B) 2x3-5x D) 2x3 + 5x

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1 Pre Calculus Final Review 2010 (April) Name Divide f(x) by d(x), and write a summary statement in the form indicated. 1) f x = x - 4; d x = x + 7 (Write answer in polynomial form) 1) A) f x = x + 7 x2-7x B) f x = x + 7 x2-7x C) f x = x + 7 x2 + 7x D) f x = x + 7 x2 + 7x Divide using synthetic division, and write a summary statement in fraction form. 2) 2x 4 - x - 1x2 + x A) 2x - 7x2 + 6x C) 2x - 7x2 + 6x B) 2x - x D) 2x + x ) Divide f(x) by d(x), and write a summary statement in the form indicated. ) f x = x4-4x - 2x2-4x - ; d x = x2 + 1 (Write answer in fractional form) ) f x A) x2 + 1 = x 2 f x - 4x - B) x2 + 1 = x x - + x2 + 1 C) f x x2 + 1 = x 2-4x x2 + 1 D) f x x2 + 1 = x 2 + 4x - Using the given zero, find all other zeros of f(x). 4) 2 + 4i is a zero of f x = x4-14x + 8x2-00x ) A) i,, and - B) 2-4i, - C) 2-4i, D) 2-4i,, and - Write the polynomial in standard form and identify the zeros of the function. ) f(x) = (x + 2)(x + 2)(i)(x - i) ) A) f(x) = x4 + 4x - x2-6x - 6; zeros -2 (mult. 2), ± B) f(x) = x4 + 1x2 + 6; zeros 2 (mult. 2), ± C) f(x) = x4 + 4x + 1x2 + 66; zeros 2 (mult. 2), ± i D) f(x) = x4 + 4x + 1x2 + 66; zeros -2 (mult. 2), ± i Solve the equation. 7x 6) x x = 28 x2-7x 6) A) x = 4 7 or B) x = 7 4 C) x = 2 7 or D) x = 4 7 1

2 7) -x 2-8 = -1x x - 4 x ) A) x = - ± 6 B) x = 8, - C) x = - 8, D) x = Rewrite the expression as a sum or difference or multiple of logarithms. 8) log 14 x14 8) A) log 14 14x B) log log 14 x C) 14 log 14 x D) log ) log 6 19 s2r 9) A) 1 6 log 19-2 log s - 2 log r B) 6 log 19-2 log s - log 6 C) log 19 - log s - log r D) 1 6 log 19-2 log s - log r Write the expression using only the indicated logarithms. 10) log6 (x + y) using natural logarithms 10) A) ln (x + y) ln 6 B) ln 6 ln (x + y) C) ln (x + y) ln 6 D) ln (x + y) + ln 6 Solve the equation. 11) ex - 1 = -40 ex A) 0.90, B) 2.079, C) 8, D) -1 11) 12) log ( 4 + x) - log (x - 2 ) = log 12) A) - B) C) D) 1 2 1) ex - 18e-x = HONORS ONLY 1) A) B) C) D) Find the amount accumulated after investing a principal P for t years at an interest rate r. 14) P = $14,000, t = 7, r 0%, compounded semiannually (k = 2) 14) A) $1, B) $26,99.09 C) $27, D) $27, ) P = $260, t 9, r = 9% compounded continuously 1) A) $147. B) $401,48,60.48 C) $417. D) $ Convert from degrees to radians. Use the value of found on a calculator and round answers to four decimal places, as needed. ) 24 ) A) 9 B) 8 C) 10 D) 18 2

3 Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. 17) 17) 18 A) 9.9 B) 0 C) 1100 D) 27 Solve for x. Round your answer to 2 decimal places. 18) 18) 10 x 7 A) 6.02 B) 12.2 C) 7.99 D).62 Solve the equation. 19) Solve sec = 2 for, where ) A) 0 B) 4 C) 60 D) 90 Suppose that is in standard position and the given point is on the terminal side of. Give the exact value of the indicated trig function for. 20) (-1, 6); find sin. 20) A) - 1 B) 1 C) D) ) (8, ); find sin. 21) A) 89 B) C) 8 D) Find the specified quantity. 22) Find the amplitude of y = cos 4x ) A) 20 B) C) 2 D) 4 2) Find the period of y = sin 4x ) A) B) 4 C) 2 D) 24) Find the phase shift of y = sin x ) A) - 2 B) - 6 C) 6 D) 4

