<p> Math 093 Practice Final Exam #1 1</p><p>1.) Factor completely: (a) 3x8 + 7x 7  6x 6 (b) 4x 2 16 a 2  9a 20 a 2  4a 2.) Simplify:  a 2  2a 15 3  a x 2  9 3.) For the rational expression: x 2  2x 15 (a) Find the values of x for which the expression is undefined. (b) Simplify completely.</p><p>4.) Simplify: (5xy  3y 2  x 2 y)  (5y 2  x 2 y  2xy  4xy 2 )</p><p>20y 5 z 8  2y 4 z 2  4y 2 z 4  8y 2 z 5.) Divide: 4y 2 z 4 6.) Multiply and simplify: (a) (x 2  5y) 2 (b) (x 3  2)(x 6  2x3  4)</p><p>7.) Solve for x: (x  5) 2  36</p><p>8.) Solve for x: 3  x 1  x</p><p>3 1 5 9.) Solve for x:   1 x 2 x</p><p>10.) Solve for x by using the quadratic formula: x 2  2x  4</p><p>11.) A rectangle has a base which is five times as long as its height. Find the base and the height of the rectangle if the perimeter is 240 meters.</p><p> y 1 12.) Add and simplify:  y 2  25 y 2  8y 15</p><p>13.) Simplify. Write your answers without negative exponents. Assume all variables are positive. 5x 2 y 8 z 3 (a) (5x 5 y 9 )2 (b) 10x 6 y 2 z 5</p><p>14.) Perform the indicated operation and simplify, if possible. Assume all variables are positive. 27x5 y 4 (a) ( 2  6)(4 2  6) (b) 3x 2 y11 Math 093 Practice Final Exam #1 2</p><p>15.) Perform the indicated operation and simplify, if possible. Assume all variables are positive. 5 (a) Rationalize: (b) 18m5n16 8  3</p><p>16.) Consider the equation of the line 5x + 2y = 8: (a) Find the x-intercept. Write your answer as an ordered pair. (b) Find the y-intercept. Write your answer as an ordered pair. (c) Find the slope (d) Graph the line. Label two points.</p><p>17.) A straight line passes through the points (-3, 5) and (-2, -6). (a) Find the slope of the line. (b) Find the equation of the line in slope-intercept form.</p><p>18.) Graph the inequality: -3x + 2y < 4.</p><p>19.) Solve the system. If there is no solution or an infinite number of solutions, state this. (1) 3x – 8y = 14 (2) x + 4y = -2</p><p>20.) Solve the system. If there is no solution or an infinite number of solutions, state this. (1) –x + 2y = 4 (2) 2x – 4y = 8</p><p>21.) A jar is filled with quarters and dimes. Ken decides to cash them in at the bank. The teller gives him $14.40 and tells him there were 78 coins in all. How many of each were in the jar?</p><p>22.) Perform the indicated operations and simplify, if possible. Assume that all variables are positive. 2 50x 5  5x 12x3  3x 2 98x</p><p>23.) Graph the parabola: y  2x 2  8x  6 . Clearly state the y-intercept, any x-intercept(s), and the vertex.</p><p>24.) If f (x)  3x 2  5x  4 , find f (2) .</p><p>25.) Solve the inequality: 4(3  2x)  5 < 31 Math 093 Practice Final Exam #1 3</p><p>ANSWERS</p><p>1 1a.) x6(3x – 2)(x + 3) 2.) 3a.) x = 5, -3 a x  3 b.) 4(x – 2)(x + 2) b.) x  5</p><p>1y 2 2 4.) 3xy-2y2+2x2y-4xy2 5.) 5y 3 z 4  1 6a.) x4-10x2y+25y2 2z 2 z 3 b.) x9 + 8</p><p>7.) x = 1, -11 8.) x = 5 9.) x = 4</p><p> y 1 10.) no real solution 11.) 20 and 100 12.) (y  5)(y  3)</p><p> y18 2 10  15 13a.) 14a.) 2  6 3 15a.) 25x10 5 1z 2 3x xy b.) b.) b.) 3m 2 n8 2m 2x 4 y10 y 4</p><p>16a.) ( 8/5, 0) 17a.) -11 18.) y-int (0,2) b.) (0, 4) b.) y = -11x – 28 slope = 3/2 c.) -5/2 dotted line shade below</p><p>19.) (2, -1) 20.) no solution 21.) 44Q , 34D</p><p>22.) 31x 2 2x 10x 2 3x 23.) y-int (0,-6) 24.) 2 x-int (3,0) and (1,0) vertex (2, 2) opens downward</p><p>25.) x > -3</p>