. Simplif the complex fraction x 4 4 x. x 4 x x 4 x x 4 x x 4 x x E) 4 x. A rectangular frame for a painting has a perimeter of 8 inches. If the length of the frame is inches, find the width of the frame. 8 in. 7 in. 6 in. 4 in. E) 66 in.. Compute a zero of the quadratic function f x x 76. 4 x i 4 x 4 x 4 x E) x 4 i 4. Coordinates of the vertex for the parabola = x + x + 40 are: ( 6, 4) (-6, 4) (-4, 6) ( 4, 6) E) ( 0, 4). Solve: x 0 x 7 0 > x 0 x 0 x 0 E) no solution 6. Solve the radical equation x 0 to find all real solutions. x 9; x 9 x x 9 x E) x ; x 7. Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: (4, 6) line: 40x 8 = 4 9 x+ x = 40x = x + 6 E) = x 40 0 8. Find the remainder of p(x) q(x). Here, p( x) x x 9 and q( x) x. - 0 E) - Page
9. Evaluate f x for the following function. f ( x) 6x 4 6x 6x 6x 6x E) 0. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (4, 9) line: 9x + 4 = 8 6x 8 x+ 9 9 49 x+ = x = 9x + 4 E) = x. Given that f ( x) x and g x ( ) x determine the value of ( f o g)(0) (if possible). 0 x E) not possible. The volume of a gas varies directl with the temperature. If the volume is 0cc at 40C, what is the volume if the temperature is 64 C? 48 cc 64 cc 6 cc 64 cc E) 6 cc. Use the zero x to completel factor the polnomial f ( x) x x x 7. (x)( x 7) (x)( x 7) (x)( x 7) (7x )( x ) E) (7x)( x ) 4. Solve the sstem of equations. 8 x+ 6 6 x+0 7 7, 6 0 solution, 6, 6 7 7, 6 0 E) no. Solve the inequalit x 0 x. 4 4,, 4 4,, 4 4,, 4 4, E), Page
6. Write the standard form of the equation of the circle with radius r = 8 and center: (, ). ( x) ( ) 64 ( x) ( ) 64 ( x) ( ) 64 E) ( x) ( ) 8 ( x) ( ) 8 7. One of the zeros of a certain quadratic polnomial with real coefficients is 0 i.what is its other zero? 0 i 0 i 0 i 0 i E) 0 i 8. The population P (in thousands) of a cit from 990 to 004 can be modeled b 0.00 t P 67. e, where t is the ear, with t = 0 corresponding to 990. According to the model, during what ear will the population be approximatel 7,000? 00 04 07 999 E) 996 9. Expand the expression log x log E) log x log x log x log as a sum, difference, and/or constant multiple of logarithms. log x log log x log 0. Solve using an method. 6 x+ 0 x 4, 7, 6 4, 9 9 4, 9 9 E) inconsistent 8. Find the determinant of the matrix 7 9. 7 E) 0. Find the fifth term of the sequence. (Assume that n begins with.) a n+ 6 0 8 E) 8 n Page
. The volume of a small drum in the shape of a right circular clinder is 4 cubic feet. The radius of the drum is 8 feet. Find the height of the drum.. ft 4. ft 4.0 ft. ft E).0 ft 4. An open box is to be made from a square piece of cardboard, 4 inches on a side, b cutting equal squares with sides of length x from the corners and turning up the sides. Determine the function, V, in terms of x, that represents the volume of the box. V( x) x + 4x V( x) 4 x + 48 x 4x V( x) 4 x + 48x E) V( x) 4 x 96 x + 76x V( x) 4 x 48 x + 4x x. Solve the sstem of equations 4. x 0 x 7, 4 x 4, 7 x 7, 4 x 8, E) x, 8 6. If possible, find AB. 7 9 7 7 9 7 4 7 A, B 0 6 4 0 9 8 9 9 E) not possible 7. Use the quadratic formula to solve x 8 x+ 0 0. x 88 i x 4 i x4 i x 9 i E) x9 i 8. Solve the logarithmic equation ln x + e e + e e + E) e 9. Solve the exponential equation below algebraicall. Round our result to three decimal places. x 00e.90 0.999.607.7 E) 0.40 Page 4
0. Determine the domain of the following function. Express our answer in interval notation. f ( x) x.,.,.,,. E),. Find the inverse function of f. f ( x) x + f ( x) x + f ( x) x E) f ( x) x + f ( x) x f ( x) x +. Solve the equation 4x8 6 for in terms of x. 7 x 9 9 x 4 E) x 4 x 4 x 4. Solve the equation x 6 0 for in terms of x. 6x 6x 6 x x E) x 6 x + 4. Determine the equation(s) of an vertical asmptotes of f( x) x x. x = - onl x = 0 onl x and x0 x = onl E) none. An airline charges $0 for a round-trip flight from New York to Los Angeles if the ticket is purchased at least 7 das in advance of travel. Otherwise, the price is $800. If a total of 8 tickets are purchased at a total cost of $9,00, find the number of $0 tickets sold. 60 6 6 4 E) 8 6. One acetic acid solution is 60% water and another is 80% water. How man liters of 80% solution should be mixed with 60% solution to produce 0 liters of a solution that is 6% water? 9 4 E) 6 Page
7. Find all solutions of the following equation. 6 x+ 6 x 7 x 0 x,6 x x E) x 0,4 8. Divide 4x 8x 4 b x 4. x x x x x x x E) x x x 9. Find the slope of the line passing through the points 4, and,. 4 0 8 8 0 E) 0 40. Find the slope of the line with equation: + 7x = 4 7 E) 7 Page 6
4. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. point: (, 4) slope: m = 4 = 4x + 4 = 4x 7 = 4x + 8 = 4x E) = 4x 4. The decibel ( db ) is a unit that is used to express the relative loudness of two sounds. One application of decibels is the relative value of the output power of an amplifier with respect to the input power. The relative value D of power level P with respect to power level P is given ( in units of db ) in terms of the logarithm of their ratio as follows: D 0log P P where the values of P and P are expressed in the same units, such as watts ( W ). If P 76W, find the value of P at which D 0.8. Round our answer to nearest integer. 8 6 96 9 E) 86 4. If the expression ( + 4 ) is expanded, the highest power of x would be: 4 E) Page 7
44. The profit in dollars from selling x DVD plaers is given b 40x 0. Set up and solve an equation to find out how man DVD plaers must be sold to obtain a profit of $400. 7 8 E) 9 4. Find the center of the graph of the circle. x + x 9 0 (-, 6) (, 6) (-,) (,-6) E) (,-) 46. Simplif the rational expression the expression is defined. x x 64 and indicate the values of the variable for which x 0 x 0, 8 x 8 x 8 E) x 8, 8 47. In 00, the average weekda volume of traffic on a particular stretch of the Princess Parkwa was 7,000 vehicles. B 006, the volume had increased to,000 vehicles per weekda. B how man vehicles did the traffic increase per ear?,00 77 4,400 46,00 E),800 Page 8
. D. C. E 4. B. E 6. E 7. D 8. B 9. E 0. C. A. A. A 4. E. A 6. D 7. A 8. C 9. D 0. D. A. D. A 4. E. A 6. E 7. E 8. A 9. B 0. A. D. E. A 4. C. E 6. B 7. D 8. D 9. E 40. E 4. C 4. D 4. E 44. B 4. A 46. E Page 9
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