Math 110: Sample exam #2 Direction: Solve the problems on separate paper. Show your steps. Submit before the exam. Staple your papers. CH 2 1.Solve and write solution in set notation: 4 w + 12 + 9 w > w + 9 2.Solve and write solution in set notation: 4 ( 6 x + 1) 8 x 3. Solve and express the solution as set notation 4. Solve and graph the solution 5 x + 7 > 2 x 2 5 2 x4 5. Solve and express the solution as set notation 6. Solve and graph the solution 7. Dara invested some money at 3% simple interest and $6000 more than that amount at 4.5% simple interest. After 1 year her total interest from the two accounts was $870. How much did she invest at each rate? Set up algebraic equation to earn full credit. ANS $8,000 at 3% and $14,000 at 4.5% 8. With income from her bibliography, an actor invests some of the money at 3% and $30,000 more than twice as much at 4%. The total annual interest earned from the investments is $5,600. How much is invested at each rate? Set up algebraic equation to earn full credit. Equation to solve 0.03 x + 0.04( 2 x + 30000 ) = 5600 8( 5 x ) 3x + 4 5( 2 x 3) + 4 6 x + 5 9. A cargo ship, heading into port, radios the 10. The distance between LA & San Diego is Coast Guard that it is experiencing engine about 120 miles. A driver leaves LA at 8AM. trouble and that it's speed has dropped to 3 Due to traffic the first part of the trip averages knots. Immediately, a Coast Guard cutter 35 mph, then 60 mph for the rest of the trip. If leaves port and speeds at a rate of 25 knots the car arrived in San Diego at 11AM, find the directly toward the disabled ship, which is 21 travel time for each part of the trip Set up nautical miles offshore. How much time will it algebraic equation to earn full credit. take the Coast Guard cutter to reach the cargo ship? Set up algebraic equation to earn full credit. ANS hrs 11. How many gallons of 50% antifreeze must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 40% antifreeze? To earn full credit, set up equation and solve. Correct answer without equation is at most 1 point. 12. Alex mixes vinegar with 5% acetic acid and pickled vinegar containing 15% acetic acid. How many cups of each vinegar are needed to make 2 cups of weed killer having 13% acetic acid? To earn full credit, set up equation and solve. CH5 13. Simplify 18 x 3 y6 6 x2 y3 14. Simplify (4 u v 4 )(u3 w2 )2 15. Simplify 2 2 3 (e )( e ) 16. Simplify 2x 3 6x4 4 y 3 y2 17. Simplify (positive exponents) a) 2 x 5 3x 6 18. Simplify (positive exponents) ( x 3 y 3)4 12 xy 6 x9 a. 4 b. 4 10 c. 3x y x (2 x1 y2)3 b) ( )( ) ( )( ) ( x 4 )2 19. Simplify (positive exponents) ( a. 5a 7 2a 4 ANS ) 3 b. 3 4 3x 4y ( ) 2 c. x 6 x 2 40 27 x12 1 5 , 3 , a 64 y x2 21. Perform the indicated operations a) 2 x 5 + 3x 4 + 4 x 3 + 5 x 2 + 4 x 4 7 x 2 + 6 b) c) 2 ( ) ( ) (2m7 + 3m4 + 7 x 4 ) (2m7 + 4m2 6x 4 ) (3 x2 7 x y7 y 2 )(4 x 2x y +9 y 2) 20. Simplify (positive exponents) a. 2 x 4 2 b. r 4 r c. x 4 y 9 x 2 y 3