PRECALCULUS SUPPLEMENTARY VI

PRECALCULUS SUPPLEMENTARY VI - AP CALCULUS PRECALCULUS...

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AP CALCULUS PRECALCULUS SUPPLEMENTARY VI Problems : 1) From a rectangular piece of cardboard having dimensions ac m = 3 and bc m = 7 , an open box is to be made by cutting out an identical square with side length x from each corner and turning up the sides (see diagram below). Which of the following choices gives the correct equation of the volume V of the box as a function of x ? A) () ( ) ( ) Vx x x x =− 37 B) ( ) ( ) x x x 32 72 C) () ( ) ( ) x x D) ( ) ( ) x x x 23 7 E) x xx =−− 4 2) Let fx x x k =+ + 2 3 . If is divisible by ( ) x 1 , then what is the remainder when is divided by x + 1 ? A) 6 B) 4 C) 0 D) E) 3) Let fx x x k x =+ ++ 32 83 and gx x 41 2 . When each of these respective functions is divided by ( ) x + 2 , their remainders are equal. What is the value of k ? A) 13 B) 5 C) D) E)
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4) Let () fx x x x =+− 38 1 0 32 . Find the remainder when [ ] 2 is divided by ( ) x + 1 . A) 0 B) 16 C) D) 4 E) 5) Which fits better: a round peg is a square hole (figure a) or a square peg in a round hole (figure b) (i.e. which figure has the greatest percentage of area covered?) Assume that the radius of each circle is r . 6) Solve for x : a) xx +− = 51 64 b) 2 22 4 4 x x x x x + + = + 7) Using the trigonometric identity, cos cos 36 72 1 2 oo −= , find the exact value of cos36 o . Hint : Observe that 72 2 36 = . Let θ = 36 o . Thus, you ultimately need to solve for cos from the trigonometric identity cos cos θθ 2 1 2 . 8) Consider Δ ABC with A Bc = , BC a = and CA b = . If = BAC ABC 2 , then prove abb c =+ . Hint : You will need to use the Sine and Cosine Laws. 9) Solve the following system of equations: xy z z z + = ++ = = 25 1 1 21 5 2 2 10) Let r be the radius of the circle ( ) xyr −+ + = 12 2 . If the line yx = − + is tangent to the circle, then what is the value of r ?
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This note was uploaded on 07/27/2010 for the course MATH MATH 1025 taught by Professor Tanny during the Spring '09 term at York University.

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PRECALCULUS SUPPLEMENTARY VI - AP CALCULUS PRECALCULUS...

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