4 Find the exact value of the composition. 2) cos arcsin 1 4 2) A) B) C) 1 2 D) 1 4 Use the fundamental identities to find the value of the trigonometric function. 26) Find tan if cos 2 and sin < 0. 26) A) - B) - C) - D) 2 27) Find cot if csc = A) and tan > 0. 27) B) 4 C) D) 17 Solve the triangle. 28) A = 42, B = 4, b = 8 28) A) C 04, a 6.7, c 14 B) C 04, a 6.7, c 11.6 C) C 04, a 9.6, c 14 D) C 4, a 6.7, c ) 29) A) B = 60, b 8., c 10. B) B = 4, b 7.7, c 8. C) B = 0, b 9.7, c 10. D) B = 4, b 8., c 7.7 4

5 0) 0) A) B = 20., C = 4.7, a = 461 B) B = 4.7, C = 20., a = 461 C) B = 4.7, C = 20., a = 21. D) B = 20., C = 4.7, a = 21. 1) A = 4, b 0, c = 7 1) A) a 12, C 44.1, B 81.9 B) No triangles possible C) a 8.2, C 44.1, B 81.9 D) a 12, C 48.1, B 77.9 Solve the equation algebraically. 2) x2 - x - 1 = 0 2) A) - 2 ± B) 2 ± C) 2 ± D) ± 129 ) x - 10x - 2 = 0 ) A) - B) - 2 ; 1 C) D) 2 ; -1 Find the domain of the given function. 4) f(x) = - x 4) A) All real numbers B) (-, ] C) (-,) (, ) D) (, ) ) f(x) = (x + 2)(x - ) A) All real numbers B) [-, -2) (-2, ) (, ) C) (-, -) (- -2) (-2, ) (, ) D) (0, ) ) Find the range of the function. 6) f(x) = 9 + x 6) A) (-, ) B) [-9, ) C) [0, ) D) (0, ) Determine algebraically whether the function is even, odd, or neither even nor odd. 7) f(x) = 2x - 8x 7) A) Even B) Odd C) Neither 8) f(x) = 7x4 + 7x + 8) A) Even B) Odd C) Neither

6 Find the inverse of the function. 9) f(x) = 2x + 7 9) A) f-1(x) = x C) f-1(x) = x B) Not a one-to-one function D) f-1(x) = x ) f(x) = x ) A) f-1(x) = x + 6 B) Not a one-to-one function C) f-1(x) = x - 6 D) f-1(x) = x - 6 For the given function, find all asymptotes of the type indicated (if there are any) 41) f(x) = x - 4, vertical 41) x2-9 A) x =, x = - B) x = - C) x = 4 D) x = 42) f(x) = x 2-4x + 9, slant HONORS ONLY 42) A) x = y + 4 B) y = x - 7 C) None D) y = x + 1 4) f(x) = 8x 2-2x - 2, horizontal 4) x2-7x + 6 A) y = 8/ B) None C) y = 2/7 D) y = 0 Evaluate the limit based on the graph of f shown. HONORS ONLY 44) 44) lim f x x -1- A) B) 1 C) 0 D) 6

7 4) 4) lim x f x A) B) 2 C) 0 D) Graph the rational function and analyze it in the following way: find the intercepts, asymptotes, use limits to describe the behavior at the vertical asymptotes and the end behavior. Find the domain and range. Determine where the function is continuous and where it is increasing and decreasing. Find any local extrema. (HONORS ONLY) 46) f(x) = x 2 + x - 2 x2 - x ) Find the product of the complex number and its conjugate. 47) -6 + i 47) A) 27 B) 4 C) 46 D) 48 Solve the equation. 48) 8x2-7 = 0 48) A) - 7 ± 47 B) - 7 ± 47 i C) 7 ± 47 D) 7 ± 47 i Find the standard form of the equation of the parabola. 49) Focus at (9, 1), directrix y = -7 49) A) (x - 9)2 = (y + ) B) (y - 1)2 = (x - 9) C) (x - 1)2 = (y + ) D) (x - 9)2 = (y - 1) 7

