x+27 11) 24m2+48mn+24n2 12) 3x3-25x2+18x+24 Section 2. 1. Given: , , , , find the following: (a) (b) (c) (d) 1a) 13 1b) 1c) 4 1d) (e) (f) (g) (h) 1e) {(5, 3), (4, 2), (7, 1)} 1f) no inverse, not 1-1 1g){(3, 1/5), (2, ?), (1, 1/7) } 1h) 2. Given and , find the following: (a) (b) (c) (d) 2a) -3 2b) 2c) -38 2d) (e) (f) (g) (h)

introduction to deriatives

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Derivative meaninig
There are two components to calculus. One is the measure the rate of change at any given point on a curve. This rate of change is called the derivative. The simplest example of a rate of change of a function is the slope of a line. We take this one step further to get the rate of change at a point on a line. The other part of calculus is used to measure the exact area under a curve. This is called the integral. If you wanted to find the area of a semicircle, you could use integration to get the answer. The two parts; the derivative and the integral are inverse functions of each other. That is, they cancel each other out. Just as (x2)1/2=x, the derivative of (integral (x)) = x and derivative of (integral (f (x)) = f(x).

Implicit Differentiation Simplified

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Inverse functions and differentiation
y + xy = 7x Implicit differentiation? (dy/dx) + (x(dy/dx)+ y(1)) = 7(1) (dy/dx)(x + 1) = 7 - y (dy/dx) = (7 - y) / (x + 1) Easy?

Calculus FRQ

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free response questions calculus 1969 1998

AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f1(x) = x, f2(x) = xcos x, f3(x) = 3e2x, f4(x) = x - |x|. Answer the following questions (a, b, c, and d) about each of these functions. Indicate your answer by writing either yes or no in the appropriate space in the given rectangular grid. No justification is required but each blank space will be scored as an incorrect answer. Questions Functions f1 f2 f3 f4___

Calculus FRQ

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free response questions calculus 1969 1998

AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f1(x) = x, f2(x) = xcos x, f3(x) = 3e2x, f4(x) = x - |x|. Answer the following questions (a, b, c, and d) about each of these functions. Indicate your answer by writing either yes or no in the appropriate space in the given rectangular grid. No justification is required but each blank space will be scored as an incorrect answer. Questions Functions f1 f2 f3 f4___

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