8 0) Vertex at the origin, opens to the right, focal width = 0) A) y2 = -4x B) y2 = x C) x2 = y D) y2 = -x Find the vertex, the focus, and the directrix of the parabola. 1) y2 + 4x + 4y + 0 = 0 1) A) Vertex: - 1, 1 ; Focus: (-, 1); Directrix: y = - B) Vertex: 2, -2 ; Focus: 4, -2 ; Directrix: y = 4 C) Vertex: 1, -2 ; Focus: (0, -2); Directrix: x = 2 D) Vertex:, 1 ; Focus: (2, 1); Directrix: y = 0 2 Find an equation in standard form for the ellipse that satisfies the given conditions. 2) An ellipse with foci at (, 2) and (, -4); major axis length of 10 2) A) (y + 1) 2 2 C) (x + 1) () 2 + (y + ) 2 B) (y + 1) 2 2 D) (x + 1) 2 + (x - ) 2 + (y + ) 2 2 Find the center, vertices, and foci of the ellipse with the given equation. ) (x + 4) 2 + (y + ) 2 ) A) Center: (-4, -); Vertices: (-, -24), (-, ); Foci: (-, -20), (-, 12) B) Center: (-4, -); Vertices: (-24, -), (, -); Foci: (-20, -), (12, -) C) Center: (-4, -); Vertices: (-, -24), (-, ); Foci: (-, -), (-, 8) D) Center: (-4, -); Vertices: (-24, -), (, -); Foci: (-, -), (8, -) Find an equation in standard form for the hyperbola that satisfies the given conditions. 4) Center (1, -4), focus (6, -4), vertex (, -4) 4) A) (x + 1) 2 C) (x - 1) (y + 4) (y + 4) 2 B) (x - 1) 2 D) (x - 1) 2 - (y + 4) (y + 4) 2 2 Solve for y, and use a function grapher to graph the conic. ) x2 + y2 + 64x + 4y - 12 = 0 ) 8

9 A) y = 2 ± 4 x2 + 4x - 1 B) y = x2-4x + 1 C) y = 2 ± 4 -x2-4x + 1 D) y = -2 ± 4 - x2-4x + 1 6) xy + 2y - 2 = 0 6) 9

10 A) y = -2 x + 2 B) y = 2 x - 2 C) y = -2 x - 2 D) y = 2 x + 2 Find point in translated system. 7) P(x,y) = (, 2), h =, k 7) A) (x, y ) = (1, - ) B) (x, y ) = ( -, 1) C) (x, y ) = ( -, -1) D) (x, y ) = ( +, ) Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 8) x2-9xy - 2y = 0 8) A) Ellipse B) Hyperbola C) Parabola 9) 8x2 + 8xy + 2y2-6y = 0 9) A) Hyperbola B) Ellipse C) Parabola 60) 7x2 - xy + 6y2-20 = 0 60) A) Ellipse B) Parabola C) Hyperbola 10

11 Rotate the coordinate axes to eliminate the xy term. 61) x2 + 2xy + y x - 4 2y = 0 61) A) y' = (x') 2 B) (x') 2 + (y') C) 4(x') = (y') 2 D) (x') (y') 2 8 Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle. 62) P(x, y) = (, -8); = 62) A) + 8, B) - 8, C) - 8, D) 2, - 4 Write the equation in standard form. 6) x2 + 9y2 + 96x - 24y = 0 6) A) (x ) 2 + (y - ) 2 B) () 2 + (y - ) C) (x ) (y - ) 2 8. D) () (y - )